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Integrating the statistical analysis of spatial data in ecology
Ecography
Abstract
In many areas of ecology there is an increasing emphasis on spatial relationships. Often ecologists are interested in new ways of analyzing data with the objective of quantifying spatial patterns, and in designing surveys and experiments in light of the recognition that there may be underlying spatial pattern in biotic responses. In doing so, ecologists have adopted a number of widely different techniques and approaches derived from different schools of thought, and from other scientific disciplines. While the adaptation of a diverse array of statistical approaches and methodologies for the analysis of spatial data has yielded considerable insight into various ecological problems, this diversity of approaches has sometimes impeded communication and retarded more rapid progress in this emergent area. Many of these different statistical methods provide similar information about spatial characteristics, but the differences among these methods make it difficult to compare the results of studies that employ contrasting approaches. The papers in this mini-series explore possible areas of agreement and synthesis between a diversity of approaches to spatial analysis in ecology.
... Meanwhile, from the sociosystem aspect, the population is the entire community in Wanagiri village. Research samples from the ecosystem (vegetation) aspect were plant species covered by squares with squared sizes of 20x20 m2, 10x10 m2, and 1x1 m2 each with a total of 86 squares [25]- [29], while samples from the sociosystem aspect were taken from community components such as representatives of official villages, representatives of traditional villages, community leaders, balian / shaman, stakeholders / priests, and the general public. The sample consisted of 50 people. ...
... Systematic sampling technique is chosen because the sampling technique by placing plots / squares / sampling plots is carried out systematically with transect lines that are alternately and continuously positioned on the right and left. This is done so that all plant species in each location can be recorded [25]- [29]. ...
... The tree category is mature plants having a diameter of 20 cm, with this square size also includes the square size for saplings (saplings, poles) with a squared size of 10x10 m2, plants with a diameter of 10 cm to 20 cm, and seedlings (seedlings). / understorey) with a square size of 1x1 m2, namely regeneration plants from sprouts to tillers measuring less than 1.5 m tall [25]- [29]. Determination of the zone / location in this study is in Taman Gumi Banten with squared placement as in Figure 1 C. ...
This study aimed to identify the composition of plant species and Useful plants in the forests of Taman Gumi Banten, Indonesia. This research conducted in the forests of Taman Gumi Banten and village Wanagiri. The population of this study, from the ecosystem aspect, is all plant species in the Taman Gumi Banten forest. From the sociosystem aspect, it is the entire community in Wanagiri village. The sample of this research from the ecosystem aspect is the plant species covered by squares. From the sociosystem aspect, it is a community component. The total sample is 50 people. Data collection methods are quadratic methods and interviews. The sampling technique is a systematic sampling technique. Data were analysed descriptively. The conclusions of this study are (1) There are 68 plant species in the entire forest of Taman Gumi Banten, (2) Of the 68 existing plant species, as many as 59 (86.76%) of the plant species were useful plants, while 9 (13.24%) of them were unknown. (5) The use of plants by the local community is 23 species (38.98%) for food, 20 species (33.89%) for boards, 9 species (15.25%) for medicine, 25 species (47.17%) ) for Hindu religious ceremonies, and industrial materials there are 1 species (1.69%).
... As fisheries management policies shift from single species assessments to the more holistic Ecosystem-Based Fisheries Management (EBFM) (Hall and Mainprize 2004, Pikitch et al. 2004, Branch and Clark 2006, the need to understand the influence of spatial structures on ecological processes continues to grow. This, along with the technological advances in computational power and geographical information systems (GIS), has led to the emergence of a field that quantitatively examines spatially explicit data in ecology, referred to as 'spatial analysis' (Liebhold and Gurevitch 2002). This field of study fully embraces Legendre's (1993) new paradigm and aims to explicitly understand, measure and model spatial patterns in ecological data (Liebhold and Gurevitch 2002). ...
... This, along with the technological advances in computational power and geographical information systems (GIS), has led to the emergence of a field that quantitatively examines spatially explicit data in ecology, referred to as 'spatial analysis' (Liebhold and Gurevitch 2002). This field of study fully embraces Legendre's (1993) new paradigm and aims to explicitly understand, measure and model spatial patterns in ecological data (Liebhold and Gurevitch 2002). ...
... Spatially structured residuals usually indicate either that the model may be misspecified, in the sense that important variables predictors may be missing from the model, or that other processes are important besides the effects of the measured environmental variables (Fortin and Dale 2005, Wagner and Fortin 2005, McIntire and Fajardo 2009, Dray et al. 2012. Given that the majority of ecological processes are spatially structured, the introduction of a spatial component as a proxy or 'substitute variable' acknowledges the presence of such potentially underlying processes that may be difficult to measure directly in field studies, but may be important predictors, e.g., missing environmental variables or biotic interactions (Liebhold and Gurevitch 2002, McIntire and Fajardo 2009, Dray et al. 2012. Although these missing 'variables' may not be identified, their combined influence can be quantified through spatial analysis and incorporated into mixed models as random effects (Zuur et al. 2009, Dray et al. 2012, Hamylton 2013), thereby enhancing model performance. ...
Tsitsikamma National Park (TNP) possesses the oldest (established 1954), and one of the largest (350 km 2) 'no-take' marine protected areas (MPA) in South Africa. A long-term monitoring (LTM) programme to observe the subtidal reef fishes in the TNP MPA was established in 2007. To date, 243 angling replicates have been completed, and a total of 2,751 fish belonging to 41 different species have been caught and released. In an era of unprecedented global biodiversity loss, data that can be used to monitor ecosystems and gauge changes in biodiversity through time are essential. This thesis aims to improve the methodological and statistical processes currently available for LTM of subtidal reef fish by providing an evaluation of the TNP MPA LTM programme. Angling data revealed definitive spatial structuring, in the form of spatial autocorrelation, and a shift in viewing spatial dependency as a statistical obstacle to a source of ecological information created a new avenue of data inference. Species-specific distribution maps identified localized habitat as the main predictor variable for species abundance, emphasizing the need for accurate a priori bathymetric information for subtidal monitoring. 'Random forest' analyses confirmed spatial variables are more important than temporal variables in predicting species abundance. The effectiveness of Generalized Linear Mixed Models (GAMMs) to account for spatial autocorrelation was highlighted, and evidence that disregarding spatial dependencies in temporal analyses can produce erroneous results was illustrated in the case of dageraad (Chrysoblephus cristiceps). Correlograms indicated that the current sampling strategy produced spatially redundant data and the sampling unit size (150 m 2) could be doubled to optimize sampling. Temporal analyses demonstrated that after 50 years of 'no take' protection the TNP MPA ichthyofauna exhibits a high level of stability. Species-specific size structure was also found to be highly stable. Dageraad was the only species to exhibit a definitive temporal trend in their size structure, which was attributed to recruitment variation and the possibility that large individuals may migrate out of the study area. The inadequacy of angling as a method for monitoring a broad spectrum of the fish species was highlighted, particularly due to its selectivity towards large predators. As a result, a new sampling iii technique known as Stereo Baited Remote Underwater Videos (stereo-BRUVs) was introduced to the LTM programme in 2013. Stereo-BRUVs enabled sampling of 2640 fish belonging to 52 different species, from 57 samples collected in less than two years. A comparison of the sampling methods concluded that, compared to angling, stereo-BRUVs provide a superior technique that can survey a significantly larger proportion of the ichthyofauna with minimal length-selectivity biases. In addition, stereo-BRUVs possess a higher statistical power to detect changes in population abundance. However, a potential bias in the form of 'hyperstability' in sites with unusually high fish densities was identified as a possible flaw when using stereo-BRUVs. In an attempt to provide a more rigorous method evaluation, simulation testing was employed to assess the ability of angling and stereo-BRUVs to accurately describe a decreasing population. The advantage of this approach is that the simulated population abundances are known, so that each sampling method can be tested in terms of how well it tracks known abundance trends. The study established that stereo-BRUVs provided more accurate data when describing a distinct population decline of roman (Chrysoblephus laticeps) over 10-and 20-year periods. In addition, spawner-biomass was found to be a more accurate population estimate than relative abundance estimates (CPUE and MaxN) due to the inclusion of population size structure information, highlighting the importance of length-frequency data. The study illustrated that an evaluation framework that utilizes simulation testing has the potential to optimize LTM sampling procedures by addressing a number of methodological questions. This includes developing a procedure that aligns data collected from different sampling methods by applying correction factors, thus ensuring LTM programmes are able to adapt sampling strategies without losing data continuity. iv
... Le développement de méthodes statistiques pour la validation est le problème le plus difficile à résoudre car il n'existe pas de règle d'or pour standardiser les prédictions (Fielding 2002in Ottaviani 2004). (Liebhold et Gurevitch 2002), l'autocorrélation doit être plutôt vue comme une part inhérente des processus spatiaux de sélection et de la structure de l'habitat qu'il faut chercher à expliquer plutôt que de chercher à la minimiser en fonction des données d'occurrence disponibles (Boyce 2006). ...
... Le manque d'indépendance spatiale entre les points d'observations d'une espèce peut être vu comme un problème pouvant nuire notamment à la compréhension des relations faune-habitat(Liebhold et Gurevitch 2002). Il s'agit de l'autocorrélation spatiale qui apparaît quand les points d'occurrence échantillonnés sont proches dans l'espace ou dans le temps et quifait que la position d'une donnée de présence peut influencer la position d'une autre. ...
Dans les Alpes du Nord françaises, les populations de tétras-lyre sont menacées par la fermeture du paysage induite par la colonisation d'espèces ligneuses sur les pâturages abandonnés. Parmi ces espèces, l'aulne vert est considérée comme une menace majeure pour la conservation de l'habitat de reproduction du galliforme. Dans ce contexte, il est nécessaire de mieux connaître les effets de l'organisation spatiale de l'aulne vert sur l'occurrence du tétras-lyre afin de mieux maîtriser cette dynamique d'embuissonnement à l'échelle d'une gestion locale de cet habitat de reproduction. Ainsi, cette thèse s'est attachée dans un premier temps à mettre en évidence que l'occurrence du galliforme peut être prédite à l'aide d'indicateurs spatialisés relatifs à la structure du paysage induite par la distribution de l'aulne vert sur une étendue occupée au sein de son habitat de reproduction. En effet, des données de présence-absence du galliforme issues d'un échantillonnage systématique ont été combinées à une analyse de l'organisation spatiale de l'aulne vert. Ceci a permis d'évaluer l'effet de certains indices paysagers sur la probabilité de présence du galliforme à l'aide de modèles de régression logistique. Nos résultats ont principalement montré que les poules de tétras-lyre sont sensibles à l'organisation spatiale de l'aulne vert alors que ce n'est pas le cas pour les coqs. Plus précisément, le taux de recouvrement de l'aulne vert, le nombre de patchs d'aulne vert et la somme des longueurs de lisières d'aulne vert sont apparus comme étant des prédicteurs significatifs de l'occurrence des poules.Ces trois prédicteurs ont ensuite été utilisés pour construire des modèles spatialement explicites décrivant l'occupation de l'espace par les poules en fonction d'une carte de distribution de l'aulne vert. Après validation des prédictions des modèles, le modèle le plus pertinent et le plus valide pour prédire l'occurrence des poules est celui utilisant la somme des longueurs de lisières associée au taux de recouvrement de l'aulne vert. D'autre part, ce modèle a été combiné à un modèle de simulation de l'expansion de l'aulne vert dans le temps et l'espace à l'aide d'un modèle à automate cellulaire stochastique. Ainsi, nous avons pu simuler l'évolution de la distribution de l'occurrence des poules en fonction de l'évolution des patrons d'organisation du paysage induite par l'expansion de l'aulne vert.La mise en évidence d'un lien entre des patrons paysagers et l'occupation de l'espace par les poules à une échelle fine suggère qu'intégrer des indices paysagers spatialisés dans un modèle spatial et temporel devrait permettre de développer un outil d'aide à la gestion locale de l'habitat du galliforme reposant sur une approche d'écologie du paysage.
... Key criticisms of citizen science research include weak study designs [73], inadequate participant training [29], poor standardisation of data and methodologies [74], and observational biases [75]. Poor survey methods can directly impact the accuracy and reliability of citizen science research, which in turn can erode confidence in the validity of findings on species abundance and density which are considered essential parameters for assessing population demographics [76,77]. ...
... Accuracy is considered essential when assessing species population demographics [76,77], and citizen science surveys have shown similar results to traditional surveys within the Bay of Biscay (e.g. Refs. ...
Cetacean communities face significant threats from adverse interactions with human activities such as bycatch, vessel collision, and environmental pollution. Monitoring of marine mammal populations can help to assess and safeguard marine biodiversity for future generations. Traditional surveys can be costly and time-consuming to undertake, but we explore the ability of citizen science to inform environmental assessments and subsequent conservation management. We use data collected from platforms of opportunity within the Bay of Biscay to investigate spatial changes in cetacean diversity, with the aim of identifying hotspots which may be suitable for further investigation and conservation. Seventeen species of cetaceans were recorded over a ten year period, many of which are data deficient in European waters (e.g. Bottlenose dolphin, Short-beaked common dolphin, Striped dolphin, Risso's dolphin, Long-finned pilot whale, Killer whale, Northern bottlenose whale, Cuvier's beaked whale, Sowerby's beaked whale and True's beaked whale). Biodiversity (determined by Simpson's Diversity index) ranged from 0.19 to 0.77. The central and southern areas of the survey area indicated the highest biodiversity (0.65–0.77), and these locations may benefit most from protection as Important Marine Mammal Areas. We present a case for this designation, and discuss the benefits and limitations of citizen science for informing conservation action.
