Adaptive constraints and the phylogenetic comparative method: a computer simulation test

Recently, the utility of modern phylogenetic comparative methods (PCMs) has been questioned because of the seemingly restrictive assumptions required by these methods. Although most comparative analyses involve traits thought to be undergoing natural or sexual selection, most PCMs require an assumption that the traits be evolving by less directed random processes, such as Brownian motion (BM). In this study, we use computer simulation to generate data under more realistic evolutionary scenarios and consider the statistical abilities of a variety of PCMs to estimate correlation coefficients from these data. We found that correlations estimated without taking phylogeny into account were often quite poor and never substantially better than those produced by the other tested methods. In contrast, most PCMs performed quite well even when their assumptions were violated. Felsenstein's independent contrasts (FIC) method gave the best performance in many cases, even when weak constraints had been acting throughout phenotypic evolution. When strong constraints acted in opposition to variance-generating (i.e., BM) forces, however, FIC correlation coefficients were biased in the direction of those BM forces. In most cases, all other PCMs tested (phylogenetic generalized least squares, phylogenetic mixed model, spatial autoregression, and phylogenetic eigenvector regression) yielded good statistical performance, regardless of the details of the evolutionary model used to generate the data. Actual parameter estimates given by different PCMs for each dataset, however, were occasionally very different from one another, suggesting that the choice among them should depend on the types of traits and evolutionary processes being considered.     

Assessing the Goodness of Fit of Phylogenetic Comparative Methods: A Meta-Analysis and Simulation Study

Background

Phylogenetic comparative methods (PCMs) have been applied widely in analyzing data from related species but their fit to data is rarely assessed.

Question

Can one determine whether any particular comparative method is typically more appropriate than others by examining comparative data sets?

Data

I conducted a meta-analysis of 122 phylogenetic data sets found by searching all papers in JEB, Blackwell Synergy and JSTOR published in 2002–2005 for the purpose of assessing the fit of PCMs. The number of species in these data sets ranged from 9 to 117.

Analysis Method

I used the Akaike information criterion to compare PCMs, and then fit PCMs to bivariate data sets through REML analysis. Correlation estimates between two traits and bootstrapped confidence intervals of correlations from each model were also compared.

Conclusions

For phylogenies of less than one hundred taxa, the Independent Contrast method and the independent, non-phylogenetic models provide the best fit.For bivariate analysis, correlations from different PCMs are qualitatively similar so that actual correlations from real data seem to be robust to the PCM chosen for the analysis. Therefore, researchers might apply the PCM they believe best describes the evolutionary mechanisms underlying their data.     

Nonlinear relationships and phylogenetically independent contrasts

The method of phylogenetically independent contrasts is commonly used for exploring cross-taxon relationships between traits. Here we show that this phylogenetic comparative method (PCM) can fail to detect correlated evolution when the underlying relationship between traits is nonlinear. Simulations indicate that statistical power can be dramatically reduced when independent contrasts analysis is used on nonlinear relationships. We also reanalyze a published data set and demonstrate that ignoring nonlinearity can affect biological inferences. We suggest that researchers consider the shape of the relationship between traits when using independent contrasts analysis. Alternative PCMs may be more appropriate if data cannot be transformed to meet assumptions of linearity.     

Special Care Is Needed in Applying Phylogenetic Comparative Methods to Gene Trees with Speciation and Duplication Nodes

How gene function evolves is a central question of evolutionary biology. It can be investigated by comparing functional genomics results between species and between genes. Most comparative studies of functional genomics have used pairwise comparisons. Yet it has been shown that this can provide biased results, as genes, like species, are phylogenetically related. Phylogenetic comparative methods should be used to correct for this, but they depend on strong assumptions, including unbiased tree estimates relative to the hypothesis being tested. Such methods have recently been used to test the “ortholog conjecture,” the hypothesis that functional evolution is faster in paralogs than in orthologs. Although pairwise comparisons of tissue specificity (τ) provided support for the ortholog conjecture, phylogenetic independent contrasts did not. Our reanalysis on the same gene trees identified problems with the time calibration of duplication nodes. We find that the gene trees used suffer from important biases, due to the inclusion of trees with no duplication nodes, to the relative age of speciations and duplications, to systematic differences in branch lengths, and to non-Brownian motion of tissue specificity on many trees. We find that incorrect implementation of phylogenetic method in empirical gene trees with duplications can be problematic. Controlling for biases allows successful use of phylogenetic methods to study the evolution of gene function and provides some support for the ortholog conjecture using three different phylogenetic approaches.     

