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The study of phenotypic variation in time and space is central to evolutionary biology. Modern geometric morphometrics is the leading family of methods for the quantitative analysis of biological forms. This set of techniques relies heavily on technological innovation for data acquisition, often in the form of 2D or 3D digital images, and on powerful multivariate statistical tools for their analysis. However, neither the most sophisticated device for computerized imaging nor the best statistical test can produce accurate, robust and reproducible results, if it is not based on really good samples and an appropriate use of the 'measurements' extracted from the data. Using examples mostly from my own work on mammal craniofacial variation and museum specimens, I will show how easy it is to forget these most basic assumptions, while focusing heavily on analytical and visualization methods, and much less on the data that generate potentially powerful analyses and visually appealing diagrams.

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... Details of molar morphology are often sufficient to diagnose extinct species and contain evidence of evolutionary relationships between mammalian taxa (Gingerich 1985;Ungar 2010). In short, multiple common sources of between-individual variation can be accounted for in the morphology of mammalian molars, making it possible to focus on variation due to other processes that accrue over genetic distance (Albrecht and Miller 1993;Cardini 2020). ...

... No sexual size dimorphism has yet been detected in O. leucogaster (Dewsbury et al. 1980). Finally, specimens of O. leucogaster are well represented in skeletal and tissue collections in museums, a practically important consideration for this type of research (Cardini 2020). ...

... Previous studies noted that morphological variation at the population level is noisy, or that extraneous sources of variation obstruct the detection of a signal of morphological differentiation between populations (Polly 2003;Cardini 2020). Our raw observations support the idea that natural populations are morphologically variable (Fig. 5), but not necessarily the interpretation that subtle geographic signal exists and could be detected if only adequate samples were included (Cardini 2020). ...

In neutral models of quantitative trait evolution, both genetic and phenotypic divergence scale as random walks, producing a correlation between the two measures. However, complexity in the genotype‐phenotype map may alter the correlation between genotypic and phenotypic divergence, even when both are evolving neutrally or nearly so. Understanding this correlation between phenotypic and genetic variation is critical for accurately interpreting the fossil record. This study compares the geographic structure and scaling of morphological variation of the shape of the first lower molar of 77 individuals of the northern grasshopper mouse Onychomys leucogaster to genome‐wide SNP variation in the same sample. We found strong genetic structure but weak or absent morphological structure indicating that the scaling of each type of variation are decoupled from one another. Low PST values relative to FST values are consistent with a lack of morphological divergence in contrast to genetic divergence between groups. This lack of phenotypic structure and the presence of notable within‐sample phenotypic variance is consistent with uniform selection or constraints on molar shape across a wide geographic and environmental range. Over time, this kind of decoupling may result in patterns of phenotypic stasis masking underlying genetic patterns. This article is protected by copyright. All rights reserved

... The mathematical and statistical theory of shape analysis had been synthesized in the following years (Adams et al., 2004;Bookstein, 1996;Dryden & Mardia, 1998;Goodall, 1991;Goodall & Mardia, 1993;Rohlf, 1999;Small, 1996), based on the earlier work by David Kendall and others (Kendall, 1981(Kendall, , 1984. Since then, geometric morphometrics has been continually refined and has found countless applications in biological, anthropological, paleontological, medical, psychological, archeological, and industrial fields (for reviews see, e.g., Adams & Otárola-Castillo, 2013;Bookstein, 2018;Cardini, 2020;Elewa, 2010;Halazonetis, 2004;Klingenberg, 2010;Lawing & Polly, 2010;MacLeod, 2018;Mitteroecker, 2020;Mitteroecker & Gunz, 2009;Schaefer et al., 2009;Slice, 2005;Wiley et al., 2005;Zelditch et al., 2012). The geometric morphometric toolkit has also been connected to other methodologies, including biomechanics (e.g., O'Higgins et al., 2019;Parr et al., 2012;Polly et al., 2016;Weber et al., 2011), systematics and phylogenetics (e.g., Adams, 2014;Klingenberg & Gidaszewski, 2010;Monteiro, 2013;Rohlf, 2002), image analysis (e.g., Mayer et al., 2014Mayer et al., , 2017, quantitative genetics (e.g., Adams, 2011;Baab, 2018;Martínez-Abadías et al., 2009;Pavličev et al., 2016;Schroeder & von Cramon-Taubadel, 2017), genetic mapping (e.g., Mitteroecker et al., 2016;Pallares et al., 2015;Var on-González et al., 2019), evolutionary psychology and brain imaging (e.g., Walla et al., 2020;Windhager et al., 2012Windhager et al., , 2018 as well as molecular and developmental biology (e.g., Arif et al., 2013;Buchberger et al., 2021;Hallgrimsson et al., 2015;Marchini et al., 2021;Martínez-Abadías et al., 2018). ...

... Some authors have criticized the use of semilandmarks. For instance, Cardini (2020) wrote that "positions of the semilandmarks can be optimized, but they are fundamentally arbitrarily decided by an operator or an algorithm" (p. 514). ...

... landmarks are the important ones. Questions, disagreements, and studies about the necessary number of landmarks, and especially of semilandmarks, have fueled numerous discussions in the geometric morphometrics community (e.g.,Cardini, 2020;Evin et al., 2020;Goswami et al., 2019;Oxnard & O'Higgins, 2009;Rolfe et al., 2021;Watanabe, 2018).Designing a landmark scheme is a crucial step in any morphometric study that requires time, biological knowledge, and a careful inspection of multiple specimens to gauge the range of variation to be represented. The biological or geometrical homology criteria underlying the landmark definitions are key to the interpretation of results(Bookstein, 1991;Oxnard & O'Higgins, 2009). ...

The foundations of geometric morphometrics were worked out about 30 years ago and have continually been refined and extended. What has remained as a central thrust and source of debate in the morphometrics community is the shared goal of meaningful biological inference through a tight connection between biological theory, measurement, multivariate biostatistics, and geometry. Here we review the building blocks of modern geometric morphometrics: the representation of organismal geometry by landmarks and semilandmarks, the computation of shape or form variables via superimposition, the visualization of statistical results as actual shapes or forms, the decomposition of shape variation into symmetric and asymmetric components and into different spatial scales, the interpretation of various geometries in shape or form space, and models of the association between shape or form and other variables, such as environmental, genetic, or behavioral data. We focus on recent developments and current methodological challenges, especially those arising from the increasing number of landmarks and semilandmarks, and emphasize the importance of thorough exploratory multivariate analyses rather than single scalar summary statistics. We outline promising directions for further research and for the evaluation of new developments, such as “landmark‐free” approaches. To illustrate these methods, we analyze three‐dimensional human face shape based on data from the Avon Longitudinal Study of Parents and Children (ALSPAC).

... Bunlar canlı veya cansız tüm materyali kapsamaktadır. Genel olarak çalışmalar değerlendirildiğinde ise, çalışmaların çoğunluğunun hayvanlar üzerinde gerçekleştiği görülmekte olup, memeliler (Cardini, 2020;Cardini et al., 2021), sürüngen ve amfibiler (Kaliontzopoulou, 2011;Gray et al., 2017) ve böcekler (Tatsuta et al., 2018Sumruayphol & Chaiphongpachara, 2019) üzerinde etkili sonuçlar verdiği çalışmalarlar ortaya konulmuştur. ...

... Bu motiflerin merkezinde yer alan penç sevilerek kullanılan motiflerden olmuştur (Fot. 15,16,17). Stilize edilmiş çiçeklerin üstten görünüşü ile oluşturulmuş penç motiflerinin formu değişmemekle birlikte değişen yaprak sayılarına göre adlandırılmaktadır (Birol ve Derman, 2015, s.47). Dört yapraklı penç motifi haça benzediği için İslamiyet'ten sonra çok kullanılmamaktadır. ...

Kültür; toplumların sosyal olarak nesilden nesile aktardığı somut ve
somut olmayan değerler bütünü, sembolik ve öğrenilmiş ürünler ya da
özellikler toplamı; insan faaliyetinin toplumsal olarak aktarılan yönleri�nin bütünü olarak tanımlanmaktadır (Koyuncu Okca vd. 2020:1761). Kül�tür aynı zamanda toplumun yaşayış şekillerini aktaran, ulusların tarihi ge�lişme süreci içinde yarattığı maddi ve manevi değerlerdir. Bu değerler, uy�garlığın gerektirdiği bilim ve sanat dalları ile toplumun yaşamı için önem
taşıyan din, duygu düşünce, gelenek, ahlak, terbiye gibi kavramları içerir.
Kültür toplumda sadece mevcut durumu içermez. Aynı zamanda sü�rekli yenilendiği için bulunduğu toplumun yaşam sürecini de ortaya ko�yar(Dilek ve Coşkun, 2018:239). Bir toplumun modern yaşama ayak uy�durabilmesi için ekonomi, eğitim ve teknoloji alanındaki başarıları kadar
kültürel yapısı ve sanat alanındaki başarıları da önemli yer tutmaktadır(-
Dilek ve Coşkun, 2008:546). Kültür değerlerinin zamanla gelişmesi ve
yücelmesi uygarlığın en önemli göstergesidir. Tarihin ilk dönemlerinden
itibaren uygarlık kavramı kent olgusunun içeriğini belirlemede ve kent
ile ilişkili bir kavram olarak oldukça etkili olmuştur (Koyuncu Okca vd,
2019:406). Selçuklu döneminde başlayan Türk kent kimliği ve imar faali�yetleri ile kentleşme başlamıştır. Türk evi, doğal çevre ve kültürün özel�liklerine uyumludur. Yapı, tarih boyunca, salt insan yaşantısının mekanik
gereksinimlerini karşılayacak bir işlevsellik anlayışı ile çözümlenip bıra�kılmamıştır. Düzenleme ölçü, oran, modül, simetri, birlik, ritim, uyum,
denge, renk gibi kavramlar yapının görsel etkisini yoğunlaştırıcı öğelerdi

... If possible, tests should be performed using the exact same set of reference specimens. That being said, error should always be interpreted in the context of the biological question explored [14,21,37]. The amount of acceptable error will indeed depend on the data used and the comparisons being made [17,21,38,39]. ...

