A phylogenetic comparative method for evaluating trait coevolution across two phylogenies for sets of interacting species

Evaluating trait correlations across species within a lineage via phylogenetic regression is fundamental to comparative evolutionary biology, but when traits of interest are derived from two sets of lineages that coevolve with one another, methods for evaluating such patterns in a dual‐phylogenetic context remain underdeveloped. Here, we extend multivariate permutation‐based phylogenetic regression to evaluate trait correlations in two sets of interacting species while accounting for their respective phylogenies. This extension is appropriate for both univariate and multivariate response data, and may use one or more independent variables, including environmental covariates. Imperfect correspondence between species in the interacting lineages can also be accommodated, such as when species in one lineage associate with multiple species in the other, or when there are unmatched taxa in one or both lineages. For both univariate and multivariate data, the method displays appropriate type I error, and statistical power increases with the strength of the trait covariation and the number of species in the phylogeny. These properties are retained even when there is not a 1:1 correspondence between lineages. Finally, we demonstrate the approach by evaluating the evolutionary correlation between traits in fig species and traits in their agaonid wasp pollinators. R computer code is provided.     

Phylogenetic ANOVA: Group‐clade aggregation,biological challenges,and a refined permutation procedure

Phylogenetic regression is frequently used in macroevolutionary studies, and its statistical properties have been thoroughly investigated. By contrast, phylogenetic ANOVA has received relatively less attention, and the conditions leading to incorrect statistical and biological inferences when comparing multivariate phenotypes among groups remain underexplored. Here, we propose a refined method of randomizing residuals in a permutation procedure (RRPP) for evaluating phenotypic differences among groups while conditioning the data on the phylogeny. We show that RRPP displays appropriate statistical properties for both phylogenetic ANOVA and regression models, and for univariate and multivariate datasets. For ANOVA, we find that RRPP exhibits higher statistical power than methods utilizing phylogenetic simulation. Additionally, we investigate how group dispersion across the phylogeny affects inferences, and reveal that highly aggregated groups generate strong and significant correlations with the phylogeny, which reduce statistical power and subsequently affect biological interpretations. We discuss the broader implications of this phylogenetic group aggregation, and its relation to challenges encountered with other comparative methods where one or a few transitions in discrete traits are observed on the phylogeny. Finally, we recommend that phylogenetic comparative studies of continuous trait data use RRPP for assessing the significance of indicator variables as sources of trait variation.     

Assessing Trait Covariation and Morphological Integration on Phylogenies Using Evolutionary Covariance Matrices

Morphological integration describes the degree to which sets of organismal traits covary with one another. Morphological covariation may be evaluated at various levels of biological organization, but when characterizing such patterns across species at the macroevolutionary level, phylogeny must be taken into account. We outline an analytical procedure based on the evolutionary covariance matrix that allows species-level patterns of morphological integration among structures defined by sets of traits to be evaluated while accounting for the phylogenetic relationships among taxa, providing a flexible and robust complement to related phylogenetic independent contrasts based approaches. Using computer simulations under a Brownian motion model we show that statistical tests based on the approach display appropriate Type I error rates and high statistical power for detecting known levels of integration, and these trends remain consistent for simulations using different numbers of species, and for simulations that differ in the number of trait dimensions. Thus, our procedure provides a useful means of testing hypotheses of morphological integration in a phylogenetic context. We illustrate the utility of this approach by evaluating evolutionary patterns of morphological integration in head shape for a lineage of Plethodon salamanders, and find significant integration between cranial shape and mandible shape. Finally, computer code written in R for implementing the procedure is provided.     

Evolutionary Models and Phylogenetic Signal Assessment via Mantel Test

Phylogenetically closely related species tend to be more similar to each other than to more distantly related ones, a pattern called phylogenetic signal. Appropriate tests to evaluate the association between phylogenetic relatedness and trait variation among species are employed in a myriad of eco-evolutionary studies. However, most tests available to date are only suitable for datasets describing continuous traits, and are most often applicable only for single trait analysis. The Mantel test is a useful method to measure phylogenetic signal for multiple (continuous, binary and/or categorical) traits. However, the classical Mantel test does not incorporate any evolutionary model (EM) in the analysis. Here, we describe a new analytical procedure, which incorporates explicitly an evolutionary model in the standard Mantel test (EM-Mantel). We run numerical simulations to evaluate its statistical properties, under different combinations of species pool size, trait type and number. Our results showed that EM-Mantel test has appropriate type I error and acceptable power, which increases with the strength of phylogenetic signal and with species pool size but depended on trait type. EM-Mantel test is a good alternative for measuring phylogenetic signal in binary and categorical traits and for datasets with multiple traits.     

