Evolutionary Quantitative Genetics Research Articles

Heritability within groups is uninformative about differences among groups: Cases from behavioral, evolutionary, and statistical genetics

Without the ability to control or randomize environments (or genotypes), it is difficult to determine the degree to which observed phenotypic differences between two groups of individuals are due to genetic vs. environmental differences. However, some have suggested that these concerns may be limited to pathological cases, and methods have appeared that seem to give-directly or indirectly-some support to claims that aggregate heritable variation within groups can be related to heritable variation among groups. We consider three families of approaches: the "between-group heritability" sometimes invoked in behavior genetics, the statistic [Formula: see text] used in empirical work in evolutionary quantitative genetics, and methods based on variation in ancestry in an admixed population, used in anthropological and statistical genetics. We take up these examples to show mathematically that information on within-group genetic and phenotypic information in the aggregate cannot separate among-group differences into genetic and environmental components, and we provide simulation results that support our claims. We discuss these results in terms of the long-running debate on this topic.

The missing fraction problem as an episodes of selection problem.

In evolutionary quantitative genetics, the missing fraction problem refers to a specific kind of bias in parameters estimated later in life that occurs when nonrandom subsets of phenotypes are missing from the population due to prior viability selection on correlated traits. The missing fraction problem thus arises when the following hold: (a) viability selection and (b) correlation between later-life traits and traits important for early-life survival. Although it is plausible that these conditions are widespread in wild populations, this problem has received little empirical attention. This may be natural: the problem could appear intractable, given that it is impossible to measure phenotypes of individuals that have previously died. However, it is not impossible to correctly measure lifetime selection, or correctly predict evolutionary trajectories, of later-life traits in the presence of the missing fraction. Two basic strategies are available. First, given phenotypic data on selected early life traits, well established but underused episodes of selection theory can yield correct values of evolutionary parameters throughout life. Second, when traits subjected to early-life viability selection are not known and/or measured, it is possible to use the genetic association of later-life traits with early-life viability to correctly infer important information about the consequences of prior viability selection for later-life traits. By carefully reviewing the basic nature of the missing fraction problem, and describing the tractable solutions to the problem, we hope that future studies will be able to be better designed to cope with the (likely pervasive) consequences of early-life viability selection.

Morphology, evolution, and the whole organism imperative: Why evolutionary questions need multi-trait evolutionary quantitative genetics.

Since Washburn's New Physical Anthropology, researchers have sought to understand the complexities of morphological evolution among anatomical regions in human and non-human primates. Researchers continue, however, to preferentially use comparative and functional approaches to examine complex traits, but these methods cannot address questions about evolutionary process and often conflate function with fitness. Moreover, researchers also tend to examine anatomical elements in isolation, which implicitly assumes independent evolution among different body regions. In this paper, we argue that questions asked in primate evolution are best examined using multiple anatomical regions subjected to model-bound methods built from an understanding of evolutionary quantitative genetics. A nascent but expanding number of studies over the last two decades use this approach, examining morphological integration, evolvability, and selection modeling. To help readers learn how to use these methods, we review fundamentals of evolutionary processes within a quantitative genetic framework, explore the importance of neutral evolutionary theory, and explain the basics of evolutionary quantitative genetics, namely the calculation of evolutionary potential for multiple traits in response to selection. Leveraging these methods, we demonstrate their use to understand non-independence in possible evolutionary responses across the limbs, limb girdles, and basicranium of humans. Our results show that model-bound quantitative genetic methods can reveal unexpected genetic covariances among traits that create a novel but measurable understanding of evolutionary complexity among multiple traits. We advocate for evolutionary quantitative genetic methods to be a standard whenever appropriate to keep studies of primate morphological evolution relevant for the next seventy years and beyond.