... A common question when starting a study is about how many landmarks or measurements should be used to accurately quantify variation. The answer is never straightforward and as this study shows, more is not always better [9,37]. Measuring effort should be contrasted with the aims of the study and the number of coordinates acquired depends on the complexity of the structure measured. ...

Quantifying phenotypes is a common practice for addressing questions regarding morphological variation. The time dedicated to data acquisition can vary greatly depending on methods and on the required quantity of information. Optimizing digitization effort can be done either by pooling datasets among users, by automatizing data collection, or by reducing the number of measurements.
Pooling datasets among users is not without risk since potential errors arising from multiple operators in data acquisition prevents combining morphometric datasets. We present an analytical workflow to estimate within and among operator biases and to assess whether morphometric datasets can be pooled. We show that pooling and sharing data requires careful examination of the errors occurring during data acquisition, that the choice of morphometric approach influences amount of error, and that in some cases pooling data should be avoided.
The demonstration is based on a worked example (Sus scrofa teeth) using a combinations of 18 morphometric approaches and datasets for which we identified and quantified several potential sources of errors in the workflow. We show that it is possible to estimate the analytical power of a study using a small subset of data to select the best morphometric protocol and to optimize the number of variables necessary for analysis. In particular, we focus on semi-landmarks, which often produce an inflation of variables in contrast to the number of available observations use in statistical testing. We show how the workflow can be used for optimizing digitization efforts and provide recommendations for best practices in error management.

... The development of semilandmark methods (Bookstein, 1996;Gunz and Mitteroecker, 2013) has been a crucial step forward for a number of specific applications. Landmarks should be equivalent across study subjects and selected so that they are relevant to the specific hypotheses (Cardini, 2020a;Oxnard and O'Higgins, 2009). Thus, depending on the study questions, the criterion for equivalence, as well as the choice of a configuration of landmarks, might vary (Oxnard and O'Higgins, 2009). ...

Landmark-based geometric morphometrics using the Procrustes approach has become the dominant family of methods in morphometrics. However, the superimposition (and sliding, if semilandmarks are present), that transforms raw coordinates into shape coordinates is biologically arbitrary. Procrustes has desirable statistical properties, but is not based on a biological model. The same is true for sliding methods. These techniques allow powerful statistical analyses of a full set of shape coordinates, but make the use of subsets of landmarks/semilandmarks problematic, inaccurate and misleading, if not totally wrong. Crucially, the biological arbitrariness of the superimposition prevents any meaningful quantification, analysis and interpretation of variation one landmark/semilandmark at a time. We exemplify how misleading this type of analyses can be by using a real dataset, as well as simulated data with isotropic variation. Both show inconsistencies in ‘per-landmark/semilandmark’ variances. The simulation in fact helps to make even more obvious that the pattern of variance is strongly influenced by the biologically arbitrary choice of the mathematical treatment. Unfortunately, despite this limitation of all superimposition methods being known since the early days of Procrustean morphometrics, there has been a recent series of papers in leading journals presenting results of ‘per-landmark’ analyses. Thus, we further clarify why these analyses are wrong and represent misleading examples that should not be followed: Procrustes shape data cannot be analyzed, visualized or interpreted one landmark at a time. For users who are in doubt, in the Conclusions, we provide a short list of recommendations on how to easily avoid this type of mistakes.

... between-group PCA and multivariate regression; e.g. Bookstein, 2019;Cardini, 2020), the symmetric component of shape variation was computed, and the four landmarks corresponding to the left side of the tail were discarded. All subsequent analyses were carried out using the five landmarks representing the right side of the tail (Figure 1a; note that these landmarks were mirrored to represent symmetric tails in all figures). ...

Variational properties hold a fundamental role in shaping biological evolution, exerting control over the magnitude and direction of evolutionary change elicited by micro-evolutionary processes that sort variation, such as selection or drift. We studied the genus Tyrannus as a model for examining the conditions and drivers that facilitate the repeated evolution of exaggerated, secondary sexual traits in the face of significant functional limitations. In particular, we explore the role of allometry, sexual selection and their interaction, on the diversification of tail morphology in the genus, assessing whether and how they promoted or constrained phenotypic evolution. Non-deep-forked species tend to show reduced sexual dimorphism and moderate allometric variation in tail shape. The exaggerated and functionally constrained long feathers of deep-forked species, T. savana and T. forficatus, which show both marked sexual dimorphism and allometric tail shape variation, independently diverged from the rest of the genus following the same direction of main interspecific variation accrued during the evolution of non-deep-forked species. Moreover, the latter direction is also aligned with axes summarising sexual dimorphism and allometric variation on deep-forked species, a feature lacking in the rest of the species. Thus, exaggerated tail morphologies are interpreted as the result of amplified divergence through reorientation and co-option of allometric variation by sexual selection, repeatedly driving morphology along a historically favoured direction of cladogenetic evolution.

... Since an opening of 120° is the standard in studies of bird tail morphology [66], the two landmarks marking the tip of the outermost rectrices of each side were further rotated 30°, using the centroid of landmarks #6-#9 (defining the 'base' of the tail) as pivot. In order to avoid problems reported elsewhere for supervised versions of Principal Component Analysis (PCA) and its algebraic equivalents (i.e., between-group PCA and Partial Least Squares; e.g., [64,65]), the four landmarks corresponding to the left side of the tail (having served to determine the central axis of symmetry) were discarded and all subsequent analyses were carried out using the five remaining landmarks ( Figure 1A; note that these landmarks were mirrored to represent tails in all figures). ...

Variational properties hold a fundamental role in shaping biological evolution, exerting control over the magnitude and direction of evolutionary change elicited by microevolutionary processes that sort variation, such as selection or drift. We studied the Tyrannus genus, as a model for examining the conditions and drivers that facilitate the repeated evolution of exaggerated, secondary sexual traits in the face of significant functional limitations. We study the role of allometry, sexual selection, and their interaction on the diversification of tail morphology in the genus, assessing whether and how they promoted or constrained phenotypic evolution. The exaggerated and functionally-constrained long feathers of deep-forked species, T. savana and T. forficatus, independently diverged from the rest of the genus following the same direction of main interspecific variation common to the entire cluster of species. However, at a macroevolutionary scale those axes summarising both sexual dimorphism and allometric variation of the deep-forked species were aligned with the between-species maximum variation axis of non deep-forked species. Thus, we are presenting evidence of amplified divergence via the co-option and reorientation of allometric shape variation involved in a sexual selection process that repeatedly drove morphology along a historically favoured direction of cladogenetic evolution.

... Yet, large variance might instead reflect genuine variability in relation to the specific evolutionary history, pattern of distribution and breadth of ecological adaptations or degree of plasticity of a species. However, variance could also be biased by how well the museum samples cover the full geographic range of a species (Albrecht and Miller 1993;Cope 1993;Harrison 1993;Cardini 2020a). For D. novemcintus, a small variance is almost certainly an artefact of sampling. ...

An accurate classification is the basis for research in biology. Morphometrics and morphospecies play an important role in modern taxonomy, with geometric morphometrics increasingly applied as a favourite analytical tool. Yet, really large samples are seldom available for modern species and even less common in palaeontology, where morphospecies are often identified, described and compared using just one or a very few specimens. The impact of sampling error and how large a sample must be to mitigate the inaccuracy are important questions for morphometrics and taxonomy. Using more than 4000 crania of adult mammals and taxa representing each of the four placental superorders, we assess the impacts of sampling error on estimates of species means, variances and covariances in Procrustes shape data using resampling experiments. In each group of closely related species (mostly congeneric), we found that a species can be identified fairly accurately even when means are based on relatively small samples, although errors are frequent with fewer specimens and primates more prone to inaccuracies. A precise reconstruction of similarity relationships, in contrast, sometimes requires very large samples (> 100), but this varies widely depending on the study group. Medium-sized samples are necessary to accurately estimate standard errors of mean shapes or intraspecific variance covariance structure, but in this case minimum sample sizes are broadly similar across all groups (≈ 20–50 individuals). Overall, thus, the minimum sample sized required for a study varies across taxa and depends on what is being assessed, but about 25–40 specimens (for each sex, if a species is sexually dimorphic) may be on average an adequate and attainable minimum sample size for estimating the most commonly used shape parameters. As expected, the best predictor of the effects of sampling error is the ratio of between- to within-species variation: the larger the ratio, the smaller the sample size needed to obtain the same level of accuracy. Even though ours is the largest study to date of the uncertainties in estimates of means, variances and covariances in geometric morphometrics, and despite its generally high congruence with previous analyses, we feel it would be premature to generalize. Clearly, there is no a priori answer for what minimum sample size is required for a particular study and no universal recipe to control for sampling error. Exploratory analyses using resampling experiments are thus desirable, easy to perform and yield powerful preliminary clues about the effect of sampling on parameter estimates in comparative studies of morphospecies, and in a variety of other morphometric applications in biology and medicine. Morphospecies descriptions are indeed a small piece of provisional evidence in a much more complex evolutionary puzzle. However, they are crucial in palaeontology, and provide important complimentary evidence in modern integrative taxonomy. Thus, if taxonomy provides the bricks for accurate research in biology, understanding the robustness of these bricks is the first fundamental step to build scientific knowledge on sound, stable and long-lasting foundations.

