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Appropriate use of regression analysis in marine biology
Abstract
The Model I linear regression theory is often used in the analysis of data under conditions when the Model II theory is clearly needed. Implications derived from the use of the two theories can differ greatly when there is not a high degree of correlation between the X and Y variables. The geometric mean Model II method is easy to use, and is probably needed in the analysis of most field data, since the X variable in field data is rarely under the control of the investigator.
... This issue, which also pervades other fields of marine science such as fishery ecology, has already been highlighted by Laws et al. (1981) [2]: "the need to use model II (here type-II) regression methods in many applications have long been recognized, but a glance at the current literature will reveal that most biological oceanographers use model I (here type-I) regression methods exclusively even when model II is clearly needed". Until the 1980s, the lack of widespread statistical software packages could have been a reason that favoured the application of the most common type-I method. ...
... This issue, which also pervades other fields of marine science such as fishery ecology, has already been highlighted by Laws et al. (1981) [2]: "the need to use model II (here type-II) regression methods in many applications have long been recognized, but a glance at the current literature will reveal that most biological oceanographers use model I (here type-I) regression methods exclusively even when model II is clearly needed". Until the 1980s, the lack of widespread statistical software packages could have been a reason that favoured the application of the most common type-I method. ...
... Until the 1980s, the lack of widespread statistical software packages could have been a reason that favoured the application of the most common type-I method. However, as reported in Laws et al. (1981) [2] and Innamorati et al. (1990) [3], the need for a more careful choice of the regression models and methods was already clear in the oceanographic community. Laws et al. (1981) [2] investigated the problem demonstrating that type-II methods should be applied to in situ data which are affected by instrument and sampling uncertainties. ...
Linear regression is widely used in applied sciences and, in particular, in satellite optical oceanography, to relate dependent to independent variables. It is often adopted to establish empirical algorithms based on a finite set of measurements, which are later applied to observations on a larger scale from platforms such as autonomous profiling floats equipped with optical instruments (e.g., Biogeochemical Argo floats; BGC-Argo floats) and satellite ocean colour sensors (e.g., SeaWiFS, VIIRS, OLCI). However, different methods can be applied to a given pair of variables to determine the coefficients of the linear equation fitting the data, which are therefore not unique. In this work, we quantify the impact of the choice of “regression method” (i.e., either type-I or type-II) to derive bio-optical relationships, both from theoretical perspectives and by using specific examples. We have applied usual regression methods to an in situ data set of particulate organic carbon (POC), total chlorophyll-a (TChla), optical particulate backscattering coefficient (bbp), and 19 years of monthly TChla and bbp ocean colour data. Results of the regression analysis have been used to calculate phytoplankton carbon biomass (Cphyto) and POC from: i) BGC-Argo float observations; ii) oceanographic cruises, and iii) satellite data. These applications enable highlighting the differences in Cphyto and POC estimates relative to the choice of the method. An analysis of the statistical properties of the dataset and a detailed description of the hypothesis of the work drive the selection of the linear regression method
... Then, the second iteration changing the parameter values by a small amount and recalculating the SS, so on and so forth the iteration goes on until the objective function was met. Generally there are two basic goals of regression analysis, which are prediction and estimation of functional relationship (Laws and Archie, 1981). When it comes to the goal of regression analysis is to estimate the functional relationship between the estimated Chl-a, Chl-a ret , and in-situ Chl-a, Chl-a is , Model-I regression methods are no longer appropriate if both Chl-a ret and Chl-a is are subject to error and the observations are uncontrolled. ...
... The ICRM model of iterative regression is a function of the Model II regression with Reduced Major Axis (RMA) technique. The Model II regression is chosen because it is more accurate when it comes to regression analysis in marine biology related studies(Laws & Archie, 1981). Polynomial coefficients in the Chl-a empirical algorithm (Equation 3.1) are the objective variable to be defined. ...
Studies on Chl-a variation, assessment of MODIS data and development of local ocean colour algorithm are few for Malacca Straits water. The aim of this study is to locally calibrate and validate the Chl-a derived from MODIS standard Chl-a algorithm (OC3M) on the latest R2013 data within the acceptable error tolerance at the Absolute Percentage Difference (APD) below 35% and to test the algorithm’s applicability.
... The choice of the regression model best suited to this goal has been extensively discussed in both the ecological and statistical literature (Fuller 1987;see Prairie et al. 1995 and references therein). Model II regression (Ricker 1973;Laws and Archie 1981), which includes a family of different statistical recipes, should be used when there is no a priori expectation as to whether either Y or X is a dependent variable or whenever X is not fixed and measured with error. On the other hand, model I regression is the method of choice when the ultimate goal is to develop an equation to predict Y from X or when the error variance of Y is much larger than the error variance of X (at least three times larger, according to Legendre and Legendre 1998). ...
... The arguments presented above clearly show that the criticisms made by Laws are unfounded and that there are many reasons that justify the use of model I regression by Calbet (2001) as well as the ecological coherence of the conclusions reached. Indeed, despite recurrent advocacy for the virtues of model II regression (Ricker 1973;Laws and Archie 1981), its use should be tampered by the realization that empirical data do not fall into a simple dichotomous analytical arsenal (model I vs. II) but rather vary along a continuum. Only a careful assessment of relative errors can guide our choice of which is more appropriate for the given set of data. ...
... This method is preferred when neither dataset is controlled or free of error. The resulting slope minimizes the absolute value of the sum of the products of the deviations between the observations and the regression line in both the X and Y directions (Ricker, 1973;Laws and Archie, 1981). Correlations between satellite and insitu optical measurements were used to assess the strength and statistical significance (pvalue <0.05) of a linear relationship between the observations. ...
... Regression from Behrenfeld and Boss (2006) is included for reference. the absolute value of the sum of the products of the deviations between the observations and the regression line in both the X and Y directions (Ricker, 1973;Laws and Archie, 1981). The correlation between results from each method was used to assess the strength and statistical significance (p-value <0.05) of a linear relationship between the datasets ( Fig. 5.12). ...
Satellite-based optical measurements were coupled with physical and optical measurements from Seaglider – a long-range autonomous glider – to study interactions between biological and physical processes off the coast of Washington, USA, and to evaluate space-time variability of regional phytoplankton and particle distributions. Using satellite ocean color data variability in near-surface chlorophyll a was characterized across a range of spatial and temporal scales ranging from 1 – 500 km and from days – years to assess region-wide responses by phytoplankton to changes in environmental conditions. Results from 1998 – 2002 revealed both strong negative and positive anomalies associated with lingering effects of the 1997-98 El Niño and an invasion of Subartic water into the California Current System in 2002, respectively. Ocean color satellite data were also used to derive ‘spectral signatures’ for waters associated with the Juan de Fuca Eddy to monitor these waters as they moved southwards towards Washington beaches. Episodic southward transport of these waters may play a role in bloom initiation of the potentially toxigenic pennate diatom Pseudo-nitzschia and the ability to track these waters by remote sensing could help determine when to initiate more intensive sampling for domoic acid along the Washington coast. From April 2002 – December 2005 Seaglider conducted highly resolved (~5 km horizontal spacing, ~1 m vertical resolution, ~15 d temporal resolution) surveys across the northern California Current System. A new matchup procedure minimized discrepancies between Seaglider fluorescence and satellite-derived estimates of chlorophyll a at the surface (r = 0.834) allowing observations from these disparate remote sensing platforms to be fused together to create a quasi-4-dimensional representation of the phytoplankton distribution within a persistent offshore eddy in September and October 2004. Unfortunately daytime fluorescence is quenched at all times of the year in these waters with maximum quenching exceeding 80% during summer making it difficult to compare near-surface fluorescence measurements with satellite-derived estimates of surface phytoplankton biomass. A detailed statistical characterization of mid-day fluorescence quenching in April 2002 and from August 2003 – December 2005 was conducted to constrain the magnitude and variability in mid-day quenching to better use fluorescence as an independent validation for phytoplankton biomass at the surface.
... Practitioners using dual-isotope analysis have traditionally used ordinaryleast squares regression to calculate the slope in dual-isotope plots. However, it is well-reported in other disciplines such as marine biology (Laws and Archie, 1981), clinical chemistry (Linnet, 1999), anthropology (Smith, 2009), and within the geological sciences (Wehr and Saleska, 2017) that ordinary-least squares introduces uncertainty (mathematical bias) when significant errors are present in the x-and yvariables. Sherwood Lollar's work demonstrated that the York regression method (York, 1966;York, 1969;York et al., 2004) is a more appropriate regression method for dual-isotope plotsproducing more accurate estimates of Λ and its uncertainty for more reliable interpretations of (bio)transformation reaction mechanisms (Ojeda et al., 2019;Ojeda et al., 2021). ...
Here, we review the contributions of Professor Barbara Sherwood Lollar to Compound Specific Isotope Analysis (CSIA) in contaminant hydrogeology and environmental chemistry. We first discuss the seminal work by Professor Sherwood Lollar’s lab on establishing CSIA as a quantitative tool for contaminant (bio)transformation at contaminated groundwater sites. We describe the critical research by her lab in the development and validation of sample collection techniques, single- and multi-element CSIA, and isotope data evaluation for reliable interpretations. We highlight the contributions of Professor Sherwood Lollar’s lab towards the development of best practices for the successful application of CSIA by industry to demonstrate the occurrence of (bio)transformation, identify (bio)transformation mechanisms, quantify the extent and rate of degradation and differentiate among potential contaminant sources. We then explore Professor Sherwood Lollar’s applications of CSIA to hydrogeology of the deep subsurface and the fast widening of the field to new environments (e.g., sediments), contaminants (e.g., chlorofluorocarbons, pesticides), and systems (e.g., plant, enzymes).
... To check whether eye length scales isometrically with bee size (and thus can be expected to predict ommatidia number, Jander & Jander, 2002) we used reduced major axis regression (model II) (Laws & Archie, 1981) to test whether the slope b of the relationship ln eye length ð Þ¼ ln a ð Þ þ b x lnð ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi body weight 3 p Þ differs from 1 (Gr€ uter et al., 2012;H€ olldobler & Wilson, 2009;Wilson, 1953). ...
Stingless bees are the most species-rich group of eusocial bees and show great diversity in behaviour, ecology, nest architecture, colony size, and worker morphology. How this variation relates to varying selection pressures and constraints is not well understood. Variation can be caused by selection acting on behavioural or morphological traits, both alone and in correlation across traits. Here we tested whether behavioural and morphological traits important for foraging and defence are linked to nest-entrance architecture, an extended phenotype relevant to both foraging and nest defence. Using 23 species we investigated whether eye size, nest entrance size, landing behaviour and foraging method show cross-species correlations. A phylogenetically-controlled comparative analysis revealed that species with relatively smaller eyes build relatively larger entrances, which in turn are associated with faster landing approaches and fewer landing errors by foragers, both of which could reduce predation risk. Concerning foraging, mass-recruiting species have c. 10-times larger entrance holes than species with a solitary foraging strategy. Larger entrances could help species with mass recruitment to rapidly increase forager traffic or mount a strong defensive response when under attack. Our results show that studying correlations among different traits helps understand phenotypic diversity in species rich groups.