Evolution of hormone-phenotype couplings and hormone-genome interactions

When selection favors a new relationship between a cue and a hormonally mediated response, adaptation can proceed by altering the hormonal signal that is produced or by altering the phenotypic response to the hormonal signal. The field of evolutionary endocrinology has made considerable progress toward understanding the evolution of hormonal signals, but we know much less about the evolution of hormone-phenotype couplings, particularly at the hormone-genome interface. We briefly review and classify the mechanisms through which these hormone-phenotype couplings likely evolve, using androgens and their receptors and genomic response elements to illustrate our view. We then present two empirical studies of hormone-phenotype couplings, one rooted in evolutionary quantitative genetics and another in comparative transcriptomics, each focused on the regulation of sexually dimorphic phenotypes by testosterone (T) in the brown anole lizard (Anolis sagrei). First, we illustrate the potential for hormone-phenotype couplings to evolve by showing that coloration of the dewlap (an ornament used in behavioral displays) exhibits significant heritability in its responsiveness to T, implying that anoles harbor genetic variance in the architecture of hormonal pleiotropy. Second, we combine T manipulations with analyses of the liver transcriptome to ask whether and how statistical methods for characterizing modules of co-expressed genes and in silico techniques for identifying androgen response elements (AREs) can improve our understanding of hormone-genome interactions. We conclude by emphasizing important avenues for future work at the hormone-genome interface, particularly those conducted in a comparative evolutionary framework.

Conceptualizing the evolutionary quantitative genetics of phenological life-history events: Breeding time as a plastic threshold trait

Successfully predicting adaptive phenotypic responses to environmental changes, and predicting resulting population outcomes, requires that additive genetic (co)variances underlying microevolutionary and plastic responses of key traits are adequately estimated on appropriate quantitative scales. Such estimation in turn requires that focal traits, and their underlying quantitative genetic architectures, are appropriately conceptualized. Here, we highlight that directly analyzing observed phenotypes as continuously distributed quantitative traits can potentially generate biased and misleading estimates of additive genetic variances and individual‐by‐environment and gene‐by‐environment interactions, and hence of forms of plasticity and genetic constraints, if in fact the underlying biology is best conceptualized as an environmentally sensitive threshold trait. We illustrate this scenario with particular reference to the key phenological trait of seasonal breeding date, which has become a focus for quantifying joint microevolutionary, plastic, and population responses to environmental change, but has also become a focus for highlighting that predicted adaptive outcomes are not always observed. Specifically, we use simple simulations to illustrate how potentially misleading inferences on magnitudes of additive genetic variance, and forms of environmental interactions, can arise by directly analyzing observed breeding dates if the transition to breeding in fact represents a threshold trait with latent‐scale plasticity. We summarize how existing and new datasets could be (re)analyzed, potentially providing new insights into how critical microevolutionary and plastic phenological responses to environmental variation and change can arise and be constrained.

Evolvability: A Quantitative-Genetics Perspective

The concept of evolvability emerged in the early 1990s and soon became fashionable as a label for different streams of research in evolutionary biology. In evolutionary quantitative genetics, evolvability is defined as the ability of a population to respond to directional selection. This differs from other fields by treating evolvability as a property of populations rather than organisms or lineages and in being focused on quantification and short-term prediction rather than on macroevolution. While the term evolvability is new to quantitative genetics, many of the associated ideas and research questions have been with the field from its inception as biometry. Recent research on evolvability is more than a relabeling of old questions, however. New operational measures of evolvability have opened possibilities for understanding adaptation to rapid environmental change, assessing genetic constraints, and linking micro- and macroevolution.

Integrating genomics and multivariate evolutionary quantitative genetics: a case study of constraints on sexual selection in Drosophila serrata.

In evolutionary quantitative genetics, the genetic variance-covariance matrix, G, and the vector of directional selection gradients, β, are key parameters for predicting multivariate selection responses and genetic constraints. Historically, investigations of G and β have not overlapped with those dissecting the genetic basis of quantitative traits. Thus, it remains unknown whether these parameters reflect pleiotropic effects at individual loci. Here, we integrate multivariate genome-wide association study (GWAS) with G and β estimation in a well-studied system of multivariate constraint: sexual selection on male cuticular hydrocarbons (CHCs) in Drosophila serrata. In a panel of wild-derived re-sequenced lines, we augment genome-based restricted maximum likelihood to estimate G alongside multivariate single nucleotide polymorphism (SNP) effects, detecting 532 significant associations from 1 652 276 SNPs. Constraint was evident, with β lying in a direction of G with low evolvability. Interestingly, minor frequency alleles typically increased male CHC-attractiveness suggesting opposing natural selection on β. SNP effects were significantly misaligned with the major eigenvector of G, gmax, but well aligned to the second and third eigenvectors g2 and g3. We discuss potential factors leading to these varied results including multivariate stabilizing selection and mutational bias. Our framework may be useful as researchers increasingly access genomic methods to study multivariate selection responses in wild populations.

