A COMPARISON OF TWO METHODS TO STUDY CORRELATED DISCRETE CHARACTERS ON PHYLOGENETIC TREES

Abstract — We use a simulation approach to study two methods proposed for the analysis of correlated discrete characters on cladograms, the concentrated changes test (CCT) and the contingent states test (CST). Both of these consider the case where there is an independent and a dependent character and assign probabilities to various events in the dependent character given one or the other state of the independent character. The CCT gives different results for symmetric and asymmetric cladograms. In the latter case, the proportion of branches reconstructed as having the derived state has less influence on the resulting probabilities. The CST is only sensitive to the proportion of derived branches, regardless of whether the tree is symmetric or asymmetric. The CCT calculates probabilities by considering character state reconstructions which are not allowed by parsimony algorithms, thereby increasing the probability of rejecting a true null hypothesis (type I error rate). We discuss some alternative questions that could be studied using these tests and also derive equations for calculating the number of possible events in the dependent character for unresolved parts of the phylogeny.     

Fast, accurate and simulation-free stochastic mapping

Mapping evolutionary trajectories of discrete traits onto phylogenies receives considerable attention in evolutionary biology. Given the trait observations at the tips of a phylogenetic tree, researchers are often interested where on the tree the trait changes its state and whether some changes are preferential in certain parts of the tree. In a model-based phylogenetic framework, such questions translate into characterizing probabilistic properties of evolutionary trajectories. Current methods of assessing these properties rely on computationally expensive simulations. In this paper, we present an efficient, simulation-free algorithm for computing two important and ubiquitous evolutionary trajectory properties. The first is the mean number of trait changes, where changes can be divided into classes of interest (e.g. synonymous/non-synonymous mutations). The mean evolutionary reward, accrued proportionally to the time a trait occupies each of its states, is the second property. To illustrate the usefulness of our results, we first employ our simulation-free stochastic mapping to execute a posterior predictive test of correlation between two evolutionary traits. We conclude by mapping synonymous and non-synonymous mutations onto branches of an HIV intrahost phylogenetic tree and comparing selection pressure on terminal and internal tree branches.     

A METHOD FOR TESTING THE CORRELATED EVOLUTION OF TWO BINARY CHARACTERS: ARE GAINS OR LOSSES CONCENTRATED ON CERTAIN BRANCHES OF A PHYLOGENETIC TREE?

A method is presented for assessing whether changes in a binary character are more concentrated than expected by chance on certain branches of a phylogenetic tree. It can be used to test for correlated evolution of two characters by asking whether changes in the first character are significantly concentrated on those branches on which the second character has a specified state. Thus, one could test whether this specified state is associated with, and thus might enable or select, gains or losses in the first character. The probability of achieving a concentration as or more extreme than that observed under the null hypotheses that changes are distributed randomly on the cladogram is obtained by calculating (a) the number of ways that n gains and m losses can be distributed on the cladogram and (b) the number of ways that p gains q losses can be distributed on the branches of interest given n gains and m losses in the cladogram overall. Summing (b) for appropriate p and q then dividing by (a) yields the desired probability. Simulations suggest that biases resulting from errors in parsimony reconstructions of ancestral states are not extreme.     

Is ACCTRAN better than DELTRAN?

When parsimony ancestral character reconstruction is ambiguous, it is often resolved in favour of the more complex character state. Hence, secondary loss (secondary “absence”) of a complex feature is favoured over parallel gains of that feature as this preserves the stronger hypothesis of homology. We believe that such asymmetry in character state complexity is important information for understanding character evolution in general. However, we here point out an inappropriate link that is commonly made between this approach and the accelerated transformation (ACCTRAN) algorithm. In ACCTRAN, changes are assigned along branches of a phylogenetic tree as close to the root as possible. This has been taken to imply that ACCTRAN will minimize hypotheses of parallel origins of complex traits and thus that ACCTRAN is philosophically better justified than the alternatives, such as delayed transformation (DELTRAN), where changes are assigned along branches as close to the tips as possible. We provide simple examples to show that such views are mistaken and that neither ACCTRAN nor DELTRAN consistently minimize parallel gain of complex traits. We therefore do not see theoretical grounds for favouring the popular ACCTRAN algorithm. © The Willi Hennig Society 2008.     