... Results were combined and analysed together by one-way analysis of variance (ANOVA) at P s 0.05, by Student's t-test at P s 0.05, and correlation coefficient test using Excel 2000. Linear regression analysis between the observed values was used to verify the fitting quality according to Laws and Archie (1981). ...
p> This research provides an advanced understanding of the physiological responses of two algal species, Chlorella vulgaris and Scenedesmus subspicatus (Chlorophyta) to changing environmental conditions likely to occur in Waste Stabilisation Ponds (WSPs).
Bicarbonate was found to be a suitable carbon source for both species. Maximum growth rates of around 0.07 h<sup>-1 </sup>were achieved at concentrations of around 10 mmol C 1<sup>-1</sup>. The results showed that nitrate uptake became increasingly light dependent with increases in temperature. Phosphate was taken up from the medium in excess of immediate growth requirements and uptake rates did not show light or temperature dependence at the range of concentrations used. Respiration rates were shown to depend on light and temperature. Photosynthetic activity was registered at light intensities as low as 7.8 µmol m<sup>-2 </sup>s<sup>-1 </sup>and 5°C of temperature. Both light and temperature affected growth rates. Both species reached maximum light-specific growth rates at 47.0 µmol m<sup>-2</sup>s<sup>-1 </sup>at all temperatures tested. Below 15°C C. vulgaris showed higher growth rates than S. subspicatus, but this was reversed at 20°C.
Experiments on survival showed that a proportion of cells of C. vulgaris could survive long periods (22 weeks) of dormancy in complete darkness and low temperatures (+4 and -20°C). Despite a hardening procedure, S.subspicatus showed no survival after exposure to -20°C and limited ability to resume growth and carry out photosynthetic oxygen production after exposure to +4°C and complete darkness up to 14-15 weeks. Overall the results indicate that C. vulgaris is better adapted to growth at low temperature and light intensities, but may be out-competed by S. subspicatus in warmer brighter conditions. </p
... Type-II regression (MATLAB function lsqfitgm.m) was applied rather than Type-I regression as it accounts for the inherent measurement uncertainties of in situ field data (Laws and Archie, 1981). While values of r and S that are close to one generally indicate better agreement between model estimates and in situ observations, r and S alone provide no information on the accuracy or bias of a given model, and thus are not viewed in isolation from the MAD and δ when assessing model performance. ...
The size structure of phytoplankton communities influences important ecological and biogeochemical processes, including the transfer of energy through marine food webs. A variety of algorithms have been developed to estimate phytoplankton size classes (PSCs) from satellite ocean color data. However, many of these algorithms were developed for application to the global ocean, and their performance in more productive, optically complex coastal and continental shelf regions warrants evaluation. In this study, several existing PSC models were applied in the Northeast U.S. continental shelf (NES) region and compared with in situ PSC estimates derived from a local HPLC pigment data set. The effect of regional re-parameterization and incorporation of sea surface temperature (SST) into existing abundance-based model frameworks was investigated and model performance was assessed using an independent data set. Abundance-based model re-parameterization alone did not result in significant improvement in model performance compared with other models. However, the inclusion of SST led to a consistent reduction in model error for all size classes. Of two absorption-based algorithms tested, the best performing approach displayed similar performance metrics to the regional SST-dependent abundance-based model. The SST-dependent model and the absorption-based method were applied to monthly composites of the NES region for April and September 2019 and qualitatively compared. The results highlight the benefit of considering SST in abundance-based models and the applicability of absorption-based PSC methods in optically complex regions.
... We calculated regressions between various variables and salinity to analyze their conservative behavior in different water masses. Since both variables are random, we used Model II regressions following Laws and Archie (1981). We used Model I regression to analyze temporal trends in water mass nutrient concentrations. ...
There is strong evidence of an increase in primary production (PP) in the Arctic Ocean (AO) over the last two decades. Further increases will depend on the interplay between decreasing light limitation for primary producers, as the sea ice extent and thickness decrease, and the availability of nutrients, which is controlled by, but not limited to, inputs from the Atlantic and the Pacific Oceans. While these inputs are the major nutrient sources to the AO, ocean vertical mixing is required to bring the nutrients into the photic zone. We analyze data collected in the Western Eurasian Basin (WEB) between 1980 and 2016 and characterize the nutrient climatology of the various water masses. We conclude that there were no significant trends in the concentrations of the two macronutrients that typically limit PP in the AO (nitrate and silicic acid, in the case of diatoms), except a decreasing trend for silicic acid in Polar Surface Water (PSW), which is consistent with the reported increase in PP in the AO. We suggest that the Whalers Bay polynya, located in the northwestern corner of Svalbard, may act as a mixing hotspot, creating patches of nutrient replenished PSW. These patches may then be advected to higher latitudes under the ice pack, later boosting PP upon release from light limitation or else, keeping a nutrient reservoir that may be used in a subsequent growth season. It is likely that this remaining nutrient reservoir will decrease as sea ice cover retreats and light limitation alleviates.
... Gray circles represent samples between the shelf water and the slope water/Gulf Stream, and black crosses represent the samples between the nearshore and the shelf water. Black lines denote least squares fits calculated with a model II regression (Laws and Archie, 1981;Sokal and Rohlf, 2012), and the red dot lines are the Redfield ratios. ...
The United States Department of Energy (DOE)’s Ocean Margins Program (OMP) cruise EN279 in March 1996 provides an important baseline for assessing long-term changes in the carbon cycle and biogeochemistry in the Mid-Atlantic Bight (MAB) as climate and anthropogenic changes have been substantial in this region over the past two decades. The distributions of O2, nutrients, and marine inorganic carbon system parameters are influenced by coastal currents, temperature gradients, and biological production and respiration. On the cross-shelf direction, pH decreases seaward, but carbonate saturation state (ΩArag) does not exhibit a clear trend. In contrast, ΩArag increases from north to south, while pH has no clear spatial patterns in the along-shelf direction. In order to distinguish between the effects of physical mixing of various water masses and those of biological activities on the marine inorganic carbon system, we use the potential temperature-salinity diagram to identify water masses, and differences between observations and theoretical mixing concentrations to measure the non-conservative (primarily biological) effects. Our analysis clearly shows the degree to which ocean margin pH and ΩArag are regulated by biological activities in addition to water mass mixing, gas exchange, and temperature. The correlations among anomalies in dissolved inorganic carbon, phosphate, nitrate, and apparent oxygen utilization agree with known biological stoichiometry. Biological uptake is substantial in nearshore waters and in shelf-slope mixing areas. This work provides valuable baseline information to assess the more recent changes in the marine inorganic carbon system and the status of coastal ocean acidification.
... Data were tested for normality using the Anderson-Darling normality test within the R package kSamples (Scholz and Zhu 2017). Model II major axis regressions (Ricker 1973;Laws and Archie 1981) were employed to test for potential relationships between litter size and sex ratio within the first, second, and third litters (parity) of each mother pooled across all years, as well as on an annual basis, to test for any apparent relationships within each calendar year. Additionally, regressions were run on litter size and sex ratio of litters from 1-, 2-, and 3-year-old mothers known to have had at least three observed litters over the sample period, to test for any apparent relationship within specific dam age cohorts. ...
Trivers and Willard proposed that female mammals should adjust their investment in male versus female offspring relative to their ability to produce high-quality offspring. We tested whether litter size–sex ratio trade-offs predicted by Adaptive Sex Allocation (ASA) theory occur among Richardson’s ground squirrel (Urocitellus richardsonii) dams over 10 distinct breeding years in a population where individuals experienced variability in food availability and habitat disruption. Litters of primiparous dams became increasingly female-biased with increasing litter size, but that trend waned among second litters born to dams, and reversed among third litters, with larger litters becoming more male-biased, suggesting that ASA is a product of interacting selection pressures. Trade-offs were not associated with habitat disruption, the availability of supplementary food, or dam age. An association between habitat disruption and male-biased sex ratios, the prevalence of litter size–sex ratio trade-offs and placental scar counts exceeding the number of juveniles at weaning in our population, but not in a geographically distinct population of conspecifics exposed to different environmental conditions reveal that the expression of ASA varies among populations and among years within populations, illustrating the conditional nature of ASA.
... This approach involved transforming NDVI-to-NDVI instead of translating using the distributed method (transforming the red and NIR bands to calculate a transformed NDVI) Band-to-NDVI [27]. The eVIIRS NDVI was transformed using the GMR developed from our eVIIRS and eMODIS correlation statistics described in the results section [28,29]. The GMR transformation was selected because the inverse can be used to transform historical eMODIS NDVI to eVIIRS-like NDVI values if this transformation is needed to create similar historical continuity in NDVI values, but for our study we adhere to transforming eVIIRS NDVI to eVIIRS' [30,31]. ...
Vegetation has been effectively monitored using remote sensing time-series vegetation index (VI) data for several decades. Drought monitoring has been a common application with algorithms tuned to capturing anomalous temporal and spatial vegetation patterns. Drought stress models, such as the Vegetation Drought Response Index (VegDRI), often use VIs like the Normalized Difference Vegetation Index (NDVI). The EROS expedited Moderate Resolution Imaging Spectroradiometer (eMODIS)-based, 7-day NDVI composites are integral to the VegDRI. As MODIS satellite platforms (Terra and Aqua) approach mission end, the Visible Infrared Imaging Radiometer Suite (VIIRS) presents an alternate NDVI source, with daily collection, similar band passes, and moderate spatial resolution. This study provides a statistical comparison between EROS expedited VIIRS (eVIIRS) 375-m and eMODIS 250-m and tests the suitability of replacing MODIS NDVI with VIIRS NDVI for drought monitoring and vegetation anomaly detection. For continuity with MODIS NDVI, we calculated a geometric mean regression adjustment algorithm using 375-m resolution for an eMODIS-like NDVI (eVIIRS’) eVIIRS’ = 0.9887 × eVIIRS − 0.0398. The resulting statistical comparisons (eVIIRS’ vs. eMODIS NDVI) showed correlations consistently greater than 0.84 throughout the three years studied. The eVIIRS’ VegDRI results characterized similar drought patterns and hotspots to the eMODIS-based VegDRI, with near zero bias.