... The study of spatial relationships in ecology has grown exponentially since ecologists, in general, rejected the conventional view of autocorrelation as simply being a statistical nuisance and instead fully embraced Legendre's (1993) paradigm whereby autocorrelation is seen as a source of ecological information. In this context, spatial analysis aims to explicitly understand, measure and model spatial patterns in ecological data (Liebhold and Gurevitch 2002). McIntire and Fajardo (2009) further expanded the concept of spatial analysis by proposing spatial dependency as a surrogate for uncovering unidentified and/or immeasurable ecological variables or processes through the analysis of spatial patterns and their residuals. ...
... Much of the emphasis of ecological long-term monitoring (LTM) is placed on temporal abundance trends for species, and spatial aspects are often poorly investigated or completely neglected (Legendre 1993;Zuur et al. 2009). This is reflected in the various methods that have been devised for eliminating the effects of spatial dependence when measuring biotic responses over time, such as spatial stratification and 'neighbourhood' averaging (Liebhold and Gurevitch 2002). In doing so, ecologists accept a high level of variability within a temporal dataset, resulting in low precision of the predicted abundance trend. ...
Spatial dependence can obscure relationships between response and explanatory variables because of structuring within the residuals reducing variance and biasing coefficient estimates. Here, we highlight the influence of the spatial component, in the presence of spatial dependence, on abundance trends. This is illustrated using abundance data for a Critically Endangered reef fish, dageraad Chrysoblephus cristiceps, which were obtained from a long-term monitoring programme in the Tsitsikamma National Park marine protected area, South Africa. Correlograms illustrate distinct spatial structuring in the abundance data, and spatial variables were determined as more important than temporal variables when ranked according to predictive power using a random forest analysis. A generalised additive model (GAM) that did not account for spatial dependencies was compared to a generalised additive mixed model (GAMM) that incorporated a spatial residual correlation structure. Results derived from the spatially explicit GAMM differed considerably from the GAM lacking a spatial component, with the latter deemed to produce over-precise and partially biased abundance trends. The study emphasises the importance of space in accurately modelling abundance estimates, particularly temporal trends, and provides an introduction to the minimal statistical requirements necessary to address the violations associated with spatial autocorrelation.
... When observations are aggregated together, we refer to these modified observations as having different units of analysis for modeling (e.g., 10 observations aggregated into a single quantity has a unit of analysis of 10; Neuendorf, 2021). However, the potential benefits of increased effort per observation, aggregated/composited unit of analysis, may be offset by the undesirable effect of masking processes operating at fine spatio-temporal scales (Rossi et al., 1992;Jelinski and Wu, 1996;Liebhold and Gurevitch, 2002;Maas-Hebner et al., 2015). Thus, the FLvMS trade-off should be a ubiquitous design consideration for both observational studies and resulting analyses. ...
In order to learn about broad scale ecological patterns, data from large-scale surveys must allow us to either estimate the correlations between the environment and an outcome and/or accurately predict ecological patterns. An important part of data collection is the sampling effort used to collect observations, which we decompose into two quantities: the number of observations or plots (n) and the per-observation/plot effort (E; e.g., area per plot). If we want to understand the relationships between predictors and a response variable, then lower model parameter uncertainty is desirable. If the goal is to predict a response variable, then lower prediction error is preferable. We aim to learn if and when aggregating data can help attain these goals. We find that a small sample size coupled with large observation effort coupled (few large) can yield better predictions when compared to a large number of observations with low observation effort (many small). We also show that the combination of the two values (n and E), rather than one alone, has an impact on parameter uncertainty. In an application to Forest Inventory and Analysis (FIA) data, we model the tree density of selected species at various amounts of aggregation using linear regression in order to compare the findings from simulated data to real data. The application supports the theoretical findings that increasing observational effort through aggregation can lead to improved predictions, conditional on the thoughtful aggregation of the observational plots. In particular, aggregations over extremely large and variable covariate space may lead to poor prediction and high parameter uncertainty. Analyses of large-range data can improve with aggregation, with implications for both model evaluation and sampling design: testing model prediction accuracy without an underlying knowledge of the datasets and the scale at which predictor variables operate can obscure meaningful results.
... Information System (GIS) to explore spatial relationships within and between data (Gough & Rushton, 2000) (Vogiatzakis, 2003). Spatial relationships in ecology are very important, since the ecologists are often interested to analyse data with the objective of quantify spatial patterns (Liebhold & Gurevitch, 2002). Their relationships show the geometric or geographic properties of the data permitting to identify their distribution by means of spatial analysis. ...
Introduced in 1960s to store, analyse, and manipulate data collected for the Canada Land Inventory by mapping information about soils, agriculture, recreation, wildlife, waterfowl, forestry and land use, since their origins Geographic Information Systems (GISs) have had a fundamental role in the study of the environment. As computers systems for capturing, storing, checking, and displaying data related to positions on Earth's surface, GISs have quickly become an effective and powerful tool for addressing ecological issues, analysing the relationship between living things and their habitats, assessing the environmental impact of man-made transformations of a territory. This article aims to show and discuss the results of a study concerning quantitative distribution of GIS for ecology in literature from Scopus database using bibliometric analysis. Bibliometric analysis is a scientific computer assisted review methodology to explore the major research interests in scientific literature, so to identify core research authors, as well as their relationship, by covering articles, conference papers, book chapters and reviews related to a given topic or field. The high number of scientific manuscripts published on the subject (5,204) in the analysed period (1979-2021), remarked the soundness of this topic. While China shows the greatest number of published documents, USA is the country with the most cited documents. Specifically, "remote sensing", "spatial analysis" and "land use" are the keywords most frequently linked to GIS and ecology, so to underline respectively three aspects: the relevance of environment monitoring by satellite, airplane or drone, the utility of relating ecological questions to the geo-localization, the necessity of produce thematic maps for describing the economic and cultural activities (e.g., agricultural, residential, industrial, and recreational uses) that are practiced at a given place. Since the study shows that trend of publications focusing on the application of GIS for ecology is increasing, further growing is expected in the next future, also considering the ductility that these computer systems provide in different fields.
... This Btk are softest on natural enemies, do not leave residue on the vegetable or environment, and are thus environmentally friendly and compatible with IPM program (Walsh 2005). Understanding the distribution of an insect pest in field situations is essential for the design of an IPM program (Brenner et al. 1998, Liebhold andGurevitch 2002) and sampling plan developments (Taylor 1984, Binns et al. 2000, Southwood and Henderson 2016. In addition, knowledge of pest distribution of an insect population is essential in developing sampling plans in particular because factors responsible for variation in pest distribution differ within the field and at landscape and regional scales (Ayalew et al. 2008, Panthi et al. 2021. ...
The diamondback moth (Plutella xylostella L.) is the most destructive insect pest on cabbage (Brassica oleracea var. capitata L.). Infestation by this pest usually results in the indiscriminate use of insecticides by farmers due to a lack of sampling plans for this pest. Sampling plans for P. xylostella management decisions on winter-spring cabbage in the Eastern Cape Province of South Africa were developed, through population monitoring that comprised weekly counts of immature stages of P. xylostella on 60 plants for 11 wk each during the winter and spring seasons. The mean density-variance relationship was used to describe the distribution of the pest, and number of infested plants was used to develop a fixed-precision sampling plan. All plant growth stages preceding maturation were vulnerable to P. xylostella damage resulting in yield losses. A high aggregation of P. xylostella on cabbage was observed in spring than in winter. The average sample number to estimate P. xylostella density within a 15% standard error of the mean was 35 plants. Furthermore, the estimated plant proportion action threshold (AT) was 51% with density action thresholds of 0.50 and 0.80 for spring and winter, respectively. Fitting P. xylostella cumulative counts in the winter and spring sampling plans resulted in 100% and 45% reduction in insecticide treatments. The similarity of sample size and ATs between both seasons provides evidence that a single sampling plan is practical for all cabbage growing seasons. The similarity of the estimated ATs to those acceptable in established integrated pest management programs indicates reliability.
... Environmental data associated with the locations of species' presence are not often independent (Carl and Kuhn 2008;Dormann et al. 2007;Dormann 2007), while handling with this spatial autocorrelation (Dale et al. 2002) represents a major challenge in SDM, even though it plays a significant role as source of information to study processes responsible for observed patterns (Schabenberger et al. 2017 ;Dormann et al. 2007). The interest in quantifying and including spatial autocorrelation in the understanding of natural phenomena is frequent nowadays (Dale et al. 2002, Liebhold andGurevitch 2002). ...
Although Iroko (Milicia excelsa) is listed endangered and has a great socioeconomic and cultural importance in Benin, there have been few attempts to definition of sustainable conservation strategies for the species. This study explored the spatial patterns of the species and tested if the species distribution may be affected under future climates forecasts. Moran index was used to measure the spatial autocorrelation of the abundance of Iroko. For the niche modeling, records of the species were added to bioclimatic variables (current and future conditions) and soil layers in the maximum entropy algorithm. Results showed overall a spatial dependency between Iroko population according to the density (P < 0.001). The population density seems similar between 0 and 3 km but differ from 3 to 150 km. A slight increase was noted from the present-day distribution to the future forecasts (4.71 % and 6.95 % respectively following the scenarios RCP4.5 and RCP8.5). Urgent conservation actions are needed to safeguard the remnant populations of Iroko in Benin.
... Measurements on a cohesive study area, such as performed in field trials (Singh et al., 2003), ecological surveys (Liebhold, 2002), or remote sensing (Wójtowicz et al., 2016), provide a wealth of knowledge on variability occurring between living organisms. On the one hand, the common origin of the data and the use of the same cultivar, soil, weather, and cultivating conditions reduce the variability to manageable levels. ...
Naturally occurring variability within a study region harbors valuable information on relationships between biological variables. Yet, spatial patterns within these study areas, e.g., in field trials, violate the assumption of independence of observations, setting particular challenges in terms of hypothesis testing, parameter estimation, feature selection, and model evaluation. We evaluate a number of spatial regression methods in a simulation study, including more realistic spatial effects than employed so far. Based on our results, we recommend generalized least squares (GLS) estimation for experimental as well as for observational setups and demonstrate how it can be incorporated into popular regression models for high-dimensional data such as regularized least squares. This new method is available in the BioConductor R-package pengls. Inclusion of a spatial error structure improves parameter estimation and predictive model performance in low-dimensional settings and also improves feature selection in high-dimensional settings by reducing “red-shift”: the preferential selection of features with spatial structure. In addition, we argue that the absence of spatial autocorrelation (SAC) in the model residuals should not be taken as a sign of a good fit, since it may result from overfitting the spatial trend. Finally, we confirm our findings in a case study on the prediction of winter wheat yield based on multispectral measurements.
... As a widely used method in other fields, K-function plays an important role in spatial data analysis in plant ecology recently [10]. But it also forms a major challenge in present ecological research [11]. Like most spatial statistical methods, the K-function assumes a homogenous environment to calculate the Euclidean distance between points (or straight-line distance "as the crow flies"), and therefore is an inappropriate tool for analyzing point patterns confined along irregular road networks [5]. ...
Previous studies have demonstrated the inherent relationships between landscape pattern and road networks. A new technique for analyzing the distribution of points on a network has been developed, called the network K-function for univariate analysis. Using this method, we analyzed the spatial patterns of three types of vegetations in Xishuangbanna in Yunnan province with different periods, to investigate the effects of road disturbance. Comparing different periods of K curves, we can explore the characteristics of different types of vegetations distributing along the road network. The results of the Kernel and network K-function analyses showed that populations of three types of vegetations were tending to cluster by road networks. The broad-leaved forests were not randomly distributed within road networks in three periods at all distance. In contrast, the coniferous forests is peculiar, with significant small-scale clustering of at distances up to 120 km and significant large-scale repulsion of clusters of populations >120 km. However the number of plantation forests increased and tend to cluster with the road networks.
... Additionally, the functions of species need to be assessed, particularly those that determine how they utilize the landscape. Unfortunately, these types of data are rarely collected, because landscape level studies are dominated by measuring alpha-diversity within specific production land uses (even if this diversity is related to the composition or configuration of the surrounding landscape), with an unnecessary emphasis of spatial-independence of sampling points (Liebold and Gurevitch, 2002). Questions that currently limit the development of theory related to landscape-moderated effects on biodiversity and ecosystem function are outlined in Box 5. ...