... Multivariate morphometric techniques provide an additional tool for quantifying a wide range of morphological variation that can incorporate a suite of phenotypic characteristics, including measures of adaptive variation (Rohlf and Marcus 1993;McGuigan et al. 2003;Komiya et al. 2011). Digital imaging technology has further simplified and standardized the collection of morphometric data and improved the ability of researchers to increase the geographic extent of samples included in analyses (Mojekwu and Anumudu 2015;Cardini 2020). Despite the improvements made in quantifying intraspecific variation using molecular and morphometric methods, the two approaches have often been pursued in isolation of each other and sometimes leading to arguments for one method over the other (Hillis 1987;Phillimore et al. 2008;Losos et al. 2012). ...

The cutthroat trout, Oncorhynchus clarkii (Richardson, 1836), is one of the most widely distributed species of freshwater fish in western North America. Occupying a diverse range of habitats, they exhibit significant phenotypic variability that is often recognized by intraspecific taxonomy. Recent molecular phylogenies have described phylogenetic diversification across cutthroat trout populations, but no study has provided a range-wide morphological comparison of taxonomic divisions. In this study, we used linear and geometric-based morphometrics to determine if phylogenetic and subspecies divisions correspond to morphological variation in cutthroat trout, using replicate populations from throughout the geographic range of the species. Our data indicate significant morphological divergence of intraspecific categories in some, but not all, cutthroat trout subspecies. We also compare morphological distance measures with distance measures of mtDNA sequence divergence. DNA sequence divergence was positively correlated with morphological distance measures, indicating that morphologically more similar subspecies have lower sequence divergence in comparison to morphologically distant subspecies. Given these results, integrating both approaches to describing intraspecific variation may be necessary for developing a comprehensive conservation plan in wide-ranging species.

The study of insular variation has fascinated generations of biologists and has been central to evolutionary biology at least since the time of Wallace and Darwin. In this context, using 3D geometric morphometrics, I investigate whether the population of mountain hares (Lepus timidus Linnaeus, 1758) introduced in 1857 on the Swedish island of Hallands Väderö shows distinctive traits in cranial size and shape. I find that size divergence follows the island rule, but is very small. In contrast, shape differences, compared to the mainland population, are almost as large as interspecific differences among lineages separated by hundreds of thousands of years of a largely independent evolutionary history. Even if, contrary to what is documented in the scientific literature, mountain hares were present in HV before 1857, the evolutionary history of this population could not have start earlier than the end of the last glaciation (i.e., at least one order of magnitude more recently than the separation of L. timidus from other hare species in this study). My results, thus, suggest that the insular population is a significant evolutionary unit and a potentially important component of the diversity of Swedish mountain hares. This is interesting for evolutionary biologists, but even more relevant for conservationists trying to protect the disappearing population of southern Swedish L. timidus, threatened by changes in climate and the environment, as well as by disease and the introduced European hare (Lepus europaeus Pallas, 1778). Island populations of mountain hares, thus, represent a potential source for future reintroductions on the mainland and, as my research shows, an important component of variability to maximize the preservation of the evolutionary potential in a species facing huge environmental changes.

Traditionally, morphological characters are widely used to distinguish between interspe-cies and intraspecies. In addition to the size of morphological characters, shape has also been used as an indicator in the last decades. We evaluated the geometric morphometry and morphometric of the bill of Chukar Partridge, Alectoris chukar from captive and wild populations to determine the bill variation and population relationships. Although there was a size difference between the sexes, no shape difference was found. However, captive populations differed from wild populations in both size and shape. Although there was no difference in shape among wild populations, some differences were found in size. Moreover, bill sizes of captive populations were statistically longer than western, centre, and eastern wild populations. It was also shown that the western populations had the most significant variation among the wild populations. The results revealed that using the size and shape together was more effective in comparing populations.

The classification of most mammalian orders and families is under debate and the number of species is likely greater than currently recognized. Improving taxonomic knowledge is crucial, as biodiversity is in rapid decline. Morphology is a source of taxonomic knowledge, and geometric morphometrics applied to two dimensional (2D) photographs of anatomical structures is commonly employed for quantifying differences within and among lineages. Photographs are informative, easy to obtain, and low cost. 2D analyses, however, introduce a large source of measurement error when applied to crania and other highly three dimensional (3D) structures. To explore the potential of 2D analyses for assessing taxonomic diversity, we use patas monkeys (Erythrocebus), a genus of large, semi‐terrestrial, African guenons, as a case study. By applying a range of tests to compare ventral views of adult crania measured both in 2D and 3D, we show that, despite inaccuracies accounting for up to ¼th of individual shape differences, results in 2D almost perfectly mirror those in 3D. This apparent paradox might be explained by the small strength of covariation in the component of shape variance related to measurement error. A rigorous standardization of photographic settings and the choice of almost coplanar landmarks are likely to further improve the correspondence of 2D to 3D shapes. 2D geometric morphometrics is, thus, appropriate for taxonomic comparisons of patas ventral crania. Although it is early to generalize, our results corroborate similar findings from previous research in mammals, and suggest that 2D shape analyses are an effective heuristic tool for morphological investigation of small differences. This article is protected by copyright. All rights reserved.

Convergence consists in the independent evolution of similar traits in distantly related species. The mammalian cranio‐mandibular complex constitutes an ideal biological structure to investigate ecomorphological dynamics and the carnivorans, due to their phenotypic variability and ecological flexibility, offer an interesting case‐study to explore the occurrence of convergent evolution. Here, we applied multiple pattern‐based metrics to test the occurrence of convergence in the cranio‐mandibular shape of extant carnivorans. To this aim, we tested for convergence in many dietary groups and analysed several cases of carnivoran convergence concerning either ecologically equivalent species or ecologically similar species of different body sizes described in the literature. Our results validate the occurrence of convergence in ecologically equivalent species in a few cases (as well as in the case of giant and red pandas), but almost never support the occurrence of convergent evolution in dietary categories of living carnivorans. Therefore, convergent evolution in this clade appears to be a rare phenomenon. This is probably the consequence of a complex interplay of one‐to‐many, many‐to‐one, and many‐to‐many relationships taking place between ecology, biomechanics and morphology.
This article is protected by copyright. All rights reserved

The quantification of cranial sexual dimorphism (CSD) among modern humans is relevant in evolutionary studies of morphological variation and in a forensic context. Despite the abundance of quantitative studies of CSD, few have specifically examined intra‐sex variability. Here we quantify CSD in a geographically homogeneous sample of adult crania, which includes Italian individuals from the 19th and 20th centuries. Cranial morphology is described with 92 3D landmarks analyzed using Procrustean geometric morphometrics (PGMM). Size and shape variables are used to compare morphological variance between sexes in the whole cranium and four individual regions. The same variables, plus Procrustes form, are used to quantify average sex differences and explore classification accuracy. Our results indicate that: i) as predicted by Wainer‘s rule, males present overall more variance in size and shape, albeit this is statistically significant only for total cranial size; ii) differences between sexes are dominated by size and to a lesser extent by Procrustes form; iii) shape only accounts for a minor proportion of variance; iv) the cranial base shows almost no dimorphism for shape; and v) facial Procrustes form is the most accurate predictor of skeletal sex. Overall, this study suggests developmental factors underlying differences in CSD among cranial regions; stresses the need for population‐specific models that describe craniofacial variation as the basis for models that facilitate the estimation of sex in unidentified skeletal remains; and provides one of the first confirmations of ‘Wainer's rule’ in relation to sexual dimorphism in mammals specific to the human cranium.

Miniaturized amphibians of the genus Brachycephalus are phenotypically diverse. The species of Brachycephalus have bufoniform or leptodactyliform baupläne and any of three skeletal states: nonhyperossified, hyperossified without dorsal shield, and hyperossified with dorsal shield. We integrate high-resolution microcomputed tomography, geometric morphometrics, and an estimate of molecular phylogenetic relationships to investigate skull diversity in shape and size-shape space in selected species of Brachycephalus. Skull diversity amongst species of Brachycephalus can be partitioned into shape and size-shape space according to the four conditions of skeletal states-baupläne, namely, nonhyperossified leptodactyliform, nonhyperossified bufoniform, hyperossified bufoniform without dorsal shield, and hyperossified bufoniform with dorsal shield. Skull diversity in shape and size-shape space in nonhyperossified leptodactyliform species of Brachycephalus is markedly larger, when compared to skull diversity in species of the three other conditions of skeletal states-baupläne. Variation in skull shape scales with size across Brachycephalus and, therefore, can be explained by allometry. Skull diversity, baupläne, and skeletal states covary to a large extent with monophyletic lineages of Brachycephalus, as revealed by a mitochondrial DNA species tree. Nonhyperossified bufoniform species and hyperossified bufoniform species with or without dorsal shield are monophyletic lineages, as inferred from a mitochondrial DNA species tree. Nonhyperossified leptodactyliform species of Brachycephalus do not share, however, a most recent common ancestor. The nonhyperossified leptodactyliform species of Brachycephalus, due to their marked skull diversity and lack of monophyly, emerge as evolutionarily complex. Therefore, further sampling of the nonhyperossified leptodactyliform condition of skeletal states-baupläne will be necessary to further understand the evolutionary history of Brachycephalus.

Using sampling experiments, we found that, when there are fewer groups than variables, between-groups PCA (bgPCA) may suggest surprisingly distinct differences among groups for data in which none exist. While apparently not noticed before, the reasons for this problem are easy to understand. A bgPCA captures the g − 1 dimensions of variation among the g group means, but only a fraction of the ∑ n i − g dimensions of within-group variation (n i are the sample sizes), when the number of variables, p, is greater than g − 1. This introduces a distortion in the appearance of the bgPCA plots because the within-group variation will be underrepresented, unless the variables are sufficiently correlated so that the total variation can be accounted for with just g − 1 dimensions. The effect is most obvious when sample sizes are small relative to the number of variables, because smaller samples spread out less, but the distortion is present even for large samples. Strong covariance among variables largely reduces the magnitude of the problem, because it effectively reduces the dimensionality of the data and thus enables a larger proportion of the within-group variation to be accounted for within the g − 1-dimensional space of a bgPCA. The distortion will still be relevant though its strength will vary from case to case depending on the structure of the data (p, g, covariances etc.). These are important problems for a method mainly designed for the analysis of variation among groups when there are very large numbers of variables and relatively small samples. In such cases, users are likely to conclude that the groups they are comparing are much more distinct than they really are. Having many variables but just small sample sizes is a common problem in fields ranging from morphometrics (as in our examples) to molecular analyses.

Good empirical applications of geometric morphometrics (GMM) typically involve several times more variables than specimens, a situation the statistician refers to as “high p/n,” where p is the count of variables and n the count of specimens. This note calls your attention to two predictable catastrophic failures of one particular multivariate statistical technique, between-groups principal components analysis (bgPCA), in this high-p/n setting. The more obvious pathology is this: when applied to the patternless (null) model of p identically distributed Gaussians over groups of the same size, both bgPCA and its algebraic equivalent, partial least squares (PLS) analysis against group, necessarily generate the appearance of huge equilateral group separations that are fictitious (absent from the statistical model). When specimen counts by group vary greatly or when any group includes fewer than about ten specimens, an even worse failure of the technique obtains: the smaller the group, the more likely a bgPCA is to fictitiously identify that group as the end-member of one of its derived axes. For these two reasons, when used in GMM and other high-p/n settings the bgPCA method very often leads to invalid or insecure biological inferences. This paper demonstrates and quantifies these and other pathological outcomes both for patternless models and for models with one or two valid factors, then offers suggestions for how GMM practitioners should protect themselves against the consequences for inference of these lamentably predictable misrepresentations. The bgPCA method should never be used unskeptically—it is always untrustworthy, never authoritative—and whenever it appears in partial support of any biological inference it must be accompanied by a wide range of diagnostic plots and other challenges, many of which are presented here for the first time.

Using sampling experiments, we found that, when there are fewer groups than variables, between-groups PCA (bgPCA) may suggest surprisingly distinct differences among groups for data in which none exist. While apparently not noticed before, the reasons for this problem are easy to understand. A bgPCA captures the g-1 dimensions of variation among the g group means, but only a fraction of the ∑ n i − g dimensions of within-group variation ( n i are the sample sizes), when the number of variables, p , are greater than g -1. This introduces a distortion in the appearance of the bgPCA plots because the within-group variation will be underrepresented, unless the variables are sufficiently correlated so that the total variation can be accounted for with just g -1 dimensions. The effect is most obvious when sample sizes are small relative to the number of variables, because smaller samples spread out less, but the distortion is present even for large samples. Strong covariance among variables largely reduces the magnitude of the problem, because it effectively reduces the dimensionality of the data and thus enables a larger proportion of the within-group variation to be accounted for within the g -1-dimensional space of a bgPCA. The distortion will still be relevant though its strength will vary from case to case depending on the structure of the data ( p , g , covariances etc.). These are important problems for a method developed mainly to analyze variation among groups when there are very large numbers of variables and relatively small samples, a common situation in fields ranging from morphometrics (as in our examples) to molecular analyses.

Studies of morphological integration and modularity are a hot topic in evolutionary developmental biology. Geometric morphometrics using Procrustes methods offers powerful tools to quantitatively investigate morphological variation and, within this methodological framework, a number of different methods has been put forward to test if different regions within an anatomical structure behave like modules or, vice versa, are highly integrated and covary strongly. Although some exploratory techniques do not require a priori modules, commonly modules are specified in advance based on prior knowledge. Once this is done, most of the methods can be applied either by subdividing modules and performing separate Procrustes alignments or by splitting shape coordinates of anatomical landmarks into modules after a common superimposition. This second approach is particularly interesting because, contrary to completely separate blocks analyses, it preserves information on relative size and position of the putative modules. However, it also violates one of the fundamental assumptions on which Procrustes methods are based, which is that one should not analyse or interpret subsets of landmarks from a common superimposition, because the choice of that superimposition is purely based on statistical convenience (although with sound theoretical foundations) and not on a biological model of variance and covariance. In this study, I offer a first investigation of the effects of testing integration and modularity within a configuration of commonly superimposed landmarks using some of the most widely employed statistical methods available to this aim. When applied to simulated shapes with random non-modular isotropic variation, standard methods frequently recovered significant but arbitrary patterns of integration and modularity. Re-superimposing landmarks within each module, before testing integration or modularity, generally removes this artifact. The study, although preliminary and exploratory in nature, raises an important issue and indicates an avenue for future research. It also suggests that great caution should be exercised in the application and interpretation of findings from analyses of modularity and integration using Procrustes shape data, and that issues might be even more serious using some of the most common methods for handling the increasing popular semilandmark data used to analyse 2D outlines and 3D surfaces.

Accurate characterization of morphological variation is crucial for generating reliable results and conclusions concerning changes and differences in form. Despite the prevalence of landmark-based geometric morphometric (GM) data in the scientific literature, a formal treatment of whether sampled landmarks adequately capture shape variation has remained elusive. Here, I introduce LaSEC (Landmark Sampling Evaluation Curve), a computational tool to assess the fidelity of morphological characterization by landmarks. This task is achieved by calculating how subsampled data converge to the pattern of shape variation in the full dataset as landmark sampling is increased incrementally. While the number of landmarks needed for adequate shape variation is dependent on individual datasets, LaSEC helps the user (1) identify under- and oversampling of landmarks; (2) assess robustness of morphological characterization; and (3) determine the number of landmarks that can be removed without compromising shape information. In practice, this knowledge could reduce time and cost associated with data collection, maintain statistical power in certain analyses, and enable the incorporation of incomplete, but important, specimens to the dataset. Results based on simulated shape data also reveal general properties of landmark data, including statistical consistency where sampling additional landmarks has the tendency to asymptotically improve the accuracy of morphological characterization. As landmark-based GM data become more widely adopted, LaSEC provides a systematic approach to evaluate and refine the collection of shape data––a goal paramount for accumulation and analysis of accurate morphological information.

Many fossil specimens exhibit deformations caused by taphonomic processes. Due to these deformations, even important specimens have to be excluded from morphometric analyses, impoverishing an already poor paleontological record. Techniques to retrodeform and virtually restore damaged (i.e. deformed) specimens are available, but these methods genenerally imply the use of a sparse set of bilateral landmarks, ignoring the fact that the distribution and amount of control points directly affects the result of the retrodeformation. We propose a method developed in the R environment and available in the R-package “Morpho” that, in addition to the landmark configurations, also allows using a set of semi-landmarks homogeneously distributed along curves and on surfaces. We evaluated the outcome of the retrodeformation, regarding the number of semi-landmarks used and its robustness against asymmetric noise, based on simulations using a virtually deformed gorilla cranium. Finally, we applied the method to a well-known Neanderthal cranium that exhibits signs of taphonomically induced asymmetry.

The textbook literature of principal components analysis (PCA) dates from a period when statistical computing was much less powerful than it is today and the dimensionality of data sets typically processed by PCA correspondingly much lower. When the formulas in those textbooks involve limiting properties of PCA descriptors, the limit involved is usually the indefinite increase of sample size for a fixed roster of variables. But contemporary applications of PCA in organismal systems biology, particularly in geometric morphometrics (GMM), generally involve much greater counts of variables. The way one might expect pure noise to degrade the biometric signal in this more contemporary context is described by a different mathematical literature concerned with the situation where the count of variables itself increases while remaining proportional to the count of specimens. The founders of this literature established a result of startling simplicity. Consider steadily larger and larger data sets consisting of completely uncorrelated standardized Gaussians (mean zero, variance 1) such that the ratio of variables to cases (the so-called “p/n ratio”) is fixed at a value y. Then the largest eigenvalue of their covariance matrix tends to (Formula presented.), the smallest tends to (Formula presented.), and their ratio tends to the limiting value (Formula presented.), whereas in the uncorrelated model both of these eigenvalues and also their ratio should be just 1.0. For (Formula presented.) not an atypical value for GMM data sets, this ratio is 9; for (Formula presented.) which is still not atypical, it is 34. These extrema and ratios, easily confirmed in simulations of realistic size and consistent with real GMM findings in typical applied settings, bear severe negative implications for any technique that involves inverting a covariance structure on shape coordinates, including multiple regression on shape, discriminant analysis by shape, canonical variates analysis of shape, covariance distance analysis from shape, and maximum-likelihood estimation of shape distributions that are not constrained by strong prior models. The theorem also suggests that we should use extreme caution whenever considering a biological interpretation of any Partial Least Squares analysis involving large numbers of landmarks or semilandmarks. I illuminate these concerns with the aid of one simulation, two explicit reanalyses of previously published data, and several little sermons.

Geometric morphometrics is routinely used in ecology and evolution and morphometric datasets are increasingly shared among researchers, allowing for more comprehensive studies and higher statistical power (as a consequence of increased sample size). However, sharing of morphometric data opens up the question of how much nonbiologically relevant variation (i.e., measurement error) is introduced in the resulting datasets and how this variation affects analyses. We perform a set of analyses based on an empirical 3D geometric morphometric dataset. In particular, we quantify the amount of error associated with combining data from multiple devices and digitized by multiple operators and test for the presence of bias. We also extend these analyses to a dataset obtained with a recently developed automated method, which does not require human-digitized landmarks. Further, we analyze how measurement error affects estimates of phylogenetic signal and how its effect compares with the effect of phylogenetic uncertainty. We show that measurement error can be substantial when combining surface models produced by different devices and even more among landmarks digitized by different operators. We also document the presence of small, but significant, amounts of nonrandom error (i.e., bias). Measurement error is heavily reduced by excluding landmarks that are difficult to digitize. The automated method we tested had low levels of error, if used in combination with a procedure for dimensionality reduction. Estimates of phylogenetic signal can be more affected by measurement error than by phylogenetic uncertainty. Our results generally highlight the importance of landmark choice and the usefulness of estimating measurement error. Further, measurement error may limit comparisons of estimates of phylogenetic signal across studies if these have been performed using different devices or by different operators. Finally, we also show how widely held assumptions do not always hold true, particularly that measurement error affects inference more at a shallower phylogenetic scale and that automated methods perform worse than human digitization.

Significance
The strong focus on species extinctions, a critical aspect of the contemporary pulse of biological extinction, leads to a common misimpression that Earth’s biota is not immediately threatened, just slowly entering an episode of major biodiversity loss. This view overlooks the current trends of population declines and extinctions. Using a sample of 27,600 terrestrial vertebrate species, and a more detailed analysis of 177 mammal species, we show the extremely high degree of population decay in vertebrates, even in common “species of low concern.” Dwindling population sizes and range shrinkages amount to a massive anthropogenic erosion of biodiversity and of the ecosystem services essential to civilization. This “biological annihilation” underlines the seriousness for humanity of Earth’s ongoing sixth mass extinction event.

Nonhuman primates, our closest biological relatives, play important roles in the livelihoods, cultures, and religions of many societies and offer unique insights into human evolution, biology, behavior, and the threat of emerging diseases. They are an essential component of tropical biodiversity, contributing to forest regeneration and ecosystem health. Current information shows the existence of 504 species in 79 genera distributed in the Neotropics, mainland Africa, Madagascar, and Asia. Alarmingly, ~60% of primate species are now threatened with extinction and ~75% have declining populations. This situation is the result of escalating anthropogenic pressures on primates and their habitats— mainly global and local market demands, leading to extensive habitat loss through the expansion of industrial agriculture , large-scale cattle ranching, logging, oil and gas drilling, mining, dam building, and the construction of new road networks in primate range regions. Other important drivers are increased bushmeat hunting and the illegal trade of primates as pets and primate body parts, along with emerging threats, such as climate change and anthroponotic diseases. Often, these pressures act in synergy, exacerbating primate population declines. Given that primate range regions overlap extensively with a large, and rapidly growing, human population characterized by high levels of poverty, global attention is needed immediately to reverse the looming risk of primate extinctions and to attend to local human needs in sustainable ways. Raising global scientific and public awareness of the plight of the world's primates and the costs of their loss to ecosystem health and human society is imperative.

We describe patterns of skull size and shape variation in an Atlantic forest endemic rodent to test the influence of genetic structure, historical and environmental variables upon intraspecific morphological variability. South America, Brazil, Atlantic forest. We analyse subtle differences in skull morphology of Akodon cursor through geometric morphometrics applied to 324 individuals from 12 localities distributed throughout the species range. Using cytochrome-b gene (cyt-b) sequences from 125 individuals (38 localities), we describe underlying patterns of genetic structure and transform them into distance measures that are included in our morphological analyses. We estimate the relative importance of genetic structure, historical variables and environmental variables on skull size and shape through mixed model selection and Akaike's information criterion. Geographical patterns in skull size are mainly explained by non-random factors related to primary productivity and precipitation, whereas spatial shifts in shape correlate with mitochondrial divergence. Cytochrome-b data revealed a phylogeographic break around the Jequitinhonha River, yet striking morphological shifts were observed further south. Differences in palaeostability between regions, and the configuration of rivers, appear as secondary sources of explanation for observed patterns. Multiple forces explain morphological variation within A. cursor. Teasing apart the effects of local adaptation and gene flow may be difficult, but is a key to improve our understanding of the drivers of intraspecific morphological variation. Our findings support the view that size is a more labile feature than shape, and that it may more easily break away from constraints imposed by gene flow. The combination of random and non-random factors, together with documented breaks in the distribution of the Atlantic forest over the Late Quaternary, accounts for the majority of morphological differences observed in A. cursor.

Allometry refers to the size-related changes of morphological traits and remains an essential concept for the study of evolution and development. This review is the first systematic comparison of allometric methods in the context of geometric morphometrics that considers the structure of morphological spaces and their implications for characterizing allometry and performing size correction. The distinction of two main schools of thought is useful for understanding the differences and relationships between alternative methods for studying allometry. The Gould-Mosimann school defines allometry as the covariation of shape with size. This concept of allometry is implemented in geometric morphometrics through the multivariate regression of shape variables on a measure of size. In the Huxley-Jolicoeur school, allometry is the covariation among morphological features that all contain size information. In this framework, allometric trajectories are characterized by the first principal component, which is a line of best fit to the data points. In geometric morphometrics, this concept is implemented in analyses using either Procrustes form space or conformation space (the latter also known as size-and-shape space). Whereas these spaces differ substantially in their global structure, there are also close connections in their localized geometry. For the model of small isotropic variation of landmark positions, they are equivalent up to scaling. The methods differ in their emphasis and thus provide investigators with flexible tools to address specific questions concerning evolution and development, but all frameworks are logically compatible with each other and therefore unlikely to yield contradictory results.

Geometric morphometrics-a set of methods for the statistical analysis of shape once saluted as a revolutionary advancement in the analysis of morphology -is now mature and routinely used in ecology and evolution. However, a factor often disregarded in empirical studies is the presence and the extent of measurement error. This is potentially a very serious issue because random measurement error can inflate the amount of variance and, since many statistical analyses are based on the amount of "explained" relative to "residual" variance, can result in loss of statistical power. On the other hand, systematic bias can affect statistical analyses by biasing the results (i.e. variation due to bias is incorporated in the analysis and treated as biologically-meaningful variation). Here, I briefly review common sources of error in geometric morphometrics. I then review the most commonly used methods to measure and account for both random and non-random measurement error, providing a worked example using a real dataset.

The development and the present state of the “tps” series of software for use in geometric morphometrics on Windows-based computers are described. These programs have been used in hundreds of studies in mammals and other organisms.

Climate change resulting in a reduction of alpine habitat is believed to pose a considerable risk to alpine-dependent species, including many marmots. Hoary marmots ( Marmota caligata ) range throughout much of the mountainous Pacific Northwest (PNW) and Rocky Mountains while the closely related Olympic and Vancouver Island marmots ( M. olympus and M. vancouverensis , respectively) are restricted to small isolated regions of the PNW. The endemic Vancouver Island marmot is currently classified as Critically Endangered and the Olympic marmot has recently experienced dramatic population declines. Previous phylogenetic studies of PNW marmot species have had limited power as they focused on resolving interspecific relationships, implicitly assumed an absence of gene flow among currently recognized species, included relatively few individuals, and relied heavily or entirely on mitochondrial DNA. We sequenced 2 mitochondrial and 4 nuclear markers from 167 hoary, 4 Vancouver Island, and 5 Olympic marmots in order to investigate phylogenetic relationships and historic gene flow among these species. We recovered 2 monophyletic (and predominantly allopatric) mitochondrial clades of hoary marmots that are not sister groups. Instead, Vancouver Island marmots formed a monophyletic mitochondrial sister clade to 1 of the hoary marmot clades. Nuclear loci did not recover the 2 mitochondrial clades of hoary marmots and suggest that Vancouver Island marmots may have experienced mitochondrial introgression from coastal mainland hoary marmots. Additionally, our nuclear results suggest possible gene flow between hoary and Olympic marmots despite different chromosomal formulas. Rather than resolving what has previously been considered a straightforward 3-taxon phylogenetic question, our findings suggest a complicated history of rapid divergence of the 3 species followed by intermittent and possibly ongoing gene flow between hoary marmots and both Olympic and Vancouver Island marmots. These results therefore have significant implications for the conservation of the latter 2 species, both of which are conservation concerns.

Random measurement error is ubiquitous in morphometric data, and it can cause serious statistical problems. We stress that measurement error is a potential problem primarily when true phenotypic variation in shape is relatively small, such as in studies of intraspecific variation in shape. A model for the partitioning of measurement error in landmark based morphometrics is presented. The impact of measurement error can be reduced in a number of ways, depending on the methods used to collect, process and analyse data, and we give some practical advice. We also recommend that repeated measures of all individuals are taken routinely in morphometric studies where measurement error may be a potential problem. This enables both a quantification, by estimating repeatabilities from analyses of variance, and a reduction, by averaging repeated measures, of the relative impact of measurement error. We perform an analysis of shape variation in a uniform sample of young perch (Perca fluviatilis), solely aimed at illustrating how different components of measurement error can be quantified, and demonstrate (a) that estimates of repeatability will only be informative of the error components that are actually repeated in each repeated measure, (b) that the relative impact of different components of measurement error can be partitioned and assessed by planned hierarchical repeated measurement protocols followed by nested analyses of variance, (c) that measurement error is unevenly distributed among different shape variables and (d) that the relative magnitude of ME in a given shape variable can be reduced to an estimable extent by averaging several repeated measures.

An important aspect of geometric morphometrics, since its beginnings, has been the visualization of shape changes. A range of methods has been developed with advances in the theory of statistical shape analysis and new possibilities in computer graphics. Most approaches are based either on relative shifts of landmark positions in starting and target shapes after superimposition or on D'Arcy Thompson's idea of transformation grids. Both approaches are in wide use in current morphometrics, and both have their distinctive advantages and shortcomings. This paper discusses the assumptions and some caveats of both approaches. The paper also offers some recommendations for authors of geometric morphometric studies.

Conservation of marmots, large ground-dwelling squirrels restricted to the northern hemisphere, was impacted by direct human activity through hunting or modifying ecosystem dynamics. Regulating human activities reduced the threat of extinction. Climate change, an indirect human impact, threatens marmot survival through global warming and extreme weather events. Most marmot species occupy a harsh environment characterized by a short growing season and a long, cold season without food. Marmots cope with seasonality by hibernating. Their large size increases the efficiency of fat accumulation and its use as the sole energy source during hibernation. Marmot physiology is highly adapted to coping with low environmental temperatures; they are stressed by high heat loads. Global warming since the last ice age reduced the geographic distribution of some of the 15 species of marmots. Recent warming resulted in a movement upslope of their lower elevation boundary. This process likely will continue because warming is associated with drier unpalatable vegetation. Drought reduces reproduction and increases mortality; thus decreased summer rainfall in the montane environments where marmots live may cause local extinction. Snow cover, a major environmental factor, is essential to insulate hibernation burrows from low, stressful temperatures. However, prolonged vernal snow cover reduces reproduction and increases mortality. Montane areas currently lacking marmot populations because vernal snow cover persists beyond the time that marmots must begin foraging may become colonized if warming causes earlier snow melt. This benefit will be short-lived because decreased precipitation likely will result in unpalatable vegetation. Although some marmot populations are physiologically adapted to a warmer climate, global warming will increase too rapidly for any significant evolutionary response to dryness. The species that live in high, alpine meadows where tree and shrub invasions occur are most threatened with extinction. Captive breeding can preserve marmot species in the shortrun, but is impractical over the long-term. Widespread species are unlikely to be endangered in the foreseeable future, but local, low elevation populations will be lost.

One of the most basic but problematic issues in modern morphometrics is how many specimens one needs to achieve accuracy in samples. Indeed, this is one of the most regularly posed questions in introductory courses. There is no simple and certainly no absolute answer to this question. However, there are a number of techniques for exploring the effect of sampling, and our aim is to provide an example of how this might function in a simplified but informative way. Thus, using resampling methods and sensitivity analyses based on randomized subsamples, we assessed sampling error in horse teeth from several modern and fossil populations. Centroid size and shape of an upper premolar (PM2) were captured using Procrustes geometric morphometrics. Means and variances (using three different statistics for shape variance) were estimated, as well as their confidence intervals. Also, the largest population sample was randomly split into progressively smaller subsamples to assess how reducing sample size affects statistical parameters. Results indicate that mean centroid size is highly accurate; even when sample size is small, errors are generally considerably smaller than differences among populations. In contrast, mean shape estimation requires large samples of tens of specimens (ca. >20), although this requirement may be less stringent when variance in a population is very small (e.g. populations that underwent strong genetic bottlenecks). Variance in either centroid size or shape can be highly inaccurate in small samples, to the point that sampling error makes it as variable as differences among spatially and chronologically well-separated populations, including two which are highly distinctive as a consequence of strong artificial selection. Likely, centroid size and shape variance require no

Quantitative shape analysis using geometric morphometrics is based on the statistical analysis of landmark coordinates. Many structures, however, cannot be quantified using traditional landmarks. Semilandmarks make it possible to quantify two or three-dimensional homologous curves and sur- faces, and analyse them together with traditional landmarks. Here we first introduce the concept of sliding semilandmarks and discuss applications and limitations of this method. In a second part we show how the sliding semilandmark algorithm can be used to estimate missing data in incomplete specimens.

Many ecological and evolutionary studies seek to explain patterns of shape variation and its covariation with other variables. Geometric morphometrics is often used for this purpose, where a set of shape variables are obtained from landmark coordinates following a Procrustes superimposition.We introduce geomorph: a software package for performing geometric morphometric shape analysis in the r statistical computing environment.Geomorph provides routines for all stages of landmark-based geometric morphometric analyses in two and three-dimensions. It is an open source package to read, manipulate, and digitize landmark data, generate shape variables via Procrustes analysis for points, curves and surfaces, perform statistical analyses of shape variation and covariation, and to provide graphical depictions of shapes and patterns of shape variation. An important contribution of geomorph is the ability to perform Procrustes superimposition on landmark points, as well as semilandmarks from curves and surfaces.A wide range of statistical methods germane to testing ecological and evolutionary hypotheses of shape variation are provided. These include standard multivariate methods such as principal components analysis, and approaches for multivariate regression and group comparison. Methods for more specialized analyses, such as for assessing shape allometry, comparing shape trajectories, examining morphological integration, and for assessing phylogenetic signal, are also included.Several functions are provided to graphically visualize results, including routines for examining variation in shape space, visualizing allometric trajectories, comparing specific shapes to one another and for plotting phylogenetic changes in morphospace.Finally, geomorph participates to make available advanced geometric morphometric analyses through the r statistical computing platform.

Twenty years ago, Rohlf and Marcus proclaimed that a "revolution in morphometrics" was underway, where classic analyses based on sets of linear distances were being supplanted by geometric approaches making use of the coordinates of anatomical landmarks. Since that time the field of geometric morphometrics has matured into a rich and cohesive discipline for the study of shape variation and covariation. The development of the field is identified with the Procrustes paradigm, a methodological approach to shape analysis arising from the intersection of the statistical shape theory and analytical procedures for obtaining shape variables from landmark data. In this review we describe the Procrustes paradigm and the current methodological toolkit of geometric morphometrics. We highlight some of the theoretical advances that have occurred over the past ten years since our prior review (Adams et al., 2004), what types of anatomical structures are amenable to these approaches, and how they extend the reach of geometric morphometrics to more specialized applications for addressing particular biological hypotheses. We end with a discussion of some possible areas that are fertile ground for future development in the field.

Superimposition methods for comparing configurations of landmarks in two or more specimens are reviewed. These methods show differences in shape among specimens as residuals after rotation, translation, and scaling them so that they align as well as possible. A new method is presented that generalizes Siegel and Benson's (1982) resistant-fit theta-rho analysis so that more than two objects can be compared at the same time. Both least-squares and resistant-fit approaches are generalized to allow for affine transformations (uniform shape change). The methods are compared, using artificial data and data on 18 landmarks on the wings of 127 species of North American mosquitoes. Graphical techniques are also presented to help summarize the patterns of differences in shape among the objects being compared.

The purpose of this book is to introduce Fourier descriptors as a method for measuring the shape of whole or parts of organisms. Fourier descriptors refer to the utilization of Fourier analysis, primarily the Fourier series as a curve-fitting technique, that can numerically describe the outline (shape) of irregular structures such as are commonly found in living organisms. The quantitative characterization of irregular forms is often a first step towards elucidation of the underlying biological processes, whether they be genetic, evolutionary, or functional. The first five chapters discuss the theory behind the use of Fourier descriptors and the remaining chapters show case studies of how they can be used in various fields of biology such as anatomy, cell biology, medicine and dentistry. This book is solely devoted to this subject and will be of interest to all those interested in biological morphometrics.

Quantitative analyses of morphological variation using geometric morphometrics are often performed on 2D photos of 3D structures. It is generally assumed that the error due to the flattening of the third dimension is negligible. However, despite hundreds of 2D studies, few have actually tested this assumption and none has done it on large animals, such as those typically classified as megafauna. We explore this issue in living equids, focusing on ventral cranial variation at both micro- and macro-evolutionary levels. By comparing 2D and 3D data, we found that size is well approximated, whereas shape is more strongly impacted by 2D inaccuracies, as it is especially evident in intra-specific analyses. The 2D approximation improves when shape differences are larger, as in macroevolution, but even at this level precise inter-individual similarity relationships are altered. Despite this, main patterns of sex, species and allometric variation in 2D were the same as in 3D, thus suggesting that 2D may be a source of 'noise' that does not mask the main signal in the data. However, the picture that emerges from this and other recent studies on 2D approximation of 3D structures is complex and any generalization premature. Morphometricians should therefore test the appropriateness of 2D using preliminary investigations in relation to the specific study questions in their own samples. We discuss whether this might be feasible using a reduced landmark configuration and smaller samples, which would save time and money. In an exploratory analysis, we found that in equids results seem robust to sampling, but become less precise and, with fewer landmarks, may slightly overestimate 2D inaccuracies.

Principal components analysis (PCA) is a common method to summarize a larger set of correlated variables into a smaller and more easily interpretable axes of variation.. However, the different components needs to be distinct from each other to be interpretable otherwise they only represents random directions. This is a fundamental assumption of PCA and thus needs to be tested every time. Sample correlation matrices will always result in a pattern of decreasing eigenvalues even if there is no structure. Tests are therefore needed to discern real patterns from illusionary ones. Furthermore,, the loadings of the vectors need to be larger than expected by random data to be useful in the calculation of PC‐scores. PC‐scores calculated from non‐distinct PC's have very large standard errors and cannot be used for biological interpretations. I give a number of examples to illustrate the potential problems with PCA. Robustness of the PC's increases with increasing sample size, but not the number of traits. I review a few simple test statistics appropriate for testing PC's, and use a real world example to illustrate how this can be done using randomization tests. PCA can be very useful but great care is needed to avoid spurious results. This article is protected by copyright. All rights reserved

Allometry refers to the ways in which organismal shape is associated with size. It is a special case of integration, or the tendency for traits to covary, in that variation in size is ubiquitous and evolutionarily important. Allometric variation is so commonly observed that it is routinely removed from morphometric analyses or invoked as an explanation for evolutionary change. In this case, familiarity is mistaken for understanding because rarely do we know the mechanisms by which shape correlates with size or understand their significance. As with other forms of integration, allometric variation is generated by variation in developmental processes that affect multiple traits, resulting in patterns of covariation. Given this perspective, we can dissect the genetic and developmental determinants of allometric variation. Our work on the developmental and genetic basis for allometric variation in craniofacial shape in mice and humans has revealed that allometric variation is highly polygenic. Different measures of size are associated with distinct but overlapping patterns of allometric variation. These patterns converge in part on a common genetic basis. Finally, environmental modulation of size often generates variation along allometric trajectories, but the timing of genetic and environmental perturbations can produce deviations from allometric patterns when traits are differentially sensitive over developmental time. These results question the validity of viewing allometry as a singular phenomenon distinct from morphological integration more generally.

When first described, the small calvaria KNM-ER 42700 from Ileret, Kenya, was considered a late juvenile or young adult and assigned to Homo erectus. However, this species attribution has subsequently been challenged because the specimen's neurocranial shape differs substantially from that of H. erectus adults. Here, (1) we describe the postmortem damage and deformation that could have influenced previous shape analyses, (2) present digital reconstructions based on computed tomographic scans correcting for these taphonomic defects, and (3) analyze the reconstructed endocranial shape and form, considering both static allometry among adults and ontogenetic allometry. To this end, we use geometric morphometrics to analyze the shape of digital endocasts based on landmarks and semilandmarks. Corroborating previous studies of the external surface, we find that the endocranial shape of KNM-ER 42700 falls outside the known adult variation of H. erectus. With an endocranial volume estimate between 721 and 744 ml, size cannot explain its atypical endocranial shape when static allometry within H. erectus is considered. However, the analysis of ontogenetic allometry suggests that it may be a H. erectus individual that is younger than previously thought and had not yet reached adult endocranial shape. Future work should therefore comprehensively review all cranial indicators of its developmental age, including closure of the spheno-occipital synchondrosis. An alternative hypothesis is that KNM-ER 42700 represents an as yet unidentified species of early Homo. Importantly, KNM-ER 42700 should not be included in the adult hypodigm of H. erectus.

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There is over 60 years of discussion in the statistical literature concerning the misuse and limitations of null hypothesis significance tests (NHST). Based on the prevalence of NHST in biological anthropology research, it appears that the discipline generally is unaware of these concerns. The p values used in NHST usually are interpreted incorrectly. A p value indicates the probability of the data given the null hypothesis. It should not be interpreted as the probability that the null hypothesis is true or as evidence for or against any specific alternative to the null hypothesis. P values are a function of both the sample size and the effect size, and therefore do not indicate whether the effect observed in the study is important, large, or small. P values have poor replicability in repeated experiments. The distribution of p values is continuous and varies from 0 to 1.0. The use of a cut-off, generally p ≤ 0.05, to separate significant from nonsignificant results, is an arbitrary dichotomization of continuous variation. In 2016, the American Statistical Association issued a statement of principles regarding the misinterpretation of NHST, the first time it has done so regarding a specific statistical procedure in its 180-year history. Effect sizes and confidence intervals, which can be calculated for any data used to calculate p values, provide more and better information about tested hypotheses than p values and NHST.

Although fluctuating asymmetry has become popular as a measure of developmental instability, few studies have examined its developmental basis. We propose an approach to investigate the role of development for morphological asymmetry by means of morphometric methods. Our approach combines geometric morphometrics with the two-way ANOVA customary for conventional analyses of fluctuating asymmetry and can discover localized features of shape variation by examining the patterns of covariance among landmarks. This approach extends the notion of form used in studies of fluctuating asymmetry from collections of distances between morphological landmarks to an explicitly geometric concept of shape characterized by the configuration of landmarks. We demonstrate this approach with a study of asymmetry in the wings of tsetse flies (Glossina palpalis gambiensis). The analysis revealed significant fluctuating and directional asymmetry for shape as well as ample shape variation among individuals and between the offspring of young and old females. The morphological landmarks differed markedly in their degree of variability but multivariate patterns of landmark covariation identified by principal component analysis were generally similar between fluctuating asymmetry (within-individual variability) and variation among individuals. Therefore there is no evidence that special developmental processes control fluctuating asymmetry. We relate some of the morphometric patterns to processes known to be involved in the development of fly wings.

The mathematical/statistical software platform R has seen an immense increase in popularity within the last decade. Its main advantages are its flexibility, a large repository of freely available extensions, its open-source nature and a thriving community. This tutorial gives an introduction into landmark/surface-mesh based statistical shape analysis in R – specifically using the packages Morpho and Rvcg . Beginning with examples based on sparse sets of anatomical landmarks, the tutorial will go on dealing with surface and curve landmarks and more challenging tasks such as mesh manipulations and surface registration. Apart from statistical analyses, emphasis will also be put on comprehensive visualization of the results. Extensive examples and code snippets are provided to allow the reader to easily replicate the analyses.

Biogeography is spatial by nature. Over the past 20 years, the literature related to the analysis of spatially structured data has exploded, much of it focused on a perceived problem of spatial autocorrelation and ways to deal with it. However, there are a number of other issues that permeate the biogeographical and macroecological literature that have become entangled in the spatial autocorrelation web. In this piece I discuss some of the assumptions that are often made in the analysis of spatially structured data that can lead to misunderstandings about the nature of spatial data, the methods used to analyse them, and how results can be interpreted.

This review considers some recent advances in shape analysis based on landmark data, and focuses on the application of these methods to the study of skeletal evolution in primates. These advances have provoked some controversy. The major aims of this review are to put these debates in context and to provide an overview for the nonmathematician. The purpose of morphometric studies is considered, together with issues relating to the nature, significance and identification of landmarks before turning to a review of available technologies for the analysis of morphological variation. These are considered in terms of underlying models and assumptions in order to clarify when each is appropriate. To illustrate the application of these methods, 3 example studies are presented. The first examines differences amongst ancient and modern adult human crania using 2-dimensional data. The second illustrates the extension of these methods into 3 dimensions in a study of facial growth in monkeys. The third presents an application to the analysis of the form of the hominoid talus. The review ends with an account of available software resources for shape analysis.

The decomposition of deformations by principal warps is demonstrated. The method is extended to deal with curving edges between landmarks. This formulation is related to other applications of splines current in computer vision. How they might aid in the extraction of features for analysis, comparison, and diagnosis of biological and medical images is indicated.