... While not explicitly dealt with here, these findings are also relevant to multi-element isotope analyses in environmental chemistry [37], ecology [38], and food forensics [39]. In fact, these findings are relevant to any field using linear regression for data analysis, encompassing fields including marine biology [40], clinical chemistry [41], anthropology [42]. ...
Measuring changes in the stable isotope ratios of multiple elements (e.g. Δδ¹³C, Δδ³⁷Cl, and Δδ²H) during the (bio)transformation of environmental contaminants has provided new insights into reaction mechanisms and tools to optimize remediation efforts. Dual-isotope analysis, wherein changes in one isotopic system are plotted against another (to derive an interpretational parameter expressed as Λ), is a key tool in multi-element isotopic assessment. To date, most dual-isotope analyses use ordinary linear regression (OLR) for the derivation, which can be subject to regression attenuation and thus an inherent artifact that depresses slope values, expressed as Λ. Here, a series of Monte Carlo simulations were constructed to represent common data conditions and variations within dual-isotope data to test the degree of bias when deriving Λ using OLR compared to an alternative regression technique, the York method. The degree of bias was quantified compared to the modeled or “true” Λ value. For all simulations, the York method provided the least bias in slope estimates (<1%) over all data conditions tested. In contrast, OLR produced unbiased estimates only under a limited set of conditions, which was validated through a mathematical model proof. Both the mathematical model and simulations show that bias of at least 5% in OLR occurs when the extent of enrichment in the x-variable (XM) is equal to or less than ≈15 times the 1σ precision in the isotope measurement (σX), for both Cl/C and C/H plots. The results give practitioners tools to evaluate whether bias is present in data and to estimate the extent to which this negatively impacts the interpretations and predictions of remediation potential for new and previously published datasets. This study demonstrates that integration of such robust statistical tools is essential for dual-isotope interpretations widely used in contaminant hydrogeology but relevant to other disciplines including environmental chemistry and ecology.
... This approach was applied for all instrument-instrument comparisons, and for instrument-overall-instrument-concentration mean comparisons. Given that there was error associated with all concentrations measured, Model II regression was applied for particle concentration assessments (Laws and Archie 1981). For particle size assessments, Model I regression was used to obtain the slope of all Niskin-bottle particle size spectra, since the particle sizes were measured with higher precision than the size-specific concentrations. ...
Holographic microscopy has emerged as a tool for in situ imaging of microscopic organisms and other particles in the marine environment: appealing because of the relatively larger sampling volume and simpler optical configuration compared to other imaging systems. However, its quantitative capabilities have so far remained uncertain, in part because hologram reconstruction and image recognition have required manual operation. Here, we assess the quantitative skill of our automated hologram processing pipeline (CCV Pipeline), to evaluate the size and concentration measurements of environmental and cultured assemblages of marine plankton particles, and microspheres. Over 1 million particles, ranging from 10 to 200 μm in equivalent spherical diameter, imaged by the 4‐Deep HoloSea digital inline holographic microscope (DIHM) are analyzed. These measurements were collected in parallel with a FlowCam (FC), Imaging FlowCytobot (IFCB), and manual microscope identification. Once corrections for particle location and nonuniform illumination were developed and applied, the DIHM showed an underestimate in ESD of about 3% to 10%, but successfully reproduced the size spectral slope from environmental samples, and the size distribution of cultures (Dunaliella tertiolecta, Heterosigma akashiwo, and Prorocentrum micans) and microspheres. DIHM concentrations (order 1 to 1000 particles ml−1) showed a linear agreement (r2 = 0.73) with the other instruments, but individual comparisons at times had large uncertainty. Overall, we found the DIHM and the CCV Pipeline required extensive manual correction, but once corrected, provided concentration and size estimates comparable to the other imaging systems assessed in this study. Holographic cameras are mechanically simple, autonomous, can operate at very high pressures, and provide a larger sampling volume than comparable lens‐based tools. Thus, we anticipate that these characterization efforts will be rewarded with novel discovery in new oceanic environments.
... where W(i) = total weight (g), L(i) = length (mm), a = intercept (coefficient of initial growth) and b = slope (coefficient of growth, i.e. relative growth rate of the variables). For analysis of the morphometric relationship's length-height, length-width and height-width, only adult individuals (L ≥ 12 mm) were considered, and fits were made corresponding to a linear function (Ricker 1973;Laws & Archie, 1981): ...
There have been no published studies of the genus Donax in the eastern tropical Pacific. This work describes the morphometric relationships, growth and mortality of the bean clam Donax punctatostriatus Hanley, 1843 in the sandy beach of Isla de la Piedra, south of Mazatlán Bay, Mexico. Direct collections by hand were performed during 20 monthly sample periods (November 2008 to June 2010) in the intertidal zone of the beach. A total of 2,324 clams of different sizes were removed from the sand, then measured and weighed in the laboratory. The length range of the shells was 2.78-25.64 mm (mean = 12.61 ± 4.04 mm). The length-weight relationship of the total sample indicated isometric growth (a = 0.0002 g; b = 3.0 g mm−1, R2 = 0.97); there was positive allometric growth in the recruits (<6.99 mm) (b = 3.4) and in juveniles (b = 3.2); in adults there was negative allometric growth (b = 2.6). Negative allometry of the length/width (log Wd = −0.239 + 0.922 log L) and height/width (log Wd = −0.054 + 0.900 log H) ratio of adults is consistent with a more compressed form of their shell, which assists rapid burying behavior in the sand. The maximum-recorded size of an empty shell (39 mm) was used to set the value of L∞ and to estimate K with the Shepherd (SLCA) method. The average growth rate during the life cycle was 0.43 mm yr−1. Values of L∞ between 29.16 and 34.22 mm were estimated with the Powell-Wetherall method using different class intervals. The mortality coefficient estimated with various methods was variable (0.84-1.15 yr−1). The growth of the clam is rapid and the mortality high, probably because of the characteristics of the habitat, in a subtropical region with high hydrodynamics and sediment transport.
... We assume that this difference is due to the application of correlation tests instead of 777 linear models to study asymmetric topics. This can be appropriate when not only the response 778 45 variable, but also the predictors, are random (Legendre and Legendre, 2012), even if model II 779 regression is a more generally accepted alternative (Laws and Archie, 1981 previous studies. For instance, James and McCulloch (1990), who summarised and reviewed the 786 use of multivariate techniques in ecology and systematics, also found that PCA was the most 787 frequently used ordination method and that linear models were widely used. ...
Many ecological processes that play important roles in ecosystems occur over long time periods and can therefore not always be properly studied with short-term studies. However, researchers have to face many challenges while setting up long-term ecological studies, including the choice of relevant data analysis methods and the design of the study (i.e. sampling frequency, number of sites, etc.). This literature review, based on 99 original studies, provides an overview of methodological choices used to analyse the effects of abiotic parameters on biological communities on a long-term scale. To this end, the main characteristics of study design were recorded (e.g. sampling frequency, duration, taxa, variables) and the different data analysis tools summarised and analysed. We found that long-term ecological studies focusing on the effects of environmental factors on biotic parameters mostly concerned aquatic habitats. Studies substantially varied in their design, although many of them had similar aims. Univariate methods, almost entirely performed by means of linear modelling and correlation tests, were used more often than multivariate methods. Finally, constrained and unconstrained ordination methods were used equally, and other data analysis tools were rare. Finally, we created a decision key to help researchers choose the appropriate analysis tools for their specific long-term study.
... Slope values from the log-log analysis ranged from −0.78 to −0.14 (mean, −0.43) for OLS regressions and from −1.15 to −0.33 (mean, −0.64) for RMA regressions, in line with those observed in assemblages of highly productive inshore waters (Huete-Ortega et al., 2010;Reul et al., 2005Reul et al., , 2008. Although both types of regression describe the same spatial pattern, slopes from OLS regressions were in all cases lower than RMA, a fact also verified by Laws and Archie (1981) when reanalyzing with RMA two ecological data sets previously Fig. 8. Biplot of the PCA based on eukaryotic unicellular plankton abundances from nine sites at SAB (S1-S9). Rows indicate the loading of each species on the first two axes. ...
Tidal flats are exceptionally dynamic coastal ecosystems. Tides are their main source of energy, whose influence decreases landwards (as land elevation increases), thus shaping physical, chemical and biological gradients. In this study we assess whether the structure of nano- and microplankton varies along a spatial gradient in San Antonio Bay (SAB, SW Atlantic), a semi-desert coastal ecoystem with a wide tidal flat and a macrotidal regime. We hypothesize that the tidal effect shapes SAB's both taxonomical groups and size spectrum. The seasonal sampling of nine sites revealed that diatoms and small flagellates were the most abundant groups, together accounting for over 75% of total density in practically all sites and seasons. High densities of meroplanktonic stages of Ulva lactuca were recorded in spring at the innermost sites, accounting for over 95% of all planktonic cells. Slopes of the size spectrum analysis were in line with highly productive inshore waters (mean:-0.64) and showed that larger phytoplankton was the main contributor to total biomass, despite its decreasing importance towards inner sites. The spatial and seasonal variations found for lower trophic web compartments provide evidence of the importance of tidal transport in ruling phytoplankton structure in tidal flats under strong macrotidal regimes.
... where β 0 and β 1 are estimated parameters and y and x are any combination of the length measurements. In contrast to OLS, the MA equation is reciprocal in the sense that there is no dependency of one variable over the other and allows for error in both y and x (Laws & Archie, 1981). The MA models were fit using the package lmodel2 (Legendre, 2018) in R (www.r-project.org). ...
Length‐measurement conversions and seasonal mass–length relationships (MLR) for Pacific herring Clupea pallasii, northern anchovy Engraulis mordax, Pacific sardine Sardinops sagax, Pacific mackerel Scomber japonicus and jack mackerel Trachurus symmetricus in the California Current are presented. The conversions between total (LT), fork (LF,) and standard lengths (LS) should facilitate comparisons of data across disciplines and institutions. These equations resulted from an analysis of measurements spanning 14 years and the western seaboard of North America, from the north end of Vancouver Island to the USA–Mexico border. Major‐axis regressions were used to calculate reciprocal length‐measurement conversions (e.g., LT to LS and LS to LT) and generalised linear models and ordinary least‐squares models were used to create MLRs that account for seasonal variations. The MLR models indicated seasonal differences for all species except C. pallasii, for which there was no multi‐season data. Discrepancies between these and published models were examined, along with the suitability and benefit of the various types of models used for length‐measurement conversion and MLRs.
... The performances of the tested algorithms were evaluated based on the following statistical parameters: Pearson's correlation coefficient (r), slope (S) and intercept (I) of Type-2 linear regression (York, 1966;Laws and Archie, 1981;Glover et al., 2011) fitted on log-transformed Chl-a data; root-mean-square error (RMSE, ); bias (δ); and mean ratio. The latter three parameters are defined, respectively, as ...