Despite a developing understanding of how landscape level processes moderate biodiversity patterns and ecosystem functioning, key questions remain unresolved, therefore limiting our ability to manage for biodiversity conservation and ecosystem functioning at the most appropriate scales. These questions have remained unanswered because studies in agricultural landscapes generally over-emphasize alpha diversity within managed land uses, and are focused at scales that are irrelevant to species studied. We argue that the key to resolving unanswered questions in landscape-moderated effects on biodiversity and ecosystem functioning lies in establishing the distribution of available species and functions across the landscape and between land uses, and in understanding how this distribution of species varies with changing landscape context. We emphasize the need for studies that empirically test the mechanisms underpinning landscape-moderated effects on biodiversity and ecosystem function and link these with ecosystem service delivery. We facilitate this approach by outlining the empirical investigations that will lead to a better understanding of biodiversity patterns and ecosystem functioning at the landscape scale, and we highlight statistical approaches to support these different approaches to sampling. Our paper is divided in four sections: (A) we identify where and why gaps exist in our mechanistic understanding of landscape level processes, by reviewing current hypotheses; (B) we outline why, and how, landscape level research would benefit from shifting the focus to the distribution and partitioning of species and functions within a landscape; (C) we outline why, and how, larger scale processes, such as dispersal and meta-population dynamics need to be addressed in a more interactive fashion; and finally, (D) we round out by highlighting the experimental settings where landscape effects most urgently need testing.
... The modeling of species distributions, a significant endeavor in ecology and conservation, has become a more prominent feature of population analyses as improvements in technology and cost efficiency have increased the ability to collect spatial ecological data. Statistical research has greatly developed the theory of models containing spatial autocorrelation during the past half century [52], however the application of these methods has only recently been considered valuable to modeling ecological processes [12,23,29,30]. A popular statistical method for modeling species distributions and abundance is the varying coefficient model (VCM) [6,19] introduced by Hastie and Tibshirani [21]. ...
Varying coefficient models (VCMs) are commonly used for their high degree of flexibility in modeling complex systems. Many applications in fisheries utilize VCMs to capture spatial variation in populations of marine fishes. All of these applications use the penalized least squares method for estimation. However, this approach is known to be sensitive to non-normal distributions and outliers, a common feature of ecological data. Robust estimation methods are more appropriate for handling noisy and non-normal data. We present the application of a signed-rank-based procedure for obtaining robust estimates in VCMs on a fisheries dataset from the North Pacific Ocean. We demonstrates that the signed-rank-based estimation method provides better fit and improved prediction in comparison to the classical likelihood VCM fits in both simulations and the real data application, particularly when the distributions are non-normal and may be misspecified. Rank-based estimation of VCMs is therefore valuable for modeling ecological data and obtaining useful inferences where non-normality and outliers are common.
... For example, the emergence of fine-scale GPS tracking technology has refined both the spatial and temporal scales at which animal relocations can be measured [17,18]. Likewise, increased statistical software capabilities have facilitated the manipulation and analysis of spatial data which previously was cumbersome or infeasible, or only provided coarse-scaled information [19][20][21]. Advancements in methodology have also occurred through the emergence of home range estimators that incorporate time, variance in Brownian motion, or other animal movement parameters into their models and now result in more representative utilization distributions that reflect associated movements across a landscape, rather than independent relocation points (e.g., Brownian and dynamic Brownian bridge movement models, movement kernel density estimators [22][23][24][25]). ...
Infrequent, long-distance animal movements outside of typical home range areas provide useful insights into resource acquisition, gene flow, and disease transmission within the fields of conservation and wildlife management, yet understanding of these movements is still limited across taxa. To detect these extra-home range movements (EHRMs) in spatial relocation datasets, most previous studies compare relocation points against fixed spatial and temporal bounds, typified by seasonal home ranges (referred to here as the “Fixed-Period” method). However, utilizing home ranges modelled over fixed time periods to detect EHRMs within those periods likely results in many EHRMs going undocumented, particularly when an animal’s space use changes within that period of time. To address this, we propose a novel, “Moving-Window” method of detecting EHRMs through an iterative process, comparing each day’s relocation data to the preceding period of space use only. We compared the number and characteristics of EHRM detections by both the Moving-Window and Fixed-Period methods using GPS relocations from 33 white-tailed deer ( Odocoileus virginianus ) in Alabama, USA. The Moving-Window method detected 1.5 times as many EHRMs as the Fixed-Period method and identified 120 unique movements that were undetected by the Fixed-Period method, including some movements that extended nearly 5 km outside of home range boundaries. Additionally, we utilized our EHRM dataset to highlight and evaluate potential sources of variation in EHRM summary statistics stemming from differences in definition criteria among previous EHRM literature. We found that this spectrum of criteria identified between 15.6% and 100.0% of the EHRMs within our dataset. We conclude that variability in terminology and definition criteria previously used for EHRM detection hinders useful comparisons between studies. The Moving-Window approach to EHRM detection introduced here, along with proposed methodology guidelines for future EHRM studies, should allow researchers to better investigate and understand these behaviors across a variety of taxa.
... Previously, the majority of efforts to conserve biodiversity have been focused on species, communities or their habitats, but recently, there has been an increasing awareness of the importance of considering larger scales, such as entire ecosystems and landscapes, with the aim of benefiting both biodiversity and human well-being [4][5][6]. Likewise, the recent tendency in conservation planning is focused on ecosystem-level assessments, which ensures not only the protection of a sufficient portion of all ecosystems within a country but also the persistence of lower-level biodiversity, for example, genetic diversity [7][8][9]. forest decline and land use change driving ecosystem collapse, few studies have assessed conservation status at the ecosystem-level based on the IUCN criteria [35]. ...
World ecosystems are suffering from anthropogenic and natural pressure. The IUCN (International Union for Conservation of Nature) has developed analogous criteria for the Red List of Threatened Species in order to perform similar risk assessments on ecosystems, creating the Red List of Ecosystems (RLE) methodology. One of the most significant challenges for the construction of these lists is gathering the available information to apply the criteria. By applying IUCN RLE criteria B (the extent of restricted geographic distribution of an ecosystem), we analyzed the threat level of 64 forest ecosystems of the Ecuadorian mainland. According to the results, limited distribution is the key risk to threatened ecosystems, which are associated with anthropogenic pressures. Our study showed that 22% of forest ecosystems are classified as threatened. This evaluation of the forest ecosystem status at a national level could lead to public awareness towards ecosystem conservation and provide reasonable strategies to managers.
... Multivariate method (redundancy and analysis) was used to assess the relationships between coffee quality traits and environmental variables. This is because correlation and regression analysis alone may not be suitable when large numbers of variables are involved, and thus different methods should be integrated for comprehensive analysis (Liebhold and Gurevitch, 2002;Zhang and Oxley, 1994). Multivariate analysis provides statistical methods for study of the joint relationships of variables (James and McCulloch, 1990). ...
Coffee quality is a complex trait involving sensory and bean characteristics as well as biochemical contents. The objective of this study was to assess the major factors influencing the quality of wild Arabica coffee (Coffea arabica L.) in the natural coffee forests of southwest and southeast Ethiopia. Results revealed that both natural (soil, aspect, elevation, climate, geographic location) and human factors (cherry harvesting/ handing, theft, forest management) considerably influenced the quality of wild Arabica coffee. The soil factor affected every component of coffee quality (cup quality, bean characteristics and biochemical contents). The cup quality of coffee varied with soil properties, especially with available P and soil texture. The bean size distribution was also affected by soil properties; there was significant positive relationship between soil pH, sand or Mn and the proportion of bold beans (retained on screen 17). Soil organic matter, total N and sand content were inversely correlated with caffeine content, but available P and clay content were positively correlated with caffeine. Increase in elevation led to increase in bean size up to the elevation of about 1600 m above sea level, but thereafter no more increase in bean size (hump-shaped relationship, not monotonic). Bean size increased with increase in longitude, but it decreased with increase in latitude. Cup quality was also significantly influenced by coffee harvesting and handling, but its influence was not noticed on bean size and biochemical contents. Coffee quality is therefore the resultant of an interaction of different natural and human factors prevailing in the respective area.
... Hence, ecological processes cannot be inferred from spatial patterns without additional external information. Thus, the underlying processes responsible for the observed spatial patterns are of key interest to ecologists (Liehold & Gurevitch, 2002;McIntire & Fajardo, 2009;Tilman & Kareiva, 1997;Tuda, 2007). ...
A major objective of plant ecology research is to determine the underlying processes responsible for the observed spatial distribution patterns of plant species. Plants can be approximated as points in space for this purpose, and thus, spatial point pattern analysis has become increasingly popular in ecological research. The basic piece of data for point pattern analysis is a point location of an ecological object in some study region. Therefore, point pattern analysis can only be performed if data can be collected. However, due to the lack of a convenient sampling method, a few previous studies have used point pattern analysis to examine the spatial patterns of grassland species. This is unfortunate because being able to explore point patterns in grassland systems has widespread implications for population dynamics, community‐level patterns, and ecological processes. In this study, we developed a new method to measure individual coordinates of species in grassland communities. This method records plant growing positions via digital picture samples that have been sub‐blocked within a geographical information system (GIS). Here, we tested out the new method by measuring the individual coordinates of Stipa grandis in grazed and ungrazed S. grandis communities in a temperate steppe ecosystem in China. Furthermore, we analyzed the pattern of S. grandis by using the pair correlation function g (r ) with both a homogeneous Poisson process and a heterogeneous Poisson process. Our results showed that individuals of S. grandis were overdispersed according to the homogeneous Poisson process at 0–0.16 m in the ungrazed community, while they were clustered at 0.19 m according to the homogeneous and heterogeneous Poisson processes in the grazed community. These results suggest that competitive interactions dominated the ungrazed community, while facilitative interactions dominated the grazed community. In sum, we successfully executed a new sampling method, using digital photography and a geographical information system, to collect experimental data on the spatial point patterns for the populations in this grassland community.
... En effet, le forestier ne prend pas souvent en compte la question de la structure spatiale, en considérant que la répartition des arbres est simplement aléatoire ou régulière (Bouchon, 1979). Depuis une vingtaine d'années, plusieurs études ont été réalisées par des forestiers ou des écologues pour comparer les différentes méthodes d'analyse de la structure spatiale de l'écosystème forestier (Liebhold & Gurevitch, 2002). Les différentes méthodes utilisées se classent usuellement en fonction de la nature des données nécessaires à leur établissement. ...
... La caractérisation de la distribution spatiale d'une variable écologique est une étape fondamentale car elle peut avoir des conséquences sur les inférences statistiques associées aux valeurs échantillonnées Liebhold et Gurevitch, 2002). En présence d'autocorrélation spatiale positive, des échantillons proches dans l'espace fournissent des informations partiellement redondantes, diminuant le nombre de degrés de liberté de l'échantillon total. ...
... Urbanisation and its environmental effects resulted from population increase, socioeconomic developments and land use changes (Fragkias & Seto, 2009). In the past decades, catering for the rapid demographic and environmental changes using weak land use planning have led to the development of a haphazard landscape, stress on the structure of the ecosystem and the deterioration of the environment (Liebhold & Gurevitch, 2002). Forest and agricultural lands have been changed to human settlements and urban areas over decades of years (Fragkias & Seto, 2009). ...
Spatial patterns of human settlements, their changes and their geographical implications are important for understanding the drivers of land use and land cover change. This paper examines the spatiotemporal pattern of settlement development in three different settlements of Thabo Mofutsanyane municipal district namely Harrismith, Vrede and Ladybrand using GIS, remote sensing and spatial metrics techniques. The study is based on 30 years of time-series data compiled from satellite images with emphasis on pre and post 1994’s (the year of change in government from apartheid to majority rule) spatial change in settlement development. Landsat 4–5 imageries for 1989, 1999, 2009 and Landsat 8 OLI for 2018 were downloaded and classified for land use/land cover change (LULCC). Also, landscape and class metrics were computed using Fragstats QGIS 2.18.9 to generate spatial analysis. A dynamic spatial pattern is observed in the settlements under study. Urban built-up areas had a rapid trend of growth in Harrismith from 1989 (5 years before transition from apartheid to majority rule) to 1999 (5 years after transition from apartheid to majority rule) but later slowed down in the subsequent years under study while Ladybrand and Vrede had moderate growth trend in the subsequent years under study. The settlement development process has developed fragmented and heterogeneous land use combinations in the years after 1994. At landscape level, land fragmentation occurred due to land use changes and significant urban expansion; Ladybrand experienced more physical connectedness than Harrismith and Vrede. While at class level, Harrismith and Vrede are more aggregated or physically connected than Ladybrand; this means Ladybrand was relatively more fragmented than the other two settlements. The study results show that a LULCC and landscape metrics integrated approach is effective to analyse and describe the spatial patterns of urban landscapes.
... Once the variogram function is calculated, it can be used for kriging, which is an interpolation method used to estimate values at unsampled locations [31][32][33]. Variogram analysis and kriging have been used to conduct spatial analysis in forest entomology and agricultural systems [33][34][35]. I used kriging to interpolate pre-and post-MPB basal areas to build contour maps, which I examined visually. ...
