Geometric estimates of heritability in biological shape

The recently developed geometric morphometrics methods represent an important contribution of statistics and geometry to the study of biological shapes. We propose simple protocols using shape distances that incorporate geometric techniques into linear quantitative genetic models that should provide insights into the contribution of genetics to shape variation in organisms. The geometric approaches use Procrustes distances in a curved shape space and distances in tangent spaces within and among families to estimate shape heritability. We illustrate the protocols with an example of wing shape variation in the honeybee, Apis mellifera. The heritability of overall shape variation was small, but some localized components depicting shape changes on distal wing regions showed medium to large heritabilities. The genetic variance-covariance matrix of the geometric shape variables was significantly correlated with the phenotypic shape variance-covariance matrix. A comparison of the results of geometric methods with the traditional multivariate analysis of interlandmark distances indicated that even with a larger dimensionality, the interlandmark distances were not as rich in shape information as the landmark coordinates. Quantitative genetics studies of shape should greatly benefit from the application of geometric methods.     

Shape disparity of bovid (Mammalia,Artiodactyla) horn sheaths and horn cores allows discrimination by species in 3D geometric morphometric analyses

The bony cranial structures of even‐toed hoofed mammals are important for understanding ecology and behavior of ruminants. Horns, the cranial appendages of the family Bovidae, are covered in a layer of keratin that is often not preserved in the fossil record; however, this keratin sheath is intimately involved in the processes that influence horn shape evolution. To understand the relationship between these two components of horns, we quantified both core and sheath shape for four extant species using three‐dimensional geometric morphometric analyses in separate, core‐ and sheath‐specific morphospaces as well as a combined morphospace. We assessed correlations between the horn and sheath morphospaces using two‐block partial least squares regression, a Mantel test of pairwise distances between species, and Procrustes ANOVA. We measured disparity in the combined morphospace as Procrustes distances between mean shapes of cores and sheaths within and between species and as Procrustes variance. We also tested whether core and sheath shapes could be discriminated by taxon with a canonical variate analysis. Results show that horn core and sheath morphospaces are strongly correlated. The differences in shape between a species' core and sheath were statistically significant, but not as great as those between the cores and sheaths of different species when close relatives were not considered, and core and sheath Procrustes variances are not significantly different within species. Cores and sheath shapes were highly identifiable and were assigned to the correct clade 93% of the time in the canonical variate analysis. Based on these tests, horn cores are distinguishable in geometric morphometric analyses, extending the possibility of using geometric morphometrics to study the ecology and evolution of bovid horns to the fossil record.     

Relationship of cranial robusticity to cranial form,geography and climate in Homo sapiens

Variation in cranial robusticity among modern human populations is widely acknowledged but not well‐understood. While the use of “robust” cranial traits in hominin systematics and phylogeny suggests that these characters are strongly heritable, this hypothesis has not been tested. Alternatively, cranial robusticity may be a response to differences in diet/mastication or it may be an adaptation to cold, harsh environments. This study quantifies the distribution of cranial robusticity in 14 geographically widespread human populations, and correlates this variation with climatic variables, neutral genetic distances, cranial size, and cranial shape. With the exception of the occipital torus region, all traits were positively correlated with each other, suggesting that they should not be treated as individual characters. While males are more robust than females within each of the populations, among the independent variables (cranial shape, size, climate, and neutral genetic distances), only shape is significantly correlated with inter‐population differences in robusticity. Two‐block partial least‐squares analysis was used to explore the relationship between cranial shape (captured by three‐dimensional landmark data) and robusticity across individuals. Weak support was found for the hypothesis that robusticity was related to mastication as the shape associated with greater robusticity was similar to that described for groups that ate harder‐to‐process diets. Specifically, crania with more prognathic faces, expanded glabellar and occipital regions, and (slightly) longer skulls were more robust than those with rounder vaults and more orthognathic faces. However, groups with more mechanically demanding diets (hunter‐gatherers) were not always more robust than groups practicing some form of agriculture. Am J Phys Anthropol, 2010. © 2009 Wiley‐Liss, Inc.     

Evolutionary convergence of body shape and trophic morphology in cichlids from Lake Tanganyika

A recent phylogenetic analysis of mitochondrial DNA sequences from eretmodine cichlids from Lake Tanganyika indicated independent origins of strikingly similar trophic specializations, such as dentition characters. Because genetic lineages with similar trophic morphologies were not monophyletic, but instead were grouped with lineages with different trophic phenotypes, raises the question of whether trophic morphology covaries with additional morphological characters. Here, we quantified morphological variation in body shape and trophically associated traits among eretmodine cichlids using linear measurements, meristic counts and landmark‐based geometric morphometrics. A canonical variates analysis (CVA) delineated groups consistent with dentition characters. Multivariate regression and partial least squares analyses indicated that body shape was significantly associated with trophic morphology. When the phylogenetic relationships among taxa were taken into account using comparative methods, the covariation of body shape and trophic morphology persisted, indicating that phylogenetic relationships were not wholly responsible for the observed pattern. We hypothesize that trophic ecology may be a key factor promoting morphological differentiation, and postulate that similar body shape and feeding structures have evolved multiple times in independent lineages, enabling taxa to invade similar adaptive zones.     

Allometric and non‐allometric consequences of inbreeding on Drosophila melanogaster wings

Inbreeding is expected to increase the variability in size and shape within populations. The distinct effects of inbreeding on size and shape suggest that they are governed by different developmental pathways. One unresolved question is whether the non‐allometric shape component is partially unconstrained developmentally and therefore whether shape is evolvable. In the present study, we utilized a mass outbred population of Drosophila melanogaster maintained at standard laboratory conditions. Eight lines with equivalent expected levels of inbreeding (F ≈ 0.67) were obtained by restricting the size of each population to two pairs for nine generations. Nine landmarks were measured on Drosophila wings of the inbreed lines and compared with those of the mass population. Wing landmarks comprise an excellent model system for studying evolution of size and shape. Landmark measurements were analyzed with a Procrustes generalized least squares procedure. To visualize global shape changes among samples, we reconstructed the mean shape and the shape changes related to both the allometric and non‐allometric components. An increased variability in the non‐allometric shape component was found with inbreeding. This indicated that shape was not entirely developmentally constrained, and therefore that shape appears to be evolvable. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 102 , 626–634.     

Lower molar shape and size in prosimian and platyrrhine primates

The goal of this research is to evaluate the relative strength of the influences of diet, size, and phylogenetic signal on dental geometric shape. Accurate comprehension of these factors and their interaction is important for reconstructing diet and deriving characters for a cladistic analysis in fossil primates. Geometric morphometric analysis is used to identify axes of shape variation in the lower second molars of (a) prosimian primates and (b) platyrrhines. Landmarks were placed on µCT‐generated surface renderings. Landmark configurations were aligned using generalized Procrustes analysis. Principal components analysis and phylogenetic principal components analysis (pPCA) were performed on species average landmark co‐ordinates. pPCs were examined with phylogenetic generalized least squares analysis for association with size and with diet. PCs from both phylogenetic and non‐phylogenetic analyses were sufficient to separate species by broad dietary categories, including insectivores and folivores. In neither analysis was pPC1 correlated with tooth size, but some other pPCs were significantly correlated with size. The pattern of association between pPCs and size altered when centroid size and dietary variables were combined in the model; effects of diet factors typically exceeded effects of size. These results indicate a dominant phylogenetic and dietary signal in molar shape but also show some shape change correlated with size in the absence of obvious dietary associations. Geometric morphometric analysis appears to be useful for tracking functional traits in molars, particularly in tracking differences between folivorous and insectivorous species.     

Shape and size variation on the wing of <Emphasis Type="Italic">Drosophila mediopunctata</Emphasis>: influence of chromosome inversions and genotype-environment interaction

The second chromosome of Drosophila mediopunctata is highly polymorphic for inversions. Previous work reported a significant interaction between these inversions and collecting date on wing size, suggesting the presence of genotype-environment interaction. We performed experiments in the laboratory to test for the joint effects of temperature and chromosome inversions on size and shape of the wing in D. mediopunctata. Size was measured as the centroid size, and shape was analyzed using the generalized least squares Procrustes superimposition followed by discriminant analysis and canonical variates analysis of partial warps and uniform components scores. Our findings show that wing size and shape are influenced by temperature, sex, and karyotype. We also found evidence suggestive of an interaction between the effects of karyotype and temperature on wing shape, indicating the existence of genotype-environment interaction for this trait in D. mediopunctata. In addition, the association between wing size and chromosome inversions is in agreement with previous results indicating that these inversions might be accumulating alleles adapted to different temperatures. However, no significant interaction between temperature and karyotype for size was found--in spite of the significant presence of temperature-genotype (cross) interaction. We suggest that other ecological factors--such as larval crowding--or seasonal variation of genetic content within inversions may explain the previous results.     

Variation in scale shape among alternative sympatric phenotypes of Arctic charr Salvelinus alpinus from two lakes in Scotland

Landmark‐based geometric morphometric analysis was used to detect differences in scale shape between ecologically distinct phenotypes of Arctic charr Salvelinus alpinus coexisting in the same lake. Relative warp analysis and standard multivariate analyses of the partial warps, obtained after a Procrustes superimposition, showed that scale landmarks were efficient in discriminating among two closely related alternative phenotypes within each of the two lakes. In Loch Tay, S. alpinus exhibited a bimodal body size‐frequency distribution among sexually mature fish, whereas in Loch Awe, S. alpinus are unimodal in body size but segregated into two distinct spawning phenotypes. In both lakes, alternative phenotypes showed significant differences in foraging ecology, habitat use and life history. It is probable that differences in scale shape reflect differences in ecology of these forms.     

Advances in Geometric Morphometrics

Geometric morphometrics is the statistical analysis of form based on Cartesian landmark coordinates. After separating shape from overall size, position, and orientation of the landmark configurations, the resulting Procrustes shape coordinates can be used for statistical analysis. Kendall shape space, the mathematical space induced by the shape coordinates, is a metric space that can be approximated locally by a Euclidean tangent space. Thus, notions of distance (similarity) between shapes or of the length and direction of developmental and evolutionary trajectories can be meaningfully assessed in this space. Results of statistical techniques that preserve these convenient properties—such as principal component analysis, multivariate regression, or partial least squares analysis—can be visualized as actual shapes or shape deformations. The Procrustes distance between a shape and its relabeled reflection is a measure of bilateral asymmetry. Shape space can be extended to form space by augmenting the shape coordinates with the natural logarithm of Centroid Size, a measure of size in geometric morphometrics that is uncorrelated with shape for small isotropic landmark variation. The thin-plate spline interpolation function is the standard tool to compute deformation grids and 3D visualizations. It is also central to the estimation of missing landmarks and to the semilandmark algorithm, which permits to include outlines and surfaces in geometric morphometric analysis. The powerful visualization tools of geometric morphometrics and the typically large amount of shape variables give rise to a specific exploratory style of analysis, allowing the identification and quantification of previously unknown shape features.     

Using image analysis on the ventral colour pattern in Salamandrina perspicillata (Amphibia: Salamandridae) to discriminate among populations

The ventral colour pattern in Salamandrina perspicillata is characteristic of each individual and remains invariant throughout the salamanders' life. The present study aimed to determine, using statistical methods applied to quantitative image analysis, whether the coloration pattern is population-specific. The images of ventral colour pattern of 180 salamanders belonging to five populations were analysed. The images were previously warped by geometric morphometry. To our knowledge, this is the first study to use an approach based on geometric morphometrics to standardize ventral shapes. This technique is useful for eliminating form distortions. The results of an analysis of similarities recognized more coloration similarity among individuals of the same population than among individuals from different populations. Analysis by partial least squares correctly classified the 88.88% of individuals into the correct population. The similarities or differences among individuals of different populations are not related to the geographical distances. The results obtained showed that the coloration of the ventral side of the head of the salamanders can be used for discriminating among populations.  © 2009 The Linnean Society of London, Biological Journal of the Linnean Society , 2009, 96 , 35–43.     

Evolution of the male genitalia: morphological variation of the aedeagi in a natural population of <Emphasis Type="Italic">Drosophila mediopunctata</Emphasis>

To investigate the size and shape of the aedeagus of Drosophila mediopunctata, we used basic statistics and geometric morphometrics. We estimated the level of phenotypic variation, natural and laboratory heritability as well as the phenotypic correlations between aedeagus and wing measures. The wing was used as an indicator for both body size and shape. Positive significant correlation was obtained for centroid size of aedeagus and wing for field parents and their offspring reared in the laboratory. Many positive significant phenotypic correlations were found among linear measures of both organs. The phenotypic correlations were few for aedeagus and wing shape. Coefficients of variation of the measures were on average larger in the aedeagus than in the wing for offspring reared in laboratory, but not for flies coming from the field. Significant “natural” heritabilities were found for five linear measures of the aedeagus and only one for the wing. Few significant heritabilities were found for aedeagus and wing shape, mostly ones concerning the uniform components. In an exploratory analysis, we found that inversion DS-PC0 is associated with both uniform and nonuniform components of shape, respectively, in the wing and aedeagus. Our results do not support the lock-and-key hypothesis for the male genitalia evolution, but cannot refute the sexual selection and pleiotropy hypotheses.     

Altitudinal genetic and morphometric variation among populations of Culex theileri Theobald (Diptera: Culicidae) from northeastern Turkey

Enviromental conditions, including such important climatic variables as temperature and precipitation, change with altitude; thus, elevation plays a significant role in determining population and community structure in a variety of organisms. Using single nucleotide polymorphisms (SNPs) and geometric morphometrics, nine populations of Culex theileri Theobald occurring in different ecological subregions at altitudes between 808-2,130 m in northeastern Turkey were compared. The wing size and shape data indicate that there are significant phenotypic differences among them, while Cx theileri populations are not genetically differentiated in the northeast part of Turkey. The size and shape variation analysis of wings showed that there is a positive correlation between wing (body) size/shape and altitude.     

Wing size and shape variation of Phlebotomus papatasi (Diptera: Psychodidae) populations from the south and north slopes of the Atlas Mountains in Morocco

The wing shape and size morphology of populations of the medically important phlebotomine sand fly, Phlebotomus papatasi, were examined in two endemic (south of the Atlas Mountains) and nonendemic (north of the Atlas Mountains) foci of cutaneous leishmaniasis by using geometric morphometrics in Morocco. Although it is present in all of Morocco, P. papatasi is the main vector of Leishmania major in only southern part of the Atlas Mountains. There are four major mountain ranges that serve as geographical barriers for species distribution in the study area and at least four gaps were recognized among these barriers. We found statistically significant differences in wing shape morphology between southern and northern populations. Analysis clearly recognized two main groups of populations on both sides of the mountains. The graphical depiction of Principal Component Analysis (PCA) and Canonical Variates Analysis (CVA) confirmed our morphometric study suggesting that the difference in wing morphology between the populations indicates that the population of P. papatasi shows phenotypic plasticity in the study area. According to centroid size analyses, which were used as measures of wing size differences among different sites, the north population of P. papatasi had relatively larger wings than the south population.     