Jinhae Bay, one of the most important aquaculture areas in Korean coastal waters, has suffered from serious environmental problems due to intensive anthropogenic activities since the 1970s. Determining the response of coastal ecosystems in Korea to anthropogenic activities requires understanding the characteristics of chlorophyll-a concentration (Chl-a), and the high spatiotemporal resolution of the Geostationary Ocean Color Imager (GOCI) can aid these efforts. However, producing reliable satellite-based Chl-a estimates is challenging in optically complex coastal waters and the Chl-a estimation algorithms must be assessed regionally. Based on in situ Chl-a measurements collected in Jinhae Bay between 2011 and 2016, we evaluated GOCI-derived Chl-a estimates obtained using six ocean color Chl-a algorithms: two standard open ocean algorithms, one GOCI-standard algorithm, and three Tassan's algorithms regionally modified for Korean waters. All of the algorithms tended to underestimate high Chl-a values >0.9 mg m−3. The Yellow Sea Large Marine Ecosystem Ocean Color Project (YOC) algorithm, one of the modified Tassan's algorithms, provided the best fit to the in situ Chl-a measurements in Jinhae Bay (r = 0.51, p < 0.05), including appropriate representations of the spatial and temporal variation. Therefore, this algorithm can be considered a baseline approach for satellite-based long-term coastal monitoring systems in Jinhae Bay.
... Others report only the SE 11,16 or report no error at all. 21 The debate over appropriate best-fit regression methods and error reporting is widespread in the scientific literature in fields including marine biology, 22 clinical chemistry, 23 anthropology, 24 within the geological sciences, 25 and within contaminant hydrogeology. 19 However, recommendations are often specific to each field. ...
Compound-specific isotope analysis (CSIA) is a powerful tool to understand the fate of organic contaminants. Using CSIA, the isotope ratios of multiple elements (δ¹³C, δ²H, δ³⁷Cl, δ¹⁵N) can be measured for a compound. A dual-isotope plot of the changes in isotope ratios between two elements produces a slope, lambda (Λ), which can be instrumental for practitioners to identify transformation mechanisms. However, practices to calculate and report Λ and related uncertainty are not universal, leading to the potential for misinterpretations. Here, the most common methods are re-evaluated to provide the basis for a more accurate best practice representation of Λ and its uncertainty. The popular regression technique, ordinary linear regression, can introduce mathematical bias. The York method, which incorporates error in both variables, better adapts to the wide set of data conditions observed for dual-isotope data. Importantly, the existing technique of distinguishing between Λs using the 95% confidence interval alone produces inconsistent results, whereas statistical hypothesis testing provides a more robust method to differentiate Λs. The propensity for Λ to overlap for a variety of conditions and mechanisms highlights the requirement for statistical justification when comparing datasets. Findings from this study emphasize the importance of this evaluation of best practice and provide recommendations for standardizing, calculating, and interpreting dual-isotope data.
... If unbiased, these slopes would imply that export efficiency varied as NPP raised to the −0.74 power in the SO and −0.64 power at HOT, i.e., there would be a negative correlation between NPP and export efficiency. However, when the independent variable is merely measured and is not under the control of the investigator, OLS regression produces a biased estimate of the slope of the true relationship between two variables (Laws et al., 2016;Laws and Archie, 1981;Ricker, 1973). The OLS slope systematically underestimates the magnitude of the true slope. ...
We analyzed net primary production (NPP) and export production rates measured in the Southern Ocean (SO) and at Station ALOHA (22° 45′N, 158° 00′W) and discovered that in both cases there was a highly significant negative correlation between NPP and the ratio of export production to NPP (i.e., the export ratio). We show that in both cases this negative correlation can be explained by a time lag between the production and export of organic matter from the euphotic zone. The negative correlation appears (disappears) in simulated data if the estimates of the relationship between NPP and export production are based on measurements over timeframes that are comparable to or shorter (much longer) than the time lag between NPP and export production. At Station ALOHA, where data are available from a time series that extends back to 1988, the negative correlation disappears when the data are climatologies over monthly time intervals, which are long compared to the assumed lag of five days between the production and export of organic matter at low latitudes. We conclude that because of the temporal variability of NPP and the time lags between the production and export of organic matter, meaningful estimates of export ratios will need to be based on rates of NPP and export production averaged over timeframes that are long compared to the lag between production and export.
... sea conditions and operator ability, which in turn can introduce several contamination factors; hence, here we consider satellite and in situ observations to both be affected by uncertainties (Loew et al., 2017). Thus, for the matchup analysis, a type-2 regression (also called orthogonal regression) is implemented here (Laws and Archie, 1981). The statistical parameters for the assessment of satellite versus in situ data are listed in Table 2. ...
The Mediterranean near-real-time multi-sensor processing chain has
been set up and is operational in the framework of the Copernicus Marine
Environment Monitoring Service (CMEMS). This work describes the main steps
operationally performed to enable single ocean colour sensors to enter the
multi-sensor processing applied to the Mediterranean Sea by the Ocean Colour
Thematic Assembly Centre within CMEMS. Here, the multi-sensor chain takes
care of reducing the inter-sensor bias before data from different sensors are
merged together. A basin-scale in situ bio-optical dataset is used both to
fine tune the algorithms for the retrieval of phytoplankton chlorophyll and
the attenuation coefficient of light, Kd, and to assess the uncertainty
associated with them. The satellite multi-sensor remote sensing reflectance
spectra agree better with the in situ observations than those of the single
sensors. Here, we demonstrate that the operational multi-sensor processing
chain compares sufficiently well with the historical in situ datasets to also
confidently be used for reprocessing the full data time series.
... Because both the dependent variable, CPUE (fish per hour) and the independent variable, density (fish per 100 m 2 ), have associated variability, we used a Model II regression to determine the relationship between CPUE and fish density totalled for all dive plots per site (Ricker, 1973;Laws and Archie, 1981). Since the fishing was conducted by drifting overtop of all dive plots, site density was calculated as total number of fish counted by total area searched summed across plots for each site. ...
Using density measurements derived by SCUBA diving, we have verified that research angling catch per unit of effort (CPUE) is a useful measurement of the relative abundance of nearshore reef species when the appropriate habitat is targeted. We found a strictly proportional relationship between lingcod and copper rockfish CPUE and density using a ranged major axis regression. This relationship did not hold for quillback rockfish since this study did not target their preferred depth range; nor for kelp greenling. Researchers must be aware of such limitations when using CPUE as a measure of relative abundance.
... Use of the Model I re gression is justified in this analysis, as temperature was kept constant and controlled by the experimental design. If both variables are random and not controlled by the researcher, then a Model II type re gression that assumes error in both variables is required (Laws & Archie 1981, Legendre & Legendre 1998. A Model II regression should always be used under these circumstances, although in biological oceanography, Model I regression is most commonly used. ...
Microbial respiration of particulate organic carbon (POC) is one of the key processes controlling the magnitude of POC export from the surface ocean and its storage on long timescales in the deep. Metabolic processes are a function of temperature, such that warming sea temperatures should increase microbial respiration, potentially reducing POC export. To investigate this in the Southern Ocean, we measured microbial oxygen consumption of large particles over a 10°C temperature range (summer maximum + 8°C) to then estimate the decrease in export by 2100. Our results showed that POC-normalised respiration increased with warming. We estimate that POC export (scaled to primary production) could decrease by 17 ± 7% (SE) by 2100, using projected regional warming (+1.9°C) from the IPCC RCP 8.5 ('business-as-usual' scenario) for our sub- Antarctic site. Increased microbial respiration is one of many processes that will be altered by future climate change, which could all modify carbon storage in the future. Our estimate of the potential decline in carbon sequestration is within previous estimates from lab and field experiments, but higher than simple mechanistic models. To explore our results further, we used the metabolic theory of ecology (MTE) to determine the activation energy of microbial respiration, which was 0.9 eV. This is higher than classical MTE (0.6-0.7 eV), suggesting that sub-Antarctic microbes are particularly sensitive to temperature change. Such regional characteristics in the response of organisms to increased temperatures should be accounted for in large-scale or global model analyses to ensure that the results do not underestimate microbial responses to warming.
... The uncertainty associated with the in situ data is due to several factors, e.g., the sea conditions, the operator ability which in turn can introduce several contamination factors; hence, here we consider satellite and in situ observations to be both affected by uncertainties (Loew et al., 2017). Thus, for the matchup analysis, a type-2 regression (also called orthogonal regression) is implemented here (Laws and Archie, 1981). The statistical parameters for the assessment of satellite versus in situ data are listed in Table 2. ...
This work describes the main processing steps operationally performed to enable single ocean colour sensors to enter the multi-sensor chain for the Mediterranean Sea of Ocean Colour Thematic Assembling Centre. Here, the multi-sensor chain takes care of reducing the inter-sensor bias before data from different sensors are merged together. The basin-scale in situ bio-optical dataset is used both to fine-tuning the algorithms for the retrieval of phytoplankton chlorophyll and attenuation coefficient of light, Kd, and to assess the uncertainty associated with them. The satellite multi-sensor remote sensing Reflectance spectra better agree with the in situ observations than that of the single sensors, and are comparable with the ESA-OC-CCI multi-sensor product, highlighting the importance of reducing the inter-sensor bias. The Mediterranean near-real-time multi-sensor processing chain has been set up and is operational in the framework of the Copernicus Marine Environment Monitoring Service.
... where W(i) = total weight (g), L(i) = length (mm), a = intercept (coefficient of initial growth) and b = slope (coefficient of growth, i.e. relative growth rate of the variables). For analysis of the morphometric relationship's length-height, length-width and height-width, only adult individuals (L ≥ 12 mm) were considered, and fits were made corresponding to a linear function (Ricker 1973;Laws & Archie, 1981): ...
En el Pacífico Tropical Oriental no existen estudios de las especies del género Donax. Específicamente, el conocimiento biológico y ecológico de la almeja Donax punctatostriatus en el Pacifico mexicano es nulo. En el presente trabajo se estimaron las relaciones biométricas y los parámetros de crecimiento y mortalidad de esta almeja en una playa arenosa de Isla de la Piedra localizada al sur de Mazatlán, México. Se realizaron 36 muestreos quincenales (noviembre 2008 - junio 2010). Se recolectaron de forma directa 2,324 almejas de diferentes tallas en la zona intermareal, las cuales fueron medidas y pesadas. El rango de longitud de las conchas fue de 2.78 ̶ 25.64 mm (media=12.61 mm, D.E.=4.04 mm). La relación largo-peso del total de los organismos indicó un crecimiento isométrico (a=0.0002 gr; b=3.0 g/cm; r2=0.97), los reclutas (< 11.0 mm) crecimiento alométrico positivo (b=3.4) y los juveniles y adultos alométrico negativo (b= 2.8). La talla máxima registrada de una concha vacía se usó para fijar el valor de L∞ a 39 mm y calcular K con el método Shepherd (SLCA). La tasa de crecimiento fue de 0.430 año-1, la L∞ también fue estimado con el método de Powell y Whetheral con diferentes intervalos de clase, dando valores de 29.16–34.22 mm. El coeficiente de mortalidad se estimó con varios métodos y los valores obtenidos fueron poco variables entre sí (0.84 – 1.15 año-1). La alometría negativa de esta población de almejas indicó una forma comprimida de la concha, lo cual explica la estrategia de enterrarse con mayor facilidad en el sedimento. Su crecimiento es rápido y la mortalidad alta se debería principalmente al alto hidrodinamismo del hábitat en esta región subtropical.