CORRELATED EVOLUTION OF MIGRATION AND SEXUAL DICHROMATISM IN THE NEW WORLD ORIOLES (ICTERUS)

The evolution of sexual dimorphism has long been attributed to sexual selection, specifically as it would drive repeated gains of elaborate male traits. In contrast to this pattern, New World oriole species all exhibit elaborate male plumage, and the repeated gains of sexual dichromatism observed in the genus are due to losses of female elaboration. Interestingly, most sexually dichromatic orioles belong to migratory or temperate‐breeding clades. Using character scoring and ancestral state reconstructions from two recent studies in Icterus, we tested a hypothesis of correlated evolution between migration and sexual dichromatism. We employed two discrete phylogenetic comparative approaches: the concentrated changes test and Pagel's discrete likelihood test. Our results show that the evolution of these traits is significantly correlated (CCT: uncorrected P < 0.05; ML: LRT = 12.470, P < 0.005). Indeed, our best model of character evolution suggests that gains of sexual dichromatism are 23 times more likely to occur in migratory taxa. This study demonstrates that a life‐history trait with no direct relationship with sexual selection has a strong influence on the evolution of sexual dichromatism. We recommend that researchers further investigate the role of selection on elaborate female traits in the evolution of sexual dimorphism.     

Test a clade in phylogenetic trees

We develop a new method for testing a portion of a tree (called a clade) based on multiple tests of many 4-taxon trees in this paper. This is particularly useful when the phylogenetic tree constructed by other methods have a clade that is difficult to explain from a biological point of view. The statement about the test of the clade can be made through the multiple P values from these individual tests. By controlling the familywise error rate or the false discovery rate (FDR), 4 different tree test methods are evaluated through simulation methods. It shows that the combination of the approximately unbiased (AU) test and the FDR-controlling procedure provides strong power along with reasonable type I error rate and less heavy computation.     

Genetic parameters in a rubber tree population: heritabilities,genotype-by-environment interactions and multi-trait correlations

Rubber tree breeding programs are mainly driven by selection of individuals with high yield and quality of rubber. Data from 51 open-pollinated progenies tested on six sites in Brazil were analyzed over several traits to estimate the following: genetic parameters such as narrow-sense heritability and additive genetic variance in single- and multi-site analyses, type B correlations to determine the relevance of genotype-by-environment interactions and its effects on alternative selection strategies, additive genetic repeatability correlation for rubber yield based on three consecutive yearly measurements, and type A correlations to evaluate trait-to-trait genetic associations for all measured traits. Average rubber yield (RYm) showed an estimated narrow-sense heritability of 0.31, with an estimated type B correlation of 0.84, indicating low levels of genotype-by-environment interaction. The trait survival and number of latex vessel rings (RG) showed larger genotype-by-environment interaction and the lowest heritabilites. High to moderate type B correlation was found for most traits, with a value of 0.85 between diameter (or girth) and RYm; therefore, it is possible to achieve interesting rubber yield genetic gains (over 3 years of measurements) from indirect selection based on diameter at age 2.     

Plant persistence traits in fire-prone ecosystems of the Mediterranean basin: a phylogenetic approach