The mountain pine beetle (MPB) (Dendroctonus ponderosae) is a bark beetle that attacks and kills ponderosa pine (Pinus ponderosa), among other pine species throughout the western conifer forests of the United States and Canada, particularly in dense stands comprising large trees. There is information on the stand conditions that the insect prefers. However, there is a paucity of information on how small-scale variation in stand conditions influences the distribution of tree mortality within a stand. I examined the small-scale distribution of ponderosa pine basal area pre- and post a mountain pine beetle infestation, and used geostatistical modeling to relate the spatial distribution of the host to subsequent MPB-caused tree mortality. Results indicated increased mortality in the denser parts of the stand. Previous land management has changed historically open low-elevation ponderosa pine stands with aggregated tree distribution into dense stands that are susceptible to mountain pine beetles and intense fires. Current restoration efforts are aimed at reducing tree density and leaving clumps of trees, which are more similar to historical conditions. The residual clumps, however, may be susceptible to mountain pine beetle populations. Land managers will want to be cognizant of how mountain pine beetles will respond to restoration treatments, so as to prevent and mitigate tree mortality that could negate restoration efforts.
... In order to observe possible differences in the morphometric characteristics of the different species of seagrass, a non-parametric ANOVA was performed between the study sites (north, center and south), using the Kruskal-Wallis test. The results were represented with box and whisker diagrams (Liebhold and Gurevitch 2002). An analysis of Landscape Ecology metrics was performed to identify the spatial complexity of the seagrasses in the study area, obtaining statistical indices at class level for the landscape in each area. ...
Seagrass meadows are sites that help mitigate the effects of climate change. The protected area of the Laguna Madre of Tamaulipas is an important site for its biodiversity, which has undergone changes both in the structure and distribution of its seagrass meadows. Five seagrass species were found (Halodule wrightii, Syringodium filiforme, Thalassia testudinum, Ruppia maritima and Halophila engelmannii), forming multispecific meadows. The south zone presented the longest and broadest leaves, but the lowest biomass. Biomass was greatest in the center zone, whereas the highest density were observed in the north zone. The structure analysis showed that the longest and the densest seagrass meadows were S.filiforme. The greatest biomass was recorded for T.testudinum. The meadows with the greatest cover consisted of H.wrightii-S.filiforme. There is little fragmentation of the landscape, and a large succession of species. This indicates change processes, due to the variation in environmental conditions, caused by anthropic modifications, in the lagoon. Due to its importance as an environmental bioindicator, it is necessary to monitor changes in the patterns of structure, fragmentation and succession of species. The present research provides evidence of the change in the distribution of tropical seagrass cover, which may be related to the tropicalization of temperate ecosystems and the need to conserve these habitats.
... Two green zones in the city of Kolkata were chosen-the CKBS and the East Kolkata Wetland Area. Since birds are highly diverse and conspicuous species of the ecosystem and are sentinel to environmental stresses (Hanski 1999, Liebhold et al., 2002, Collinge 2001, Bellier et al., 2007, Soetaert et al., 2009, Jane et al., 2009, they could be studied with respect to their niche, to get a better understanding of the interaction with the habitat as well as the habitat. 6 Species of birds were chosen, which were common to both the places, but their population varied in those places. ...
Plants and trees support the survival of many species. The aim of this study is to get an elementary idea of the role of habitat, mainly the niche, in the growth and survival of the population of the bird species. Two sampling stations were chosen, one at the Chintamani Kar Bird Sanctuary, Kolkata and the other at the East Kolkata Wetlands. Species of birds common to both these regions were chosen and their number was recorded. The population varied to a great extent at these two habitats. Thus, this study aims to focus on the importance of the relationship between the habitat requirements and niche specification of the bird species. It also gives the idea, that conspicuous species like birds are helpful in the study of ecosystem and effects of the rise of pollution in the ecosystem, can be studied, through monitoring the changes, in the interaction of the species with the environmental factors. The present study was concluded with the fact, that their food habits, nesting spaces, local landscape, vegetation and breeding practices affect their growth and population, even in the regions with similar altitude-longitude-latitude scale, temperature and climatic zone (macrohabitat remaining the same, changes occurring in the microhabitat). Micro factors like-nesting space, breeding habits, feeding practices as well as their body features, play an important role in the interactions. Mathematical analysis has been performed upon sample data to figure out the correlation between the two attributes. Thus, consolidated evidence has been created to support the aim of this study. This study has been conducted at a very elementary level and factors in the variation of population like-interspecific and intraspecific interactions and any kind associations could not be included within the scope of this study. But, future findings including the physico-chemical factors as well as, better metrics would give us a better view of our ecological parameters and environmental health. As birds are conspicuous species, their population or change in population from one microhabitat to another, is one of the easiest ways to spot the changing dynamics of our ecosystem. Their niche, habitat requirement and growth and survival is very specific and thus any change in the parameters would in turn change their numbers, in a definite geographical zone. The study focuses on the habitat specifications and how a particular species of bird, interacts with it. Finally, at the end of the study we have tried to establish a correlation between the habitat specifications of the individual bird species with the niche that is how the species, under study interacts with their habitats on a micro-scale i.e., the microhabitat (a very definitive component in our ecosystem that we often overlook at the superficial level).
... Threshold based hotspot delineations are a common approach, where a somewhat arbitrary threshold is applied to density, abundance or richness maps to identify areas where the top 2.5% (e.g., Ceballos and Ehrlich 2006), 5% (e.g., ) 10% (e.g., Tolimieri et al. 2015) or 20% (Ward-Paige and Bundy 2016) of the feature of interest are located. In contrast, the spatial hotspot approach is a spatially explicit methodology acknowledging the spatial dependence in ecological datasets (Liebhold andGurevitch 2002, Wagner andFortin 2005). Thresholds for hotspot delineation in spatial methods are statistically determined and account for spatial patterns in the data (Nelson and Boots 2008). ...
Canada is committed to maintaining biological diversity and productivity in the marine environment under the Oceans Act (1997). Identifying Ecologically and Biologically Significant Areas (EBSAs) is a key component of this commitment and Fisheries and Oceans (DFO) and the Convention on Biological Diversity (CBD) have developed guidelines and criteria to identify these areas. EBSAs were identified in the Northern Shelf Bioregion (NSB) in 2006 using a two-phase expert-driven approach. In response to a science advice request from Oceans Sector, and following DFO Science’s recommendation that EBSAs should be re-evaluated and updated with new information every five years, we re-assess the original EBSAs with available empirical data to increase understanding of the underlying ecological support for the existing EBSAs. In addition, we present an approach for identifying productivity and diversity hotspots, two EBSA criteria not evaluated in the first process. In general, we found empirical evidence for at least one important species listed in the original EBSA justification for all EBSAs except for the Hecate Strait Front. Although the results of our empirical analysis showed that existing EBSAs do an adequate job of capturing at least a portion of areas important to the ecology of multiple species, the shape and configuration of the EBSA boundaries could likely be improved to better match the ecological features within. In addition to the EBSA reassessment, we present hotspot maps of 1) nearshore habitat diversity, 2) diversity (fish and invertebrates), and 3) biomass (using catch per unit effort of fish and invertebrates). We also provide updated maps for 1) important areas for primary productivity, and 2) Sponge Reef EBSAs. These new data layers can be used to update the EBSAs and be used to inform the MPA network planning process ongoing in the NSB.
... Geostatistical modeling theory originally developed for applied geology is increasingly being used in both basic and applied ecology (Perry et al. 2002, Liebhold andGurevitch 2002) to provide models for studying the spatial pattern of biodiversity variables. Pinho and co-authors (Pedro Pinho et al., 2008b) used geostatistical modeling to describe spatial relations between biodiversity data, land cover categories and atmospheric pollutant concentrations, although at a limited and predetermined spatial scales of analysis. ...
The high potential of geostatistical methods to be applied in spatial epidemiology and the great potential for utilizing lichen ecological indicators in health studies, motivated the research and development of novel methods and applications shown in this thesis. To address an epidemiological question related with the association between air quality and birth weight, this explores the development of novel approaches by 1) exploring the potential of lichen as air quality indicators in environmental health studies, 2) exploring the use of geostatistical simulation to assess spatial uncertainty of exposure, and 3) enhancing the exploratory analysis capabilities of multivariate geostatistics for analysis of spatial processes underlying ecological associations in both environmental and epidemiological fields.
The first part of the thesis provides a novel guideline for health research when geostatistical stochastic simulation is combined with lichens ecological indicator to measure air quality and associations with birth weight outcome. The results showed that, combined with high-spatial-resolution lichen data, geostatistical methods allowed to produce high spatial resolution air quality maps for posterior statistical analysis and presented themselves as cost-effective alternatives and appropriate to measure associations with the health outcome birth weight.
The second part of the thesis introduces novel applications of multivariate geostatistical methods to model spatial processes underlying ecological associations in environmental and epidemiological fields. The results showed that the multivariate geostatistics may play a role to model the intensity and direction of spatially non-stationary processes underlying ecological associations especially in large regions, where variations in their intensity and direction are likely to occur.
... Thus, to understand the processes that shape biodiversity in agricultural landscapes, scientists must explicitly investigate the organization of species assemblages in space and time (Socolar et al. 2016). For example, the few studies that assess the relationship between agricultural intensification and community structure at landscape scales often ignore spatial community turnover, focusing only on alpha or gamma diversity and disregarding the spatial distance between communities in their analyses (Liebhold and Gurevitch 2002;Soininen et al. 2007). This may be risky, as high spatial turnover in species identities (high β-diversity) has been associated with high levels of ecosystem functions and services (Van Der Plas et al. 2016), which are very important for increasing productivity in agricultural land, reducing the need for further arable land. ...
Understanding beta-diversity, i.e. species turnover in space and time, is essential for informing conservation actions. Soaring cultivation of mass flowering crops (e.g. oil seed rape OSR) and loss of semi-natural habitats (SNH) can strongly affect populations of native pollinators, yet it remains unclear how OSR and SNH affect spatial and temporal turnover of pollinator communities. Here, we examined how the landscape-scale proportions of OSR and SNH affect spatial and temporal community turnover in solitary bees and hoverflies, two key provider groups of pollination and pest control services in temperate agro-ecosystems. Using a novel grid-based landscape-wide sampling approach, we quantified pollinator communities within ten 1 km × 1 km landscapes representing independent gradients in OSR and SNH availability. We sampled during and after OSR flowering, in two subsequent years, yielding app. 8800 specimens representing 160 species. Spatial community turnover, measured as the slope of the dissimilarity-distance relationship, was not influenced by the proportion of OSR at any time. In contrast, SNH decreased community turnover for bees during OSR flowering and for hoverflies after flowering, likely caused by pollinator movement between land use types. This suggests that a high availability of SNH may help to promote an even distribution of native bees and hoverflies within temperate agricultural landscapes, hereby potentially stabilizing landscape-wide pollination services.
... In the so-called ''mapped data'' method, every point's coordinates are recorded and used to determine the spatial pattern. The method of Ripley (1981) has been used in recent ecological studies to investigate numerous spatial patterns (Liebhold and Gurevitch 2002). In this study, we used spatial point pattern analysis. ...
In a reserved forest parcel in a virgin eastern Hyrcanian mixed beech forest, 80 ha was surveyed to determine the pit and mound topography, canopy gaps and dead trees. The aim was to investigate the spatial patterns and correlation of pit and mound features with canopy gaps. Seventy-five canopy gaps and 61 pit and mound features were identified. The univariate first order nearest neighbor (RCE) and bivariate second order test (Ripley’s K) statistic were applied. RCE statistics highlighted a general aggregation pattern for canopy gaps and pits and mounds, while pits and mounds alone were more clumped. Distances between canopy gaps were 130 m average, whereas distances between pit and mound features and dead trees were 60 and 78 m, respectively. Spatial positive correlation of canopy gaps with pits and mounds were observed with all distances. The result of spatial correlations between canopy gaps with pits and mounds confirmed that windthrows cause micro successions in fallen tree ecosystem-scale correlated with gap phase dynamics in the forest community-scale.
... The conservation of woody species requires an understanding of driven factors of their distribution (Ruston, Ormerod, & Kerby, 2004) which was one of issues in ecology and conservation for plant ecologists Law et al. 2009). Therefore, spatial analysis patterns of trees was an important tool to understand the arrangement of the system (Linares-Palomino, 2005) and had become a widely used approach in ecological research (Liebhold & Gurevitch, 2002;Revilla & Palomares, 2002;Liang & Dong, 2004;Wiegand & Moloney, 2004). In tropical forest, many studies have shown the dependence of plant distribution to local environment especially on edaphic factors, altitude, latitude and topography (Schemske 2002;Phillips et al., 2003;Lomolino, Sax, & Brown, 2004;Svenning et al., 2004). ...
... Some thresholds reach as high as 25% and 50% (e.g., Nur et al. 2011). However, movement in this discipline has shifted toward acknowledging spatial dependence in ecological datasets and incorporating spatially explicit methodology to understand spatial relationships (Liebhold andGurevitch 2002, Wagner andFortin 2005). Spatial methods for hotspot delineation enable thresholds to be statistically determined and account for the spatial patterns of species distributions (Nelson and Boots 2008). ...
