ANCESTRAL CHARACTER ESTIMATION UNDER THE THRESHOLD MODEL FROM QUANTITATIVE GENETICS

Evolutionary biology is a study of life's history on Earth. In researching this history, biologists are often interested in attempting to reconstruct phenotypes for the long extinct ancestors of living species. Various methods have been developed to do this on a phylogeny from the data for extant taxa. In the present article, I introduce a new approach for ancestral character estimation for discretely valued traits. This approach is based on the threshold model from evolutionary quantitative genetics. Under the threshold model, the value exhibited by an individual or species for a discrete character is determined by an underlying, unobserved continuous trait called “liability.” In this new method for ancestral state reconstruction, I use Bayesian Markov chain Monte Carlo (MCMC) to sample the liabilities of ancestral and tip species, and the relative positions of two or more thresholds, from their joint posterior probability distribution. Using data simulated under the model, I find that the method has very good performance in ancestral character estimation. Use of the threshold model for ancestral state reconstruction relies on a priori specification of the order of the discrete character states along the liability axis. I test the use of a Bayesian MCMC information theoretic criterion based approach to choose among different hypothesized orderings for the discrete character. Finally, I apply the method to the evolution of feeding mode in centrarchid fishes.     

Comparative methods with sampling error and within-species variation: contrasts revisited and revised

Comparative methods analyses have usually assumed that the species phenotypes are the true means for those species. In most analyses, the actual values used are means of samples of modest size. The covariances of contrasts then involve both the covariance of evolutionary changes and a fraction of the within-species phenotypic covariance, the fraction depending on the sample size for that species. Ives et al. have shown how to analyze data in this case when the within-species phenotypic covariances are known. The present model allows them to be unknown and to be estimated from the data. A multivariate normal statistical model is used for multiple characters in samples of finite size from species related by a known phylogeny, under the usual Brownian motion model of change and with equal within-species phenotypic covariances. Contrasts in each character can be obtained both between individuals within a species and between species. Each contrast can be taken for all of the characters. These sets of contrasts, each the same contrast taken for different characters, are independent. The within-set covariances are unequal and depend on the unknown true covariance matrices. An expectation-maximization algorithm is derived for making a reduced maximum likelihood estimate of the covariances of evolutionary change and the within-species phenotypic covariances. It is available in the Contrast program of the PHYLIP package. Computer simulations show that the covariances are biased when the finiteness of sample size is not taken into account and that using the present model corrects the bias. Sampling variation reduces the power of inference of covariation in evolution of different characters. An extension of this method to incorporate estimates of additive genetic covariances from a simple genetic experiment is also discussed.     

Evaluating the efficacy of continuous quantitative characters for reconstructing the phylogeny of a morphologically homogeneous spider taxon (Araneae, Mygalomorphae, Antrodiaetidae, Antrodiaetus)

The use of continuous quantitative characters for phylogenetic analyses has long been contentious in the systematics literature. Recent studies argue for and against their use, but there have been relatively few attempts to evaluate whether these characters provide an accurate estimate of phylogeny, despite the fact that a number of methods have been developed to analyze these types of data for phylogenetic inference. A tree topology will be produced for a given methodology and set of characters, but little can be concluded with regards to the accuracy of phylogenetic signal without an independent evaluation of those characters. We assess the performance of continuous quantitative characters for the mygalomorph spider genus Antrodiaetus, a group that is morphologically homogeneous and one for which few discrete (morphological) characters have been observed. Phylogenetic signal contained in continuous quantitative characters is compared to an independently derived phylogeny inferred on the basis of multiple nuclear and mitochondrial gene loci. Tree topology randomizations, regression techniques, and topological tests all demonstrate that continuous quantitative characters in Antrodiaetus conflict with the phylogenetic signal contained in the gene trees. Our results show that the use of continuous quantitative characters for phylogenetic reconstruction may be inappropriate for reconstructing Antrodiaetus phylogeny and indicate that due caution should be exercised before employing this character type in the absence of other independently derived sources of characters.     