... Correlation between deviations from the somatic and otolith growth curves converts an 'errors in variables' issue, commonly encountered in allometric relationships such as that between length and otolith radius (Laws and Archie 1981;Xiao 1996;Katsanevakis et al. 2007), into a 'correlated errors in variables' problem, adding to the statistical issues encountered when fitting equations to describe the relationship (Fuller 1980;Thoresen and Laake 2007). The bivariate growth model developed for this study takes such individual variation and potential for correlation of deviations into account, thereby directly addressing this issue. ...
Back-calculation of lengths at ages prior to capture has been found to be a valuable tool for many fish studies. The approach relies on the relationship between fish length and measures of growth zones formed at validated, regular intervals in hard structures within the fish, such as otoliths. While it has been suggested that the inclusion of age in back-calculation procedures might improve the quality of the estimates that are produced, there are relatively few back-calculation approaches that have employed this variable, and it appears that none has made use of traditional growth curves when describing somatic and otolith growth.
This thesis employed data for six teleost species with different biological characteristics to determine whether results of analyses were broadly applicable to a wide range of species. The performance of a new proportionality-based back-calculation approach based on a model of somatic and otolith growth that employs traditional forms of growth curves and assumes a bivariate distribution of deviations from these two growth curves was explored. The forms of the curves used to describe fish length and otolith size at capture were selected from a suite of traditional and flexible growth curves on the basis of Akaike Information Criteria for the fitted models. Coefficients of determination indicated good fits of the bivariate growth model for five of the six species. Deviations from the two growth curves were positively correlated and, for three of the six species, statistically significant.
The accuracy and precision of predictions made using the fitted bivariate growth model were assessed by comparing predicted lengths at capture given both age and otolith radius, and predicted otolith radius at capture given both age and fish length, with the corresponding observed values for fish that were not included when fitting the model. The resulting measures of root mean square error (RMSE) for six fish species with different biological characteristics were compared with those obtained using the methods employed in a set of existing proportionality-based back-calculation approaches that also incorporated age when describing the relationship between fish length and otolith radius. Based on the results from this cross-validation, the RMSEs of predictions of fish length and otolith size of the new bivariate model were found typically to be equal to or better than those produced using the regression equations of the alternative approaches.
The new bivariate growth model was extended to provide a proportionality-based back-calculation approach, with the option of constraining the growth curves to pass through a biological intercept, i.e., the length, otolith radius and age of recently-hatched larvae. Back-calculated estimates of lengths at ages prior to capture calculated for individuals from a population of Acanthopagrus butcheri using the bivariate growth model were compared with the estimates produced by other proportionality-based back-calculation approaches that employed age and with a constraint-based back-calculation approach that was known to have good performance. The resulting estimates of length at ages produced by the proportionality-based back-calculation approach developed using the bivariate growth model, when constrained to pass through the biological intercept for this species, were typically more consistent with mean observed lengths at corresponding ages than those of the alternative back-calculation approaches. In combination with the cross-validation results, these findings suggest that, for this population of A. butcheri, back-calculated lengths produced using the bivariate growth model are likely to be more reliable than those produced using the other back-calculation approaches.
A common assumption of mixed effects models of otolith growth suggests that, through inclusion of a random effect for different fish, the growth rate of otolith of an individual fish relative to that of other fish will persist throughout life. It was proposed that, throughout the life of an individual from a selected population of A. butcheri, the sizes of its otolith remain in constant proportion to the average sizes of the otoliths of fish of the same ages. This hypothesis was investigated by exploring the extent to which the natural logarithms of the ratios of otolith size for individual fish to average otolith size from A. butcheri of the same age remained constant throughout life. Although, for individuals of this species, the hypothesis of constant proportionality with age was found to be invalid as the ratios of relative otolith size varied among different periods of life, these ratios became increasingly constant with increasing age.
Other factors likely to affect predictions derived from the new back-calculation approach, such as length-dependent selection and level of fishing mortality, were explored using simulation. Results from this simulation suggest that, due to the cumulative effect of fishing mortality on survival, the mean age of fish of a given length or otolith size is likely to decrease as length-dependent fishing mortality increases for fish with larger lengths or otolith sizes, with the effect apparently less on otolith size than on fish length. Similarly, mean lengths for fish with otoliths of a given size and, to a lesser extent, mean otolith sizes for a given fish length, decreased with increasing fishing mortality for fish with larger lengths or otolith sizes. Mean otolith sizes at age of younger fish, however, appeared little affected by reduced selectivity. Although otolith size at age of older fish predicted by bivariate models fitted to simulated otolith sizes at capture appeared little affected by increasing fishing mortality, predicted fish lengths at age of older fish and fish lengths at otolith size of fish with larger otoliths decreased with increasing fishing mortality, with the magnitude and direction of the effect varying among species with different levels of fishing mortality.
The model developed in this study provides a link between studies of somatic growth and investigations of the relationship between length and otolith size undertaken in traditional back-calculation approaches, thereby facilitating future investigation of factors affecting this relationship and, through this, improving our understanding of the influence of environmental factors on somatic and otolith growth.
... We compared otolith-derived measurements of larval duration (non-normally distributed) among species and among years using a nonparametric Kruskal-Wallis test, followed by a nonparametric multiple comparison analysis (Dunn 1964, Zar 1984. We used reduced major axes (RMA) procedures to adjust for the inherent variability in the independent variable (length) of the age-on-length linear regressions (Ricker 1973, Laws andArchie 1981). Length-on-age regressions provided an estimate of growth rate (slope) and size at settlement (intercept), and the jackknife method produced estimates of standard error for each statistic (Sokal and Rohlf 1981). ...
Despite the fact that recruitment can significantly influence the population dynamics of benthic marine populations, relatively little is known about the biological and physical processes controlling recruitment. We selected eight closely related coral reef fishes (wrasses in the family Labridae) to examine the temporal and spatial patterns of juvenile recruitment to the Caribbean island of Barbados. We used a comparative approach to study the relationships among patterns of recruitment, early life history traits, and aspects of the physical environment. For 10 wk during each of three peak recruitment (spring) seasons (1990-1992), we used a biweekly census of recently settled juveniles (8-25 mm standard length, SL) to measure the abundance of six congeners, Halichoeres bivittatus, H. radiatus, H. poeyi, H. garnoti, H. pictus, and H. maculipinna, and two confamilial labrids, Thalassoma bifasciatum and Bodianus rufus. Analysis of the otoliths of a sample of collected specimens provided estimates of larval durations, postsettlement ages, sizes at settlement, and juvenile growth rates, enabling back-calculation of settlement day for all collected juveniles. We compared temporal patterns of recruitment among species, and spatial patterns of recruitment for the most common species. Temporal patterns of recruitment were consistent among seasons for most of the labrids examined, although the magnitude of recruitment was less predictable (particularly for H. poeyi, H. maculipinna, and B. rufus). The eight labrids could be divided into two groups based on their early life history traits and within-season temporal patterns of recruitment. Halichoeres bivittatus, H. radiatus, H. poeyi, H. garnoti, and H. pictus had larval durations that were relatively short and invariant (means of 23-27 d), and all settled at fairly large sizes (9-12 mm SL) during the new moon and first maximum amplitude tide. In contrast, T. bifasciatum, B. rufus, and H. maculipinna had larval durations that were longer or more variable, and all three were able to delay metamorphosis. These three species settled at relatively smaller sizes (8-10 mm SL) during the third-quarter moon and second minimum amplitude tide. We compared temporal patterns of T. bifasciatum recruitment between Barbados and Caribbean Panama in an attempt to identify further the proximate environmental cues operating during settlement. Contrasting patterns of T. bifasciatum recruitment between the two geographical locations probably result from differences in the relative timing of the lunar and tidal amplitude cycles. Recruitment of labrids to Barbados occurred along the entire west coast of the island. Although some labrids had rather specific habitat requirements (e.g., B. rufus associated exclusively with large seaward-facing coral heads such as Montastrea spp.), most species were ubiquitous along the west coast. Species-specific juvenile densities did not often vary significantly among sites following major recruitment events, although overall densities were generally lower at a central site. Lower recruitment to that site likely results from reduced rates of larval supply due to prevailing offshore tidal flows. Thus, temporal and spatial patterns of labrid recruitment to Barbados appear to be more predictable than previously thought for reef fishes. In particular, variation in the tidal amplitude cycle may influence both the timing of settlement and, to a lesser degree, the spatial scale of larval supply. Finally, the interaction of larval biology with such physical processes is evident in the correlation between temporal patterns of recruitment and early life history traits. The functional nature of this relationship clearly warrants further study.
... Much discussion has surrounded the question whether model I (fixed independent variable) or model II (independent variable measured with error) is the appropriate regression analysis for this application. Laws and Archie (1981) argue that most oceanographic data are best analyzed using model II, since frequently both variables are measured and have error; therefore, one of the assumptions of parametric regression analysis is violated. This is also true for the data presented here; however, the sources for both errors are not correlated. ...
... A key, consistent observation is that Phaeocystis colony blooms usually follow the spring diatom maximum, implying that perhaps chemical modification of seawater via biological conditioning or secretion of allelochemic substances (Smayda 1980) is a prerequisite for colony formation. In this regard, there is the provocative suggestion that some species of the diatom genus Chaetoceros produce a chemical compound which initiates the change from the motile to non-motile stage (Boalch 1984). Free-living Phaeocystis cells can attach to surfaces by means of their flagella (not haptonema) (Kornmann 1955;Parke et al. 1971). ...