Phylogenetic structural equation modelling reveals no need for an ‘origin’ of the leaf economics spectrum

The leaf economics spectrum (LES) is a prominent ecophysiological paradigm that describes global variation in leaf physiology across plant ecological strategies using a handful of key traits. Nearly a decade ago, Shipley et al. (2006) used structural equation modelling to explore the causal functional relationships among LES traits that give rise to their strong global covariation. They concluded that an unmeasured trait drives LES covariation, sparking efforts to identify the latent physiological trait underlying the ‘origin’ of the LES. Here, we use newly developed phylogenetic structural equation modelling approaches to reassess these conclusions using both global LES data as well as data collected across scales in the genus Helianthus. For global LES data, accounting for phylogenetic non‐independence indicates that no additional unmeasured traits are required to explain LES covariation. Across datasets in Helianthus, trait relationships are highly variable, indicating that global‐scale models may poorly describe LES covariation at non‐global scales.     

Evolutionary transition between bee pollination and hummingbird pollination in Salvia: Comparing means,variances and covariances of corolla traits

Covariation among traits can modify the evolutionary trajectory of complex structures. This process is thought to operate at a microevolutionary scale, but its long‐term effects remain controversial because trait covariation can itself evolve. Flower morphology, and particularly floral trait (co)variation, has been envisioned as the product of pollinator‐mediated selection. Available evidence suggests that major changes in pollinator assemblages may affect the joint expression of floral traits and their phenotypic integration. We expect species within a monophyletic lineage sharing the same pollinator type will show not only similarity in trait means but also similar phenotypic variance‐covariance structures. Here, we tested this expectation using eighteen Salvia species pollinated either by bees or by hummingbirds. Our findings indicated a nonsignificant multivariate phylogenetic signal and a decoupling between means and variance‐covariance phenotypic matrices of floral traits during the evolution to hummingbird pollination. Mean trait value analyses revealed significant differences between bee‐ and hummingbird‐pollinated Salvia species although fewer differences were detected in the covariance structure between groups. Variance‐covariance matrices were much more similar among bee‐ than hummingbird‐pollinated species. This pattern is consistent with the expectation that, unlike hummingbirds, bees physically manipulate the flower, presumably exerting stronger selection pressures favouring morphological convergence among species. Overall, we conclude that the evolution of hummingbird pollination proceeded through different independent transitions. Thus, although the evolution of hummingbird pollination led to a new phenotypic optimum, the process involved the diversification of the covariance structure.     

A critique of life history approaches to human trait covariation

Covariation of life history traits across species may be organised on a ‘fast-slow’ continuum. A burgeoning literature in psychology and social science argues that trait covariation should be similarly organised across individuals within human populations. Here we describe why extrapolating from inter-species to inter-individual trait covariation is not generally appropriate. The process that genetically tailors species to their environments (i.e. Darwinian evolution) is fundamentally different from processes that tailor individuals to their environments (e.g. developmental plasticity), so their outcomes in terms of trait covariation need not be parallel or even related. We discuss why correlational selection, physical linkage, pleiotropy, and non-random mating do not substantively affect this claim in the context of complex human traits. We also discuss life history trade-offs and their relation to inter-individual trait covariation. We conclude that researchers should avoid hypotheses and explanations that assume trait covariation will correspond across and within species, unless they can mount a theoretically coherent argument to support this claim in the context of their research question.     

Integrating genomic and phenotypic data to evaluate alternative phylogenetic and species delimitation hypotheses in a recent evolutionary radiation of grasshoppers