The mouse skull as a source of morphometric data for phylogeny inference

Brownian motion has been a model widely used for describing phenotypic evolution of continuous characters under random drift. Evolution of traits evolving under weak stabilizing selection, together with drift, can also be modeled by the Ornstein-Uhlenbeck process, in which a population moves at random on an adaptive peak under the influence of drift with selection returning the population towards the optimum. Obviously, reliability of an evolutionary model stands or falls with the extent to which the underlying assumptions are supported or violated. Another potential problem of continuous characters as a source of data for phylogeny inference is the correlation between them. To assess whether the Brownian motion model or the Ornstein-Uhlenbeck model are suitable for modeling the evolution of continuous cranial and dental characters and to what extent these characters are correlated with one another, 11 measurements encompassing various aspects of the mouse skull morphology were collected and subjected to a comparative analysis using the generalized least squares method. It could be shown that only about one-half of the characters evolved according to the Brownian motion model or the Ornstein-Uhlenbeck model. Moreover, about 44% of the correlation coefficients exceeded 0.8, suggesting a need for removing at least phenotypic covariances from the data prior to a phylogenetic analysis. Finally, ancestral states of the characters under study were estimated with the generalized least square method. There has been a general trend towards enlarging the overall size of the skull and increasing the braincase volume in the species of the genus Mus.     

PHYLOGENETIC ANALYSIS OF THE EVOLUTIONARY CORRELATION USING LIKELIHOOD

Many evolutionary processes can lead to a change in the correlation between continuous characters over time or on different branches of a phylogenetic tree. Shifts in genetic or functional constraint, in the selective regime, or in some combination thereof can influence both the evolution of continuous traits and their relation to each other. These changes can often be mapped on a phylogenetic tree to examine their influence on multivariate phenotypic diversification. We propose a new likelihood method to fit multiple evolutionary rate matrices (also called evolutionary variance–covariance matrices) to species data for two or more continuous characters and a phylogeny. The evolutionary rate matrix is a matrix containing the evolutionary rates for individual characters on its diagonal, and the covariances between characters (of which the evolutionary correlations are a function) elsewhere. To illustrate our approach, we apply the method to an empirical dataset consisting of two features of feeding morphology sampled from 28 centrarchid fish species, as well as to data generated via phylogenetic numerical simulations. We find that the method has appropriate type I error, power, and parameter estimation. The approach presented herein is the first to allow for the explicit testing of how and when the evolutionary covariances between characters have changed in the history of a group.     

Principal component analysis as an alternative treatment for morphometric characters: phylogeny of caseids as a case study

In a recent study, the phylogeny of Caseidae (a herbivorous family of Palaeozoic synapsids belonging to the paraphyletic grade known as pelycosaurs) was analysed with a dataset employing more than three hundred continuous morphological characters in an effort to follow the principles of total evidence. Continuous characters are a source of great debate, with disagreements surrounding their suitability for and treatment in phylogenetic analysis. A number of shortcomings were identified in the handling of continuous characters in this study of caseids, including the use of gap weighting to discretize the characters and potential issues with redundancy and character non‐independence. Therefore, an alternative treatment for these characters is suggested here. First, rather than using gap weighting, the continuous characters were analysed in the program TNT, in which the raw values can be treated as continuous rather than discrete. Second, prior to the phylogenetic analysis, the continuous characters were subjected to a log‐ratio principal component analysis, and then the principal components were included in the character matrix rather than the raw ratios. Analysing the original data in TNT produced little difference in the results, but using the principal components as continuous characters resulted in alternative positions for Caseopsis agilis, Ennatosaurus tecton and Caseoides sanangeloensis. The differences are judged to be due to the reduced redundancy of the characters, the smaller number of principal components not overwhelming the discrete characters and the use of a scaling method which allows principal components with a higher variance to have a greater influence on the analysis. The positions of highly fragmentary fossils depended heavily on the method used to treat the missing characters in the principal component analysis, and so the method proposed here is not recommended for analysing very incomplete taxa.     