Is horizontal transmission really a problem for phylogenetic comparative methods? A simulation study using continuous cultural traits

Phylogenetic comparative methods (PCMs) provide a potentially powerful toolkit for testing hypotheses about cultural evolution. Here, we build on previous simulation work to assess the effect horizontal transmission between cultures has on the ability of both phylogenetic and non-phylogenetic methods to make inferences about trait evolution. We found that the mode of horizontal transmission of traits has important consequences for both methods. Where traits were horizontally transmitted separately, PCMs accurately reported when trait evolution was not correlated even at the highest levels of horizontal transmission. By contrast, linear regression analyses often incorrectly concluded that traits were correlated. Where simulated trait evolution was not correlated and traits were horizontally transmitted as a pair, both methods inferred increased levels of positive correlation with increasing horizontal transmission. Where simulated trait evolution was correlated, increasing rates of separate horizontal transmission led to decreasing levels of inferred correlation for both methods, but increasing rates of paired horizontal transmission did not. Furthermore, the PCM was also able to make accurate inferences about the ancestral state of traits. These results suggest that under certain conditions, PCMs can be robust to the effects of horizontal transmission. We discuss ways that future work can investigate the mode and tempo of horizontal transmission of cultural traits.     

SIMULATION‐BASED LIKELIHOOD APPROACH FOR EVOLUTIONARY MODELS OF PHENOTYPIC TRAITS ON PHYLOGENY

Phylogenetic comparative methods (PCMs) have been used to test evolutionary hypotheses at phenotypic levels. The evolutionary modes commonly included in PCMs are Brownian motion (genetic drift) and the Ornstein–Uhlenbeck process (stabilizing selection), whose likelihood functions are mathematically tractable. More complicated models of evolutionary modes, such as branch‐specific directional selection, have not been used because calculations of likelihood and parameter estimates in the maximum‐likelihood framework are not straightforward. To solve this problem, we introduced a population genetics framework into a PCM, and here, we present a flexible and comprehensive framework for estimating evolutionary parameters through simulation‐based likelihood computations. The method does not require analytic likelihood computations, and evolutionary models can be used as long as simulation is possible. Our approach has many advantages: it incorporates different evolutionary modes for phenotypes into phylogeny, it takes intraspecific variation into account, it evaluates full likelihood instead of using summary statistics, and it can be used to estimate ancestral traits. We present a successful application of the method to the evolution of brain size in primates. Our method can be easily implemented in more computationally effective frameworks such as approximate Bayesian computation (ABC), which will enhance the use of computationally intensive methods in the study of phenotypic evolution.     

The degree and pattern of phylogenetic signal in primate long-bone structure

Interspecific scaling is a fundamental tool for comparative studies of primate long-bone structure and adaptation. However, scaling analyses based on conventional statistical methods can lead to false positives regarding adaptive relationships when traits exhibit strong phylogenetic signal. This problem can be addressed through the use of phylogenetic comparative methods (PCMs). To date, PCMs have not been incorporated into comparative studies of primate long-bone structure because it has been assumed that long-bone structure is free of phylogenetic signal once appropriately scaled. To test this assumption, we evaluated the degree of phylogenetic signal in three types of long-bone structural traits (bone length, articular surface areas, and cross-sectional geometric properties) from 17 quadrupedal primate species. We compared the pattern of phylogenetic signal in raw trait values and residual trait values after regression against body mass, bone length, and the product of body mass x bone length. Our results show that significant phylogenetic signal is present in all traits before scaling, due in part to their strong covariance with body mass. After scaling, bone length still exhibits strong phylogenetic signal, but articular surface areas do not, and cross-sectional properties exhibit different levels of signal depending on the variable used to scale the data. These results suggest that PCMs should be incorporated into interspecific studies of bone length and perhaps cross-sectional geometric properties. Our results also demonstrate that tests for phylogenetic signal prior to implementing a PCM should focus on residual variance, not individual traits.     

phylosem: A fast and simple R package for phylogenetic inference and trait imputation using phylogenetic structural equation models

Phylogenetic comparative methods (PCMs) can be used to study evolutionary relationships and trade-offs among species traits. Analysts using PCM may want to (1) include latent variables, (2) estimate complex trait interdependencies, (3) predict missing trait values, (4) condition predicted traits upon phylogenetic correlations and (5) estimate relationships as slope parameters that can be compared with alternative regression methods. The Comprehensive R Archive Network (CRAN) includes well-documented software for phylogenetic linear models (phylolm), phylogenetic path analysis (phylopath), phylogenetic trait imputation (Rphylopars) and structural equation models (sem), but none of these can simultaneously accomplish all five analytical goals. We therefore introduce a new package phylosem for phylogenetic structural equation models (PSEM) and summarize features and interface. We also describe new analytical options, where users can specify any combination of Ornstein-Uhlenbeck, Pagel's-δ and Pagel's-λ transformations for species covariance. For the first time, we show that PSEM exactly reproduces estimates (and standard errors) for simplified cases that are feasible in sem, phylopath, phylolm and Rphylopars and demonstrate the approach by replicating a well-known case study involving trade-offs in plant energy budgets.     

PHYLOGENIES,SPATIAL AUTOREGRESSION,AND THE COMPARATIVE METHOD: A COMPUTER SIMULATION TEST

Brownian motion computer simulation was used to test the statistical properties of a spatial autoregressive method in estimating evolutionary correlations between two traits using interspecific comparative data. When applied with a phylogeny of 42 species, the method exhibited reasonable Type I and II error rates. Estimation abilities were comparable to those of independent contrasts and minimum evolution (parsimony) methods, and generally superior to a traditional nonphylogenetic approach (not taking phylogenies into account at all). However, the autoregressive method performed extremely poorly with a smaller phylogeny (15 species) and with nearly independent (“star”) phylogenies. In both of these situations, any phylogenetic autocorrelation present in the data was not detected by the method. Results show how diagnostic techniques (e.g., Moran's I) can be useful in detecting and avoiding such situations, but that such techniques should not be used as definitive evidence that phylogenetic correlation is not present in a set of comparative data. The correction factor (α) proposed by Gittleman and Kot (1990) for use in weighting phylogenetic information had little effect in most analyses of 15 or 42 species with incorrect phylogenetic information, and may require much larger sample sizes before significant improvement is shown. With the sample sizes tested in this study, however, the autoregressive method implemented with this correction factor and correct phylogenetic information led to downwardly biased estimates of the absolute magnitude of the evolutionary correlation between two traits. Cautions and recommendations for implemention of the spatial autoregressive method are given; computer programs to conduct the analyses are available on request.     

Mitochondrial DNA as a tool for reconstructing past life‐history traits in mammals

Reconstructing the ancestral characteristics of species is a major goal in evolutionary and comparative biology. Unfortunately, fossils are not always available and sufficiently informative, and phylogenetic methods based on models of character evolution can be unsatisfactory. Genomic data offer a new opportunity to estimate ancestral character states, through (i) the correlation between DNA evolutionary processes and species life‐history traits and (ii) available reliable methods for ancestral sequence inference. Here, we assess the relevance of mitochondrial DNA – the most popular molecular marker in animals – as a predictor of ancestral life‐history traits in mammals, using the order of Cetartiodactyla as a benchmark. Using the complete set of 13 mitochondrial protein‐coding genes, we show that the lineage‐specific nonsynonymous over synonymous substitution rate ratio (dN/dS) is closely correlated with the species body mass, longevity and age of sexual maturity in Cetartiodactyla and can be used as a marker of ancestral traits provided that the noise introduced by short branches is appropriately dealt with. Based on ancestral dN/dS estimates, we predict that the first cetartiodactyls were relatively small animals (around 20 kg). This finding is in accordance with Cope's rule and the fossil record but could not be recovered via continuous character evolution methods.     

Taxon sampling, correlated evolution, and independent contrasts

Independent contrasts are widely used to incorporate phylogenetic information into studies of continuous traits, particularly analyses of evolutionary trait correlations, but the effects of taxon sampling on these analyses have received little attention. In this paper, simulations were used to investigate the effects of taxon sampling patterns and alternative branch length assignments on the statistical performance of correlation coefficients and sign tests; "full-tree" analyses based on contrasts at all nodes and "paired-comparisons" based only on contrasts of terminal taxon pairs were also compared. The simulations showed that random samples, with respect to the traits under consideration, provide statistically robust estimates of trait correlations. However, exact significance tests are highly dependent on appropriate branch length information; equal branch lengths maintain lower Type I error than alternative topological approaches, and adjusted critical values of the independent contrast correlation coefficient are provided for use with equal branch lengths. Nonrandom samples, with respect to univariate or bivariate trait distributions, introduce discrepancies between interspecific and phylogenetically structured analyses and bias estimates of underlying evolutionary correlations. Examples of nonrandom sampling processes may include community assembly processes, convergent evolution under local adaptive pressures, selection of a nonrandom sample of species from a habitat or life-history group, or investigator bias. Correlation analyses based on species pairs comparisons, while ignoring deeper relationships, entail significant loss of statistical power and as a result provide a conservative test of trait associations. Paired comparisons in which species differ by a large amount in one trait, a method introduced in comparative plant ecology, have appropriate Type I error rates and high statistical power, but do not correctly estimate the magnitude of trait correlations. Sign tests, based on full-tree or paired-comparison approaches, are highly reliable across a wide range of sampling scenarios, in terms of Type I error rates, but have very low power. These results provide guidance for selecting species and applying comparative methods to optimize the performance of statistical tests of trait associations.     

Phylogenetic comparative methods and the geographic range size – body size relationship in new world terrestrial carnivora

Most recent papers avoid describing macroecological relationships and interpreting then without a previous control of non-independence in data caused by phylogenetic patterns in data. In this paper, we analyzed the geographic range size – body size relationship for 70 species of New World terrestrial Carnivora (fissipeds) using various phylogenetic comparative methods and simulation procedures to assess their statistical performance. Autocorrelation analyses suggested a strong phylogenetic pattern for body size, but not for geographic range size. The correlation between the two traits was estimated using standard Pearson correlation across species (TIPS) and four different comparative methods: Felsenstein's independent contrasts (PIC), autoregressive method (ARM), phylogenetic eigenvector regression (PVR) and phylogenetic generalized least-squares (PGLS). The correlation between the two variables was significant for all methods, except PIC, in such a way that ecological mechanisms (i.e., minimum viable population or environmental heterogeneity- physiological homeostasis), could be valid explanations for the relationship. Simulations using different O-U processes for each trait were run in order to estimate true Type I errors of each method. Type I errors at 5% were similar for all phylogenetic methods (always lower than 8%), but equal to 13.1% for TIPS. PIC usually performs better than all other methods under Brownian motion evolution, but not in this case using a more complex combination of evolutionary models. So, recent claims that using independent contrasts in ecological research can be too conservative are correct but, on the other hand, using simple across-species correlation is too liberal even under the more complex evolutionary models exhibited by the traits analyzed here.     

Phylogeny-Based Comparative Methods Question the Adaptive Nature of Sporophytic Specializations in Mosses

Adaptive evolution has often been proposed to explain correlations between habitats and certain phenotypes. In mosses, a high frequency of species with specialized sporophytic traits in exposed or epiphytic habitats was, already 100 years ago, suggested as due to adaptation. We tested this hypothesis by contrasting phylogenetic and morphological data from two moss families, Neckeraceae and Lembophyllaceae, both of which show parallel shifts to a specialized morphology and to exposed epiphytic or epilithic habitats. Phylogeny-based tests for correlated evolution revealed that evolution of four sporophytic traits is correlated with a habitat shift. For three of them, evolutionary rates of dual character-state changes suggest that habitat shifts appear prior to changes in morphology. This suggests that they could have evolved as adaptations to new habitats. Regarding the fourth correlated trait the specialized morphology had already evolved before the habitat shift. In addition, several other specialized “epiphytic” traits show no correlation with a habitat shift. Besides adaptive diversification, other processes thus also affect the match between phenotype and environment. Several potential factors such as complex genetic and developmental pathways yielding the same phenotypes, differences in strength of selection, or constraints in phenotypic evolution may lead to an inability of phylogeny-based comparative methods to detect potential adaptations.     

The ascent of the abundant: how mutational networks constrain evolution

Evolution by natural selection is fundamentally shaped by the fitness landscapes in which it occurs. Yet fitness landscapes are vast and complex, and thus we know relatively little about the long-range constraints they impose on evolutionary dynamics. Here, we exhaustively survey the structural landscapes of RNA molecules of lengths 12 to 18 nucleotides, and develop a network model to describe the relationship between sequence and structure. We find that phenotype abundance—the number of genotypes producing a particular phenotype—varies in a predictable manner and critically influences evolutionary dynamics. A study of naturally occurring functional RNA molecules using a new structural statistic suggests that these molecules are biased toward abundant phenotypes. This supports an “ascent of the abundant” hypothesis, in which evolution yields abundant phenotypes even when they are not the most fit.     

Assessing the accuracy of ancestral protein reconstruction methods

The phylogenetic inference of ancestral protein sequences is a powerful technique for the study of molecular evolution, but any conclusions drawn from such studies are only as good as the accuracy of the reconstruction method. Every inference method leads to errors in the ancestral protein sequence, resulting in potentially misleading estimates of the ancestral protein's properties. To assess the accuracy of ancestral protein reconstruction methods, we performed computational population evolution simulations featuring near-neutral evolution under purifying selection, speciation, and divergence using an off-lattice protein model where fitness depends on the ability to be stable in a specified target structure. We were thus able to compare the thermodynamic properties of the true ancestral sequences with the properties of “ancestral sequences” inferred by maximum parsimony, maximum likelihood, and Bayesian methods. Surprisingly, we found that methods such as maximum parsimony and maximum likelihood that reconstruct a “best guess” amino acid at each position overestimate thermostability, while a Bayesian method that sometimes chooses less-probable residues from the posterior probability distribution does not. Maximum likelihood and maximum parsimony apparently tend to eliminate variants at a position that are slightly detrimental to structural stability simply because such detrimental variants are less frequent. Other properties of ancestral proteins might be similarly overestimated. This suggests that ancestral reconstruction studies require greater care to come to credible conclusions regarding functional evolution. Inferred functional patterns that mimic reconstruction bias should be reevaluated.     

Linkage Rules for Plant–Pollinator Networks: Trait Complementarity or Exploitation Barriers?

Recent attempts to examine the biological processes responsible for the general characteristics of mutualistic networks focus on two types of explanations: nonmatching biological attributes of species that prevent the occurrence of certain interactions (“forbidden links”), arising from trait complementarity in mutualist networks (as compared to barriers to exploitation in antagonistic ones), and random interactions among individuals that are proportional to their abundances in the observed community (“neutrality hypothesis”). We explored the consequences that simple linkage rules based on the first two hypotheses (complementarity of traits versus barriers to exploitation) had on the topology of plant–pollination networks. Independent of the linkage rules used, the inclusion of a small set of traits (two to four) sufficed to account for the complex topological patterns observed in real-world networks. Optimal performance was achieved by a “mixed model” that combined rules that link plants and pollinators whose trait ranges overlap (“complementarity models”) and rules that link pollinators to flowers whose traits are below a pollinator-specific barrier value (“barrier models”). Deterrence of floral parasites (barrier model) is therefore at least as important as increasing pollination efficiency (complementarity model) in the evolutionary shaping of plant–pollinator networks.     