Unialgal cultures of the prymnesiophyte, Phaeocystis cf. pouchetii, were isolated from Norwegian and United States coastal waters. Manipulation of the nutrient medium resulted in populations overwhelmingly dominated by either colonies or solitary cells of Phaeocystis. Both morphotypcs were grown under a range of irradiances at 0°, 2°, 5°, 10° and 20°C. Photosynthesis was measured as incorporation of H14CO3 and excretion as accumulation of DO14C during 24-hour incubations; growth rates of solitary cells were determined concurrently from changes in abundance. Both morphotypes exhibited temperature-dependent asymptotic increases in pigment-specific photosynthesis with irradiance. Saturation intensities increased with temperature. Cell division by Phaeocystis solitary cells exhibited a functional response similar to photosynthesis, although growth apparently saturated at lower irradiances. C:Chla ratios were positively correlated with irradiance and inversely related to temperature, while C:N ratios were insensitive to these environmental parameters. Colonies had higher C:Chla and C:N ratios than solitary cells. Pigment-specific excretion rates were linear functions of irradiance, and exhibited temperature-dependent positive correlations with photosynthesis. Percent extracellular release (PER) by both morphotypes was inversely related to temperature. At low temperatures (0-5 °C), solitary cells had higher photosynthesis rates than colonies at all irradiances. Their excretion rates, however, were also higher, such that the PER of solitary cells exceeded those of colonies at 0°C and low irradiances at 2°C. No differences were detectable at 5°C. At higher temperatures, photosynthesis by solitary cells still generally exceeded that by colonies, but the colonies excreted considerably more DOC. Thus, while solitary cells are more efficient at utilizing light for photosynthesis, they do not necessarily channel a larger proportion into biomass production. Colonies, however, appear to be particularly stressed by higher temperatures and irradiances.
... This effect, which results from the relationship between the size of the otolith of an individual fish and its rate of somatic growth, is exemplified by the fact that slow-growing fish have larger otoliths than faster-growing fish of the same size (e.g., Reznick et al. 1989;Campana 1990). Correlation between deviations from the somatic and otolith growth curves converts an "errors in variables" issue, commonly encountered in allometric relationships such as that between length and otolith radius (Laws and Archie 1981;Xiao 1996;Katsanevakis et al. 2007), into a "correlated errors in variables" problem, adding to the statistical issues encountered when fitting equations to describe the relationship (Fuller 1980;Thoresen and Laake 2007). The bivariate growth model developed for this study takes such individual variation and potential for correlation of deviations into account, thereby directly addressing this issue. ...
The performance of a new proportionality-based back-calculation approach, describing the relationship among length, otolith size, and age using traditional growth curves and assuming a bivariate distribution of deviations from those curves, was evaluated. Cross-validation was used for six teleost species to compare predictions of expected lengths or otolith sizes at age, given otolith size or length, respectively, with those of other proportionality-based approaches that incorporate age. For four species, and particularly Acanthopagrus butcheri when using a biological intercept, better estimates were produced using the new model than were produced using the regression equations in the other back-calculation approaches. Back-calculated lengths for A. butcheri estimated using this model were more consistent with observed lengths, particularly when employing a biological intercept, than those obtained using other proportionality-based approaches and also a constraint-based approach known to produce reliable ...
... Meanwhile, the number of papers and chapters expounding on the subject as if the solution did not exist is staggering. Examples include widely consulted books like Biometry (Sokal and Rohlf, 1995) and Numerical Recipes (Press et al., 2007) as well as articles in fields as diverse as anthropology (Smith, 2009), water resources (Hirsch and Gilroy, 1984), clinical chemistry (Stöckl et al., 1998), marine biology (Laws and Archie, 1981), aerosol science (Leng et al., 2007), and astronomy (Feigelson and Babu, 1992). ...
It has been almost 50 years since York published an exact and general solution for the best-fit straight line to independent points with normally distributed errors in both x and y. York's solution is highly cited in the geophysical literature but almost unknown outside of it, so that there has been no ebb in the tide of books and papers wrestling with the problem. Much of the post-1969 literature on straight-line fitting has sown confusion not merely by its content but by its very existence. The optimal least-squares fit is already known; the problem is already solved. Here we introduce the non-specialist reader to York's solution and demonstrate its application in the interesting case of the isotopic mixing line, an analytical tool widely used to determine the isotopic signature of trace gas sources for the study of biogeochemical cycles. The most commonly known linear regression methods – ordinary least-squares regression (OLS), geometric mean regression (GMR), and orthogonal distance regression (ODR) – have each been recommended as the best method for fitting isotopic mixing lines. In fact, OLS, GMR, and ODR are all special cases of York's solution that are valid only under particular measurement conditions, and those conditions do not hold in general for isotopic mixing lines. Using Monte Carlo simulations, we quantify the biases in OLS, GMR, and ODR under various conditions and show that York's general – and convenient – solution is always the least biased.
... The natural variability typically includes the uncertainties caused by various unknown variables, which co-vary with the predictor. Type II regressions such as the geometric mean (GM) regression or ranged major axis (RMA) regression have been recommended for such situations (Ricker 1973;Laws and Archie 1981;Legendre and Legendre 1998). ...
The temperature sensitivity of phytoplankton growth rates, parameterized as the activation energy (Ea) in the Boltzmann-Arrhenius equation, is critical to determining how global warming will affect marine ecosystems and the efficiency of the biological pump in the ocean. We applied both linear and nonlinear regression models to two laboratory temperature-growth experimental datasets to estimate the Ea of each taxon of phytoplankton and heterotrophic protists. We found that phytoplankton Ea and normalized growth rates depended strongly on community composition. Diatoms grew more rapidly and had lower Ea values, whereas cyanobacteria grew more slowly and had higher Ea values. The phytoplankton Ea was underestimated by a single OLS regression on the pooled dataset because slowly growing cyanobacteria dominated in warm, oligotrophic ocean gyres, and rapidly growing diatoms dominated in cold, nutrient-rich waters. By contrast, the median Ea values estimated from individual experiments did not differ between phytoplankton and heterotrophic protists. Our results suggest that phytoplankton community composition needs to be considered when trying to predict the effects of ocean warming on ecosystem productivity and metabolism.
... This effect, which results from the relationship between the size of the otolith of an individual fish and its rate of somatic growth, is exemplified by the fact that slow-growing fish have larger otoliths than faster-growing fish of the same size (e.g., Reznick et al. 1989;Campana 1990). Correlation between deviations from the somatic and otolith growth curves converts an "errors in variables" issue, commonly encountered in allometric relationships such as that between length and otolith radius (Laws and Archie 1981;Xiao 1996;Katsanevakis et al. 2007), into a "correlated errors in variables" problem, adding to the statistical issues encountered when fitting equations to describe the relationship (Fuller 1980;Thoresen and Laake 2007). The bivariate growth model developed for this study takes such individual variation and potential for correlation of deviations into account, thereby directly addressing this issue. ...
Curves describing the length–otolith size relationships for juveniles and adults of six fish species with widely differing biological characteristics were fitted simultaneously to fish length and otolith size at age, assuming that deviations from those curves are correlated rather than independent. The trajectories of the somatic and otolith growth curves throughout life, which reflect changing ratios of somatic to otolith growth rates, varied markedly among species and resulted in differing trends in the relationships formed between fish and otolith size. Correlations between deviations from predicted values were always positive. Dependence of length on otolith growth rate (i.e., “growth effect”) and “correlated errors in variables” introduce bias into parameter estimates obtained from regressions describing the allometric relationships between fish lengths and otolith sizes. The approach taken in this study to describe somatic and otolith growth accounted for both of these effects and that of age to pro...
... Meanwhile, the number of papers and chapters expounding on the subject as if the solution did not exist is staggering. Examples include widely consulted books like Biometry (Sokal and Rohlf, 1995) and Numerical Recipes (Press et al., 2007) as well as articles in fields as diverse as: anthropology (Smith, 2009), water resources (Hirsch and Gilroy, 1984), clinical 30 chemistry (Stöckl et al., 1998), marine biology (Laws and Archie, 1981), aerosol science (Leng et al., 2007), and astronomy (Feigelson and Babu, 1992). ...
It has been almost 50 years since York published an exact and general solution for the best-fit straight line to independent points with normally distributed errors in both x and y. York’s solution is highly cited in the geophysical literature but almost unknown outside of it, so that there has been no ebb in the tide of books and papers wrestling with the problem. Much of the post-1969 literature on straight-line fitting has sown confusion not merely by its content but by its very existence. The optimal least-squares fit is already known; the problem is already solved. Here we introduce the non-specialist reader to York’s solution, and demonstrate its application in the interesting case of the isotopic mixing line, an analytical tool widely used to determine the isotopic signature of trace gas sources for the study of biogeochemical cycles. The most commonly known linear regression methods — ordinary least squares regression (OLS), geometric mean regression (GMR), and orthogonal distance regression (ODR) — have each been recommended as the best method for fitting isotopic mixing lines. In fact, OLS, GMR, and ODR are all special cases of York’s solution that are valid only under particular measurement conditions, and those conditions do not hold in general for isotopic mixing lines. Using Monte Carlo simulations, we quantify the biases in OLS, GMR, and ODR under various conditions and show that York’s general — and convenient — solution is always the least biased.
... Fecundity was estimated for each fish using the formula F = ~ x C where F = fecundity of the B fish, A = weight of both ovaries, B = weight of sections, and C = total number of ova in the sections. Regression equations were calculated to determine the relation of fecundity to length and weight of cero and are based on standard Model-l regression techniques (Laws and Archie, 1981). Our fecundity estimates represent all ova 0.2 mm or greater in diameter which we believe are released during the spawning season. ...
... By taking these two criteria into consideration, four types of water may be identified: (A) nitrate-and light-replete waters, (B) nitrate-deficient and light-replete water, (C) nitrate-replete and light-deficient water, and (D) nitrate-and light-deficient water. The relationships between NU and NRA in the first three types of water were estimated by the reduced major axis method or model II regression analysis (Laws and Archie 1981) through the origin and the results are shown in Fig. 11 and summarized in Table 4. As expected from the previous discussions, NU was strongly correlated with NRA under nitrate-and light-replete conditions. ...
Nitrate reductase activity (NRA) and ¹⁵ NO 3 ⁻ uptake (NU) were determined in the East China Sea and the adjoining Kuroshio in May 1996, at six stations covering a range of hydrographic conditions: the nutrient‐rich and fresherplume of Changjiang Diluted Water along the Chinese coast, the nutrient‐rich upwelling Kuroshio Subsurface Water at the shelf edge northeast of Taiwan, the oligotrophic Kuroshio Surface Water and the mixing zones among these water masses on the shelf. The values of NRA in the surface mixed layer ranged between 16 and 0.1 nM‐N h ⁻¹ , whereas those of NU ranged between 37 and 1 nM‐N h ⁻¹ . Higher NRA and NU were found in the frontal zone between the coastal and shelf waters and in the upwelling zone, whereas the lowest values were found in the surface Kuroshio. The NRA/Chl a ratio increased linearly with increasing NU/primary production ratio in the sequence: Kuroshio, coastal plume, upwelling zone and mixing zones in the shelf. This is probably a reflection of the varying nutrient condition and the relative importance of NU in sustaining the biomass in these regions.