Although resolving phylogenetic relationships and establishing species limits are primary goals of systematics, these tasks remain challenging at both conceptual and analytical levels. Here, we integrated genomic and phenotypic data and employed a comprehensive suite of coalescent‐based analyses to develop and evaluate competing phylogenetic and species delimitation hypotheses in a recent evolutionary radiation of grasshoppers (Chorthippus binotatus group) composed of two species and eight putative subspecies. To resolve the evolutionary relationships within this complex, we first evaluated alternative phylogenetic hypotheses arising from multiple schemes of genomic data processing and contrasted genetic‐based inferences with different sources of phenotypic information. Second, we examined the importance of number of loci, demographic priors, number and kind of phenotypic characters and sex‐based trait variation for developing alternative species delimitation hypotheses. The best‐supported topology was largely compatible with phenotypic data and showed the presence of two clades corresponding to the nominative species groups, one including three well‐resolved lineages and the other comprising a four‐lineage polytomy and a well‐differentiated sister taxon. Integrative species delimitation analyses indicated that the number of employed loci had little impact on the obtained inferences but revealed the higher power provided by an increasing number of phenotypic characters and the usefulness of assessing their phylogenetic information content and differences between sexes in among‐taxa trait variation. Overall, our study highlights the importance of integrating multiple sources of information to test competing phylogenetic hypotheses and elucidate the evolutionary history of species complexes representing early stages of divergence where conflicting inferences are more prone to appear.     

When Are Random Data Not Random,or Is the PTP Test Useful?

Recently, empirical evidence was presented that the permutation tail probability (PTP) test has extremely low discriminatory power when assessing character covariance in phylogenetic data based on bootstrap measures of confidence. Here we are concerned with the problem of using one statistical approach, especially when applied to empirical data, to judge the performance of another. Applying an appropriate statistical approach, we statistically demonstrated that the PTP test is extremely weak in detecting the absence of character covariation. In addition, we show that PTP is highly dependent on the number of terminals and the proportion of character states in phylogenetic matrices. In conclusion, we advocate the use of simulation studies when testing the performance of statistical tools applied to phylogenetic data.     

Structure and stability of genetic variance–covariance matrices: A Bayesian sparse factor analysis of transcriptional variation in the three‐spined stickleback

The genetic variance–covariance matrix ( G ) is a quantity of central importance in evolutionary biology due to its influence on the rate and direction of multivariate evolution. However, the predictive power of empirically estimated G ‐matrices is limited for two reasons. First, phenotypes are high‐dimensional, whereas traditional statistical methods are tuned to estimate and analyse low‐dimensional matrices. Second, the stability of G to environmental effects and over time remains poorly understood. Using Bayesian sparse factor analysis (BSFG) designed to estimate high‐dimensional G ‐matrices, we analysed levels variation and covariation in 10,527 expressed genes in a large (n = 563) half‐sib breeding design of three‐spined sticklebacks subject to two temperature treatments. We found significant differences in the structure of G between the treatments: heritabilities and evolvabilities were higher in the warm than in the low‐temperature treatment, suggesting more and faster opportunity to evolve in warm (stressful) conditions. Furthermore, comparison of G and its phenotypic equivalent P revealed the latter is a poor substitute of the former. Most strikingly, the results suggest that the expected impact of G on evolvability—as well as the similarity among G ‐matrices—may depend strongly on the number of traits included into analyses. In our results, the inclusion of only few traits in the analyses leads to underestimation in the differences between the G ‐matrices and their predicted impacts on evolution. While the results highlight the challenges involved in estimating G , they also illustrate that by enabling the estimation of large G ‐matrices, the BSFG method can improve predicted evolutionary responses to selection.     

Multiple trait multiple interval mapping of quantitative trait loci from inbred line crosses

ABSTRACT: BACKGROUND: Although many experiments have measurements on multiple traits, most studies performed the analysis of mapping of quantitative trait loci (QTL) for each trait separately using single trait analysis. Single trait analysis does not take advantage of possible genetic and environmental correlations between traits. In this paper, we propose a novel statistical method for multiple trait multiple interval mapping (MTMIM) of QTL for inbred line crosses. We also develop a novel score-based method for estimating genome-wide significance level of putative QTL effects suitable for the MTMIM model. The MTMIM method is implemented in the freely available and widely used Windows QTL Cartographer software. RESULTS: Throughout the paper, we provide compelling empirical evidences that: (1) the score-based threshold maintains proper type I error rate and tends to keep false discovery rate within an acceptable level; (2) the MTMIM method can deliver better parameter estimates and power than single trait multiple interval mapping method; (3) an analysis of Drosophila dataset illustrates how the MTMIM method can better extract information from datasets with measurements in multiple traits. CONCLUSIONS: The MTMIM method represents a convenient statistical framework to test hypotheses of pleiotropic QTL versus closely linked nonpleiotropic QTL, QTL by environment interaction, and to estimate the total genotypic variance-covariance matrix between traits and to decompose it in terms of QTL-specific variance-covariance matrices, therefore, providing more details on the genetic architecture of complex traits.     

Adaptations and history

The historical definition of adaptations has come into wide use as comparative biologists have applied methods of phylogenetic analysis to a variety of evolutionary problems. Here we point out a number of difficulties in applying historical methods to the study of adaptation, especially in cases where a trait has arisen but once. In particular, the potential complexity of the genetic correlations among phenotypic traits, performance variables and fitness makes inferring past patterns of selection from comparative data difficult. A given pattern of character distribution may support many alternative hypotheses of mechanism. While phylogenetic data are limited in their ability to reveal evolutionary mechanisms, they have always been an important source of adaptive hypotheses and will continue to be so.     

Using genetic networks and homology to understand the evolution of phenotypic traits

Homology can have different meanings for different kinds of biologists. A phylogenetic view holds that homology, defined by common ancestry, is rigorously identified through phylogenetic analysis. Such homologies are taxic homologies (=synapomorphies). A second interpretation, "biological homology" emphasizes common ancestry through the continuity of genetic information underlying phenotypic traits, and is favored by some developmental geneticists. A third kind of homology, deep homology, was recently defined as "the sharing of the genetic regulatory apparatus used to build morphologically and phylogenetically disparate features." Here we explain the commonality among these three versions of homology. We argue that biological homology, as evidenced by a conserved gene regulatory network giving a trait its "essential identity" (a Character Identity Network or "ChIN") must also be a taxic homology. In cases where a phenotypic trait has been modified over the course of evolution such that homology (taxic) is obscured (e.g. jaws are modified gill arches), a shared underlying ChIN provides evidence of this transformation. Deep homologies, where molecular and cellular components of a phenotypic trait precede the trait itself (are phylogenetically deep relative to the trait), are also taxic homologies, undisguised. Deep homologies inspire particular interest for understanding the evolutionary assembly of phenotypic traits. Mapping these deeply homologous building blocks on a phylogeny reveals the sequential steps leading to the origin of phenotypic novelties. Finally, we discuss how new genomic technologies will revolutionize the comparative genomic study of non-model organisms in a phylogenetic context, necessary to understand the evolution of phenotypic traits.     

A semiparametric test to detect associations between quantitative traits and candidate genes in structured populations

MOTIVATION: Although population-based association mapping may be subject to the bias caused by population stratification, alternative methods that are robust to population stratification such as family-based linkage analysis have lower mapping resolution. Recently, various statistical methods robust to population stratification were proposed for association studies, using unrelated individuals to identify associations between candidate genes and traits of interest. The association between a candidate gene and a quantitative trait is often evaluated via a regression model with inferred population structure variables as covariates, where the residual distribution is customarily assumed to be from a symmetric and unimodal parametric family, such as a Gaussian, although this may be inappropriate for the analysis of many real-life datasets. RESULTS: In this article, we proposed a new structured association (SA) test. Our method corrects for continuous population stratification by first deriving population structure and kinship matrices through a set of random genetic markers and then modeling the relationship between trait values, genotypic scores at a candidate marker and genetic background variables through a semiparametric model, where the error distribution is modeled as a mixture of Polya trees centered around a normal family of distributions. We compared our model to the existing SA tests in terms of model fit, type I error rate, power, precision and accuracy by application to a real dataset as well as simulated datasets.     

Phylogenetic imputation of plant functional trait databases

Continental‐scale maps of plant functional diversity are a fundamental piece of data of interest to ecosystem modelers and ecologists, yet such maps have been exceedingly hard to generate. The large effort to compile global plant functional trait databases largely for the purpose of mapping and analyzing the spatial distribution of function has resulted in very sparse data matrices thereby limiting progress. Identifying robust methodologies to gap fill or impute trait values in these databases is an important objective. Here I argue that existing statistical tools from phylogenetic comparative methods can be used to rapidly impute values into global plant functional trait databases due to the large amount of phylogenetic signal often in trait data. In particular, statistical models of phylogenetic signal in traits can be generated from existing data and used to predict missing values of closely related species often with a high degree of accuracy thereby facilitating the continental‐scale mapping of plant function. Despite the promise of this approach, I also discuss potential pitfalls and future challenges that will need to be addressed.     