Common evolutionary patterns in the human nasal region across a worldwide sample.

Variation in the external nasal region among human populations has long been proposed in the literature to reflect adaptations to facilitate thermoregulation, air conditioning, and moisture retention in local climates and environments. More specifically, adaptations in populations living in colder climates have often been assumed due to correlational relationships found between variation in the nasal region and climatic variables. Here, we test this hypothesis by applying a quantitative genetics approach based on the Lande model to assess whether variation in the nasal region can be explained by random neutral processes (e.g., genetic drift) or if non-random forces (i.e., adaptation) have contributed significantly to its diversity. A mixed-sex sample representing 28 population groups from Howells' craniometric dataset were analyzed (n=2504). Twenty standard measurements were chosen to reflect the external skeletal morphology of the nasal region. We apply statistical tests developed from evolutionary quantitative genetics theory to analyze patterns of within- and between-population divergence under a null hypothesis of genetic drift. This study finds a rejection of genetic drift in all analyses, across tests that involve all 28 populations, exclusively cold-climate populations, and with cold-climate populations excluded, indicating that non-random evolutionary forces have contributed significantly to variation in the nasal region overall. These results show that nasal region adaptation is not exclusive to cold-climate populations, which have often been implicated in the literature to drive nasal variation, instead suggesting that the propensity for adaptation in the nasal region is shared among all human populations.

Complex pleiotropic genetic architecture of evolved heat stress and oxidative stress resistance in the nematode Caenorhabditis remanei.

The adaptation of complex organisms to changing environments has been a central question in evolutionary quantitative genetics since its inception. The structure of the genotype–phenotype maps is critical because pleiotropic effects can generate widespread correlated responses to selection and potentially restrict the extent of evolutionary change. In this study, we use experimental evolution to dissect the genetic architecture of natural variation for acute heat stress and oxidative stress response in the nematode Caenorhabiditis remanei. Previous work in the classic model nematode Caenorhabiditis elegans has found that abiotic stress response is controlled by a handful of genes of major effect and that mutations in any one of these genes can have widespread pleiotropic effects on multiple stress response traits. Here, we find that acute heat stress response and acute oxidative response in C. remanei are polygenic, complex traits, with hundreds of genomic regions responding to selection. In contrast to expectation from mutation studies, we find that evolved acute heat stress and acute oxidative stress response for the most part display independent genetic bases. This lack of correlation is reflected at the levels of phenotype, gene expression, and in the genomic response to selection. Thus, while these findings support the general view that rapid adaptation can be generated by changes at hundreds to thousands of sites in the genome, the architecture of segregating variation is likely to be determined by the pleiotropic structure of the underlying genetic networks.

A multivariate view of parallel evolution

A growing number of empirical studies have quantified the degree to which evolution is geometrically parallel by estimating and interpreting pairwise angles between multiple replicate lineages' evolutionary change vectors in multivariate trait space. Similar comparisons, of distance in trait space, are used to assess the degree of convergence. These approaches amount to element-by-element interpretation of distance matrices, typically testing for differences among replicate evolutionary vectors, compared to a null hypothesis of perfect parallelism. We suggest a complimentary set of approaches, co-opted from evolutionary quantitative genetics, involving eigen analysis and comparison of among-lineage covariance matrices. Such approaches allow one to identify multiple major axes of evolutionary change (e.g., alternative adaptive solutions), and also allow for the definition of biologically tenable null hypotheses, such as drift, against which empirical patterns can be tested. Reanalysis of a dataset of multivariate evolution across a replicated lake/stream gradient in threespine stickleback reveals that most of the variation in the direction of evolutionary change can be captured in just a few dimensions, indicating a greater extent of parallelism than previously appreciated. We suggest that applying such multivariate approaches may often be necessary to fully understand the extent and form of parallel and convergent evolution.

An evolutionary quantitative genetics model for phenotypic (co)variances under limited dispersal, with an application to socially synergistic traits.

