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The Structure Of Individual Variation In Miocene Globorotalia
Abstract
Analysis of probability distributions of individual organisms provides a common language to describe synchronic and diachronic diversity. When based on an appropriate quantitative description of morphology, this language can be used to explore the temporal component of diversity embedded in the fossil record. Miocene Globorotalia (planktonic foraminifera) from Deep Sea Drilling Project site 593 are described using two-point registration of landmarks in two views (spiral and apertural) and medial-axis analysis of the shape of the final chamber. The equiangular spiral parameters Θ (the angle of increment), r (the expansion rate), and t (the rate of translation down the spiral axis) appear as principal components of the landmark data. Chamber shape variation is described by three principal components of medial-axis curvature. Partial-least-squares analysis demonstrates that the first components of within-morphospace variation also explain the patterns of correlation between the landmark and chamber-shape morphospaces. In the landmark morphospaces, the distribution of sampled individuals is continuous and roughly elliptical with few stratigraphic changes. In the chamber-shape morphospace, the distribution is continuous but shows complex features beyond the elliptical; the occupied morphospace changes stratigraphically, but neither strict cladogenesis nor strict anagenesis explains the derivation of new morphologies. Exemplars of named morphospecies are scattered across these spaces with continuous variation among all forms. These names cannot be assumed to represent discrete entities.
... Operationally, species delimitation pivots on the assumption that, once sexual dimorphism, ontogeny and other causes of group difference have been taken into account to leave directly comparable individuals for analysis (semaphoronts [6]), expression of genotypes or phenotypes [7] or both [8] should be more similar in two individuals of species X than between one individual of species X and one individual of species Y. Hence individuals within species are expected to cluster in genotypic or phenotypic space, with sparsely inhabited or empty space between them. The range of intra-species variation can surpass the range of inter-species variation [9] however, which is problematic for morphological species concepts which rely critically on the assumption that gaps between species do exist [1][2][3]. ...
... The mathematical translation of species delimitation is identification of well-separated clusters ( Fig. 1): multiple species are inferred when two or more well-separated groups are a better way of describing a given sample than one group [21]. The problematic nature of non-discrete differentiation [9] has provoked the development of threshold models, which permit small numbers of supposedly distinct groups to show similar character expression: Wright [22] developed a threshold model to split continuous genotypic distributions into discrete character states; Simpson et al. [23] claimed that a coefficient of variation over 10 in a morphological trait indicated more than one taxon in a sample; Wiens & Servedio [24] used a 5% polymorphism cut-off to account for the rarity of characters being genuinely fixed; and Templeton [25] used a 5% homoplasy cut-off to partition data into independent haplotype networks. The use of threshold levels remains the crux of numerical taxonomy [7], but the idea that the appropriate threshold for species' delimitation is consistent across all questions and groups is problematic. ...
The species is a fundamental unit of biological pattern and process, but its delimitation has proven a ready source of argument and disagreement. Here, we discuss four key steps that utilize statistical thresholds to describe the morphological variability within a sample and hence assess whether there is evidence for one or multiple species. Once the initial set of biologically relevant traits on comparable individuals has been identified, there is no need for the investigator to hypothesise how specimens might be divided among groups, nor the traits on which groups might be separated.
Principal components are obtained using robust covariance estimates and retained only if they exceed threshold amounts of explanatory power, before model-based clustering is performed on the dimension-reduced space. We apply these steps in an attempt to resolve ongoing debates among taxonomists working on the extinct Eocene planktonic foraminifera Turborotalia, providing statistical evidence for two species shortly before the lineage's extinction near the Eocene/Oligocene boundary.
By estimating variance robustly (samples containing incipient species are unlikely to be scaled optimally by means and standard deviations) and identifying thresholds relevant to a particular system rather than universal standards, the steps of the framework aim to optimize the chances of delineation without imposing pre-conceived patterns onto estimates of species limits.
... Se registraron 13 hitos tipo I y tipo II sobre las siguientes estructuras ( Fig. 2): 1) unión anterior medial del premaxilar; 2) base de la aleta dorsal; 3) unión anterior de la base de la aleta adiposa con el cuerpo; 4) extremo dorsal del pedúnculo caudal; 5) punto de origen de los radios medios caudales; 6) extremo ventral del pedúnculo caudal; 7) base de la aleta anal; 8) base de la aleta anal; 9) base de la aleta pélvica; 10) base de la aleta pectoral; 11) extremo inferior del maxilar; 12) narina y 13) centro de la órbita ocular. Los hitos 1 y 5 son las coordenadas de referencia (0, 0) y (0, l) (Tabachnick & Bookstein 1990, Bookstein 1986, Dryden & Mardia 1998. ...