In nitrate‐ and light‐replete waters, the average NU/NRA was 1.0 ± 0.3. NRA was linearly related to NU so that NU = 1.08 (± 0.07)NRA ( r ² = 0.79). Thus, NRA may be used for estimating NU in these waters. In nitrate‐deficient and light‐replete waters, the average NU/NRA was 4 ± 4. These high and variable values of NU/NRA might have been caused by an over‐estimation of NU as a result of the stimulatory effect of the added ¹⁵ NO 3 ⁻ on phytoplankton growth. Thus, NRA may be a more reliable indicator of the rate of ¹⁵ NO 3 ⁻ uptake in oligotrophic waters. In nitrate‐replete and light‐deficient waters, NU did not correlate well with NRA. The average NU/NRA was 0.7 ± 0.7. These low and variable values of NU/NRA suggest a possible decoupling between NRA and NU.
By using the relationship between NU and NRA in nitrate‐ and light‐replete waters and the depth‐integrated inventory of NRA in the photic zone at each station, NU in oligotrophic waters, the coastal plume, upwelling waters and shelf waters can be estimated to be 0.45, 1.55, 3.12, and 3.59 mg‐N m ⁻² h ⁻¹ respectively. These values fall well within the range of previously reported values in similar types of water.
... This may be acceptable when the X dataset is considered to be a reference, but not when trying to establish agreement without assuming a reference because of a violation of the symmetry between X and Y, i.e. a regression of X on Y is not equivalent to that of Y on X. To solve this issue, Ji & Gallo 9 propose to use a geometric mean functional relationship (GMFR) model 21,22 , for which b and a are derived as follows: ...
Quantifying how close two datasets are to each other is a common and necessary undertaking in scientific research. The Pearson product-moment correlation coefficient r is a widely used measure of the degree of linear dependence between two data series, but it gives no indication of how similar the values of these series are in magnitude. Although a number of indexes have been proposed to compare a dataset with a reference, only few are available to compare two datasets of equivalent (or unknown) reliability. After a brief review and numerical tests of the metrics designed to accomplish this task, this paper shows how an index proposed by Mielke can, with a minor modification, satisfy a series of desired properties, namely to be adimensional, bounded, symmetric, easy to compute and directly interpretable with respect to r. We thus show that this index can be considered as a natural extension to r that downregulates the value of r according to the bias between analysed datasets. The paper also proposes an effective way to disentangle the systematic and the unsystematic contribution to this agreement based on eigen decompositions. The use and value of the index is also illustrated on synthetic and real datasets.
Body mass is a pivotal quantity in palaeobiology but must be inferred from an imperfect fossil record. We analyse the performance of regression models derived from various dentoskeletal predictors in mammals to inform fossils from the early, Mesozoic history of this radiation. Our focus is on the critical small end of the size spectrum; critical because the earliest mammals were small, because small size persisted onto the stems of the major extant radiations, and because small mammals compose a large proportion of crown diversity. The sampling strategy is diverse in terms of both phylogeny and skeletal predictors: the former allows a general application, while the latter enables comparison of various models. Linear regressions based on extant small mammals indicate a universal correlation of body mass with observed measurements, but with clear differences in precision. Postcranial predictors outperform jaw and dental metrics, with certain femoral joint dimensions providing surprisingly precise predictions. Our results indicate complex patterns of size evolution within the small‐bodied category, including the possibility that multiple Mesozoic species approached the theoretical lower limit of mammalian body size. The ability to study such dynamics only becomes possible when predicting body mass within a strict, highly focused phylogenetic context. The heuristic value of the models we provide here is not limited to the Mesozoic but is applicable to small‐bodied mammals of any geologic age.
A new multidimensional Model II regression based on bisector point of view (BRM-II) is introduced for multivariate problems that may contain measurement error. The suggested method is constructed depending on using the bisector of the minor angle between two hyperplanes identified by linear regression. The performance of the proposed method are examined by simulations up to ten variables for different sample sizes and distribution types in terms of the Mean Square Error. Moreover, the BRM-II is applied to two real problems with two and three variables, and compared with the existing methods. The results indicate that the BRM-II is easy applicable and offers relatively better accuracy. The relevant method can be easily coded in any programming language provides convenience in its application. Thus, the proposed method provide powerful tool for prediction of relevant real life problems.
The focus of this chapter is the contribution of remote sensing (RS) technologies in climate risk mainly for archaeological landscapes and built heritage. It will study the use of RS technologies for sea level rise scenario risk assessment and the use of multi-temporal multisource data and statistical indices for the detection of changes in built heritage. This chapter is divided in two sections: the first one focuses on sea level rise and potential threats, while the second one focuses on monitoring of temporal changes in built heritage using multisource multi-temporal data and indices.
Organic matter degradation is the engine behind the biogeochemical evolution of sediments during burial. Previous research has shown that eogenesis is the seat of a complex interplay between organic matter, microbes and the most reactive part of inorganic compounds, such as clay minerals. To explore the variability and stability of bromine and clay minerals as geochemical and mineral tracers, we selected an eastern Mediterranean core that has a high degree of stability in the quality and quantity of organic matter through time at a one-million-year scale and great variability in organic matter content at a 10ky scale. According to the very low maximal burial depth reached by these sediments (the core length is only 36.5 m), physical parameters, such as temperature and pressure, did not significantly influence the evolution of the studied parameters during the burial history. The bulk clay mineralogy of organic-rich and organic-poor sediments is similar all along the investigated core material; smectite predominates over kaolinite. The only identified authigenic minerals are biogenetic framboidal pyrite and manganese oxides. The X-ray data and the chemical compositions of the smectite are characteristic of a montmorillonite which is representative of a detrital Nile source. At a one-million-year scale, the organic matter content has no significant influence on clay eogenesis, and detrital smectite and kaolinite remain unchanged. Bromine is present in marine organic matter as organobromine compounds. During eogenesis, bromine is released from organic matter as bromide ion, resulting in an increase in the bromide concentration in the pore water with depth. Dissolved bromide can be used as a conservative tracer of the debromination of sedimentary organic matter. For the first time, we established that solid-phase BrOrg is a reliable tracer of debromination rates in marine sediments. The rate of debromination depends on the organic matter content. The rate increases from less than 2.3 × 10⁻⁴ μmolBrOrgmol.C⁻¹.y⁻¹ to 6.3 × 10⁻⁴ μmolBrOrgmol.C⁻¹.y⁻¹ when TOC varies from 0.17 to 3%. This increase is related to the development of the bacterial population and provides the basis for further investigation of other oceanic basins. For TOC values >4%, the rate of debromination decreases. We propose that the bioavailability of organic matter is another factor of variability in the debromination rate.
Excess inputs of nitrogen or phosphorus can harm aquatic ecosystems. Development of numeric nutrient criteria under the Clean Water Act helps to quantify water quality needed to prevent these effects and supports scientifically defensible management actions. Numeric criteria provide targets for setting National Pollutant Discharge Elimination System permit limits, total maximum daily load restoration, best management practices, waterbody assessment, land stewardship, wetlands protection, voluntary collaboration, nutrient trading, and urban stormwater runoff control.
Georgia and South Carolina’s estuaries are characterized by their high turbidity, widely varying residence times associated with high tidal amplitudes, lack of seagrasses, high ratios of tidal wetland to estuary surface area, and relatively low coastal anthropogenic land use. They generally can be classified into Piedmont riverine systems (headwaters above the fall line, with large inflow), blackwater systems (headwaters in the coastal plain with significant terrestrial contributions of organic matter), and coastal embayments (ocean-dominated systems with only freshwater contributions from land stormwater runoff and subterranean (e.g., shallow water aquifer) sources). Conceptual models of estuarine eutrophication established for other U.S. estuaries are often based upon hypoxia below the pycnocline, production dominated by phytoplankton, and seagrass endpoints – none of which apply well to Georgia and South Carolina’s estuaries, which tend to be well-mixed, mediated by heterotrophs, and have light-limited phytoplankton production.
An alternative conceptual model is presented here to derive nutrient targets (total nitrogen and total phosphorus), via measures (ecosystem primary production, chlorophyll a, dissolved oxygen, and indices of biological integrity) that are surrogates for designated use endpoints (aquatic community structure and function). The suite of indicators provides a flexible framework where a lack of data, or insensitivity of an indicator in a given location, can be overcome by using the remaining indicators to develop defensible criteria for that estuary. Criteria can be derived based on reference conditions, stressor-response relationships, and water quality simulation modeling. A reference condition approach may be particularly viable given that a number of estuaries have natural land-uses in their catchments. Protective criteria will help maintain the designated uses, which may be indicated by their trophic status, thereby ensuring that the beneficial services of Georgia and South Carolina’s estuaries to humans are sustained.
Excess inputs of nitrogen or phosphorus can harm aquatic ecosystems. Development of numeric nutrient criteria under the Clean Water Act helps to quantify water quality needed to prevent these effects and supports scientifically defensible management actions. Numeric criteria provide targets for setting National Pollutant Discharge Elimination System permit limits, total maximum daily load restoration, best management practices, waterbody assessment, land stewardship, wetlands protection, voluntary collaboration, nutrient trading, and urban stormwater runoff control.
Georgia and South Carolina’s estuaries are characterized by their high turbidity, widely varying residence times associated with high tidal amplitudes, lack of seagrasses, high ratios of tidal wetland to estuary surface area, and relatively low coastal anthropogenic land use. They generally can be classified into Piedmont riverine systems (headwaters above the fall line, with large inflow), blackwater systems (headwaters in the coastal plain with significant terrestrial contributions of organic matter), and coastal embayments (ocean-dominated systems with only freshwater contributions from land stormwater runoff and subterranean (e.g., shallow water aquifer) sources). Conceptual models of estuarine eutrophication established for other U.S. estuaries are often based upon hypoxia below the pycnocline, production dominated by phytoplankton, and seagrass endpoints – none of which apply well to Georgia and South Carolina’s estuaries, which tend to be well-mixed, mediated by heterotrophs, and have light-limited phytoplankton production.
An alternative conceptual model is presented here to derive nutrient targets (total nitrogen and total phosphorus), via measures (ecosystem primary production, chlorophyll a, dissolved oxygen, and indices of biological integrity) that are surrogates for designated use endpoints (aquatic community structure and function). The suite of indicators provides a flexible framework where a lack of data, or insensitivity of an indicator in a given location, can be overcome by using the remaining indicators to develop defensible criteria for that estuary. Criteria can be derived based on reference conditions, stressor-response relationships, and water quality simulation modeling. A reference condition approach may be particularly viable given that a number of estuaries have natural land-uses in their catchments. Protective criteria will help maintain the designated uses, which may be indicated by their trophic status, thereby ensuring that the beneficial services of Georgia and South Carolina’s estuaries to humans are sustained.