Recent developments in the analysis of comparative data

Comparative methods can be used to test ideas about adaptation by identifying cases of either parallel or convergent evolutionary change across taxa. Phylogenetic relationships must be known or inferred if comparative methods are to separate the cross-taxonomic covariation among traits associated with evolutionary change from that attributable to common ancestry. Only the former can be used to test ideas linking convergent or parallel evolutionary change to some aspect of the environment. The comparative methods that are currently available differ in how they manage the effects brought about by phylogenetic relationships. One method is applicable only to discrete data, and uses cladistic techniques to identify evolutionary events that depart from phylogenetic trends. Techniques for continuous variables attempt to control for phylogenetic effects in a variety of ways. One method examines the taxonomic distribution of variance to identify the taxa within which character variation is small. The method assumes that taxa with small amounts of variation are those in which little evolutionary change has occurred, and thus variation is unlikely to be independent of ancestral trends. Analyses are then concentrated among taxa that show more variation, on the assumption that greater evolutionary change in the character has taken place. Several methods estimate directly the extent to which ancestry can predict the observed variation of a character, and subtract the ancestral effect to reveal variation of phylogeny. Yet another can remove phylogenetic effects if the true phylogeny is known. One class of comparative methods controls for phylogenetic effects by searching for comparative trends within rather than across taxa. With current knowledge of phylogenies, there is a trade-off in the choice of a comparative method: those that control phylogenetic effects with greater certainty are either less applicable to real data, or they make restrictive or untestable assumptions. Those that rely on statistical patterns to infer phylogenetic effects may not control phylogeny as efficiently but are more readily applied to existing data sets.     

On the correlation between composition and site-specific evolutionary rate: implications for phylogenetic inference

Model-based phylogenetic reconstruction methods traditionally assume homogeneity of nucleotide frequencies among sequence sites and lineages. Yet, heterogeneity in base composition is a characteristic shared by most biological sequences. Compositional variation in time, reflected in the compositional biases among contemporary sequences, has already been extensively studied, and its detrimental effects on phylogenetic estimates are known. However, fewer studies have focused on the effects of spatial compositional heterogeneity within genes. We show here that different sites in an alignment do not always share a unique compositional pattern, and we provide examples where nucleotide frequency trends are correlated with the site-specific rate of evolution in RNA genes. Spatial compositional heterogeneity is shown to affect the estimation of evolutionary parameters. With standard phylogenetic methods, estimates of equilibrium frequencies are found to be biased towards the composition observed at fast-evolving sites. Conversely, the ancestral composition estimates of some time-heterogeneous but spatially homogeneous methods are found to be biased towards frequencies observed at invariant and slow-evolving sites. The latter finding challenges the result of a previous study arguing against a hyperthermophilic last universal ancestor from the low apparent G + C content of its rRNA sequences. We propose a new model to account for compositional variation across sites. A Gaussian process prior is used to allow for a smooth change in composition with evolutionary rate. The model has been implemented in the phylogenetic inference software PHASE, and Bayesian methods can be used to obtain the model parameters. The results suggest that this model can accurately capture the observed trends in present-day RNA sequences.     

Challenges and opportunities for comparative studies of survival rates: An example with male pinnipeds

Survival rates are a central component of life‐history strategies of large vertebrate species. However, comparative studies seldom investigate interspecific variation in survival rates with respect to other life‐history traits, especially for males. The lack of such studies could be due to the challenges associated with obtaining reliable datasets, incorporating information on the 0–1 probability scale, or dealing with several types of measurement error in life‐history traits, which can be a computationally intensive process that is often absent in comparative studies. We present a quantitative approach using a Bayesian phylogenetically controlled regression with the flexibility to incorporate uncertainty in estimated survival rates and quantitative life‐history traits while considering genetic similarity among species and uncertainty in relatedness. As with any comparative analysis, our approach makes several assumptions regarding the generalizability and comparability of empirical data from separate studies. Our model is versatile in that it can be applied to any species group of interest and include any life‐history traits as covariates. We used an unbiased simulation framework to provide “proof of concept” for our model and applied a slightly richer model to a real data example for pinnipeds. Pinnipeds are an excellent taxonomic group for comparative analysis, but survival rate data are scarce. Our work elucidates the challenges associated with addressing important questions related to broader ecological life‐history patterns and how survival–reproduction trade‐offs might shape evolutionary histories of extant taxa. Specifically, we underscore the importance of having high‐quality estimates of age‐specific survival rates and information on other life‐history traits that reasonably characterize a species for accurately comparing across species.