Las relaciones filogenéticas del grupo Astyanax son poco conocidas y su taxonomía es muy con-fusa (Garutti & Britski 2000), por lo que no sor-prende que en algunas revisiones recientes se re-porten 86 especies en el género (e.g. Lima et al. 2003) mientras que en otras se reporten 115 (e.g. Froese & Pauly 2006). Asimismo, es común en-contrar en la literatura reportes sobre "complejos de especies" de Astyanax que son morfológica y genéticamente variables (e.g. Moreira-Filho & Bertollo 1991). Algunas especies de este género poseen una am-plia distribución, como es el caso de la especie Astyanax siapae Garutti, 2003. La distribución geográfica de esta especie, que se extiende desde la cuenca del Río Casiquiare hasta la cuenca media del Río Orinoco, ocupa una de las regiones de Suramérica con mayor heterogeneidad espacial y diversidad biológica. Junto con A. siapae, Garutti (2003) también des-cribió la especie A. clavitaeniatus y validó el nombre A. rupununi Fowler, 1914, utilizando ar-gumentos de taxonomía tradicional y numérica basados en características morfológicas cualita-tivas, merística, medidas de distancia y propor-ciones. Garutti (2003) utilizó estos dos últimos ti-pos de medidas para: a) describir la forma general del cuerpo de estos peces y compararlos entre sí, b) realizar un análisis de componentes principa-les con el fin de mostrar como se agrupan los in-dividuos en cada taxón, y c) construir una clave dicotómica. Dado que uno de los supuestos implícitos en este tipo de análisis sistemático es que la clasificación de estas especies puede ser inferida a partir de la variabilidad de las formas de sus cuerpos, cabe preguntarse qué tan variable es la forma de A. sia-pae a lo largo de su distribución geográfica. Si bien la respuesta a esta pregunta no contribuye a resolver el problema sistemático que existe con las especies de este género, representa uno de los primeros aportes al conocimiento de la biología de esta especie y en especial, al conocimiento de su disparidad. La disparidad de A. siapae a lo largo de su distri-bución geográfica es el resultado de diferentes procesos biológicos que no están necesariamen-te relacionados con eventos de especiación. Si la especie está distribuida en una región muy ex-tensa y heterogénea, es de esperar que sus po-blaciones estén estructuradas geográficamente como una aparente metapoblación, dado que la existencia de flujo genético entre los subgrupos de A. siapae es un supuesto sine qua non de su estatus específico. Su amplia distribución conlleva a que la especie esté expuesta a ambientes diversos, por lo que es posible esperar que diferentes subgrupos posean características particulares, resultantes de proce-sos locales de plasticidad, que actúan a una escala temporal menor que la generacional (e.g. Morei-ra-Filho & Bertollo 1991), adaptación y deriva genética que actúan a una escala temporal mayor que la generacional, o escala evolutiva. Otro proceso biológico que afecta la disparidad percibida de una especie, es la alometría, i. e. que resulta en cambios de forma no proporcionales con la talla que ocurren a lo largo del crecimien-to. Si bien la diagnosis de nuevos taxa suele fun-damentarse en organismos adultos, es imposible discriminar la variabilidad morfológica natural de los individuos de aquella relacionada con las diferencias de edad entre ellos. Este problema también se presenta cuando se tra-baja con especies en las que es posible reconocer el estado adulto de sus individuos y particular-mente, cuando su crecimiento es continuo a lo largo de su vida y dependiente de la temperatura del medio, como ocurre con los peces y demás or-ganismos poiquilotermos (e.g. Gabillard et al. 2005). El objetivo de este estudio es describir la dispari-dad morfológica de una muestra de individuos de A. siapae provenientes de varias localidades en la cuenca de los ríos Orinoco y Siapa, en Venezuela. La disparidad de la muestra será cuantificada uti-lizando técnicas de morfometría geométrica y la 64 Dahlia, No. 9, 2007
... These "distortions" must be kept in mind when interpreting shape changes localized to the acromion and metacromion. For each specimen, digitized landmark coordinates were transformed to shape coordinates (Bookstein et al. 1985;Tabachnick and Bookstein 1990). Landmarks I and 9 at the ends of the scapular spine were designated end points of a baseline and assigned fixed coordinates: (0, 0) and (0, I). ...
The mammalian scapula, like many bones, is a single structural element that serves as an attachment site for several muscles. The goal of this study was to determine whether the scapula evolves as an integrated unit, or as a collection of distinct parts. Shape differences among the scapulae of tree squirrels, chipmunks, and ground squirrels were described using thin-plate spline analysis. This technique produces a geometric description of shape differences that can be decomposed into a series of components ranging in scale from features that span the entire form to features that are highly localized. Shape differences among tree squirrel scapulae were found only in large-scale features, indicating spatially integrated shape change. Chipmunks and ground squirrels differ from tree squirrels in several features, but shared differences reflecting divergence of their common ancestor were found only in the small-scale features. Divergence of ground squirrels from the common ancestor involved some large-scale changes but was dominated by small-scale changes. Divergence of chipmunks was dominated by large-scale changes. Thus, the scapula evolved as an integrated unit during some transitions but as a collection of distinct parts during others. These results suggest that evolutionary patterns of the postcranial skeleton may be as complex as the patterns that have been described for skulls and feeding mechanisms.
... Test diameter and cross-sectional area are well correlated in foraminifers ( Schmidt et al., 2006) and the low trochospiral morphology of the genus Globorotalia make them ideal for studies of size (Tabachnick and Bookstein, 1990). In planktonic foraminifera, chambers grow exponentially during ontogeny and the number and growth of chambers affects the size of the test (Olsson, 1971(Olsson, , 1973. ...
We propose a phenomenon termed “pre-extinction dwarfing” in Cenozoic planktonic foraminifera. High-resolution morphometric analysis shows a reduction in maximum or mean test size in the 2–20 kyr interval preceding the extinction of Pliocene Globorotalia exilis and Globorotalia miocenica from the Caribbean Sea and middle Eocene Morozovelloides crassatus from the western North Atlantic. Through a series of case studies and review of qualitative observations from the literature, we suggest that dwarfing occurs in a number of species of planktonic foraminifera foreshadowing their demise and that such size changes are not just a phenomenon associated with mass extinction events. We propose that this is a common stress-induced pattern that results in diminutive size in the pre-extinction interval.
Taxonomic data analysis has benefited greatly from standardization of systematic and stratigraphic practices. In contrast, the unique features of each group of organisms and the specific nature of many workers' questions have helped make analysis of morphological data relatively less standardized and more idiosyncratic. In addition, paleobiological analysis of morphological data at larger (roughly, suprafamilial) scales seems to have lagged behind analysis, of taxonomic data because of the relative difficulty with which morphological data are collected (both from fossils themselves and from published sources). In this review, I will briefly touch upon some of the areas in which morphological analysis has contributed significantly to our understanding of life's history. Space limitations preclude a thorough treatment of all aspects of morphological analysis, and the decision to omit certain topics, such as functional morphology, is not a reflection of the importance of these fields.