Darwinian evolution consists of the gradual transformation of heritable traits due to natural selection and the input of random variation by mutation. Here, we use a quantitative genetics approach to investigate the coevolution of multiple quantitative traits under selection, mutation, and limited dispersal. We track the dynamics of trait means and of variance-covariances between traits that experience frequency-dependent selection. Assuming a multivariate-normal trait distribution, we recover classical dynamics of quantitative genetics, as well as stability and evolutionary branching conditions of invasion analyses, except that due to limited dispersal, selection depends on indirect fitness effects and relatedness. In particular, correlational selection that associates different traits within-individuals depends on the fitness effects of such associations between-individuals. We find that these kin selection effects can be as relevant as pleiotropy for the evolution of correlation between traits. We illustrate this with an example of the coevolution of two social traits whose association within-individuals is costly but synergistically beneficial between-individuals. As dispersal becomes limited and relatedness increases, associations between-traits between-individuals become increasingly targeted by correlational selection. Consequently, the trait distribution goes from being bimodal with a negative correlation under panmixia to unimodal with a positive correlation under limiteddispersal.

Alterations in Life-History Associated With Non-target-site Herbicide Resistance in Alopecurus myosuroides.

The evolution of resistance to herbicides is a classic example of rapid contemporary adaptation in the face of a novel environmental stress. Evolutionary theory predicts that selection for resistance will be accompanied by fitness trade-offs in environments where the stress is absent. Alopecurus myosuroides, an autumn-germinating grass weed of cereal crops in North-West Europe, has evolved resistance to seven herbicide modes-of-action, making this an ideal species to examine the presence and magnitudes of such fitness costs. Here, we use two contrasting A. myosuroides phenotypes derived from a common genetic background, one with enhanced metabolism resistance to a commercial formulation of the sulfonylurea (ALS) actives mesosulfuron and iodosulfuron, and the other with susceptibility to these actives (S). Comparisons of plant establishment, growth, and reproductive potential were made under conditions of intraspecific competition, interspecific competition with wheat, and over a gradient of nitrogen deprivation. Herbicide dose response assays confirmed that the two lines had contrasting resistance phenotypes, with a 20-fold difference in resistance between them. Pleiotropic effects of resistance were observed during plant development, with R plants having a greater intraspecific competitive effect and longer tiller lengths than S plants during vegetative growth, but with S plants allocating proportionally more biomass to reproductive tissues during flowering. Direct evidence of a reproductive cost of resistance was evident in the nitrogen deprivation experiment with R plants producing 27% fewer seed heads per plant, and a corresponding 23% reduction in total seed head length. However, these direct effects of resistance on fecundity were not consistent across experiments. Our results demonstrate that a resistance phenotype based on enhanced herbicide metabolism has pleiotropic impacts on plant growth, development and resource partitioning but does not support the hypothesis that resistance is associated with a consistent reproductive fitness cost in this species. Given the continued difficulties associated with unequivocally detecting costs of herbicide resistance, we advocate future studies that adopt classical evolutionary quantitative genetics approaches to determine genetic correlations between resistance and fitness-related plant life history traits.

AGA2017: Evolutionary Quantitative Genetics in the Wild

AGA2017: Evolutionary Quantitative Genetics in the Wild

Evolutionary quantitative genetics of juvenile body size in a population of feral horses reveals sexually antagonistic selection

Inter-individual variation in juvenile body size can have important consequences for individual fitness, population dynamics, and adaptive evolution. In wild vertebrate populations, larger juvenile size is usually expected to be selected for. However, understanding how such selection may translate into adaptive evolution requires an understanding of the genetic underpinnings of early development and the factors modulating selection. In this study, we characterised the genetic basis of and selection pressures acting upon juvenile body size in a large insular population of feral horses on Sable Island, Canada, to gain insights into the evolution of juvenile body size in wild vertebrate populations. We used pedigree-based quantitative genetic ‘animal models’ to quantify the sources of phenotypic variation in withers-knee length, and assessed the influence of maternal age, sex, and temporal (birth year) and spatial environmental heterogeneity in modulating overwinter survival selection. We found that withers-knee length is moderately heritable and that there was a significant positive genetic correlation between males and females. There was no indication of directional selection in a pooled-sex analysis, but we did find evidence for significant sexually antagonistic selection, with a tendency for smaller body size to be favoured in males and larger body size to be favoured in females. These results suggest that juvenile body size has the potential to evolve in this population, and that selection on juvenile size may play an important role in modulating sex-specific contributions to population dynamics. However, our results also suggest that there is unlikely to be evolutionary change in the mean body size of Sable Island foals.