The potential influence of morphology on the evolutionary divergence of an acoustic signal

The evolution of acoustic behaviour and that of the morphological traits mediating its production are often coupled. Lack of variation in the underlying morphology of signalling traits has the potential to constrain signal evolution. This relationship is particularly likely in field crickets, where males produce acoustic advertisement signals to attract females by stridulating with specialized structures on their forewings. In this study, we characterize the size and geometric shape of the forewings of males from six allopatric populations of the black field cricket (Teleogryllus commodus) known to have divergent advertisement calls. We sample from each of these populations using both wild‐caught and common‐garden‐reared cohorts, allowing us to test for multivariate relationships between wing morphology and call structure. We show that the allometry of shape has diverged across populations. However, there was a surprisingly small amount of covariation between wing shape and call structure within populations. Given the importance of male size for sexual selection in crickets, the divergence we observe among populations has the potential to influence the evolution of advertisement calls in this species.     

Morphometric analysis of populations of Centris aenea Lepeletier (Hymenoptera: Apidae) from Northeastern Brazil

Centris aenea Lepeletier is a solitary bee that has raised interest in management to pollinate crops, such as acerola, Malpighia emarginata. This study investigated the level of morphometric variability among populations of C. aenea from Northeastern Brazil. Traditional and geometric morphometric analyses were used. Head length, leg length, wing length, and wing shape were measured in samples (5-10 females) from eight localities. We did not find statistically significant differences among the populations (P > 0.01). The partial wing warps were similar in the populations and indicated that the bees were not morphometrically different. Our results suggest that C. aenea shows low population morphometric variability and highlight the need for further investigations on population variation in this species, preferably including populations sampled at the extremes of their geographic distribution. Significant insight into the population variation of C. aenea will probably require the use of molecular markers to allow a comparative approach between morphometric variability and genetic variability.     

How does selfing affect the genetic variance of quantitative traits? An updated meta‐analysis on empirical results in angiosperm species

Most theoretical works predict that selfing should reduce the level of additive genetic variance available for quantitative traits within natural populations. Despite a growing number of quantitative genetic studies undertaken during the last two decades, this prediction is still not well supported empirically. To resolve this issue and confirm or reject theoretical predictions, we reviewed quantitative trait heritability estimates from natural plant populations with different rates of self‐fertilization and carried out a meta‐analysis. In accordance with models of polygenic traits under stabilizing selection, we found that the fraction of additive genetic variance is negatively correlated with the selfing rate. Although the mating system explains a moderate fraction of the variance, the mean reduction of narrow‐sense heritability values between strictly allogamous and predominantly selfing populations is strong, around 60%. Because some nonadditive components of genetic variance become selectable under inbreeding, we determine whether self‐fertilization affects the relative contribution of these components to genetic variance by comparing narrow‐sense heritability estimates from outcrossing populations with broad‐sense heritability estimated in autogamous populations. Results suggest that these nonadditive components of variance may restore some genetic variance in predominantly selfing populations; it remains, however, uncertain how these nonadditive components will contribute to adaptation.     

大蹄蝠头骨形态地理变化

本文采用几何形态测量法对中国大蹄蝠9个不同地理种群头骨形态变化进行研究。结果表明,不同地理种群的头骨大小及形状存在显著差异,其中云南思茅种群与海南陵水种群差异最大。回归分析表明头骨形态的地理变化与气候因素相关。随着年均温度、年均湿度的升高以及年均降水量的增多,大蹄蝠头骨变小,上颌、齿、咬肌附着部分以及耳蜗部分的形状发生变化。此外,头骨大小与海拔高度呈正相关,头骨形状变化与纬度显著相关。本研究表明对栖息地生态条件的适应是中国大蹄蝠头骨形态地理变化的重要原因。     

Body shape and size divergence among populations of Poecilia vivipara in coastal lagoons of south-eastern Brazil

Geometric shape analyses were used to study body shape and size variation among populations of the livebearing fish Poecilia vivipara inhabiting the recently formed coastal lagoons of Grussaí and Iquipari in Northern Rio de Janeiro State, Brazil. The largest components of morphological variation among females were between different habitats in the same lagoon, whereas for males there were larger differences between lagoons than between habitats. The shape differences were mostly localized in the head region and midbody, which indicated different patterns of locomotion and foraging behaviour optimized for the habitat experienced by each population. The pattern of size variation was similar to that of size-independent shape variation.