Allometric covariation: a hallmark behavior of plants and leaves

Size is one of the most important axes of variation among plants. As such, plant biologists have long searched for unifying principles that can explain how matter and energy flux and organ partitioning scale with plant size. Several recent models have proposed a universal biophysical basis for numerous scaling phenomena in plants based on vascular network geometry. Here, we review statistical analyses of several large-scale plant datasets that demonstrate that a true hallmark of plant form variability is systematic covariation among traits. This covariation is constrained by allometries that combine and trade off with one another, rather than any single universal allometric scaling exponent for a trait or suite of traits. Further, we show that covariation can be successfully modeled using network approaches that allow for species-specific designs in plants and geometric approaches that constrain relationships among economic traits in leaves. Finally, we report large-scale efforts utilizing semi-automated software tools that quantify physical networks and can inform our attempts to link vascular network structure to plant form and function. Collectively, this work highlights how the linking of morphology, biomass partitioning and the structure of physical distribution networks can improve our empirical and theoretical understanding of important drivers of plant functional diversity.     

Trait dimensionality and population choice alter estimates of phenotypic dissimilarity

The ecological niche is a multi‐dimensional concept including aspects of resource use, environmental tolerance, and interspecific interactions, and the degree to which niches overlap is central to many ecological questions. Plant phenotypic traits are increasingly used as surrogates of species niches, but we lack an understanding of how key sampling decisions affect our ability to capture phenotypic differences among species. Using trait data of ecologically distinct monkeyflower (Mimulus) congeners, we employed linear discriminant analysis to determine how (1) dimensionality (the number and type of traits) and (2) variation within species influence how well measured traits reflect phenotypic differences among species. We conducted analyses using vegetative and floral traits in different combinations of up to 13 traits and compared the performance of commonly used functional traits such as specific leaf area against other morphological traits. We tested the importance of intraspecific variation by assessing how population choice changed our ability to discriminate species. Neither using key functional traits nor sampling across plant functions and organs maximized species discrimination. When using few traits, vegetative traits performed better than combinations of vegetative and floral traits or floral traits alone. Overall, including more traits increased our ability to detect phenotypic differences among species. Population choice and the number of traits used had comparable impacts on discriminating species. We addressed methodological challenges that have undermined cross‐study comparability of trait‐based approaches. Our results emphasize the importance of sampling among‐population trait variation and suggest that a high‐dimensional approach may best capture phenotypic variation among species with distinct niches.     

Interpretation of the results of common principal components analyses

Common principal components (CPC) analysis is a new tool for the comparison of phenotypic and genetic variance-covariance matrices. CPC was developed as a method of data summarization, but frequently biologists would like to use the method to detect analogous patterns of trait correlation in multiple populations or species. To investigate the properties of CPC, we simulated data that reflect a set of causal factors. The CPC method performs as expected from a statistical point of view, but often gives results that are contrary to biological intuition. In general, CPC tends to underestimate the degree of structure that matrices share. Differences of trait variances and covariances due to a difference in a single causal factor in two otherwise identically structured datasets often cause CPC to declare the two datasets unrelated. Conversely, CPC could identify datasets as having the same structure when causal factors are different. Reordering of vectors before analysis can aid in the detection of patterns. We urge caution in the biological interpretation of CPC analysis results.     

The search for Pleiades in trait constellations: functional integration and phenotypic selection in the complex flowers of Morrenia brachystephana (Apocynaceae)

Pollinator‐mediated natural selection on single traits, such as corolla tube or spur length, has been well documented. However, flower phenotypes are usually complex, and selection is expected to act on several traits that functionally interact rather than on a single isolated trait. Despite the fact that selection on complex phenotypes is expectedly widespread, multivariate selection modelling on such phenotypes still remains under‐explored in plants. Species of the subfamily Asclepiadoideae (Apocynaceae) provide an opportunity to study such complex flower contrivances integrated by fine‐scaled organs from disparate developmental origin. We studied the correlation structure among linear floral traits (i) by testing a priori morphological, functional or developmental hypotheses among traits and (ii) by exploring the organization of flower covariation, considering alternative expectations of modular organization or whole flower integration through conditional dependence analysis (CDA) and integration matrices. The phenotypic selection approach was applied to determine whether floral traits involved in the functioning of the pollination mechanism were affected by natural selection. Floral integration was low, suggesting that flowers are organized in more than just one correlation pleiad; our hypothetical functional correlation matrix was significantly correlated with the empirical matrix, and the CDA revealed three putative modules. Analyses of phenotypic selection showed significant linear and correlational gradients, lending support to expectations of functional interactions between floral traits. Significant correlational selection gradients found involved traits of different floral whorls, providing evidence for the existence of functional integration across developmental domains.