Coastal zones represent a small part of the area and volume of the oceans. However, their importance as a land-sea interface is enormous. Over 60% of human population lives within 60 km of the sea, and coastal zones guarantee several essential services to humanity. These ecosystems work as a convergence mechanism of all human actions in adjacent watersheds, being necessary to be considered in their management, in accordance to the Water Framework Directive spirit. Several integrated coastal management tools are presented in this paper, developed for an European project using as an example Parque Natural da Ria Formosa (south of Portugal). These tools include an hydrological model, a coastal ecological model, a geographic information system, and a decision support system. The hydrological model predicts water flow and water quality to be input to the ecological model of the lagoon system. The decision support system is being developed to integrate the environmental and social-economic information. The end-users, with management responsibilities, allow an information interchange between researchers and decision makers.
Respiration of fed Aequorea victoria showed the usual dependence of oxygen consumption on ash-free dry weight ($R = aW^{b}$, with constant b = 0.8). However, weightspecific oxygen consumption increased during 3 days' starvation from 0.632 ± 0.068 μl mg⁻¹ h⁻¹ to 0.802 ± 0.069 μl mg⁻¹ h⁻¹. During starvation ash-free dry weight decreased 21%, the ratio of ash-free dry weight to diameter increasing significantly. No changes in swimming activity with starvation were observed.
In the English Channel, the brittle-star Ophiothrix fragilis is a common epifaunal species typically found on pebbles in habitats with strong tidal currents. This species forms dense aggregations on the seafloor, supporting populations that can reach up to 7 500 ind.m−2 in the eastern part of the Baie de Seine, offshore from Antifer harbour. Here, O. fragilis occurs in an area with unexpected amounts of fine-grained sediment. Some of these mud deposits are made up of unusually compact black muds, an indication of the development of anoxic conditions in surficial sediments. To highlight a potential link between silting up and dense O. fragilis populations, and identify the interactions between environmental conditions and the population dynamics of this species, we analyse the data from three surveys corresponding to exceptional situations: 1) just after a Seine flood; 2) just after a storm and 3) after a period of ten months without any flood or storm. Four parameters are taken into account: number of brittle stars per 0.25 m2, Fine Fraction percentage, Total Organic Carbon and Total Sulphur. The main environmental forcings appear to be Seine river inflow, regional circulation dependent on tidal currents and the occurrence of storms. O. fragilis is able to geoengineer its environment in various ways and at different rates. Silting up is enhanced by increasing abundance of O. fragilis and takes place at a very fast rate. As a result, floods and storms reflecting instantaneous events give rise to a steady-state situation established between the abundance of this species and the fine fraction percentage. Anoxic conditions are dependent on the degradation of organic matter and require more time to be established. After many months in the absence of any disturbing events, anoxic conditions are developed in non-compacted muddy sediments (stability situation) and represent the normal surficial situation when the sediment becomes compacted (compact black muds). The development of anoxic conditions is dependent on the abundance of the O. fragilis population and occurs at a very slow rate.
An organism’s size affects virtually all aspects of its physiology and ecology. There are presently no theoretical models which can explain the broad patterns of shape and functional changes observed; empirical descriptions of these patterns have suffered from a lack of rigor in choice and analysis of data.
The trend of persistent size increase in lineages of animals may be an artifact; the frequency of dwarfing may be hidden by taphonomic (preservational) and observational biases. The selective factors underlying persistent size changes are likely to differ between terrestrial vertebrates and marine invertebrates. The genetics of size change is poorly known and cannot be deduced from strictly allometric studies.
Body size is likely to have profound effects on the probabilities of speciation and extinction, and these effects would probably be amplified during periods of mass extinction.
This paper focuses on the estimation of parameters in the bivariate linear model, especially in the context of bivariate size-shape
relationships or allometry. Existing estimation procedures (regression, major axis, reduced major axis) all depend on a priori
assumptions on the ratio of the residuals, usually called “errors,” in both variables. These assumptions are reviewed and
evaluated. The Bartlett method is not independent of assumptions on the residuals as has been often claimed. A method which
does not require assumptions on the ratio of residuals, providing data from a third variable are available, is given. All
of the methods discussed are illustrated with data measured on planktonic Foraminifera.
If, in sampling from an existent population, we wish to know the regression of u on v, a line is fitted by least squares, minimizing the sum of the squared residuals of v (or y). If there is no error in measuring the independent variate u, regardless of whether the dependent variate has been measured without error as v or with error as y, the regression is an estimate of the true regression. If, however, the independent variate is measured with error in x, the regression obtained is a biassed one. The bias will characterize the fitted line, and will be present whether the sample is a random one of the entire population or has been taken at preassigned selected values of x.If, however, the experiment is one in which one of the variates is a controlled observation, it differs from sampling from an existent population in that, 1), the line estimated by least squares, minimizing the sum of the squared residuals of the dependent uncontrolled variate, is the same, whether x or y is the controlled variate, that is, there is only one regression; and 2), the estimated line is not biassed by the existence of an error of observation in the independent controlled variate, despite our taking no account of it in the least squares fit.
The ordinary major axis of a bivariate normal distribution is unsuitable for describing the functional relationship (in Lindley’s general sense) between two naturally variable quantities, because it is not invariant with scale and because qualitatively unlike quantities are subtracted in computing it. The bivariate structural relationship is unsuitable because one of the parameters required, λ, cannot be estimated from naturally variable data; in fact λ has no objective meaning for such data. The standard major axis (or GM regression line) has neither of these defects, and it is the line that minimizes the sum of products of the absolute vertical and horizontal deviations of data points from itself.
A number of regression situations in fish and fishery biology are examined, in which both of the variates are subject to error of measurement, or inherent variability, or both. For most of these situations a functional regression line is more suitable than the ordinary predictive regressions that have usually been employed, so that many estimates now in use are in some degree biased. Examples are (1) estimation of the exponent in the weight:length relationship, where almost all published values are somewhat too small; and (2) estimating the regression of logarithm of metabolic rate on log body weight of fish, where the best average figure proves to be 0.85 rather than 0.80. In the very common situation where the distribution of the variates is non-normal and open-ended, a functional regression is the most appropriate one even for purposes of prediction. Two ways of estimating the functional regression are (1) from arithmetic means of segments of the distribution, when computed symmetrically; and (2) from the geometric mean of one predictive regression and the reciprocal of the other. The GM regression gives a more accurate estimate when it is applicable; it is appropriate in all situations where the variability is mainly inherent in the material (little of it due to errors of measurement), or where the measurement variances are approximately proportional to the total variance of each variate; and it is the best estimate available for short series with moderate or large variability even when neither of these conditions applies. When error in X results solely from the measuring process the predictive regression of Y on X is also the functional regression if observations of X are not taken at random but rather have pre-established values, as is usual in experimental work. The uses of the various regressions are summarized in Table 8.
1.
Au cours de la mission Cineca I du Jean Charcot, 281 estimations de la respiration plusieurs tempratures ont t faites chez des coppodes rcolts diffrentes profondeurs.
2.
Les courbes mtabolisme-temprature dnotent plusiers types d'adaptation aux conditions thermiques.
3.
Il existe une corrlation forte entre le logarithme de la respiration et le logarithme du poids. Le coefficient de rgression est diffrent selon la temprature envisage. Il ne s'intgre aux limites donnes par la loi de surface qu' la temprature de 18C o il est maximum.
The results of 281 respiration analyses of pelagic copepods sampled in the South Moroccan and Canarian area are described. The copepods used in experimentation were collected from various bathymetric levels: hyponeustonic species (Anomalocera patersoni, Pontellopsis villosa, P. regalis, Labidocera wollastoni, Pontella lo biancoi), epipelagic species (Centropages typicus, Temora stylifera, Calanus helgolandicus, Acartia clausi), meso and bathypelagic species (Pleuromma xiphias, P. abdominalis, Euchaeta acuta, Undeuchaeta plumosa and some other rare species). Analysis of the metabolismtemperature curve makes it possible to describe different modes of adaptation in relation to geographical distribution, altitudinal repartition, and dietary characteristics. When all species are studied together, a strong correlation exists between the log of respiration and the log of weight. The regression coefficient varies with temperature; it is strongest at a temperature near that of the natural thermic conditions.
The productivity of a sea loch, Loch Nevis, on the west of Scotland, is estimated from nitrate and phosphate data. These results show that even though the nitrate:phosphate ratio in the water is never more than 10:1 (by atoms) and is less than 1:1 in the euphotic zone in summer, the assimilation and regeneration ratio of these elements is always close to the “normal” ratio of 16:1. Chlorophyll a and particulate organic carbon data are used to study the possible carbon:chlorophyll ratios in the plants. During the summer the ratio is calculated to be 74:1 and the remaining data suggest lower values for spring and autumn.
For a different area, the northern North Sea, carbon and chlorophyll samples during the spring flowering provide an estimated value of 23:1 for the carbon:chlorophyll ratio under very favorable conditions for growth.
The possible causes of the differences between the carbon:chlorophyll ratios for Loch Nevis and the northern North Sea are discussed.
For field samples, regression analyses of plots of chemically determined particulate organic carbon on chlorophyll are often employed to estimate the algal carbon-to-chlorophyll ratio (F) in the presence of appreciable amounts of nonalgal particulate organic carbon. Spurious results will be obtained, however, if the temporal rate of change of the algae or the nonplant matter reverses its sign during the sampling interval and the samples cannot be ordered correctly in time or space. Previously recognized sources of bias inherent in the chemical approach are also discussed. The great uncertainty of our present knowledge of F is pointed out. It is shown that the concentration of microscopically visible, nonliving particles in the sea isnot known. Renewed studies are suggested as a means of improving on the chemical approach to determining F. The general argument holds for the ratios of nitrogen (particle volume, etc.)-to-chlorophyll, carbon (nitrogen, particle volume, etc.)-to-ATP, and similar conversion factors.
In situations such as allometry where a line is to be fitted to a bivariate sample but where an asymmetric choice of one or other variable as regressor cannot be made, the reduced major axis is often used. Existing tests of the slope of this line, particularly between samples, are not sufficiently accurate in view of the scarcity of the material to which such methods are often applied. Alternative test statistics are suggested and some of their properties derived from a computer implementation of k statistics.
Statistics manual, 288 pp
- E L Crow
- F A Davis
- M W Maxfield
Rohlf: Biometry. The principles and practice of statistics in biological research
- R R Sokal
- R. R. Sokal