The two main fire response traits found in the Mediterranean basin are the resprouting capacity (R) and the propagule-persistence capacity (P). Previous studies suggested that these two traits might be correlated. In this paper we first test whether R and P have evolved independently. Then, we ask if the correlation occurs because (a) one trait is not the target of selection but it is genetically linked to the other trait which is the one under selection pressure (indirect selection), or (b) because different evolutionary responses to the same selective pressure are acting in parallel on populations at different genetic starting points (parallel selection). Finally, we test to what extent resprouting is associated with some vegetative and reproductive traits.
To answer these questions we used a traits database for the eastern Iberian Peninsula and we assembled the phylogenetic tree on the basis of published information. The results indicate that the two traits are negatively associated and support the parallel selection scenario in which changes in R precedes changes in P. The phylogenetic–informed associations of resprouting with other traits (plant height, age at maturity) support the existence of allocation tradeoffs.
The results are consistent with the biogeographical history of the Mediterranean basin flora where most of lineages already resprouted to persist after a disturbance during the Tertiary, thus making it improbable that an additional costly persistence strategy would evolve under the Quaternary climatic conditions.     

Linking the investigations of character evolution and species diversification

Variation in diversification rates is often studied by investigating traits related to species' ecology and life history. Often, however, it is unknown whether these traits evolve gradually or in punctuated bursts during speciation. Using phylogenetic data and species' present-day trait information, we present a novel approach to assessing the mode of character change while accounting for trait-dependent speciation and extinction. Our model, "Binary-State Speciation and Extinction-node enhanced state shift" (BiSSE-ness), estimates both the rate of change occurring along lineages and the probability of change occurring during speciation, as well as independent speciation and extinction rates for each character state. Using simulations, we found that BiSSE-ness is able to distinguish along-lineage and speciational change and accurately estimate the parameters associated with character change and diversification rates. We applied BiSSE-ness to an empirical primate data set and found evidence for along-lineage changes in primate mating systems and social behaviors, whereas shifts in habitat were associated with speciation. In cases where trait changes may be linked to the speciation process itself (e.g., niche-related traits), BiSSE-ness provides a suitable framework with which to simultaneously address questions regarding species diversification and character change.     

Analysis of character correlations among wood decay mechanisms,mating systems,and substrate ranges in homobasidiomycetes

Homobasidiomycetes include the majority of wood-decaying fungi. Two basic forms of wood decay are known in homobasidiomycetes: white rot, in which lignin and cellulose are degraded, and brown rot, in which lignin is not appreciably degraded. An apparent correlation has been noted between production of a brown rot, decay of conifer substrates, and possession of a bipolar mating system (which has a single mating-type locus, in contrast to tetrapolar systems, which have two mating-type loci). The goals of this study were to infer the historical pattern of transformations in decay mode, mating type, and substrate range characters, and to determine if a causal relationship exists among them. Using nuclear and mitochondrial rDNA sequences, we performed a phylogenetic analysis of 130 species of homobasidiomycetes and performed ancestral state reconstructions by using parsimony on a range of trees, with various loss:gain cost ratios. We evaluated pairwise character correlations by using the concentrated changes test (CCT) of Maddison and the maximum likelihood (ML) method of Pagel. White rot, tetrapolar mating systems, and the ability to decay conifers and hardwoods appear to be plesiomorphic in homobasidiomycetes, whereas brown rot, bipolar mating systems, and exclusive decay of conifers appear to have evolved repeatedly. The only significant correlation among characters was that between brown rot (as the independent character) and exclusive decay of conifer substrates (P < 0.03). This correlation was supported by the CCT on a range of plausible trees, although not with every reconstruction of ancestral states, and by the ML test. Our findings suggest that the evolution of brown rot has promoted repeated shifts to specialization for confier substrates.     

The influence of cambial age on breeding for wood properties in Picea glauca

We investigated the influence of cambial age on correlations between different wood traits and the possibility of early selection in order to help decision-making for the improvement of juvenile wood in white spruce (Picea glauca (Moench) Voss). Increment cores were analysed from 375 trees covering 25 open-pollinated families from a 30-year-old provenance–progeny trial in Quebec, Canada. Genetic and phenotypic correlations between different mechanical and fibre anatomy-related wood traits were found to vary with cambial age. Most correlations became stronger in magnitude in rings closer to the bark. An exception is the correlation between microfibril angle (MFA) and the modulus of elasticity where correlations were strongly negative from the pith to the bark. Age–age correlations for different wood traits were found to be high and possible gains from early selection were estimated to be good in ring 8 and older for most traits. MFA was the trait with the strongest potential for selection as early as ring 4, but a detrimental correlation with wood density may represent a drawback of such a juvenile selection approach. Estimates showed that selection concentrated on a few easily measurable traits such as wood density and core length holds promise to obtain superior genetic gains for mechanical properties, but negative impacts would be expected on fibre anatomy traits related to pulp quality. These findings show the need for more carefully planned breeding and selection strategies if one wishes to improve several traits for different end uses.     

Intra-specific leaf trait responses to species richness at two different local scales

Plant functional traits, especially leaf traits, are accepted proxies for ecosystem properties. Typically, they are measured at the species level, neglecting within-species variation. While there is extensive knowledge about functional trait changes (both within and across species) along abiotic gradients, little is known about biotic influences, in particular at local scales. Here, we used a large biodiversity-ecosystem functioning experiment in subtropical China to investigate intra-specific trait changes of 16 tree species as a response to species richness of the local neighbourhood. We hypothesized that because of positive complementarity effects, species shift their leaf traits towards a more acquisitive growth strategy, when species richness of the local neighbourhood is higher. The trait shift should be most pronounced, when a focal tree's closest neighbour is from a different species, but should still be detectable as a response to species richness of the directly surrounding tree community. Consequently, we expected that trees with a con-specific closest neighbour have the strongest response to species richness of the surrounding tree community, i.e., the steepest increase of acquisitive traits. Our results indicate that species diversity promoted reduced competition and complementarity in resource use at both spatial scales considered. In addition, the closest neighbour had considerably stronger effects than the surrounding tree community. As expected, trees with a con-specific nearest neighbour showed the strongest trait shifts. However, the predicted positive effect of local hetero-specificity disappeared at the highest diversity levels of the surrounding tree community, potentially resulting from a higher probability to meet a strong competitor in a diverse environment. Our findings show that leaf traits within the same species vary not only in response to changing abiotic conditions, but also in response to local species richness. This highlights the benefit of including within-species trait variation when analysing relationships between plant functional traits and ecosystem functions.     

Functional traits and climate drive interspecific differences in disturbance-induced tree mortality

With climate change, natural disturbances such as storm or fire are reshuffled, inducing pervasive shifts in forest dynamics. To predict how it will impact forest structure and composition, it is crucial to understand how tree species differ in their sensitivity to disturbances. In this study, we investigated how functional traits and species mean climate affect their sensitivity to disturbances while controlling for tree size and stand structure. With data on 130,594 trees located on 7617 plots that were disturbed by storm, fire, snow, biotic or other disturbances from the French, Spanish, and Finnish National Forest Inventory, we modeled annual mortality probability for 40 European tree species as a function of tree size, dominance status, disturbance type, and intensity. We tested the correlation of our estimated species probability of disturbance mortality with their traits and their mean climate niches. We found that different trait combinations controlled species sensitivity to disturbances. Storm-sensitive species had a high height-dbh ratio, low wood density and high maximum growth, while fire-sensitive species had low bark thickness and high P50. Species from warmer and drier climates, where fires are more frequent, were more resistant to fire. The ranking in disturbance sensitivity between species was overall consistent across disturbance types. Productive conifer species were the most disturbance sensitive, while Mediterranean oaks were the least disturbance sensitive. Our study identified key relations between species functional traits and disturbance sensitivity, that allows more reliable predictions of how changing climate and disturbance regimes will impact future forest structure and species composition at large spatial scales.     

Phylogenetic correlation between male–male fighting and mode of prey subjugation in snakes

Male–male fighting (MMF) in snakes is a sexually dimorphic trait in adults that is expressed during breeding periods and confers reproductive advantages to winners. This trait, however, is not ubiquitous among the approximately 2,700 species of extant snakes, and past research shows evidence of taxonomic trends. We evaluated the phylogenetic distribution of MMF in extant snakes using two previously published estimates of snake evolutionary history. We clearly identified multiple independent gains and losses of MMF in snakes and phylogenetically important taxa for which information on MMF is lacking. We followed this with two tests of the association of MMF with mode of prey capture using the concentrated-changes test (CCT) of Maddison (1990), and a third test using the subtree decomposition method of Read and Nee (1995). In the CCT analyses, first we tested whether MMF was randomly distributed with respect to mode of prey subjugation in snake lineages. This hypothesis was rejected, with MMF being significantly more concentrated in taxa that subjugate prey by constriction and/or envenomation. Second, we tested a more temporally exact hypothesis: whether changes in state of MMF were randomly distributed with respect to occurrences of state changes in mode of prey subjugation. Results of this test depended on the exact test parameters used. In general, however, this hypothesis also was rejected, suggesting that loss of constriction and/or envenomation typically results in loss of MMF, or vice versa. Last, the subtree decomposition test indicated a significant correlation between evolution of MMF and evolution of constriction and/or envenomation as the primary mode of prey subjugation. We propose that the relationship between these states is not causal but results from both characters being independent adaptations to energy resource scarcity. Received in revised form: 20 March 2001 Electronic Publication     

Irrational exuberance for resolved species trees

Phylogenomics has largely succeeded in its aim of accurately inferring species trees, even when there are high levels of discordance among individual gene trees. These resolved species trees can be used to ask many questions about trait evolution, including the direction of change and number of times traits have evolved. However, the mapping of traits onto trees generally uses only a single representation of the species tree, ignoring variation in the gene trees used to construct it. Recognizing that genes underlie traits, these results imply that many traits follow topologies that are discordant with the species topology. As a consequence, standard methods for character mapping will incorrectly infer the number of times a trait has evolved. This phenomenon, dubbed “hemiplasy,” poses many problems in analyses of character evolution. Here we outline these problems, explaining where and when they are likely to occur. We offer several ways in which the possible presence of hemiplasy can be diagnosed, and discuss multiple approaches to dealing with the problems presented by underlying gene tree discordance when carrying out character mapping. Finally, we discuss the implications of hemiplasy for general phylogenetic inference, including the possible drawbacks of the widespread push for “resolved” species trees.     

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.     

Factors influencing changes in trait correlations across species after using phylogenetic independent contrasts

Comparative interspecific data sets have been analyzed routinely by phylogenetic methods, generally using Felsenstein’s phylogenetic independent contrasts (PIC) method. However, some authors have suggested that it may not be always necessary to incorporate phylogenetic information into statistical analyses of comparative data due to the low influence of shared history on the distribution of␣character states. The main goal of this paper was to undertake a comparison of results from non-phylogenetic Pearson correlation of tip values (TIPs) and phylogenetic independent contrasts analyses (PICs), using 566 correlation coefficients derived from 65 published papers. From each study we collected the following data: taxonomic group, number of species, type of phylogeny, number of polytomies in the phylogenetic tree, if branch length was transformed or not, trait types, the original correlation coefficient between the traits (TIPs) and the correlation coefficient between the traits using the independent contrasts method (PICs). The slope estimated from a regression of PIC correlations on TIP correlations was lower than one, and a paired t-test showed that correlations from PIC are significantly smaller than those obtained by TIP. Thus, PIC analyses tend to decrease the correlation between traits and usually increases the P-value and, thus, favoring the acceptance of the null hypothesis. Multiple factors, including taxonomic group, trait type and use of branch length transformations affected the change in decision regarding the acceptance of the null hypotheses and differences between PIC and TIP results. Due to the variety of factors affecting the differences between results provided by these methods, we suggest that comparative methods should be applied as a conservative approach to cross-species studies. Despite difficulties in quantifying precisely why these factors affect the differences between PIC and TIP, we also suggest that a better evaluation of evolutionary models underlying trait evolution is still necessary in this context and might explain some of the observed patterns.     

IN SEARCH OF HOMOPLASTIC TENDENCIES: STATISTICAL INFERENCE OF TOPOLOGICAL PATTERNS IN HOMOPLASY

The “tendency” for homoplasy to appear in closely related taxa has been widely discussed but rarely quantified. This paper proposes statistical tests that examine the topological distribution of homoplasy within characters in phylogenies. They test whether character changes are localized (confined to some subtree), or clustered (occur in proximity to each other), relative to two null models of character evolution. Null Model I assumes that the observed number of character changes are dispersed randomly among the internodes of the tree, whereas Model II weights the probability that an internode contains a change by the length of that internode—estimated by the total number of character changes along that internode. Localization is measured by the largest furthest-neighbor distance between changes, clustering by the mean nearest neighbor distance. Distances are measured either by the number of intervening branches or the number of intervening character changes. Analyses of four cladistic data sets from the literature reveal very few characters that exhibit significant levels of clustering or localization—no more than would be expected by chance. In every data set a majority of characters exhibited at least weak tendencies, but in only one data set was there a significant excess of such characters. The present findings do not provide compelling evidence for the existence of “tendencies” in homoplasy, at least among characters used to reconstruct phylogenies. They should be sought elsewhere, in cladistic analyses of larger scope, probably among a class of characters defined a priori on a structural or functional basis.     

Approximate likelihood-ratio test for branches: A fast, accurate, and powerful alternative

We revisit statistical tests for branches of evolutionary trees reconstructed upon molecular data. A new, fast, approximate likelihood-ratio test (aLRT) for branches is presented here as a competitive alternative to nonparametric bootstrap and Bayesian estimation of branch support. The aLRT is based on the idea of the conventional LRT, with the null hypothesis corresponding to the assumption that the inferred branch has length 0. We show that the LRT statistic is asymptotically distributed as a maximum of three random variables drawn from the chi(0)2 + chi(1)2 distribution. The new aLRT of interior branch uses this distribution for significance testing, but the test statistic is approximated in a slightly conservative but practical way as 2(l1- l2), i.e., double the difference between the maximum log-likelihood values corresponding to the best tree and the second best topological arrangement around the branch of interest. Such a test is fast because the log-likelihood value l2 is computed by optimizing only over the branch of interest and the four adjacent branches, whereas other parameters are fixed at their optimal values corresponding to the best ML tree. The performance of the new test was studied on simulated 4-, 12-, and 100-taxon data sets with sequences of different lengths. The aLRT is shown to be accurate, powerful, and robust to certain violations of model assumptions. The aLRT is implemented within the algorithm used by the recent fast maximum likelihood tree estimation program PHYML (Guindon and Gascuel, 2003).     

樟子松无性系生长性状与结实量变异研究

为选育高产、优质的樟子松种质资源,本研究以吉林省白城市林木种子园的304个樟子松无性系为材料,对其生长性状（树高、地径、胸径、3 m处直径、冠幅、分枝角度和侧枝粗度）和结实性状（2015、2016和2017年的结实量）进行调查分析。方差分析结果表明除冠幅外无性系间各性状差异均达极显著水平（P<0.01）;各指标表型变异系数的变化范围为3.79%~65.22%,重复力变化范围为0.24~0.70;相关性分析结果表明除侧枝粗度与3 m处直径相关未达到显著水平外,树高、胸径、地径、冠幅与侧枝粗度间相关均达极显著水平,不同树龄的结实量与大部分生长性状相关未达显著水平。依据生长性状,以5%的入选率对无性系进行综合评价,15个无性系入选,入选无性系在树高、地径、胸径、3 m处直径、分枝角度和侧枝粗度等指标的遗传增益分别为5.47%、4.48%、15.18%、11.78%、2.38%和6.66%;依据3年结实量,以5%的入选率对无性系进行综合评价,15个无性系入选,入选无性系在2015年、2016年和2017年的平均结实量的遗传增益分别为2.89%、46.32%和13.88%。该研究为樟子松种子园优良无性系的选择提供材料,也为吉林西部樟子松良种选育提供基础。