There are 14 species of marmots distributed across the Holarctic, and despite extensive systematic study, their phylogenetic
relationships remain largely unresolved. In particular, comprehensive studies have been lacking. A well-supported phylogeny
is needed to place the numerous ecological and behavioral studies on marmots in an evolutionary context. To address this situation,
we obtained complete cytochrome (cyt) b sequences for 13 of the species and a partial sequence for the 14th. We applied a statistical approach to both phylogeny
estimation and hypothesis testing, using parsimony and maximum likelihood-based methods. We conducted statistical tests on
a suite of previously proposed hypotheses of phylogenetic relationships and biogeographic histories. The cyt b data strongly
support the monophyly of Marmota and a western montane clade in the Nearctic. Although some other scenarios cannot be rejected, the results are consistent
with an initial diversification in North America, followed by an invasion and subsequent rapid diversification in the Palearctic.
These analyses reject the two major competing hypotheses of M. broweri's phylogenetic relationships—namely, that it is the sister species to M. camtschatica of eastern Siberia, and that it is related closely to M. caligata of the Nearctic. The Alaskan distribution of M. broweri is best explained as a reinvasion from the Palearctic, but a Nearctic origin can not be rejected. Several other conventionally
recognized species groups can also be rejected. Social evolution has been homoplastic, with large colonial systems evolving
in two groups convergently. The cyt b data do not provide unambiguous resolution of several basal nodes in the Palearctic radiation, leaving some aspects of pelage
and karyotypic evolution equivocal.

Procrustean geometric morphometrics has made large use of 2D images for studying three-dimensional structures such as mammalian bones or arthropod exoskeleta. This type of use of 2D data is still widespread today and will likely remain common for several years due to its simplicity, efficiency and low cost. However, using 2D pictures to measure morphological variation in a 3D object is an approximation that inevitably implies measurement error. Despite this being an obvious problem, which was emphasized since the early days of the first applications of geometric morphometrics to biology, whether 2D is a good proxy for 3D has been a rather neglected topic in the literature until very recently. In this paper, using marmot mandibles and crania as an example, I show how to assess the potentially crucial impact of 'missing the third dimension' in 2D landmarks and suggest a new method to test the accuracy of these data: the method is simple and can be easily performed in a user-friendly free software such as MorphoJ. This test is complimentary to other more exploratory analyses, that can also be performed using free programs and might offer a routine protocol to estimate the goodness of the 2D to 3D approximation in geometric morphometrics. Example data and a fully worked out MorphoJ project are provided for readers to learn how to replicate the analysis.

Although fluctuating asymmetry has become popular as a measure of developmental instability, few studies have examined its developmental basis. We propose an approach to investigate the role of development for morphological asymmetry by means of morphometric methods. Our approach combines geometric morphometrics with the two-way ANOVA customary for conventional analyses of fluctuating asymmetry and can discover localized features of shape variation by examining the patterns of covariance among landmarks. This approach extends the notion of form used in studies of fluctuating asymmetry from collections of distances between morphological landmarks to an explicitly geometric concept of shape characterized by the configuration of landmarks. We demonstrate this approach with a study of asymmetry in the wings of tsetse flies (Glossina palpalis gambiensis). The analysis revealed significant fluctuating and directional asymmetry for shape as well as ample shape variation among individuals and between the offspring of young and old females. The morphological landmarks differed markedly in their degree of variability, but multivariate patterns of landmark covariation identified by principal component analysis were generally similar between fluctuating asymmetry (within-individual variability) and variation among individuals. Therefore, there is no evidence that special developmental processes control fluctuating asymmetry. We relate some of the morphometric patterns to processes known to be involved in the development of fly wings.

A guide to the popular, free statistics and visualization software that gives scientists control of their own data analysis.

We characterize and compare patterns of clinal size variation among diverse widespread sub-Saharan monkeys with the aim of identifying commonalities and differences in biogeographical variation. Thus, we accurately quantify nonlinear clines in representatives of the main lineages of widespread sub-Saharan terrestrial and arboreal monkeys, and provide a crude numerical estimate of the strength of similarities across taxonomic groups.
Sub-Saharan Africa.
Variations of skull centroid size, as a proxy for body mass, were modelled over sub-Saharan Africa within two terrestrial monkey species (Papio hamadryas and Chlorocebus aethiops) and two arboreal monkey taxa (Procolobus (Piliocolobus) sp., and the superspecies Cercopithecus nictitans–Cercopithecus mitis) using inverse distance weighting, thin-plate splines and kriging. The model with the highest cross-validated accuracy was used to produce contour plots that visualized clines and predicted size at equally spaced localities across overlapping areas of distribution ranges. Correlations among these predictions were used as a similarity measure among clines.
Irrespective of phylogenetic distances and ecological differences, all groups showed similarities in clinal size over central Africa: large animals mostly live in and around the tropical forest of the Congo basin; size declines rapidly towards the Horn of Africa and the coasts of Kenya and Tanzania. Size also tends to decrease in western Africa but clinal patterns in this region vary, with vervets (Chlorocebus aethiops) exceptionally showing a size increase.
Similarities in patterns of size across diverse monkey groups were found. Nonetheless, complexity in clines and a degree of heterogeneity across groups were evident, which is unlikely to be compatible with the exclusive effect on size of a single main environmental factor. Primary productivity may be most significant in relation to the consistent observation of large sizes in and adjacent to the central African tropical forest belt. Complex clines, such as those of African monkeys, are difficult to compare visually and data collection from evenly sampled sets of localities, where all species of interest may be found, is often impractical or simply not feasible for primates and other protected animals. The development of improved quantitative methods for the description and comparison of clines in mammals and other organisms is required.

The analysis of morphological diversity frequently relies on the use of multivariate methods for characterizing biological shape. However, many of these methods are intolerant of missing data, which can limit the use of rare taxa and hinder the study of broad patterns of ecological diversity and morphological evolution. This study applied a mutli-data set approach to compare variation in missing data estimation and its effect on geometric morphometric analyses across taxonomically variable groups, landmark position and sample sizes.Missing morphometric landmark data were simulated from five real, complete data sets, including modern fish, primates and extinct theropod dinosaurs. Missing landmarks were then estimated using several standard approaches and a geometric-morphometric-specific method. The accuracy of missing data estimation was determined for each estimation method, landmark position and morphological data set. Procrustes superimposition was used to compare the eigenvectors and principal component scores of a geometric morphometric analysis of the original landmark data, to data sets with A) missing values estimated, or B) simulated incomplete specimens excluded, for varying levels of specimens incompleteness and sample sizes.Standard estimation techniques were more reliable estimators and had lower impacts on morphometric analysis compared with a geometric-morphometric-specific estimator. For most data sets and estimation techniques, estimating missing data produced a better fit to the structure of the original data than exclusion of incomplete specimens, and this was maintained even at considerably reduced sample sizes. The impact of missing data on geometric morphometric analysis was disproportionately affected by the most fragmentary specimens.Missing data estimation was influenced by variability of specific anatomical features and may be improved by a better understanding of shape variation present in a data set. Our results suggest that the inclusion of incomplete specimens through the use of effective missing data estimators better reflects the patterns of shape variation within a data set than using only complete specimens; however, the effectiveness of missing data estimation can be maximized by excluding only the most incomplete specimens. It is advised that missing data estimators be evaluated for each data set and landmark independently, as the effectiveness of estimators can vary strongly and unpredictably between different taxa and structures.

All species demonstrate intraspecific anatomical variation. While generalisations such as Bergman's and Allen's rules have attempted to explain the geographic structuring of variation with some success, recent work has demonstrated limited support for these in certain Old World monkeys. This study extends this research to the baboon: a species that is widely distributed across sub-Saharan Africa and exhibits clinal variation across an environmentally disparate range. This study uses trend surface analysis to map the pattern of skull variation in size and shape in order to visualise the main axes of morphological variation. Patterns of shape and size-controlled shape are compared to highlight morphological variation that is underpinned by allometry alone. Partial regression is used to dissociate the effects of environmental terms, such as rainfall, temperature and spatial position. The diminutive Kinda baboon is outlying in size, so analyses were carried out with and without this taxon. Skull size variation demonstrates an east-west pattern, with small animals at the two extremes and large animals in Central and Southern Africa. Shape variation demonstrates the same geographical pattern as skull size, with small-sized animals exhibiting classic paedomorphic morphology. However, an additional north-south axis of variation emerges. After controlling for skull size, the diminutive Kinda baboon is no longer an outlier for size and shape. Also, the east-west component is no longer evident and discriminant function analysis shows an increased misclassification of adjacent taxa previously differentiated by size. This demonstrates the east-west component of shape variation is underpinned by skull size, while the north-south axis is not. The latter axis is explicable in phylogenetic terms: baboons arose in Southern Africa and colonised East and West Africa to the north, diverging in the process, aided by climate-mediated isolating mechanisms. Environmental terms appear poorly correlated with shape variation compared with geography. This might indicate that there is no simple environment-morphology association, but certainly demonstrates that phylogenetic history is an overbearing factor in baboon morphological variation.

Cave bear (Ursus spelaeus) behavioural ecology, as evidenced through population dynamics, is crucial for improving our understanding of why this species went extinct. Despite the fact that the bones of this species have been recovered in very large quantities, allowing for extensive study, fundamental questions regarding its life-ways remain unanswered. We present research using geometric morphometrics (GMM) on molars to investigate population structure based on morphological variation over space and through time. This preliminary work deliberately restricts the geographic catchment area for sampling, allowing for a meaningful appraisal of scale of variation within a spatially conservative framework. Our results demonstrate no significant morphological variation evident temporally and a small but statistically significant degree of shape variation geographically despite the proximity of the study localities. These findings suggest that an accurate quantitative exploration of morphospace may be an important source of evidence on environmental and climatic shifts and the resulting influence on animal morphology.