Global biodiversity is undergoing rapid decline due to direct and indirect anthropogenic impacts to species and ecosystems. Marine species, in particular, are experiencing accelerated population declines leading to many species being considered at risk by regional, national, and international standards. As one conservation approach, decisions made using spatially explicit information on marine wildlife populations have the potential to facilitate recovery and contribute to national and international commitments toward conservation targets. Delineating areas of intense use by species at risk can inform future marine spatial planning and conservation efforts, including the identification of marine protected areas. Methods for detecting hotspots (e.g., areas with high density and/or abundance) enable categorical mapping of the most intensely used areas. Yet, many of the current methods for delineating hotspots, such as the top 5% threshold, are subjective and fail to account for spatial patterns. Our goal was to map spatially continuous distributions of marine mammal densities and employ quantitative statistical methods to extract hotspot locations on the northern coast of British Columbia. We integrated systematically surveyed species information with environmental variables using generalized additive models to predict marine mammal distribution and density. Hotspots were identified from the density surfaces using two approaches: aspatial top 5% method and spatially local G i à statistic using three neighborhood definitions. Heterogeneous density patterns were observed for all species, and high-density regions were generally clustered in areas exhibiting oceanographic characteristics that may promote concentrated food resources. Combining species density surfaces and extracting hotspot locations identified regions important to multiple species and present candidate locations for future conservation efforts. Contributions from this research provide robust statistical methods to objectively map hotspot locations and generate GIS data products for informing coastal conservation decisions.
... Abundance and density are the most important demographic measures of a population (Liebhold and Gurevitch, 2002;MacKenzie et al., 2006) and are essential information for population assessments, viability analyses, and evaluations of management procedures (Barlow et al., 1995;Carretta et al., 2009;Wade, 1998). Although important, one common difficulty in abundance studies is accounting for negative bias due to undetected individuals because sampling procedures do not guarantee a perfect detection in most cases (Dorazio et al., 2006;Royle and Dorazio, 2008). ...
... Also diurnal changes of the coastal area cause selection of a preferable home range habitat for scalloped spiny lobsters. Spatial habitat analysis can be applied for measuring and modeling spatial patterns in biotic variables, to understand the mechanisms that manage critical aspects of the ecology of species, such as their distribution (Legendre and Legendre, 1998;Liebhold and Gurevitch, 2002) and for lobster stock assessment (Evans et al., 1996). The Geographic Information System (GIS) can be successfully applied as a fundamental analysis tool in estimation of the spatial relationships between the occurrence of macrobenthos species and related environmental factors (Jong-Kuk et al., 2011). ...
The present study was aimed to investigate the quality of home range habitat characteristics of the scalloped spiny lobster Panulirus homarus (Linnaeus, 1758) in southern coastal region of Sri Lanka. Four sites were selected from south-east (Patanagalle, Godawaya) and south-west (Weligama, Hikkaduwa) regions of the southern coast of Sri Lanka (SCSL). The bottom water quality data and benthic substrate types of their home range habitats were monitored and noted in a 25 x 25 m area covering 16 subsampling points with locality information. With the use of geographical information system (GIS) tools, the spatial distribution maps of environmental parameters were created and submerged bottom substrate types of the four sites were graphed. Salinity, temperature and dissolved oxygen correlated well with depth. Hikkaduwa site was found rich
in corals with less number of scalloped spiny lobsters. Sites of south-east region of the SCSL (Patanagalle, Godawaya) were found less polluted having rocks and sandy bottom with high occurrence of scalloped spiny lobsters. Results of the study showed that Patanagalle site (south-east of SCSL) could be suggested as the most suitable site for culturing scalloped spiny lobsters.
... This kind of contrasting diversity patterns can occur because of, for example, different historic legacies, spatial scales, regional species pools, local environmental conditions, biotic relationships and spatial processes (Alahuhta & Heino, 2013;Alahuhta, Hellsten, Kuoppala, & Riihim€ aki, 2016;Heino, Melo, Siqueira, et al., 2015;Jackson, Peres-Neto, & Olden, 2001). In addition to these deterministic and stochastic factors, the use of various statistical methods to investigate freshwater biodiversity patterns and increasing statistical complexity in ecology makes it challenging to compare results originating from different studies (Liebhold & Gurevitch, 2002). For example, the increasing use of adjusted R 2 values have resulted in decreased overall explained variations across different ecosystems (Low-Decarie, Chivers, & Granados, 2014). ...
1. The biodiversity of aquatic ecosystems is under threats and there is an urgent need to quantify the various facets of biodiversity to assess the conservation value of freshwater ecosystems. The effects of taxonomic relatedness have so far not been taken into account in biodiversity assessments of lake macrophytes.
2. We therefore tested the response of species richness and average taxonomic distinctness (AvTD) of aquatic macrophytes along environmental gradients using linear regression models and Bayesian Information Criterion variable selection method. We selected data from four regions, each with 50 to 60 lakes, situated in northern Europe (Finland, Sweden) and northern America (Minnesota, Wisconsin). We separately studied all macrophyte species, hydrophytes and helophytes.
3. Species richness and AvTD of aquatic macrophytes were generally negatively related in all regions, although it was not statistically significant. Both biodiversity measures responded to environmental gradients to various degrees among the studied macrophyte groups and regions. Species richness was best explained by alkalinity and lake area in Finland, by elevation, annual mean temperature and total phosphorus in Minnesota, and by alkalinity in Wisconsin. AvTD was best explained by alkalinity, annual mean temperature and total phosphorus in Finland and by alkalinity in Wisconsin. Very weak relationships were found in Sweden.
4. Our findings strongly suggest that complementary indices are needed to indicate more effectively the effects of environmental conditions on freshwater biodiversity. Species richness was found to be a better measure than AvTD to account for conservation value in freshwaters. However, further research is required to evaluate the usefulness of AvTD to indicate conservation value (e.g., randomization tests), because alternative measures are clearly needed for those freshwater taxa lacking complete information on true phylogenetic diversity.
... individuals influence community dynamics, and for understanding the importance of intraspecific demographic variation. The explicit incorporation of space into models of species interactions has also been helpful because it allows for the specification of biotic and abiotic neighborhoods that are ecologically relevant (Legendre and Fortin, 1989;Liebhold and Gurevitch, 2002). For example, the influence of density, composition, nearest distance to neighboring tree, and size, on the growth of a target individual can be estimated (Canham et al., 2004;Zhao et al., 2007). ...
The Eastern Deciduous Forest (EDF) region is undergoing a shift in species composition, the most dramatic trend being an increase in mesic taxa such as maple (Acer spp.) and American beech (Fagus grandifolia), and a subsequent decline in xeric species such as oaks (Quercus spp.). While several hypotheses have been proposed to explain these trends, most focus on allogenic processes such as disturbance and climate change, and little attention has been given to local species interactions. To help bridge this gap, we first quantify long-term changes in community composition of an old-growth forest using census data collected over a fifteen-year interval. Within two 50 × 70 m plots, all stems ⩾2.5 cm DBH were tagged and measured in 1996, and their spatial coordinates were mapped. Seedlings were measured in smaller subplots, and soil cores were sampled at these locations. Hemispherical photographs were then taken to quantify the light environment, and these procedures were replicated in 2011. As expected, we find an increase in the dominance of both American beech and sugar maple (Acer saccharum), and a marked decline for most others, particularly white oak (Quercus alba). Neighborhood models incorporating the density, basal area, and composition (i.e., conspecific versus heterospecific) of stems surrounding focal individual trees reveal that local density-dependent interactions were indeed weak for both American beech and sugar maple. At the same time, however, all other species experienced similarly weak effects. Likewise, soil resource gradients had little influence on long-term demographics, contrary to our expectations. Together, our results indicate that the changes observed across the Eastern Deciduous Forest region may indeed be most strongly impacted by allogenic disturbance processes, although we still encourage further research on the potential influence of local species interactions at mediating these dynamics, and expect neighborhood models to become an important tool in understanding the causes of compositional shifts in the EDF region.
We revisit a spatial metapopulation model on continuous space as a stochastic point pattern dynamics. In the model, local patches as points are distributed with a certain spatial configuration and status of each patch changes stochastically between occupied and empty: an occupied patch becomes empty by local extinction and an empty patch becomes occupied both by local and global colonization. We carry out simulation analysis and derive an analytical model in terms of singlet, pair and triplet probabilities that describe the stochastic dynamics. Using a simple closure that approximates triplet probabilities by singlet and pair probabilities, we show that equilibrium singlet and pair probabilities can be analytically derived. The derived equilibrium properties successfully describe simulation results under a certain condition where the range of local colonization and the proportion of global colonization play key roles. Our model is an extension of the classical non-spatial Levins model to a spatially explicit metapopulation model. We appeal the advantage of point pattern approach to study spatial dynamics in general ecology and call for the need to deepen our understanding of mathematical tools to explore point pattern dynamics.
Understanding the relative roles of local environmental effects and spatial effects on phytoplankton community is of essential importance to study the biogeography of them at regional scale. However, the determinants that driving the biogeography of phytoplankton communities in the coastal area of northern Zhejiang still remained unclear. We surveyed phytoplankton community compositions in water columns associated with environmental and spatial influences across five subzones that geographically covering this region over four seasons. Diatoms and dinoflagellates were recorded as the main dominant groups and Coscinodiscus oculs-iridis, Coscinodiscus jonesianus, and Skeletonema costatum, were identified as the major abundant species existing in all seasons. Spatially structured environmental conditions, rather than pure spatial or environmental factors, substantially shaped the biogeography of phytoplankton community, with the former mainly comprised of water temperature, dissolved oxygen, phosphate, pH, and salinity, and the latter referring to a non-negligible factor. This study was the first integrated research that combining environmental filtering with spatial factors in structuring phytoplankton communities at a complete tempo-spatial scale. Our results may facilitate to the further study of harmful algal blooms early-warning in this region.
Natural enemies can effectively reduce pest populations when they coincide spatially and temporally with those populations. Therefore, along with temporal synchronization, the spatial association of pests and natural enemies is also necessary to increase the efficiency of biological control. The aims of this review were to assess the current state of knowledge concerning the spatial association of pests and their natural enemies in agro-ecosystems, evaluate its application in precision pest management programs and highlight the relevant gaps in the existing literature. Spatial analysis by distance indices (SADIE) and geostatistics are adequate sets of statistical tools used to study spatial patchiness and association of pests and natural enemies, especially in field crops. Spatial association between pests and natural enemies is dynamic and many biotic and abiotic factors can influence it. According to the literature, there are important gaps in the research about the spatial association of pests and natural enemies in orchards and stored products, as well as about the effects of environmental factors on the spatial association between these organisms. Mapping the spatial distribution and association of pests and natural enemies’ populations has not been used in precision biological control until recently. Precision applications focus on the targeted application of agricultural inputs in management zones rather than whole-field treatments. Information about spatial distribution and association of pests and natural enemies can be used to improve pest management practices through precision or site-specific applications of chemical and biological control measures.
La gestion durable des forêts tropicales et la conservation de la biodiversité sont des enjeux majeurs, qui ne peuvent être atteints que par une meilleure connaissance du fonctionnement et de la résilience de ces écosystèmes. L'objectif de cette étude, conduite sur le dispositif permanent de Mbaïki (RCA), est d'évaluer l'effet de deux traitements sylvicoles (coupe sélective; coupe sélective + délianage) sur la diversité et la dynamique des peuplements arborescents (dbh ≥ 9,55 cm) en forêt dense semi-caducifoliée. Après s'être assuré que les parcelles sans traitement pouvaient effectivement servir de témoin, nous avons entrepris des études démographiques (mortalité, recrutement, croissance et survie) et des analyses spatiales uni- (relations intraspécifiques) et bi-variées (relations interspécifiques) sur le peuplement global et 37 espèces abondantes. La diversité spécifique des arbres a également été quantifiée. Nos résultats montrent que les deux types de traitement n'influencent significativement ni la diversité spécifique, ni la mortalité au sein du peuplement. L'intensité du recrutement et lacroissance individuelle sont négativement et positivement corrélées, respectivement, à l'intensité de perturbations. L'hétérogénéité environnementale induite par les perturbations (trouées) impacte significativement les patrons de distribution spatiale des espèces arborescentes con- et hétérospécifique, avec des effets espèce- et site-dépendants, sans altérersignificativement la diversité spécifique aux différentes échelles spatiales testées. Globalement, nos résultats montrent la grande résilience des peuplements à l'exploitation extensive
İklim, toprak, yükseklik vb faktörler yönüyle yaşam alanlarında mesafeye bağlı olarak ortaya çıkan varyasyonların ekolojik açıdan istilacı yabancı bitkiler için önemi (özellikle yeni taşınılan bölgelere adaptasyon ve yerleşme sürecinde) ve istila sürecine (bitkilerin yayılmasına) etkilerine değinilmiştir.
Gene Regulatory Matrices (GRMs) are a well known technique for modelling the interactions between genes. This technique is used here, but with genes and hormones, to create Gene and Hormone Regulatory Matrices (GHRMs). In addition, a network (a directed weighted graph) is constructed from the underlying interactions of several mRNA encoding enzymes and receptors and two hormones: estradiol (E2) and progesterone (P4). This also permits comparison of the impact of each given environmental condition on E2 and P4 production, as well as mRNA expression levels. Apart from differential equations techniques (which require knowledge of rates of decay of a given hormone and mRNA) there is no existing technique to accurately predict the concentration of hormones based on the concentration of mRNA. This novel approach using GHRMs permits the use of nodes to accurately model the concentrations of the remaining ones. Experiments were performed to collect data on the gene expression and hormone concentration levels for primary bovine granulosa cells under different treatments. This data was used to build the GHRM models.
Accurate identification of spatial patterns remains a challenging problem in many ecological applications. One example is a problem of biological invasion where distinguishing between patchy spatial density pattern and continuous front spatial density pattern is important for monitoring and control of the invasive species. In this paper we address the problem of pattern recognition in biological invasion in terms of a biologically meaningful mathematical model consisting of two coupled integro-difference equations. The model allows for generating topologically different spatial structures and we employ several topological characteristics of spatial pattern to investigate various spatial density distributions. It is argued that, among the other topological quantities, the number of objects in the visual image of a spatial distribution gives us the most reliable conclusion about spatial pattern when it is required to distinguish between continuous and discontinuous (patchy) spatial structures. Furthermore, sensitivity of the pattern classification above to the definition of a monitoring protocol is discussed in the paper. Two basic properties of the monitoring protocol (i.e. the threshold density value and the number of sampling locations) are investigated and it is demonstrated how their variation affects correct reconstruction of spatial density pattern.
We address the problem of pattern recognition and comparison when spatial patterns of biological invasions are studied. A model of biological invasion is employed to simulate spatio-temporal dynamics of invasive species and generate a variety of spatial patterns including so called 'no front' patchy spatial distributions. We introduce several topological indices to understand whether various spatial distributions of invasive species can be compared to each other based on information about their topology. We also investigate how topological indices used to make conclusions about the spatial pattern are related to controlling parameters in the underlying process of biological invasion. Our analysis reveals that a small increment in the model parameters results in a small increment in topological indices when the topology of continuous front spatial pattern with no patches behind the front is considered. Meanwhile, no front patchy spatial distributions present a different case where a small change in the model parameters results in random fluctuations of topological indices. The 'random' behaviour of patchy patterns is further studied to understand whether a patchy spatial structure can transform itself into a continuous front spatial distribution over time. In the paper it will be argued that apart the topological quantities used to classify spatial distributions, the transition time required to establish topological properties of the spatial pattern must be taken into account in pattern recognition and analysis. Furthermore, it will be demonstrated that for some parameter values it is impossible to conclude about the topological type of spatial pattern, i.e. continuous front spatial distributions cannot be distinguished from 'no front' patchy distributions of invasive species, no matter what their topological indices are.
In the subalpine zone on Mt. Hakusan, Japan, P. hakusanensis Koidz., a native alpine species and Plantago asiatica L., regarded as a domestic alien plant grow synpatrically along with their hybrids. Here, we observed their flowering phenology on Mt. Hakusan from 2011 to 2014 in order to clarify the factors of natural hybridization. We established 1, 3 and 6 m² plots (total of 18 plots) in the natural habitat, recorded the number of flowering inflorescences of P. hakusanensis, P. asiatica and their hybrids. In addition, we calculated the effective cumulative temperature for the first flowering from snow disappeared, and investigated their number of seeds production per plant. In P. hakusanensis, many plants bloomed a lot of inflorescences immediately after the timing of snow disappearance every year, and in some years a part of the plants bloomed a few of inflorescences again after 37.8 ± 8.1 days and 302.4 ± 67.2 degree-days from snow disappearance. In the second flowering time of P. hakusanensis, P. asiatica started flowering after 56.4 ± 13.1 days and 403.0 ± 96.7 degree-days from snow disappearance, so their flowering times overlapped. P. asiatica was able to produce many seeds in the warm year. The flowering time of their natural hybrids overlapped with P. hakusanensis. Moreover they produced seeds every year and their death rate was low. Therefore, they may remain and pollinate with P. hakusanensis.
We revisit the classical epidemiological SIS model as a stochastic point pattern dynamics with special focus on its spatial distribution at equilibrium. In this model, each point on a continuous space is either susceptible S or infectious I, and infection occurs with an infection kernel as a function of distance from I to S. This stochastic process has been mathematically described by the hierarchical dynamics of the probabilities that a point, a pair made by two points, and a triplet made by three points, etc., is in a specific configuration of status. Using a simple closure thereby triplet probabilities that appear in the dynamics are approximated, we show that the average singlet probabilities and the pair probabilities that describe spatial distributions of Ss and Is at equilibrium can be explicitly derived using the infection kernel; Is are spatially clustered in the same order of the infection kernel. The results highlight the advantage of point pattern approach to model spatial population dynamics in general ecology where local interactions among individuals likely depend on distance between them.
The oak processionary moth (Thaumetopoea processionea; OPM) is an invasive pest species that was introduced to West London in 2006. Its gregarious larvae pose a risk to forestry and public health by defoliating oak trees and shedding toxic setae. It is not known how OPM populations will spread or what impact they will have in the UK, therefore the aim of this thesis was to explore the population ecology of oak processionary moth in West London.
The thesis focuses on three key topics. Firstly how habitat influences the temporal and spatial distribution of OPM populations. Secondly, the development of molecular methods to identify the parasitoids of OPM. Thirdly, the characterisation of interactions between OPM and its main parasitoid, Carcelia iliaca. These topics were addressed by a combination of a two-year field study at three sites in West London and lab based molecular techniques.
Oak processionary moth was found to have a strong spatially and temporally stable habitat preference for open woodland containing a high proportion of oak trees. Fieldwork and molecular techniques revealed a new tachinid fly in the UK, C. iliaca, a major parasitoid of OPM. Carcelia iliaca was responsible for the mortality of around 37% of moth pupae on average, suggesting that currently parasitism is not having a stabilising effect on OPM populations.
OPM exhibited similar habitat preferences to continental populations as well as other processionary moths, likely driven by tree apparency. It is not clear how parasitism of OPM would respond in an outbreak and current parasitism rates are lower than those in continental populations. This may be a result of OPM nest removal, which was common management practice at the time of the study. The findings of this study have been used to recommend that nests remain in situ for longer, to allow C. iliaca numbers to increase.
Other OPM management options include tree felling, pesticide application and biocontrol. This study found no evidence that OPM control currently warrants tree felling. Biocontrol could be augmented with the use of specific parasitoids such as the newly discovered C. iliaca or entomopathogenic agents identified in Chapter 3, and may be the favoured management option for stakeholders and managers, but is difficult to manage in the long term.
The book presents a geographer’s perspective on the systematic character of man-nature interrelations. The author reveals the inexhaustible potential of the geosystems approach as a source of custom-made solutions to the constantly emerging spatial issues and challenges of daily social practice. At the core of the book are the landscape concept and the challenge modern Landscape Ecology is facing: the role of human society as an integral part of the Earth system and, simultaneously, a powerful factor in its transformation. The author shares the view that modeling of human space and organization of man-designed systems must conform to the natural dynamics, structures, and functions of geosystems.
The first chapter of the book discusses basic concepts of nature’s systemic character and interprets the systems approach in terms of the landscape perspective and its core values: identification of concrete spatial scales that are most appropriate for the study of specific man-nature systems. Next, the author covers the main features and principles of organization of natural systems, as well as the natural laws and regularities of their spatial-temporal organization and development. The investigation places special emphasis on the design of landscape space and the functions, dynamics, and system development which determine particular spatial organizations.
The chapter devoted to Applied Landscape Ecology reveals the theoretical foundations of landscape planning, with accents on its spatial parameters and the need for their compliance with the spatial dimensions of landscape sustainability. This chapter examines also the potential of spatial analyses and evaluations of landscape structures to furnish information for the needs of spatial planning and sustainable management of natural resources. Traditional areas of application of landscape studies, such as nature conservation, strategic environmental assessment, and geo-ecological monitoring, are investigated with particular attention, due to their significance for contemporary planning practice in Bulgaria and abroad.
Overall, the structure of this book illustrates the concept of landscape multi-functionality. It gives a new direction to the territorial planning and management policies, moving them towards inter-sector integration in utilization of landscape features and maintenance of their natural capital qualities. The book is oriented towards applied aspects of landscape ecology, which is reflected in the design of its structure and the placement of the thematic accents. It is aimed at a wide range of specialists and university students in the fields of spatial planning and integrated management of natural resources, environmental assessment, and environmental protection.
Determination of trees spatial patterns in each development stage illustrates the dynamic of stands during
the time and can provide valuable information on the underlying processes, particularly in case of
uneven-aged forests. For this purpose, three one- hectare (100m×100m) plots were closely selected at
three development stages of initial, optimal and decay in an untouched, unmanaged and uneven-aged
beech (Fagus orientalis Lipsky) dominated forest in the Kelardasht region. Diameter of all trees with dbh
greater than 7.5cm together with their coordinates, using azimuth-distance method, were recorded and
fully mapped. Spatial point pattern analyses by Ripley's K- function showed that, while the number of
stems decreases from initial stage toward decay stage, the spatial pattern of trees in initial, optimal and
decay stages are highly aggregated, random and slightly aggregated, respectively. This research
emphasizes the application of spatial statistics for investigating tree spatial patterns. It's believed that
forest managers for any insight of natural processes, need to such information from untouched stands as a
key reference for any close to nature intervention in under managing forests and for sustainable
management of forest ecosystems, as well.
Presents an overview of the regionalised variable theory as it applies to the analyses of 2 ecological data sets: 1) a study of temporal changes in Rhodomonas (Cryptophyceae) density in the epilimnion of a temperate hardwater lake; 2) the spatial variability of soil mineral N in a Michigan old-field community.-from Author
Among-sample spatial variation in gypsy moth egg mass population density was quantified from four databases: the Melrose Highlands data (104 plots [0.0405 ha] sampled throughout coastal New England over a 20-yr period in the early 1900s; maximum point separation of ≍250 km), Massachusetts state survey data (150 plots of 20 banded trees located throughout Massachusetts and sampled from 1985 to 1987; maximum point separation ≍300 km), Fox Chapel Survey Data (517 plots [0.0101 ha] sampled throughout Fox Chapel Borough, Pennsylvania from 1988 to 1990; maximum point separation ≍8 km) and Cape Cod within-stand data (groups of 169 plots [0.008 ha] located in a 25-m grid; maximum point separation ≍1 km). Sample semivariograms were calculated that quantified spatial dependency in density at a variety of spatial scales. Both the Melrose and Massachusetts data showed evidence of spatial contagion in density at distances ranging from 20 to 100 km. The range and magnitude of this spatial dependence varied considerably from year to year. The extent of small-scale (<200 m) spatial contagion of egg mass densities in the Cape Cod data was also quite variable. Some of the sites in some years showed evidence of spatial dependence at various distances, whereas data from other years and other sites showed no spatial contagion. In contrast, semivariograms from the Fox Chapel plots were quite similar: in each of the 3 yr the maximum distance of spatial dependence (“range”) was ≍1 km. In summary, we quantified spatial dependency in egg mass densities at scales ranging from 25 m to 100 km. There was little evidence of spatial dependency at greater distances. The ordinary kriging procedure can use these semivariograms to generate maps of interpolated estimates of egg mass densities. These maps may be valuable in area-wide gypsy moth management programs. Specific recommendations were developed for the spacing of spatially stratified egg mass samples in area-wide management systems.
This paper aims to provide guidance to ecologists with limited experience in spatial analysis to help in their choice of techniques. It uses examples to compare methods of spatial analysis for ecological field data. A taxonomy of different data types is presented, including point‐ and area‐referenced data, with and without attributes. Spatially and non‐spatially explicit data are distinguished. The effects of sampling and other transformations that convert one data type to another are discussed; the possible loss of spatial information is considered.
Techniques for analyzing spatial pattern, developed in plant ecology, animal ecology, landscape ecology, geostatistics and applied statistics are reviewed briefly and their overlap in methodology and philosophy noted. The techniques are categorized according to their output and the inferences that may be drawn from them, in a discursive style without formulae. Methods are compared for four case studies with field data covering a range of types. These are: 1) percentage cover of three shrubs along a line transect; 2) locations and volume of a desert plant in a 1 ha area; 3) a remotely‐sensed spectral index and elevation from 10 ⁵ km ² of a mountainous region; and 4) land cover from three rangeland types within 800 km ² of a coastal region. Initial approaches utilize mapping, frequency distributions and variance‐mean indices. Analysis techniques we compare include: local quadrat variance, block quadrat variance, correlograms, variograms, angular correlation, directional variograms, wavelets, SADIE, nearest neighbour methods, Ripley's (t), and various landscape ecology metrics.
Our advice to ecologists is to use simple visualization techniques for initial analysis, and subsequently to select methods that are appropriate for the data type and that answer their specific questions of interest. It is usually prudent to employ several different techniques.
Two-dimensional spectral analyses of spatial patterns are made using (i) the autocorrelation function, (ii) the periodogram, and its polar summary (iii) the R-spectrum and (iv) the -spectrum. Together these give a sensitive analysis of both the complete range of scales of pattern and directional components which exist in data sets and we illustrate how the significance of observed spectral features can be assessed.We investigate the spatial pattern of Calluna vulgaris in a regenerating woodland and of Epilobium angustifolium spreading in a woodland following the thinning of trees. Evidence in the spectra is found for directional, clumping and inhibition patterns, and is discussed in relation to spectra obtained from simulations of known pattern generating processes. Hypotheses about the important biological, environmental and management influences on the structure of the communities are examined.
Geostatistics brings to ecology novel tools for the interpretation of spatial patterns of organisms, of the numerous environmental components with which they in- teract, and of the joint spatial dependence between organisms and their environment. The purpose of this paper is to use data from the ecological literature as well as from original research to provide a comprehensive and easily understood analysis ofgeostatistics' manner of modeling and methods. The traditional geostatistical tool, the variogram, a tool that is beginning to be used in ecology, is shown to provide an incomplete and misleading summary of spatial pattern when local means and variances change. Use of the non-ergodic covariance and correlogram provides a more effective description of lag-to-lag spatial dependence because the changing local means and variances are accounted for. Indicator transforma- tions capture the spatial patterns of nominal ecological variables like gene frequencies and the presence/absence of an organism and of subgroups of a population like large or small individuals. Robust variogram measures are shown to be useful in data sets that contain many data outliers. Appropriate removal of outliers reveals latent spatial dependence and patterns. Cross-variograms, cross-covariances, and cross-correlograms define the joint spa- tial dependence between co-occurring organisms. The results of all of these analyses bring new insights into the spatial relations of organisms in their environment.
Spatially explicit population models are becoming increasingly useful tools for population ecologists, conservation biologists, and land managers. Models are spatially explicit when they combine a population simulator with a landscape map that describes the spatial distribution of landscape features. With this map, the locations of habitat patches, individuals, and other items of interest are explicitly incorporated into the model, and the effect of changing landscape features on population dynamics can be studied. In this paper we describe the structure of some spatially explicit models under development and provide examples of current and future research using these models. Spatially explicit models are important tools for investigating scale-related questions in population ecology, especially the response of organisms to habitat change occurring at a variety of spatial and temporal scales. Simulation models that incorporate real-world landscapes, as portrayed by landscape maps created with geographi
MOST environments are spatially subdivided, or patchy, and there has been much interest in the relationship between the dynamics of populations at the local and regional (metapopulation) scales 1. Here we study mathematical models for host-parasitoid interactions, where in each generation specified fractions (mu-N and mu-P, respectively) of the host and parasitoid subpopulations in each patch move to adjacent patches; in most previous work, the movement is not localized but is to any other patch 2. These simple and biologically sensible models with limited diffusive dispersal exhibit a remarkable range of dynamic behaviour: the density of the host and parasitoid subpopulations in a two-dimensional array of patches may exhibit complex patterns of spiral waves or spatially chaotic variation, they may show static 'crystal lattice' patterns, or they may become extinct. This range of behaviour is obtained with the local dynamics being deterministically unstable, with a constant host reproductive rate and no density dependence in the movement patterns. The dynamics depend on the host reproductive rate, and on the values of the parameters mu-N and mu-P. The results are relatively insensitive to the details of the interactions; we get essentially the same results from the mathematically-explicit Nicholson-Bailey model of host-parasitoid interactions, and from a very general 'cellular automaton' model in which only qualitative rules are specified. We conclude that local movement in a patchy environment can help otherwise unstable host and parasitoid populations to persist together, but that the deterministically generated spatial patterns in population density can be exceedingly complex (and sometimes indistinguishable from random environmental fluctuations).
Tests of “randomness” and methods of edge‐correction for spatial point patterns are surveyed. The asymptotic distribution theory and power of tests based on the nearest‐neighbour distances and estimates of the variance function are investigated.
This report describes a program, FRAGSTATS, developed to quantify landscape structure. Two separate versions of FRAGSTATS exist: one for vector images and one for raster images. In this report, each metric calculated by GRAGSTATS is described in terms of its ecological application and limitations. Example landscapes are included, and a discussion is provided of each metric as it relates to the sample landscapes. -from Authors
The intensity of a spatial pattern can be standardized so as to remain approximately constant under random thinning of individuals. The formula for this standardization is presented along with a general discussion of the interpretation of spatial pattern. A particular example is examined in detail, and the relation between the pattern analysis and the ecological conclusions is assessed. Several alternative measures of pattern are compared, including spectral analysis and block-size analysis of variance. It is argued that pattern analysis should not normally be used to examine large-scale environmental control. The mathematical theory of the standardization is given in an appendix.
1. The wavelet transform is introduced as a technique to identify spatial structure in transect data. Its main advantages over other methods of spatial analysis are its ability to preserve and display hierarchical information while allowing for pattern decomposition. 2. Two applications are presented: simple one-dimensional simulations and a set of 200-m transect data of canopy opening measurements taken in 12 stands dominated by Pseudotsuga menziesii ranging over three developmental stages. 3. The calculation of the wavelet variance, derived from the transform, facilitates comparison based on dominant scale of pattern between multiple datasets such as the stands described. 4. The results of the analysis indicate that while canopy pattern trends follow stand development, small to intermediate disturbances significantly influence canopy structure.
Artificial ‘communities’ of discs have been constructed and sampled by random throws of quadrats of different sizes and by a grid of contiguous quadrats.
The use of a grid opens the way to more detailed study of the nature of the non-random distribution of species in the field, especially to the detection of mosaic patterns not normally revealed by subjective methods.
Basic ParametersNearest-Neighbor Methods
Second MomentsModelsComparative StudiesExamples
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In an earlier study (Holling, 1959) the basic and subsidiary components of predation were demonstrated in a predator-prey situation involving the predation of sawfly cocoons by small mammals. One of the basic components, termed the functional response, was a response of the consumption of prey by individual predators to changes of prey density, and it appeared to be at least theoretically important in population regulation: Because of this importance the functional response has been further examined in an attempt to explain its characteristics.
2002. A balanced view of scale in spatial statistical analysis. – Ecography 25: 626– 640. Concepts of spatial scale, such as extent, grain, resolution, range, footprint, support and cartographic ratio are not interchangeable. Because of the potential confusion among the definitions of these terms, we suggest that authors avoid the term ''scale'' and instead refer to specific concepts. In particular, we are careful to discriminate between observation scales, scales of ecological phenomena and scales used in spatial statistical analysis. When scales of observation or analysis change, that is, when the unit size, shape, spacing or extent are altered, statistical results are expected to change. The kinds of results that may change include estimates of the population mean and variance, the strength and character of spatial autocorrelation and spatial anisotropy, patch and gap sizes and multivariate relationships. The first three of these results (precision of the mean, variance and spatial autocorrelation) can sometimes be estimated using geostatistical support-effect models. We present four case studies of organism abundance and cover illustrating some of these changes and how conclu-sions about ecological phenomena (process and structure) may be affected. We identify the influence of observational scale on statistical results as a subset of what geographers call the Modifiable Area Unit Problem (MAUP). The way to avoid the MAUP is by careful construction of sampling design and analysis. We recommend a set of considerations for sampling design to allow useful tests for specific scales of a phenomenon under study. We further recommend that ecological studies completely report all components of observation and analysis scales to increase the possibility of cross-study comparisons.
A general statistical framework is proposed for comparing linear models of spatial process and pattern. A spatial linear model for nested analysis of variance can be based on either fixed effects or random effects. Greig-Smith (1952) originally used a fixed effects model, but there are also examples of random effects models in the soil science literature. Assuming intrinsic stationarity for a linear model, the expectations of a spatial nested ANOVA and two term local variance (TTLV, Hill 1973) are functions of the variogram, and several examples are given. Paired quadrat variance (PQV, Ludwig & Goodall 1978) is a variogram estimator which can be used to approximate TTLV, and we provide an example from ecological data. Both nested ANOVA and TTLV can be seen as weighted lag-1 variogram estimators that are functions of support, rather than distance. We show that there are two unbiased estimators for the variogram under aggregation, and computer simulation shows that the estimator with smaller variance depends on the process autocorrelation.
Spatial autocorrelation analysis tests whether the observed value of a nominal, ordinal, or interval variable at one locality is independent of values of the variable at neighbouring localities. The computation of autocorrelation coefficients for nominal, ordinal, and for interval data is illustrated, together with appropriate significance tests. The method is extended to include the computation of correlograms for spatial autocorrelation. These show the autocorrelation coefficient as a function of distance between pairs of localities being considered, and summarize the patterns of geographic variation exhibited by the response surface of any given variable.
Autocorrelation analysis is applied to microgeographic variation of allozyme frequencies in the snail Helix aspersa. Differences in variational patterns in two city blocks are interpreted.
The inferences that can be drawn from correlograms are discussed and illustrated with the aid of some artificially generated patterns. Computational formulae, expected values and standard errors are furnished in two appendices.
I draw attention to the need for ecologists to take spatial structure into account more seriously in hypothesis testing. If spatial autocorrelation is ignored, as it usually is, then analyses of ecological patterns in terms of environmental factors can produce very misleading results. This is demonstrated using synthetic but realistic spatial patterns with known spatial properties which are subjected to classical correlation and multiple regression analyses. Correlation between an autocorrelated response variable and each of a set of explanatory variables is strongly biased in favour of those explanatory variables that are highly autocorrelated - the expected magnitude of the correlation coefficient increases with autocorrelation even if the spatial patterns are completely independent. Similarly, multiple regression analysis finds highly autocorrelated explanatory variables “significant” much more frequently than it should. The chances of mistakenly identifying a “significant” slope across an autocorrelated pattern is very high if classical regression is used. Consequently, under these circumstances strongly autocorrelated environmental factors reported in the literature as associated with ecological patterns may not actually be significant. It is likely that these factors wrongly described as important constitute a red-shifted subset of the set of potential explanations, and that more spatially discontinuous factors (those with bluer spectra) are actually relatively more important than their present status suggests. There is much that ecologists can do to improve on this situation. I discuss various approaches to the problem of spatial autocorrelation from the literature and present a randomisation test for the association of two spatial patterns which has advantages over currently available methods.
In ecological field surveys, observations are gathered at different spatial locations. The purpose may be to relate biological response variables (e.g., species abundances) to explanatory environmental variables (e.g., soil characteristics). In the absence of prior knowledge, ecologists have been taught to rely on systematic or random sampling designs. If there is prior knowledge about the spatial patterning of the explanatory variables, obtained from either previous surveys or a pilot study, can we use this information to optimize the sampling design in order to maximize our ability to detect the relationships between the response and explanatory variables?
The specific questions addressed in this paper are: a) What is the effect (type I error) of spatial autocorrelation on the statistical tests commonly used by ecologists to analyse field survey data? b) Can we eliminate, or at least minimize, the effect of spatial autocorrelation by the design of the survey? Are there designs that provide greater power for surveys, at least under certain circumstances? c) Can we eliminate or control for the effect of spatial autocorrelation during the analysis? To answer the last question, we compared regular regression analysis to a modified t‐test developed by Dutilleul for correlation coefficients in the presence of spatial autocorrelation.
Replicated surfaces (typically, 1000 of them) were simulated using different spatial parameters, and these surfaces were subjected to different sampling designs and methods of statistical analysis. The simulated surfaces may represent, for example, vegetation response to underlying environmental variation. This allowed us 1) to measure the frequency of type I error (the failure to reject the null hypothesis when in fact there is no effect of the environment on the response variable) and 2) to estimate the power of the different combinations of sampling designs and methods of statistical analysis (power is measured by the rate of rejection of the null hypothesis when an effect of the environment on the response variable has been created).
Our results indicate that: 1) Spatial autocorrelation in both the response and environmental variables affects the classical tests of significance of correlation or regression coefficients. Spatial autocorrelation in only one of the two variables does not affect the test of significance. 2) A broad‐scale spatial structure present in data has the same effect on the tests as spatial autocorrelation. When such a structure is present in one of the variables and autocorrelation is found in the other, or in both, the tests of significance have inflated rates of type I error. 3) Dutilleul's modified t‐test for the correlation coefficient, corrected for spatial autocorrelation, effectively corrects for spatial autocorrelation in the data. It also effectively corrects for the presence of deterministic structures, with or without spatial autocorrelation.
The presence of a broad‐scale deterministic structure may, in some cases, reduce the power of the modified t‐test.
First, we formulate some questions posed by the procedure recently proposed by Borcard et al. (1992) and Borcard and Legendre (1994) to partition the ecological variation of a community into different portions related to spatial and environmental descriptors. Working separately on the two steps of this procedure - linear modelling and ordinations on modelled tables - allows us to propose different solutions to these questions. These solutions, which use little-known proper- ties of a linear regression model with two additive factors and no interaction, are also adapted to the case of mixed factors (qualitative and quantitative). These properties are presented in the framework of canonical correlation analysis. In particular, they allow us to propose an alternative to partial regression, which avoids confounding. A detailed illustration is presented. Rapid Science 1998
The spatial heterogeneity of populations and communities plays a central role in many ecological theories, for instance the theories of succession, adaptation, maintenance of species diversity, community stability, competition, predator-prey interactions, parasitism, epidemics and other natural catastrophes, ergoclines, and so on. This paper will review how the spatial structure of biological populations and communities can be studied. We first demonstrate that many of the basic statistical methods used in ecological studies are impaired by autocorrelated data. Most if not all environmental data fall in this category. We will look briefly at ways of performing valid statistical tests in the presence of spatial autocorrelation. Methods now available for analysing the spatial structure of biological populations are described, and illustrated by vegetation data. These include various methods to test for the presence of spatial autocorrelation in the data: univariate methods (all-directional and two-dimensional spatial correlograms, and two-dimensional spectral analysis), and the multivariate Mantel test and Mantel correlogram; other descriptive methods of spatial structure: the univariate variogram, and the multivariate methods of clustering with spatial contiguity constraint; the partial Mantel test, presented here as a way of studying causal models that include space as an explanatory variable; and finally, various methods for mapping ecological variables and producing either univariate maps (interpolation, trend surface analysis, kriging) or maps of truly multivariate data (produced by constrained clustering). A table shows the methods classified in terms of the ecological questions they allow to resolve. Reference is made to available computer programs.
Various indices of spatial patterns based on plot counts are reviewed for theoretical population models appropriate to ecological
studies. It is seen that many of the indices proposed in the literature are essentially equivalent to either the index ω=
σ2/μ or to the index γ= (σ2-μ)/μ2, thus providing a variety of motiviations and interpretations of these two indices as measures of spatial patterns.
A vector approach to measuring spatial patterns which suggests both a unifying relationship between these indices and an extension
of them is proposed. This leads to an interpretation of the measures of spatial patterns in terms of the transition probabilities
of a pure birth process.
A method for the analysis of spatial pattern using quadrats of different sizes is developed on the basis of the relationship of mean crowding (\(\mathop m\limits^* \)) to mean density (m). The\(\mathop m\limits^* \)-on-m regression obtained by successive changes in quadrat size in a single population (unit-size relation) shows a characteristic pattern according to the type of distribution. By aid of the ρ-index proposed here, we can distinguish the random, aggregated and uniform distributions of the basic components (individual or group of individuals). The ρ serves as an index of spatial correlation between neighbouring quadrats, and it also provides information on the approximate area occupied by clump (colony), distribution pattern of individuals within clumps, and possibly the distribution pattern of clumps themselves.
Even in a specified type of distribution, the unit-size\(\mathop m\limits^* - m\) relation is not necessarily identical with the\(\mathop m\limits^* - m\) relation for a series of populations at a particular quadrat size (series relation). The changes in the series\(\mathop m\limits^* - m\) relationship with successive changes of quadrat sizes are also considered for some basic patterns of distributions. The combined use of the unit-size and the series\(\mathop m\limits^* - m\) relations for a set of populations of the species under study may provide a satisfactory picture of the spatial pattern characteristic of the species.
Application of the method is illustrated by using distribution data of several species of animals and plants. The advantage of the present method over other methods are discussed, and the formulae for determining the optimum quadrat unit in sampling surveys are given.
In Applied Geostatistics the authors demonstrate how simple statistical methods can be used to analyse earth science data. In clear language, they explain how various forms of the estimation method called kriging can be employed for specific problems. A case study of a simulated deposit is the focus for the book. This model helps the student develop an understanding of how statistical tools work, serving as a tutorial to guide readers through their first independent geostatistical study.
Considers the effects of scale using various examples and ways of dealing with scale. Outlines the definition of dependence on objectives and on organisations, and the domains of scale. Discusses the development of science in ecology and the development of a scaling theory which could generate testable hypotheses. -S.J.Yates
Outlines an historical perspective of landscape ecology and the consideration of scale, and describes the characteristics of landscape structure and the measures of spatial pattern that have been applied in the analysis of landscape structure. Predicted changes in landscape structure may involve ecological processes, in particular, the patterns and processes, heterogeneity, disturbance, the movement and persistence of organisms, and the redistribution of matter and nutrients. Spatial patterns influence many processes that are ecologically important. -S.J.Yates
Fragmented landscapes alter ecological interactions by modifying the flux of organisms, material, and energy. Fragmented distributions of hypothetical resources and species were represented by several fractal models of landscape patterns at scales ranging from 90 to 2,400 m. Maps of resource aggregations at three scales resulted in multiple-scale notions of "patch," "gap," "edge," "corridor," "source," and "sink." A neutral model of species co-occurrence was developed for analyses conducted at several scales. The neutral model has implications for sampling mutualistic species and for detecting species' responses to changes in environmental conditions. An ecologically meaningful view of landscape pattern depends on the home range size, dispersal ability, or speed with which organisms use resources rather than on the cartographic depiction of the landscape used by humans.
Autocorrelation is a very general statistical property of ecological variables observed across geographic space; its most common forms are patches and gradients. Spatial autocorrelation, which comes either from the physical forcing of environmental variables or from community processes, presents a problem for statistical testing because autocorrelated data violate the assumption of independence of most standard statistical procedures. The paper discusses first how autocorrelation in ecological variables can be described and measured, with emphasis on mapping techniques. Then, proper statistical testing in the presence of autocorrelation is briefly discussed. Finally, ways are presented of explicitly introducing spatial structures into ecological models. Two approaches are proposed; in the raw-data approach, the spatial structure takes the form of a polynomial of the x and y geographic coordinates of the sampling stations; in the matrix approach, the spatial structure is introduced in the form of a geog
Statistical models of environment-abundance relationships may be influenced by spatial autocorrelation in abundance, environmental variables, or both. Failure to account for spatial autocorrelation can lead to incorrect conclusions regarding both the absolute and relative importance of environmental variables as determinants of abundance. We consider several classes of statistical models that are appropriate for modeling environment-abundance relationships in the presence of spatial autocorrelation, and apply these to three case studies: 1) abundance of voles in relation to habitat characteristics; 2) a plant competition experiment; and 3) abundance of Orbatid mites along environmental gradients. We find that when spatial pattern is accounted for in the modeling process, conclusions about environmental control over abundance can change dramatically. We conclude with five lessons: 1) spatial models are easy to calculate with several of the most common statistical packages; 2) results from spatially-structured models may point to conclusions radically different from those suggested by a spatially independent model; 3) not all spatial autocorrelation in abundances results from spatial population dynamics; it may also result from abundance associations with environmental variables not included in the model; 4) the different spatial models do have different mechanistic interpretations in terms of ecological processes - thus ecological model selection should take primacy over statistical model selection; 5) the conclusions of the different spatial models are typically fairly similar - making any correction is more important than quibbling about which correction to make.
In ecological field surveys, observations are gathered at different spatial locations. The
purpose may be to relate biological response variables (e.g., species abundances) to
explanatory environmental variables (e.g., soil characteristics). In the absence of prior
knowledge, ecologists have been taught to rely on systematic or random sampling
designs. If there is prior knowledge about the spatial patterning of the explanatory
variables, obtained from either previous surveys or a pilot study, can we use this
information to optimize the sampling design in order to maximize our ability to detect the relationships between the response and explanatory variables? The specific questions addressed in this paper are:
a) What is the effect (type I error) of spatial autocorrelation on the statistical tests commonly used by ecologists to analyse
field survey data?
b) Can we eliminate, or at least minimize, the effect of spatial autocorrelation by the design of the survey? Are there designs that provide greater power for surveys, at least under certain circumstances?
c) Can we eliminate or control for the effect of spatial autocorrelation during the analysis?
To answer the last question, we compared regular regression analysis to a modified t-test developed by Dutilleul for correlation coefficients in the presence of spatial autocorrelation. Replicated surfaces (typically, 1000 of them) were simulated using different spatial parameters, and these surfaces were subjected to different sampling designs and methods of statistical analysis. The simulated surfaces may represent, for example, vegetation response to underlying environmental variation. This allowed us 1) to measure the frequency of type I error (the failure to reject the null hypothesis when in fact there is no effect of the environment on the response variable) and
2) to estimate the power of the different combinations of sampling designs and methods of statistical analysis (power is measured by the rate of rejection of the null hypothesis when an effect of the environment on the response variable has been created).
Our results indicate that:
1) Spatial autocorrelation in both the response and environmental variables affects the classical tests of significance of correlation or regression coefficients. Spatial autocorrelation in only one of the two variables does not affect the test of significance.
2) A broad-scale spatial structure present in data has the same effect on the tests as spatial autocorrelation. When such a structure is present in one of the variables and autocorrelation is found in the other, or in both, the tests of significance have inflated rates of type I error.
3) Dutilleul’s modified t-test for the correlation coefficient, corrected for spatial autocorrelation, effectively corrects for spatial autocorrelation in the data. It also effectively corrects for the presence of deterministic structures, with or without spatial autocorrelation. The presence of a broad-scale deterministic structure may, in some cases, reduce the power of the modified t-test.
This study compares empirical type I error and power of different permutation techniques that can be used for partial correlation analysis involving three data vectors and for partial Mantel tests. The partial Mantel test is a form of first-order partial correlation analysis involving three distance matrices which is widely used in such fields as population genetics, ecology, anthropology, psychometry and sociology. The methods compared are the following: (1) permute the objects in one of the vectors (or matrices); (2) permute the residuals of a null model; (3) correlate residualized vector 1 (or matrix A) to residualized vector 2 (or matrix B); permute one of the residualized vectors (or matrices); (4) permute the residuals of a full model. In the partial correlation study, the results were compared to those of the parametric t-test which provides a reference under normality. Simulations were carried out to measure the type I error and power of these permutatio methods, using normal and non-normal data, without and with an outlier. There were 10 000 simulations for each situation (100 000 when n = 5); 999 permutations were produced per test where permutations were used. The recommended testing procedures are the following:(a) In partial correlation analysis, most methods can be used most of the time. The parametric t-test should not be used with highly skewed data. Permutation of the raw data should be avoided only when highly skewed data are combined with outliers in the covariable. Methods implying permutation of residuals, which are known to only have asymptotically exact significance levels, should not be used when highly skewed data are combined with small sample size. (b) In partial Mantel tests, method 2 can always be used, except when highly skewed data are combined with small sample size. (c) With small sample sizes, one should carefully examine the data before partial correlation or partial Mantel analysis. For highly skewed data, permutation of the raw data has correct type I error in the absence of outliers. When highly skewed data are combined with outliers in the covariable vector or matrix, it is still recommended to use the permutation of raw data. (d) Method 3 should never be used.
Spatially explicit population models are becoming increasingly useful tools for population ecologists, conservation biologists and land managers. Models are spatially explicit when they combine a population simulator with a landscape map that describes the spatial distribution of landscape features. With this map, the locations of habitat patches, individuals, and other items of interest are explicitly incorporated into the model, and the effect of changing landscape features on population dynamics can be studied. In this paper we describe the structure of some spatially explicit population models under development and provide examples of current and future research using these models. Spatially explicit models are important tools for investigating scale-related questions in population ecology, especially the response of organisms to habitat change occurring at a variety of spatial & temporal scales. Simulation models that incorporate real-world landscapes, as portrayed by landscape maps created with geographic information systems, are also proving crucial in the development of management strategies in response to regional landuse and other global change processes. Spatially explicit population models will increase our ability to accurately model complex landscapes, and therefore should improve both basic ecological knowledge of landscape phenomena and applications of landscape ecology to conservation and management.
. We investigate the characteristics of the wavelet transform as an approach to analyzing spatial pattern. Compared to the familiar methods of paired quadrat or blocked quadrat variance calculations, the wavelet method seems to offer several advantages. First, when wavelet variance is plotted as a function of scale, the peak variance height is determined by pattern intensity and does not increase with scale and, depending on the wavelet chosen, the position of the variance peak matches the scale exactly. Second, the method produces only faint resonance peaks, if any, and third, by using several different wavelet forms, different characteristics of the pattern can be investigated. Fourth, the method is able to portray very clearly trends in the data, when the pattern is non-stationary. Lastly, the wavelet position variance can be used to identify patches and gaps in data with random error. We demonstrate these characteristics using artificial data and data from previously published studies for comparison. We show that two versions of the familiar blocked quadrat variance technique are forms of wavelet analysis.
A large number of methods for the analysis of the spatial structure of natural phenomena (for example, the clumping or overdispersion of tree stems, the positions of veins of ore in a rock formation, the arrangement of habitat patches in a
landscape, and so on) have been developed in a wide range of scientific fields. This paper reviews many of the methods and describes the relationships among them, both mathematically, using the cross-product as a unifying principle, and conceptually,
based on the form of a moving window or template used in calculation. The relationships among these methods suggest that while no single method can reveal all the important characteristics of spatial data, the results of different analyses are not
expected to be completely independent of each other.
The predictability of the physical arrangement of plants, at whatever scale it is viewed, is referred to as their spatial pattern. Spatial pattern is a crucial aspect of vegetation which has important implications not only for the plants themselves, but also for other organisms which interact with plants, such as herbivores and pollinators, or those animals for which plants provide a habitat. This book describes and evaluates methods for detecting and quantifying a variety of characteristics of spatial pattern. As well as discussing the concepts on which these techniques are based, examples from real field studies and worked examples are included, which, together with numerous line figures, help guide the reader through the text. The result is a book that will be of value to graduate students and research workers in the fields of vegetation science, conservation biology and applied ecology.
Pacific Northwest Research Station
- S Dept
- Forest Agriculture
- Service
S. Dept of Agriculture, Forest Service, Pacific Northwest Research Station, Gen. Tech. Rep. PNW-GTR-351.