A phylogenetic model for investigating correlated evolution of substitution rates and continuous phenotypic characters

The comparative approach is routinely used to test for possible correlations between phenotypic or life-history traits. To correct for phylogenetic inertia, the method of independent contrasts assumes that continuous characters evolve along the phylogeny according to a multivariate Brownian process. Brownian diffusion processes have also been used to describe time variations of the parameters of the substitution process, such as the rate of substitution or the ratio of synonymous to nonsynonymous substitutions. Here, we develop a probabilistic framework for testing the coupling between continuous characters and parameters of the molecular substitution process. Rates of substitution and continuous characters are jointly modeled as a multivariate Brownian diffusion process of unknown covariance matrix. The covariance matrix, the divergence times and the phylogenetic variations of substitution rates and continuous characters are all jointly estimated in a Bayesian Monte Carlo framework, imposing on the covariance matrix a prior conjugate to the Brownian process so as to achieve a greater computational efficiency. The coupling between rates and phenotypes is assessed by measuring the posterior probability of positive or negative covariances, whereas divergence dates and phenotypic variations are marginally reconstructed in the context of the joint analysis. As an illustration, we apply the model to a set of 410 mammalian cytochrome b sequences. We observe a negative correlation between the rate of substitution and mass and longevity, which was previously observed. We also find a positive correlation between ω = dN/dS and mass and longevity, which we interpret as an indirect effect of variations of effective population size, thus in partial agreement with the nearly neutral theory. The method can easily be extended to any parameter of the substitution process and to any continuous phenotypic or environmental character.     

Regressive logistic models for familial diseases: a formulation assuming an underlying liability model

Statistical models have been developed to delineate the major-gene and non-major-gene factors accounting for the familial aggregation of complex diseases. The mixed model assumes an underlying liability to the disease, to which a major gene, a multifactorial component, and random environment contribute independently. Affection is defined by a threshold on the liability scale. The regressive logistic models assume that the logarithm of the odds of being affected is a linear function of major genotype, phenotypes of antecedents and other covariates. An equivalence between these two approaches cannot be derived analytically. I propose a formulation of the regressive logistic models on the supposition of an underlying liability model of disease. Relatives are assumed to have correlated liabilities to the disease; affected persons have liabilities exceeding an estimable threshold. Under the assumption that the correlation structure of the relatives' liabilities follows a regressive model, the regression coefficients on antecedents are expressed in terms of the relevant familial correlations. A parsimonious parameterization is a consequence of the assumed liability model, and a one-to-one correspondence with the parameters of the mixed model can be established. The logits, derived under the class A regressive model and under the class D regressive model, can be extended to include a large variety of patterns of family dependence, as well as gene-environment interactions.     

Ecological diversification and phylogeny of emydid turtles

Ecological diversification is a central topic in ecology and evolutionary biology. We undertook the first comprehensive species-level phylogenetic analysis of Emydidae (an ecologically diverse group of turtles), and used the resulting phylogeny to test four general hypotheses about ecological diversification. Phylogenetic analyses were based on data from morphology (237 parsimony-informative characters) and mitochondrial DNA sequences (547 parsimony-informative characters) and included 39 of the 40 currently recognized emydid species. Combined analyses of all data provide a well-supported hypothesis for intergeneric relationships, and support monophyly of the two subfamilies (Emydinae and Deirochelyinae) and most genera (with the notable exception of Clemmys and Trachemys ). Habitat and diet were mapped onto the combined-data tree to test fundamental hypotheses about ecological diversification. Using continuous coding of ecological characters showed that lineages changed in habitat before diet, ecological change was most frequently from generalist to specialist, and habitat and diet rarely changed on the same branch of the phylogeny. However, we also demonstrate that the results of ancestral trait reconstructions can be highly sensitive to character coding method (i.e. continuous vs. discrete). Finally, we propose a simple model to describe the pattern of ecological diversification in emydid turtles and other lineages, which may reconcile the (seemingly) conflicting conclusions of our study and two recent reviews of ecological diversification.  © 2003 The Linnean Society of London, Biological Journal of the Linnean Society , 2003, 79, 577–610.     

Joint mapping of quantitative trait Loci for multiple binary characters

Joint mapping for multiple quantitative traits has shed new light on genetic mapping by pinpointing pleiotropic effects and close linkage. Joint mapping also can improve statistical power of QTL detection. However, such a joint mapping procedure has not been available for discrete traits. Most disease resistance traits are measured as one or more discrete characters. These discrete characters are often correlated. Joint mapping for multiple binary disease traits may provide an opportunity to explore pleiotropic effects and increase the statistical power of detecting disease loci. We develop a maximum-likelihood method for mapping multiple binary traits. We postulate a set of multivariate normal disease liabilities, each contributing to the phenotypic variance of one disease trait. The underlying liabilities are linked to the binary phenotypes through some underlying thresholds. The new method actually maps loci for the variation of multivariate normal liabilities. As a result, we are able to take advantage of existing methods of joint mapping for quantitative traits. We treat the multivariate liabilities as missing values so that an expectation-maximization (EM) algorithm can be applied here. We also extend the method to joint mapping for both discrete and continuous traits. Efficiency of the method is demonstrated using simulated data. We also apply the new method to a set of real data and detect several loci responsible for blast resistance in rice.     

Inferring and testing hypotheses of cladistic character dependence by using character compatibility

The notion that two characters evolve independently is of interest for two reasons. First, theories of biological integration often predict that change in one character requires complementary change in another. Second, character independence is a basic assumption of most phylogenetic inference methods, and dependent characters might confound attempts at phylogenetic inference. Previously proposed tests of correlated character evolution require a model phylogeny and therefore assume that nonphylogenetic correlation has a negligible effect on initial tree construction. This paper develops "tree-free" methods for testing the independence of cladistic characters. These methods can test the character independence model as a hypothesis before phylogeny reconstruction, or can be used simply to test for correlated evolution. We first develop an approach for visualizing suites of correlated characters by using character compatibility. Two characters are compatible if they can be used to construct a tree without homoplasy. The approach is based on the examination of mutual compatibilities between characters. The number of times two characters i and j share compatibility with a third character is calculated, and a pairwise shared compatibility matrix is constructed. From this matrix, an association matrix analogous to a dissimilarity matrix is derived. Eigenvector analyses of this association matrix reveal suites of characters with similar compatibility patterns. A priori character subsets can be tested for significant correlation on these axes. Monte Carlo tests are performed to determine the expected distribution of mutual compatibilities, given various criteria from the original data set. These simulated distributions are then used to test whether the observed amounts of nonphylogenetic correlation in character suites can be attributed to chance alone. We have applied these methods to published morphological data for caecilian amphibians. The analyses corroborate instances of dependent evolution hypothesized by previous workers and also identify novel partitions. Phylogenetic analysis is performed after reducing correlated suites to single characters. The resulting cladogram has greater topological resolution and implies appreciably less change among the remaining characters than does a tree derived from the raw data matrix.     

Phylogeny reconstruction in the neogene bryozoan metrarabdotos: A paleontologic evaluation of methodology

An adequate stratigraphic record can not only aid in both cladistic and stratophenetic reconstruction of phytogenies, but can also serve in estimating the temporal consistency of the resulting phylogenetic trees. For hypothetical data sets, cladistically constructed trees can be as consistent with the temporal distribution of sampled populations or species as those constructed stratophenetically. Empirical testing in taxonomic groups with sufficiently dense fossil records is needed to show whether, and under what conditions, this potential can be realized. A stratophenetic tree and cladistic trees based on several approaches to character weighting were constructed for Caribbean Neogene species of the bryozoan Metrarabdotos with multiple‐character data from closely spaced sequential populations. The modular morphology and highly punctuated evolutionary pattern of these species blur the distinction between continuous and discrete characters, so that all available characters are potentially of equal significance in establishing phytogenies, rather than just those with discrete states conventionally used in cladistic analysis. However, only the cladistic trees generated with all characters weighted to emphasize contribution to species discrimination have temporal consistencies that are clearly significant statistically and approach that of the stratophenetic tree in magnitude. These results provide a start toward establishing general guidelines for cladistic analysis of taxa with stratigraphie records too sparse for stratophenetic reconstruction.     

Mapping uncertainty and phylogenetic uncertainty in ancestral character state reconstruction: an example in the moss genus Brachytheciastrum

The evolution of species traits along a phylogeny can be examined through an increasing number of possible, but not necessarily complementary, approaches. In this paper, we assess whether deriving ancestral states of discrete morphological characters from a model whose parameters are (i) optimized by ML on a most likely tree; (II) optimized by ML onto each of a Bayesian sample of trees; and (III) sampled by a MCMC visiting the space of a Bayesian sample of trees affects the reconstruction of ancestral states in the moss genus Brachytheciastrum. In the first two methods, the choice of a single- or two-rate model and of a genetic distance (wherein branch lengths are used to determine the probabilities of change) or speciational (wherein changes are only driven by speciation events) model based upon a likelihood-ratio test strongly depended on the sampled trees. Despite these differences in model selection, reconstructions of ancestral character states were strongly correlated to each others across nodes, often at r > 0.9, for all the characters. The Bayesian approach of ancestral character state reconstruction offers, however, a series of advantages over the single-tree approach or the ML model optimization on a Bayesian sample of trees because it does not involve restricting model parameters prior to reconstructing ancestral states, but rather allows a range of model parameters and ancestral character states to be sampled according to their posterior probabilities. From the distribution of the latter, conclusions on trait evolution can be made in a more satisfactorily way than when a substantial part of the uncertainty of the results is obscured by the focus on a single set of model parameters and associated ancestral states. The reconstructions of ancestral character states in Brachytheciastrum reveal rampant parallel morphological evolution. Most species previously described based on phenetic grounds are thus resolved of polyphyletic origin. Species polyphylly has been increasingly reported among mosses, raising severe reservations regarding current species definition.     

Testing the association of phenotypes with polyploidy: An example using herbaceous and woody eudicots

Although numerous studies have surveyed the frequency with which different plant characters are associated with polyploidy, few statistical tools are available to identify the factors that potentially facilitate polyploidy. We describe a new probabilistic model, BiChroM, designed to associate the frequency of polyploidy and chromosomal change with a binary phenotypic character in a phylogeny. BiChroM provides a robust statistical framework for testing differences in rates of polyploidy associated with phenotypic characters along a phylogeny while simultaneously allowing for evolutionary transitions between character states. We used BiChroM to test whether polyploidy is more frequent in woody or herbaceous plants, based on tree with 4711 eudicot species. Although polyploidy occurs in woody species, rates of chromosome doubling were over six times higher in herbaceous species. Rates of single chromosome increases or decreases were also far higher in herbaceous than woody species. Simulation experiments indicate that BiChroM performs well with little to no bias and relatively little variance at a wide range of tree depths when trees have at least 500 taxa. Thus, BiChroM provides a first step toward a rigorous statistical framework for assessing the traits that facilitate polyploidy.     

THE EVOLUTION OF THRESHOLD TRAITS: A QUANTITATIVE GENETIC ANALYSIS OF THE PHYSIOLOGICAL AND LIFE-HISTORY CORRELATES OF WING DIMORPHISM IN THE SAND CRICKET

Many traits are phenotypically discrete but polygenically determined. Such traits can be understood using the threshold model of quantitative genetics that posits a continuously distributed underlying trait, called the liability, and a threshold of response, individuals above the threshold displaying one morph and individuals below the threshold displaying the alternate morph. For many threshold traits the liability probably consists of a hormone or a suite of hormones. Previous experiments have implicated juvenile hormone esterase (JHE), a degratory enzyme of juvenile hormone, as a physiological determinant of wing dimorphism in the crickets Gryllus rubens and G. firmus. The present study uses a half-sib experiment to measure the heritability of JHE in the last nymphal stadium of G. firmus and its genetic correlation with fecundity, a trait that is itself genetically correlated with wing morph. The phenotypic and genetic parameters are consistent with the hypothesis that JHE is a significant component of the liability. Comparison of sire and dam estimates suggest that nonadditive effects may be important. Two models have been proposed to account for the fitness differences between morphs: the dichotomy model, which assumes that each morph can be characterized by a particular suite of traits, and the continuous model, which assumes that the associated fitness traits are correlated with the liability rather than the morphs themselves. The latter model predicts that the fitness differences will not be constant but change with the morph frequencies. Variation in fecundity and flight muscle histolysis are shown to be more consistent with the continuous model. Data from the present experiment on JHE are inconclusive, but results from a previous selection experiment also suggest that variation in JHE is consistent only with the continuous model.     

FEMALE AND MALE GENETIC EFFECTS ON OFFSPRING PATERNITY: ADDITIVE GENETIC (CO)VARIANCES IN FEMALE EXTRA‐PAIR REPRODUCTION AND MALE PATERNITY SUCCESS IN SONG SPARROWS (MELOSPIZA MELODIA)

Ongoing evolution of polyandry, and consequent extra‐pair reproduction in socially monogamous systems, is hypothesized to be facilitated by indirect selection stemming from cross‐sex genetic covariances with components of male fitness. Specifically, polyandry is hypothesized to create positive genetic covariance with male paternity success due to inevitable assortative reproduction, driving ongoing coevolution. However, it remains unclear whether such covariances could or do emerge within complex polyandrous systems. First, we illustrate that genetic covariances between female extra‐pair reproduction and male within‐pair paternity success might be constrained in socially monogamous systems where female and male additive genetic effects can have opposing impacts on the paternity of jointly reared offspring. Second, we demonstrate nonzero additive genetic variance in female liability for extra‐pair reproduction and male liability for within‐pair paternity success, modeled as direct and associative genetic effects on offspring paternity, respectively, in free‐living song sparrows (Melospiza melodia). The posterior mean additive genetic covariance between these liabilities was slightly positive, but the credible interval was wide and overlapped zero. Therefore, although substantial total additive genetic variance exists, the hypothesis that ongoing evolution of female extra‐pair reproduction is facilitated by genetic covariance with male within‐pair paternity success cannot yet be definitively supported or rejected either conceptually or empirically.     

THE HOLY GRAIL OF THE PERFECT CHARACTER: THE CLADISTIC TREATMENT OF MORPHOMETRIC DATA

Abstract— Data scored for cladistic analyses may be quantitative or qualitative, continuous or discrete, and show overlapping or non-overlapping values between taxa. Quantitative and qualitative are modes of expression of data, while continuous or discrete refer to properties of the set of numbers that express the data; both these pairs of terms have been confused with overlapping and non-overlapping. The degree of overlap of values between taxa is often used to filter characters in cladistic analyses: if a minimum amount of overlap is exceeded, or a minimum amount of disjunction not reached, characters are rejected as "not cladistic". However, this rests on a confusion between features of taxa and features of individual organisms (attributes). Cladistic characters are features of taxa, and comprise frequency distributions of attribute values over individuals of a taxon. Cladistic characters logically cannot overlap, although taxa may have overlapping attribute values. Thus, a priori rejection of characters that have overlapping attribute values is non-sensical. Such data may still be rejected from consideration for cladistic analysis if it could be demonstrated that they contain little recoverable phylogenetic signal. Few published analyses have empirically tested this. An analysis of overlapping morphometric data from three series of Banksia suggests that, at least in these cases, they map phylogeny almost as accurately as more conventional, qualitative morphological data. While more such tests are required, morphometric data should not be rejected a priori from cladistic analyses.     

The multifactorial/threshold concept -- uses and misuses.

The common congenital malformations have familial distributions that cannot be accounted for by simple Mendelian models, but can be explained in terms of a continuous variable, "liability," with a threshold value beyond which individuals will be affected. Both genetic and environmental factors determine liability, making the system multifactorial. Cleft palate is a useful experimental model, illustrating a number of factors that contribute to palate closure, the nature of a developmental threshold, and how genes and teratogens can alter the components of liability to increase the probability of cleft palate. The nature of the genetic component to liability in human malformations in not clear, and various possibilities, ranging from polygenic in the strict sense to a major gene with reduced penetrance are compatible with the data -- but the important feature is the threshold. Much of the confusion over the concept results from inconsistent use of terminology. The term "multifactorial" should be used for "determined by a combination of genetic and environmental factors," without reference to the nature of the genetic factor(s). "Polygenic" should be reserved for "a large number of genes, each with a small effect, acting additively." When several genes, with more major effects are involved, "multilocal" can be used. When it is not clear which of these is applicable the term "plurilocal" is suggested, in the sense of "genetic variation more complex than a simple Mendelian difference." Since teratological data often represent threshold characters the concept also has important implications for the interpretation of data on dose-response curves, synergisms, and strain differences in response to teratogens.