Evolutionary Quantitative Genetics of Genomic Imprinting.

Genomic imprinting shapes the genotype-phenotype relationship by creating an asymmetry between the influences of paternally and maternally inherited gene copies. Consequently, imprinting can impact heritable and nonheritable variation, resemblance of relatives, and evolutionary dynamics. Although previous analyses have identified some of the quantitative genetic consequences of imprinting, we lack a framework that cleanly separates the influence of imprinting from other components of variation, particularly dominance. Here we apply a simple orthogonal genetic model to evaluate the roles of genetic (additive and dominance) and epigenetic (imprinting) effects. Imprinting increases the resemblance of relatives who share the expressed allele, and therefore increases variance among families of full or half-siblings. However, only part of this increased variance is heritable and contributes to selection responses. When selection is within, or among, families sharing only a single parent (half-siblings), which is common in selective breeding programs, imprinting can alter overall responses. Selection is more efficient when it acts among families sharing the expressed parent, or within families sharing the parent with lower expression. Imprinting also affects responses to sex-specific selection. When selection is on the sex whose gene copy has lower expression, the response is diminished or delayed the next generation, although the long-term response is unaffected. Our findings have significant implications for understanding patterns of variation, interpretation of short-term selection responses, and the efficacy of selective breeding programs, demonstrating the importance of considering the independent influence of genomic imprinting in quantitative genetics.

INTEGRATING MACROECOLOGY AND QUANTITATIVE GENETICS: EVOLUTION OF BODY SIZE AND BRAIN SIZE UNDER ISLAND RULE

Island rule proposes that a negative correlation between ancestral body size in continents and the descendent body size in islands exists, and this pattern have been widely studied in a macroecological and comparative perspectives. However, there are doubts about what mechanisms underlie body size evolution in islands. Here we review methodological and theoretical framework on evolutionary quantitative genetics, showing their application on body and brain size evolution in islands, using Hippopotamus dwarfism as example. In our analyses we started by generating 10,000 combinations of model parameters (generation time, effective size and heritability) and tested by Mutation-Drift Equilibrium model if body size dwarfism is a consequence of neutral drift or directional selection. We found that 99.9 % of simulations rejected neutral model. Then, we estimated the strength of directional selection necessary to differentiate the island species and found that a relatively low proportion of population (0.01 - 0.2%) should be selectively killed to decrease body size. Our results also showed that one unit decrease in body size would increase, on average, fitness by 4% in each generation, so directional selection is a plausible explanation to island rule. Finally, we also simulated the evolution of brain size of dwarfed Hippopotamus as a consequence of body size evolution alone. Our estimates of Expected Brain Size (EBS = 484 A 64 cc) were larger than the observed brain size (equal to 380 cc), which suggests the need to estimate directional selection acting on brain size independently of body size evolution. This supports the overall idea that brain size reduction is advantageous in island environments under a scenario reduction in resources, due to the high energetic budget of brain. Our analyses using evolutionary quantitative genetic support that Island Rule as a parsimonious adaptive explanation for the reduction in brain and body sizes and illustrates how to couple evolutionary analyses at population level to better understand macroecological patterns.

Maternal-by-environment but not genotype-by-environment interactions in a fish without parental care.

The impact of environmental conditions on the expression of genetic variance and on maternal effects variance remains an important question in evolutionary quantitative genetics. We investigate here the effects of early environment on variation in seven adult life history, morphological, and secondary sexual traits (including sperm characteristics) in a viviparous poeciliid fish, the mosquitofish Gambusia holbrooki. Specifically, we manipulated food availability during early development and then assessed additive genetic and maternal effects contributions to the overall phenotypic variance in adults. We found higher heritability for female than male traits, but maternal effects variance for traits in both sexes. An interaction between maternal effects variance and rearing environment affected two adult traits (female age at maturity and male size at maturity), but there was no evidence of trade-offs in maternal effects across environments. Our results illustrate (i) the potential for pre-natal maternal effects to interact with offspring environment during development, potentially affecting traits through to adulthood and (ii) that genotype-by-environment interactions might be overestimated if maternal-by-environment interactions are not accounted for, similar to heritability being overestimated if maternal effects are ignored. We also discuss the potential for dominance genetic variance to contribute to the estimate of maternal effects variance.