The study of evolution has increasingly incorporated considerations of history, scale, and hierarchy, in terms of both the origin of variation and the sorting of that variation. Although the macroevolutionary exploration of developmental genetics has just begun, considerable progress has been made in understanding the origin of evolutionary novelty in terms of the potential for coordinated morphological change and the potential for imposing uneven probabilities on different evolutionary directions. Global or whole-organism heterochrony, local heterochrony (affecting single structures, regions, or organ systems) and heterotopies (changes in the location of developmental events), and epigenetic mechanisms (which help to integrate the developing parts of an organism into a functional whole) together contribute to profound nonlinearities between genetic and morphologic change, by permitting the generation and accommodation of evolutionary novelties without pervasive, coordinated genetic changes; the limits of these developmental processes are poorly understood, however. The discordance across hierarchical levels in the production of evolutionary novelties through time, and among latitudes and environments, is an intriguing paleontological pattern whose explanation is controversial, in part because separating effects of genetics and ecology has proven difficult. At finer scales, species in the fossil record tend to be static over geologic time, although this stasis—to which there are gradualistic exceptions—generally appears to be underlain by extensive, nondirectional change rather than absolute invariance. Only a few studies have met the necessary protocols for the analysis of evolutionary tempo and mode at the species level, and so the distribution of evolutionary patterns among clades, environments, and modes of life remains poorly understood. Sorting among taxa is widely accepted in principle as an evolutionary mechanism, but detailed analyses are scarce; if geographic range or population density can be treated as traits above the organismic level, then the paleontological and mac̀roecological literature abounds in potential raw material for such analyses. Even if taxon sorting operates on traits that are not emergent at the species level, the differential speciation and extinction rates can shape large-scale evolutionary patterns in ways that are not simple extrapolations from short-term evolution at the organismal level. Changes in origination and extinction rates can evidently be mediated by interactions with other clades, although such interactions need to be studied in a geographically explicit fashion before the relative roles of biotic and physical factors can be assessed. Incumbency effects are important at many scales, with the most dramatic manifestation being the postextinction diversifications that follow the removal of incumbents. However, mass extinctions are evolutionarily important not only for the removal of dominant taxa, which can occur according to rules that differ from those operating during times of lower extinction intensity, but also for the dramatic diversifications that follow upon the removal or depletion of incumbents. Mass extinctions do not entirely reset the evolutionary clock, so survivors can exhibit unbroken evolutionary continuity, trends that suffer setbacks but then resume, or failure to participate in the recovery.
Recent studies have shown that modes of evolution, namely directional trend, random walk, and stasis, vary across morphologic traits and over the geographic range of a taxon. If so, is it possible that our interpretation of evolutionary modes is actually driven by our selection of traits in a study? In an attempt to answer this question, we have restudied the middle Miocene planktonic foraminifera Fohsella lineage, an iconic example of gradual morphologic evolution. In contrast to previous studies that have focused on the gross morphology as embodied by the edge view of tests, we analyze here multiple phenotypic traits chosen because their biologic and ecologic significance is well understood in living populations. We find that traits in the lineage did not evolve in concert. The timing and geographic pattern of changes in shape, coiling direction, size, and ecology were different. The evolution of this lineage is a mosaic combination of different evolutionary modes for different traits. We suggest that overemphasis on the evolution of some single trait, such as the edge-view outline, from narrow geographic ranges has significantly underestimated the dynamic evolutionary history of this group.
The taxonomy and phytogeny of the planktonic foraminifera Fohsella lineage has been controversial for nearly 50 years, despite its widespread application in Middle Miocene stratigraphy. We have re-examined type specimens of this lineage together with specimens from a continuous deep-sea record (Ocean Drilling Program Site 806, Ontong Java Plateau, western equatorial Pacific Ocean) with an astronomic chronology. Landmark-based geometric morphometry is employed to visualize and quantify morphologic variation within this lineage. Combined morphologic and stratigraphie data help clarify the evolutionary occurrence of diagnostic traits that characterize two problematic taxa, F. praefohsi and F"praefohsi" resulting in a revised taxonomy and phylogeny of the lineage. We emphasize the importance of biometrie studies of populations from continuous geologic records in establishing taxonomy and phylogeny of planktonic foraminifera. In the past, over-emphasis on the importance of type specimens as reference points in delineating various evolutionary stages of the Fohsella lineage has resulted in inaccurate phylogenetic reconstructions.
Morphometrics is defined as the application of multivariate statistical procedures to the study of variation in morphological characteristics of organisms. As originally implemented, the analyses are based on standard measures (“distances”) spanning critical sites. A more recent introduction is concerned with quantifying outlines of organisms, the data then being a suite of arbitrary coordinate-pairs around the circumference of the object, obtained by some automatically operating digitization procedure (e.g., the Zahn-Rosskies method). Geometric morphometrics is the latest class to appear. It relies on diagnostically located “landmarks” that form the basis for superimposition of coordinate systems, visualizations by deformation grids. The first and third of these categories can, without particular difficulty, be allied with environmental indicators by appropriate techniques.
The use of landmarks and geometrical morphometric techniques is illustrated with examples from the Harpoceratinae (Ammonitina). This approach is useful in analysing morphological variations of characters such as rib pattern or ventral shape on the scale of the genus or species. It can be used to map forms so that similarities and dissimilarities between organisms can be read and quantified directly.
It has been proposed previously that the northern Mississippi Valley Sunwaptan trilobite genus Dikelocephalus comprises 26 species. Morphometric analyses demonstrate that many of the criteria that had been used to define species of Dikelocephalus are invalid and additional analysis of biostratigraphically and biogeographically constrained collections is necessary before the taxonomic status of Dikelocephalus can be fully resolved. Many of the characters shown to be taxonomically insignificant in Dikelocephalus are also widely used in the definition of other trilobite taxa. This suggests that the species-level taxonomy of many trilobites may be substantially oversplit. -from Authors
Many organisms continue to grow their skeletons throughout ontogeny. In the shells of molluscs, protists, and brachiopods and in bovid horns, accretionary spiral growth provides a detailed and continuous growth history. Although a shell may be described as a single static form, the overall morphology is a summation of the ongoing accretionary process. For this reason, an explicitly ontogenetic characterization of form provides insight into the final form achieved. Analysis of landmark transformations offers direct access to major components of morphological variation, both among adult individuals and through an individual's ontogeny. Parameters of preconceived, abstract geometric models can also be used to characterize morphological variation, but there is no guarantee that these parameters will coincide with the major features of shape variation.
In order to locate landmarks at equivalent ontogenetic stages, features that indicate ontogenetic stage of coiled forms must be identified (e.g., growth increments, age, size, whorls). The gastropod Epitonium ( Nitidiscala ) tinctum exhibits prominent varices that provide landmark locations throughout ontogeny. Recent specimens of this species were obtained from three localities in Baja, Mexico. The morphological variation among individuals, treated as whole shells and within individual ontogenies, was analyzed using shape coordinates of landmark configurations. Deformation of shape is expressed in the uniform and nonuniform shape subspaces. The empirical components of shape variation found are similar to those generated by two parameters of an equiangular spiral: θ , the angle between consecutive varices, and W , the whorl expansion rate. The distribution of individuals is examined within morphospaces constructed from these shape features.
Three scales of analysis are necessary to characterize adequately the shape variation within and among specimens. The smallest scale is equivalent to increment-by-increment changes in θ and W . The middle scale comprises variation equivalent to whorls resulting from systematic changes in θ and W during an individual's ontogeny. Finally, there is the overall ontogenetic trajectory. Mean shape must be a function of initial shape and ontogenetic trajectory in shape. Mean forms that are found to have similar shapes at the same arbitrary growth increment may achieve that shape in different ways.
Morphological analysis of four higher taxa of fossil marine invertebrates shows that, over the history of paleontology, there is no general tendency for morphologically extreme or modal species and genera to be described preferentially early or late. Reconstructing the expected evolutionary sequences of morphological disparity that would have been estimated at various times during the past century and a half reveals features that are sensitive to sampling (for example, peak trilobite disparity in the Ordovician, peak of post-Paleozoic crinoid disparity in the Triassic, and peak blastoid disparity in the Permian), as well as more robust features (for example, increase in trilobite disparity from the Cambrian to the Ordovician, continued increase in trilobite disparity despite a drop in taxonomic diversity after the Early Ordovician, decrease in blastoid disparity from the Devonian to the Carboniferous, and increase in crinoid disparity from the Jurassic to the Cretaceous followed by decline during the Cretaceous). Although we still have much to learn about the evolution of form, in many respects our view of the history of biological diversity is mature.
Phenotypic variation within species provides the raw material acted upon by natural selection and other evolutionary mechanisms. As such, the range and variation of morphology within a species can play an important role in determining the tempo of evolution. The range and variance of aspects of cranidial morphology for nine lower Paleozoic trilobites were measured to identify microevolutionary correlates of macroevolutionary patterns. Comparisons were made among sets of homologous landmarks or upon partial warp vector matrices containing similar proportions of variance. Rarefaction and bootstrap analyses helped estimate the effects of sampling. Levels of variance and range of morphology differed considerably within and among time periods. There is no significant temporal decline in the variance or range of morphology, suggesting that developmental or genomic constraints may not have been the primary factors controlling the tempo of trilobite macroevolution. The spatial distribution of cranidial variance differed considerably among taxa, suggesting that a complex set of developmental processes governed the morphogenesis of cranidia within trilobites.
Morphologic discrimination of species of scleractinian reef corals has long been plagued by a shortage of independent characters and by high ecophenotypic plasticity. Because of these two factors, many species appear to intergrade morphologically. We outline a newly developed protocol for the morphometric recognition of species, which uses size and shape coordinates derived from landmark data. The landmarks consist of spatially homologous points digitized in three dimensions on upper calical surfaces. The approach is more powerful than linear measurements at detecting subtle distinctions among species; and the distinctions are easy to visualize and interpret biologically, which increases the accuracy and resolution of subsequent phylogenetic and large-scale faunal analyses.
As an example, we distinguish morphospecies in collections of Porites made at three Caribbean locations. Size and shape coordinates are analyzed using principal component analysis, average linkage cluster analysis, and a series of iterative discriminant analyses. Positions of different corallites from the same colonies are examined on cluster dendrograms to determine cutoffs for group recognition, and discriminant classifications for different corallites from the same colonies are compared to maximize group assignments. The results yield seven morphospecies, which are generally in 90% agreement with classification of the same animals using allozyme electrophoresis. Measures of corallite size and the relative heights and locations of the pali and septal denticles all reveal unique patterns of variation among morphospecies.
IntroductionQuantitative attributes of intraspecific variationApplications of intraspecific variation
Approximately two decades after the first pioneering analyses, the study of shape asymmetry with the methods of geometric morphometrics has matured and is a burgeoning field. New technology for data collection and new methods and software for analysis are widely available and have led to numerous applications in plants and animals, including humans. This review summarizes the concepts and morphometric methods for studying asymmetry of shape and size. After a summary of mathematical and biological concepts of symmetry and asymmetry, a section follows that explains the methods of geometric morphometrics and how they can be used to analyze asymmetry of biological structures. Geometric morphometric analyses not only tell how much asymmetry there is, but also provide information about the patterns of covariation in the structure under study. Such patterns of covariation in fluctuating asymmetry can provide valuable insight about the developmental basis of morphological integration, and have become important tools for evolutionary developmental biology. The genetic basis of fluctuating asymmetry has been studied from empirical and theoretical viewpoints, but serious challenges remain in this area. There are many promising areas for further research that are only little explored at present.
Heterochrony, change in developmental rate and timing, is widely recognized as an agent of evolutionary change. Heterotopy, evolutionary change in spatial patterning of development, is less widely known or understood. Although Haeckel coined the term as a complement to heterochrony in 1866, few studies have detected heterotopy or even considered the possibility that it might play a role in morphological evolution. We here review the roles of heterochrony and heterotopy in evolution and discuss how they can be detected. Heterochrony is of interest in part because it can produce novelties constrained along ancestral ontogenies, and hence result in parallelism between ontogeny and phylogeny. Heterotopy can produce new morphologies along trajectories different from those that generated the forms of ancestors. We argue that the study of heterochrony has been bound to an analytical formalism that virtually precludes the recognition of heterotopy, so we provide a new framework for the construction of ontogenetic trajectories and illustrate their analysis in a phylogenetic context. The study of development of form needs tools that capture not only rates of development but the space in which the changes are manifest. The framework outlined here provides tools applicable to both. When appropriate tools are used and the necessary steps are taken, a more comprehensive interpretation of evolutionary change in development becomes possible. We suspect that there will be very few cases of change solely in developmental rate and timing or change solely in spatial patterning; most ontogenies evolve by changes of spatiotemporal pattern.
Studying the association between organismal morphology and environmental conditions has been very useful to test hypothesis regarding the influence of climate on shape. It has been long recognized that different environments produce dissimilar stress levels in insects, which can be reflected on the ability of an individual to overcome these pressures and spread further. Agriotes (Coleoptera: Elateridae) species infest agricultural fields in different parts of Croatia, inhabiting different climatic conditions. Previous biological studies have indicated that there is a relationship between some Agriotes biological parameters such as density and climatic conditions such as soil moisture and temperature. However, it is still unknown how these environmental properties influence the wireworm morphological structure. This is highly relevant because the head of this species is directly involved in the mobility in the soil, thus affecting the invasive capacity of this insect. Therefore the aim of this study was to assess the association between different climatic conditions and the morphological variation of Agriotes cephalic capsule. Advanced multivariate analysis and geometric morphometric tool were applied to study the covariation between shape and environmental variables. Partial Least Squares methods were used in order to analyse the association between the wireworm head shape and three different climatic conditions: soil type, temperature and rainfall. Our results showed that there is a high covariation between the wireworm head shape and the climatic conditions. It was suggested that the observed shape–environment association could be result of the high plasticity of this species in relation to its invasive capacity.
Two living forms of Globigerinella siphonifera (d'Orbigny), presently identified as Type I and Type II, can easily be distinguished and collected by SCUBA divers because of differences in appearance, arrangement of the rhizopodial network, and the presence or absence of commensals. Additional biological differences are apparent from laboratory culture experiments; Type I individuals survive significantly longer than Type II under conditions of darkness and starvation and have significantly slower chamber formation rates. Stable isotopic analyses of Types I and II also reveal notable differences, with Type I consistently yielding more negative δ ¹⁸ O and δ ¹³ C values. Results of Mg/Ca ratio analyses indicate that Type II specimens precipitated their shells in slightly cooler (deeper) surface waters than Type I specimens. These observations and results from DNA sequencing unequivocally demonstrate that G. siphonifera Types I and II should be regarded as biological sister species.
Contrarily, biometric analysis of the empty shells reveals few significant differences between G. siphonifera Types I and II. Of all the features measured from X-ray and SEM images of serially dissected specimens, only shell porosity yields readily discernible differences, with Type I adult chambers averaging 10–20% porosity and Type II adult chambers averaging 4–7% porosity. Statistically significant differences between Type I and II populations are revealed in maximum test diameter (Type I is typically larger) and coiling (Type I is typically more evolute), but these differences do not justify species level distinction of Types I and II using traditional paleontological species concepts.
On the basis of the above evidence, and since all specimens were collected at the same location at ∼3–8 m water depth, we conclude that G. siphonifera Types I and II are living examples of cryptic speciation, whereby biological speciation has occurred in the absence of discernable change in shell morphology. However, it is not clear when or where this speciation took place. Preliminary study of deep-sea cores from the Caribbean and Pacific sides of the Isthmus of Panama reveals a predominance of specimens with Type II porosity values, with rare occurrence of specimens yielding Type I porosity values. Systematic downcore measurement of shell porosity and tightness of coiling needs to be extended back to the middle Miocene, when G. siphonifera first appeared, to determine the timing of the Type I and II morphological divergence.
Postulated mechanisms for reproductive isolation and speciation of Types I and II include alloparapatric, depth parapatric, and sympatric speciation. These models could be tested if further analysis of fossil G. siphonifera shells allows determination of the timing of speciation, the preferred depth distribution, and the history of geographic distribution of Types I and II.
Quantifying integration and modularity of evolutionary changes in morphometric traits is crucial for understanding how organismal shapes evolve. For this purpose, comparative studies are necessary, which need to take into account the phylogenetic structure of interspecific data. This study applies several of the standard tools of geometric morphometrics, which mostly have been used in intraspecific studies, in the new context of analyzing integration and modularity based on comparative data. Morphometric methods such as principal component analysis, multivariate regression, partial least squares and modularity tests can be applied to phylogenetically independent contrasts of shape data. We illustrate this approach in an analysis of cranial evolution in 160 species from all orders of birds. Mapping the shape information onto the phylogeny indicates that there is a significant phylogenetic signal in skull shape. Multivariate regression of independent contrasts of shape on independent contrasts of size reveals clear evolutionary allometry. Regardless of whether or not a correction for allometry is used, evolutionary integration between the face and braincase is strong, and tests reject the hypothesis that the face and braincase are separate evolutionary modules. These analyses can easily be applied to other taxa and can be combined with other morphometric tools to address a wide range of questions about evolutionary patterns and processes.
In this paper we analyze the laws of growth that control planktic foraminiferal shell morphology. We assume that isometry is the key toward the understanding of their ontogeny. Hence, our null hypothesis is that these organisms construct isometric shells. To test this hypothesis, geometric models of their shells have been generated with a personal computer. It is demonstrated that early chambers in log-spirally coiled structures cannot follow a strict isometric arrangement. In the real world, the centers of juvenile chambers deviate from the logarithmic growth curve. Juvenile stages are generally more planispiral and contain more chambers per whorl than adult stages. These traits are shown to be essential in order to keep volumes of consecutive chambers in geometric progression. We are convinced that the neanic stage marks the constructional bridge from a juvenile set of growth parameters to an adult one. The adult stage can be strictly isometric, that is, the effective shape is constant and the increase in volume after a chamber addition is proportional to the preexisting volume of the shell.
The shell volume is related to the biomass, the ratio of outer shell surface area to shell volume is related to the respiration rate and the ratio of the total shell surface area to shell volume is related to the total calcification effort. The influence of the parameters of the model on these relationships is investigated. Only the initial radius and the rate of radius increase affect the relationships between shell volume and surface area. The other shape parameters merely provide a fine tune-up of these relationships. Size itself plays a major role during foraminiferal development.
Assessing the extent to which population subdivision during cladogenesis is necessary for long-term phenotypic evolution is of fundamental importance in a broad range of biological disciplines. Differentiating cladogenesis from anagenesis, defined as evolution within a species, has generally been hampered by dating precision, insufficient fossil data, and difficulties in establishing a direct link between morphological changes detectable in the fossil record and biological species. Here we quantify the relative frequencies of cladogenesis and anagenesis for macroperforate planktic Foraminifera, which arguably have the most complete fossil record currently available, to address this question. Analyzing this record in light of molecular evidence, while taking into account the precision of fossil dating techniques, we estimate that the fraction of speciation events attributable to anagenesis is <19% during the Cenozoic era (last 65 Myr) and <10% during the Neogene period (last 23 Myr). Our central conclusion-that cladogenesis is the predominant mode by which new planktic Foraminifera taxa become established at macroevolutionary time scales-differs markedly from the conclusion reached in a recent study based solely on fossil data. These disparate findings demonstrate that interpretations of macroevolutionary dynamics in the fossil record can be fundamentally altered in light of genetic evidence.
▪ Abstract The diversity of organismic form has evolved nonuniformly during the history of life. Quantitative morphological studies reveal profound changes in evolutionary rates corresponding with the generation of morphological disparity at low taxonomic diversity during the early radiation of many clades. These studies have also given insight into the relative importance of genomic and ecological factors in macroevolution, the selectivity of extinction, and other issues. Important progress has been made in the development of morphological spaces that can accommodate highly disparate forms, although this area still needs more attention. Other future directions include the relationship between morphological and ecological diversification, geographic patterns in morphological diversity, and the role of morphological disparity as a causal factor in macroevolution.
Morphometrics is defined as the application of multivariate statistical procedures to the study of variation in morphological characteristics of organisms. As originally implemented, the analyses are based on standard measures (‘distances’) spanning critical sites. A more recent introduction is concerned with quantifying outlines of organisms, the data then being a suite of arbitrary coordinate-pairs around the circumference of the object, obtained by some automatically operating digitization procedure (e.g. the Zahn–Rosskies method). Geometric morphometrics is the latest class to appear. It relies on diagnostically located ‘landmarks’ that form the basis for superimposition of coordinate systems, visualizations by deformation grids. The first and third of these categories can, without particular difficulty, be allied with environmental indicators by appropriate techniques.
Ten morphometric descriptors (five pairs of form and shape parameters) are used to describe the complex morphology of the first lower molar of two morphologically similar species, Microtus arvalis and M. agrestis. These descriptors are derived either from linear measurements or from outline analysis. The effects of these different descriptors on classical analysis as used in biology or palaeobiology are explored. First, the reliability of results in statistical classification is assessed. All of the descriptors discriminate well between the two species. The initial morphometric scheme (linear or outline) does not induce marked differences in statistical classification and the major discrepancies are between standardized and non-standardized versions of descriptors, and between amplitude- and coefficient-based or linear-based descriptors. Subsequently, the similarity of morphospaces based on partial least squares analysis and of intraspecific variance (estimated from the morphospace analysis) are observed. This is done within a morphospace-disparity framework and procedures used here for testing are directed at this research area. Similarities between morphospaces are relatively high. In this case, the initial morphometric scheme is a major factor inducing dissimilarity. However, the patterns of intraspecific dispersion inferred from morphospaces are roughly similar. Major differences in results correspond to the two classes of form or shape descriptors. Similarity of intraspecific variance is obtained when standardized descriptors are used (except for amplitude-based descriptors); conversely, dissimilarity is obtained when non-standardized descriptors are used. In many cases, the results of the various analyses are robust despite changes in descriptor. Moreover, the developmental pathway of vole teeth can frequently explain major dissimilarity or even similarity. © 2004 The Linnean Society of London, Biological Journal of the Linnean Society, 2004, 83, 243–260.
Abstract: The distribution of organic forms is clumpy at any scale from populations to the highest taxonomic categories, and whether considered within clades or within ecosystems. The fossil record provides little support for expectations that the morphological gaps between species or groups of species have increased through time as it might if the gaps were created by extinction of a more homogeneous distribution of morphologies. As the quantitative assessments of morphology have replaced counts of higher taxa as a metric of morphological disparity, numerous studies have demonstrated the rapid construction of morphospace early in evolutionary radiations, and have emphasized the difference between taxonomic measures of morphological diversity and quantitative assessments of disparity. Other studies have evaluated changing patterns of disparity across mass extinctions, ecomorphological patterns and the patterns of convergence within ecological communities, while the development of theoretical morphology has greatly aided efforts to understand why some forms do not occur. A parallel, and until recently, largely separate research effort in evolutionary developmental biology has established that the developmental toolkit underlying the remarkable breadth of metazoan form is largely identical among Bilateria, and many components are shared among all metazoa. Underlying this concern with disparity is a question about temporal variation in the production of morphological innovations, a debate over the relative significance of the generation of new morphologies vs. differential probabilities of their successful introduction, and the relative importance of constraint, convergence and contingency in the evolution of form.
In contrast with speciation in terrestrial organisms, marine plankton frequently display gradual morphological change without lineage division (e.g., phyletic gradualism or gradual evolution), which has raised the possibility that a different mode of evolution dominates within pelagic environments. Here, we reexamine a classic case of putative gradual evolution within the Globorotalia plesiotumida-G. tumida lineage of planktonic foraminifera, and find both compelling evidence for the existence of a third cryptic species during the speciation event and the abrupt evolution of the descendant G. tumida. The third morphotype, not recognized in previous analyses, differs in shape and coiling direction from its ancestor, G. plesiotumida. This species dominates the globorotaliid population for 414,000 years just before the appearance of G. tumida. The first population of the descendant, G. tumida, evolves abruptly within a 44,000-year interval. A combination of morphological data and biostratigraphic evidence suggests that G. tumida evolved by cladogenesis. Our findings provide an unexpected twist on one of the best-documented cases of within-lineage phyletic gradualism and, in doing so, revisit the limitations and promise of the study of speciation in the fossil record.
Symphyseal contours in a sample of living and fossil apes were assessed by application of the line skeleton, a form of median axis transformation. While the line skeleton offers novel opportunities for the analysis of shape, this study reaffirms previous observations that the shape of the symphysis is highly variable within great ape species, such that symphyseal morphology is not useful as a taxonomic marker. There is also little indication that symphyseal shape differs significantly between the sexes. The perception of what constitutes a salient superior or inferior transverse torus among living apes appears to be dependent on the expression of the genioglossal fossa.
Morphologists and systematists have long suspected that dietary consistency can affect skull and dental form in mammals. We examined plasticity of skull shape and tooth morphology in prairie deer mice (Peromyscus maniculatus bairdii) by feeding mice diets that differed in consistency but not nutritional quality. Shape differences were analyzed qualitatively and quantitatively, using both landmark-based morphometrics and traditional distance measurements. Mice fed a gruel made of laboratory chow soaked in water differed from those fed hard blocks of chow by a slight anterior shift in the incisor tips, a narrowed zygomatic plate, a reduction in size of the masseteric tubercles, an overall decrease in skull size in lateral view, and an increase in overall size in ventral view. Disparities between our results and previous studies may be due to the differences in behavior between the inbred, relatively inactive laboratory strains commonly used in experimental studies and the outbred, constantly active species used here. Also, in contrast to previous studies, the statistical analysis employed here took into account both family relationships of the animals and the large number of statistical comparisons performed. Failure to consider these factors would have resulted in an exaggerated estimate of the effects of diet on skull form and may taint other studies that have explored the same aspects of plasticity.
Globigerinidae with multiple apertures found in Miocene samples from Oamaru and Clifden, Southland, are described in terms of the degree to with the nth chamber envelops earlier chambers, the height of the primary and one of the supplementary apertures, the number of chambers and apertures per specimen, and direction of chamber coiling. Measured characters show patterns of continuous variation within the class studied. This emphasises the arbitrary character of the “central types” used by Blow to describe the morphological changes in the lineage leading to Orbulina and suggests that simple statistical measures may better express these trends.
Ecophenotypic variation in the ornament of living Mutilus pumilus from Australia may be related to seasonal temperature differences along the southern coasts. Standard methods of statistical analysis identify geographical differences in the morphology of the data, but are inadequate for analysing the complex patterns of shape variability in the species. Geometric morphometric methods localised the more important changes in shape in both the outline of the shell and in the configuration of the ornament.
A preliminary report is presented documenting the evolution of the Globorotalia crassaformis (Galloway and Wissler) lineage from the Early Pliocene G. cibaoensis (Bermudez) in Hydraulic Piston Core 72/516 on the Rio Grande Rise (western South Atlantic). A new technique, eigenshape analysis, is used to describe the gross changes in morphology, and the use of “Raupian” analysis of expansion rates, angular displacement, position relative to coiling axis, and translation rates of chambers is suggested as a useful vehicle for inferring the geometric causes of observed evolutionary changes. These changes include size increase, decrease in the number of chambers per whorl, inflation, reduction of relative height of aperture, and increase in the peripheral angle. The sequence is judged to be an example of phyletic gradualism.
Punctuated equilibrium and phyletic gradualism are alternative hypotheses that purport to explain the tempo and mode of evolution. We evaluate the two hypotheses, as they apply to the fossil record, on both theoretical and empirical grounds. Hidden randomness in data increases as a function of greater aggregation, and the hypothesis of punctuated equilibrium should not be applied to those examples where randomness is likely to occur. False stasis can result from a sustained pattern of emigration and immigration, and geographic variation must be studied in order to posit an unambiguous case of punctuated equilibrium. We describe a statistical method based on the general linear model for testing the relative fit of the alternative hypotheses to any set of temporally ordered metric data. Our method is hierarchical in the sense that subsets of the total explained variance can themselves be explained. The size of the first molar of the primate Pelycodus and of the condylarth Hyopsodus are analyzed. There are 17 tests in the two data sets, and we discover 12 instances of gradualism, four of punctuation and one of equilibrium.
There is great power in Sewall Wright’s metaphor of the adaptive landscape, the representation of fitness as a function of position in an abstract genotypic or phenotypic parameter space. When this conception is combined with a uniform prior model for the provenance of biological variation, then the density of samples near a point of phenotypic space becomes indicative of the fitness of the organism typical of that point. In this way, an empirical distribution of organisms or species over a morphometric parameter space becomes a description of relative fitness. [See, for instance, Raup (1967) or Bookstein et al. (1985, Section 5.4).] Peaks of relative frequency are taken to connote evolutionary successes, and gaps stand for phenotypes that either have been blocked from occurring or else, once extant, were eliminated by selection.
Before one can study evolutionary rates one must reject the null model of symmetric random walk, for which the requisite quantity does not exist. As random walks reliably simulate all the features we find so compelling in the fossil record, rejection of this irritating hypothesis is much more difficult than one might hope. This paper reviews principal theorems from the mathematical literature of random walk and shows how they may be applied to empirical data by scaling net changes according to the square root of elapsed time. The notorious pair of 'opposite' findings, equilibrium and anagenesis, may be construed as deviations from random walk in opposite directions. Malmgren's data on Globorotalia tumida, previously interpreted as an example of punctuated anagenesis, are consistent with a random walk showing neither punctuation nor anagenesis, but instead varying in speed over four subsequences. -from Author
Morphologic analysis of 281 species of ammonoids from Great Britain, the North American mid-continent, and the South Urals, at eight successive levels within the Namurian Series (ca. 18 Myr duration) using bivariate plots and principal-components analysis, permits definition of morphologic diversity and identification of morphotypic patterns in time and space. Namurian ammonoids exhibit the same general range of shell geometry that characterizes ammonoids as a whole; there were few post-Namurian innovations in the basic geometry of planispiral ammonoids. Within this overall range of geometry, there are eight preferred morphotypes: two were phylogenetically monopolized by long-ranging forms; three were generalized and reoccur in successive horizons; two others were homeomorphically utilized at different times by different lineages; and one represents morphologic innovation followed by radiation. Such patterns seem to represent combined effects of function, phylogeny, and ecology. Synchronous variations in isolated successions suggest global controls such as eustatic sea-level fluctuations, whereas provincial differences in diversity may be attributable to paleogeographic and ecologic factors. We predict that the Namurian record of ammonoid morphologic diversity and change will be found to be distinctive and differentiable from earlier and later intervals. -Authors
An index is given for all available genus-group and family-group names which are applicable to the Globigerinacea; the literary sources, the nature, source and depositories of the type specimens, and selected references to significant emendations, are given. The type-species of each genus-group name is illustrated, where possible with direct reference to type specimens. The taxa of the genus-group are reclassified in a discriminatory key, in which objective synonymy is noted and some subjective synonymy is suggested, and, from which, further subjective assessments are possible. The probable phylogenetic history of the Globigerinacea is shown graphically and is discussed with especial reference to the iterative evolution of gross homeomorphs in closely or more distantly related family groups.
Multivariate Morphometrics is concerned with the application of the theory and practice of multivariate statistical analysis to two or more morphological characters considered simultaneously. This chapter focuses on recent developments in multivariate morphometrics and the special analysis of particular problems of great interpretative significance. Multivariate morphometrics is mostly a straightforward application of standard methods of multivariate statistical analysis with particular emphasis on applications of canonical variate analysis and principal component analysis. In some cases of special biological pertinence, existing theory has been found inadequate and specific adaptations of the standard techniques are in the course of being developed that treat such situations. The particular claim to existence of multivariate morphometrics lies with the interpretation of the biological significance of the statistical computations and the analysis of problems normally beyond the ken of most statisticians. Thus, the successful explanation of a multivariate-morphometric analysis may require intimate knowledge of modern evolutionary theory, taxonomy, functional morphology and various aspects of ecology.
Detailed planktonic foraminiferal zonations have been established for the Neogene (Latest Oligocene through present) in six DSDP sites in the South Pacific ranging from equatorial to subantarctic latitudes (48°S). Two basic zonal schemes are readily recognized: tropical and temperate. The tropical zonation is best developed in DSDP Site 289 and the temperate zonation in Sites 206, 207A and 284. Tropical and temperate zonations can be linked by a warm subtropical scheme in Site 208, because this sequence includes a mixture of tropical and temperate elements. A site located close to the Subantarctic Convergence (Site 281) contains a zonation largely of temperate character, but the present of cooler elements and some differences in biostratigraphic ranges have required a slightly different biostratigraphic scheme.
Multivariate analyses have been applied to the late Neogene planktonic foraminiferal lineage Globoconella in an attempt to: (1) objectively subdivide this evolutionary continuum into segments (chronospecies); and (2) differentiate each chronospecies using reproducible quantitative criteria. A principal component analysis was employed to extract chronological variation from five time series of different morphometric variables. A cluster analysis of the principal component scores was then used to reveal possible groupings. This was followed by a stepwise discriminant analysis to evaluate the grouping and to determine the most useful and parsimonious variables for taxonomic differentiation. With this sequence of analyses, the Globoconella lineage can be differentiated into six chronospecies with a correct classification percentage of 100%. Quantitative criteria for taxonomic differentiation of the following six chronospecies are proposed: Globorotalia (Globoconella) conoidea, G. (G.) conomiozea conomiozea, G. (G.) conomiozea terminalis ssp. nov., G. (G.) sphericomiozea, G. (G.) puncticulata and G. (G.) inflata.
Globigerinidae with two or more apertures found in lower to middle Miocene samples from Oamaru and Clifden (New Zealand) are described in terms of rate of expansion of chambers, relation between observed and theoretical diameters for the penultimate chamber, and angle of attachment of the final chamber. In the samples examined the experimental class includes forms usually assigned to Globigerinoides trilobus (Reuss), G. bisphericus Todd, G. glomerosus Blow, Orbulina suturalis Bronnimann, and O. universa d'Orbigny.
Planktonic foraminifers from DSDP Site 586 on Leg 89 and Sites 587-594 on Leg 90, from the equator to subantarctic waters of the southwest Pacific, are recorded. Five zonal schemes were used because of latitudinal changes in faunal assemblages and these are discussed; intersite correlation was established by selected datum species. The appearances and extinctions of most datum species were regarded as isochronous but a few were demonstrably diachronous at their paleogeographic limits, such as the appearances of G. truncatulinoides at Site 594 and G. inflata at 587. The presence of Jenkinsina samwelli in the late Oligocene at Site 593 is further support for the hypothesis that the Circum-Antarctic Current began about 30 Ma ago. At the same time, a major unconformity was formed and is widespread in the Tasman Sea area; sedimentation did not resume at Site 592 until the early Miocene. Selected taxonomic problems are discussed and 39 species illustrated. -from Authors
A new geometry based on the primitive notions of a point and a growth is explored. Growth from a boundary generates a description of an object that is centered on the space it includes. Growth from this centered or core description generates the boundary by an inverse growth. This leads to new properties and descriptions which are particularly suitable for many biological objects. Some implications for mathematics and biology are discussed. Part II explores the use of this description to the understanding of the visual process. Some implications for a revised view of nervous system structure and function are discussed.
This paper, the second in a series of three, introduces Partial Least Squares (PLS) methods for assessing the effects of moderate levels of prenatal alcohol exposure on performance and behavior in young school-age children. Studies of human behavioral teratology pose statistical problems for which standard multiple regression methods are inadequate. Prenatal alcohol exposure, the teratogenic “dose,” can be assessed only indirectly through a variety of measures of alcohol consumption. Similarly, the behavioral outcomes we examine—IQ, achievement, classroom behavior, and vigilance—are each measured indirectly in terms of multiple items or indicators. We find that a single latent variable, estimated as a linear combination of the measures of alcohol consumption, provides an appropriate measure of “dose” for summarizing the relationships between alcohol exposure and each of the four blocks of outcome variables. A pattern of alcohol consumption emphasizing binge behavior (i.e., reporting average consumption of multiple drinks per drinking occasion, or at least five drinks on any single occasion) in the period prior to recognition of pregnancy is significantly correlated with latent variables computed from each of the four outcome blocks: IQ, academic achievement, classroom behavior and attention/vigilance.
Biometric studies of the forms of organisms usually consider size and shape variations in the geometric configuration of landmarks, points that correspond biologically from form to form. The size variables may be usefully considered the linear vector space spanned by the set of all distances between pairs of landmarks. The shape of a single triangle $\Delta ABC$ of landmarks may be reduced to a single pair of shape coordinates locating the vertex $C$ in the coordinate system with landmark $A$ sent to (0,0) and landmark $B$ to (1,0). A useful space of shape variables is the span of all such shape coordinate pairs for various triples of landmarks. On a convenient null model of identical circular normal perturbations at each landmark independently, one size variable $S$, which may be taken as the mean square of all the interlandmark distances, has covariance zero with every shape variable. Then associations between shape and size may be tested by the $F$ ratio for multiple regression of $S$ on any basis for shape space. For a single triangle of landmarks, the existence of any mean difference or mean change in shape may be tested by Hotelling's $T^2$ applied to any pair of shape coordinates for that triangle. When such a difference is statistically significant, it may be interpreted as the ratio of a pair of size variables measured along directions at an angle averaging $90^\circ$ in the samples of forms. One size variable will bear the greatest mean rate or ratio of change between the forms, the other the least. Analysis of configurations of more than three landmarks reduces to consideration of size variables involving at most three landmarks. These techniques are demonstrated in a study of the growth of the head in 62 normal Ann Arbor youth. Each comparison of interest is summarized in its own orthogonal coordinate system, the biorthogonal grid pair.
Thesis (M.S.)--University of California, Los Angeles, 1981. Typescript (photocopy). Includes bibliographical references (leaves 79-80).
425 p., 213 fig., 8 tables http://paleo.ku.edu/contributions.html
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The geometric meaning of soft modeling, with some generalizations
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Development ofthe methods ofanalysis by shape coordinates was partially underwritten by USPHS Grant GM-37251. LITERATURE QTED
- J A Kitchell
- N Macleod
to J. A. Kitchell and N. MacLeod. Development ofthe methods ofanalysis by shape
coordinates was partially underwritten by
USPHS Grant GM-37251.
LITERATURE QTED
Random walk and the biometrics of morphological characters
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data in two dimensions. Stat. Sci. 1:181-242.
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---. 1988. Random walk and the biometrics of
morphological characters. Evol. BioI. 23:369-398.
---. 1990. Morphometric Tools for Landmark
Data: Geometry and Biology. Cambridge Univ.
Press, N.Y. In press.
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