Integration and coevolution of the mammalian skeleton in “real time”: the case of the Longshanks mouse

Since the publication of Olson and Miller's seminal book “Morphological Integration” in 1958, there have been over 200 studies on integration, modularity and evolvability of the mammalian skeletal and dental systems. These studies have yielded fundamental insights into the role of genetic, developmental and functional constraints on the evolutionary history, and evolutionary potential, of complex skeletal traits in diverse mammalian lineages. Yet integration and evolvability studies in skeletal systems suffer from two important limitations. First, they are by nature post‐hoc, i.e., they rely on observed patterns of covariation among traits to reconstruct the (often deep) history of (co)evolution in skeletal traits, and/or to identify the genetic, developmental and functional sources of covariation that have influenced this history. Second, and related, evolvability studies are theoretical, relying on the multivariate breeder's equation to predict the potential response of more or less integrated skeletal phenotypes to selection. Since 2010, my lab has been selectively breeding mice for increases in tibia length relative to body mass. This long‐term selection experiment provides an opportunity to validate empirically how the magnitude and pattern of covariation among skeletal traits (i.e., integration) impacts “real time” evolutionary change in the target of selection, as well as in genetically and developmentally correlated traits. Here, I use an evolutionary quantitative genetics framework and a large multi‐generational dataset of full body micro‐CT scans of the selectively bred mice (Longshanks) and random‐bred mice to: (1) quantify correlated evolution of skeletal traits in the Longshanks postcranium and cranium, and (2) determine how the magnitude and pattern of integration across the skeleton has evolved in response to strong selection on a single trait. Results show that while tibia length has changed the most, other skeletal traits (e.g. tibia cross‐sectional shape, other fore‐ and hind limb bone lengths) have also responded to selection, though to a lesser extent (i.e., allometrically). Interestingly, skull shape in Longshanks has changed significantly. The types of changes observed over ontogeny suggest the involvement of both local and systemic factors underlying mechanisms of endochondral ossification in the limbs and cranial base. Finally, the magnitude of covariation among postcranial skeletal traits increased over generations, which suggests that unidirectional selection on a single skeletal trait in Longshanks has actually reduced the evolvability of its skeleton overall. This study in “real time” vertebrate evolution thus validates and complements the insights gleaned from classical, yet largely theoretical, integration, modularity and evolvability in the mammalian skeleton.Support or Funding InformationThis work was supported by NSERC Discovery Grant 4181932, and by the Faculty of Veterinary Medicine at the University of Calgary.

The Relative Contributions of the X Chromosome and Autosomes to Local Adaptation.

Models of sex chromosome and autosome evolution yield key predictions about the genomic basis of adaptive divergence, and such models have been important in guiding empirical research in comparative genomics and studies of speciation. In addition to the adaptive differentiation that occurs between species over time, selection also favors genetic divergence across geographic space, with subpopulations of single species evolving conspicuous differences in traits involved in adaptation to local environmental conditions. The potential contribution of sex chromosomes (the X or Z) to local adaptation remains unclear, as we currently lack theory that directly links spatial variation in selection to local adaptation of X-linked and autosomal genes. Here, we develop population genetic models that explicitly consider the effects of genetic dominance, effective population size, and sex-specific migration and selection on the relative contributions of X-linked and autosomal genes to local adaptation. We show that X-linked genes should nearly always disproportionately contribute to local adaptation in the presence of gene flow. We also show that considerations of dominance and effective population size-which play pivotal roles in the theory of faster-X adaptation between species-have surprisingly little influence on the relative contribution of the X chromosome to local adaptation. Instead, sex-biased migration is the primary mediator of the strength of spatial large-X effects. Our results yield novel predictions about the role of sex chromosomes in local adaptation. We outline empirical approaches in evolutionary quantitative genetics and genomics that could build upon this new theory.

EvolQG - An R package for evolutionary quantitative genetics.

We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable and there is evidence the phenotypic matrix is sufficiently similar to the genetic matrix. Given this mathematical representation of available variation, the \textbf{EvolQG} package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification.