The evolution of function-valued traits for conditional cooperation

In this paper we study the evolution of function-valued traits for cooperation in environments that display varying degrees of population viscosity. Traits measure an individual's intrinsic propensity to cooperate in a standard bilateral Prisoner's dilemma and can be increasing, decreasing or constant functions of the probability to interact with individuals of ones own genotype. We first analyse adaptation to homogenous environments (with constant degree of viscosity). Comparing environments characterized by different degrees of viscosity, we find that the relation between viscosity and the equilibrium type distribution is not monotone. In fact, it is possible that in fluid populations (no viscosity) there is more cooperation in equilibrium than in populations with intermediate degrees of viscosity. In a second step we analyse heterogenous environments (with varying degrees of viscosity). We find that under very weak assumptions on the distribution of the viscosity parameter strictly increasing functions are always selected and under some parameter constellations they are uniquely so.     

Variation,selection and evolution of function-valued traits

We describe an emerging framework for understanding variation, selection and evolution of phenotypic traits that are mathematical functions. We use one specific empirical example – thermal performance curves (TPCs) for growth rates of caterpillars – to demonstrate how models for function-valued traits are natural extensions of more familiar, multivariate models for correlated, quantitative traits. We emphasize three main points. First, because function-valued traits are continuous functions, there are important constraints on their patterns of variation that are not captured by multivariate models. Phenotypic and genetic variation in function-valued traits can be quantified in terms of variance-covariance functions and their associated eigenfunctions: we illustrate how these are estimated as well as their biological interpretations for TPCs. Second, selection on a function-valued trait is itself a function, defined in terms of selection gradient functions. For TPCs, the selection gradient describes how the relationship between an organism's performance and its fitness varies as a function of its temperature. We show how the form of the selection gradient function for TPCs relates to the frequency distribution of environmental states (caterpillar temperatures) during selection. Third, we can predict evolutionary responses of function-valued traits in terms of the genetic variance-covariance and the selection gradient functions. We illustrate how non-linear evolutionary responses of TPCs may occur even when the mean phenotype and the selection gradient are themselves linear functions of temperature. Finally, we discuss some of the methodological and empirical challenges for future studies of the evolution of function-valued traits.     

Optimizing selection for function-valued traits

We consider a function-valued trait z(t) whose pre-selection distribution is Gaussian, and a fitness function W that models optimizing selection, subject to certain natural assumptions. We show that the post-selection distribution of z(t) is also Gaussian, compute the selection differential, and derive an equation that expresses the selection gradient in terms of the parameters of W and of the pre-selection distribution. We make no assumptions on the nature of the “time” parameter t.      

The adaptive dynamics of function-valued traits

This study extends the framework of adaptive dynamics to function-valued traits. Such adaptive traits naturally arise in a great variety of settings: variable or heterogeneous environments, age-structured populations, phenotypic plasticity, patterns of growth and form, resource gradients, and in many other areas of evolutionary ecology. Adaptive dynamics theory allows analysing the long-term evolution of such traits under the density-dependent and frequency-dependent selection pressures resulting from feedback between evolving populations and their ecological environment. Starting from individual-based considerations, we derive equations describing the expected dynamics of a function-valued trait in asexually reproducing populations under mutation-limited evolution, thus generalizing the canonical equation of adaptive dynamics to function-valued traits. We explain in detail how to account for various kinds of evolutionary constraints on the adaptive dynamics of function-valued traits. To illustrate the utility of our approach, we present applications to two specific examples that address, respectively, the evolution of metabolic investment strategies along resource gradients, and the evolution of seasonal flowering schedules in temporally varying environments.     

A flexible estimating equations approach for mapping function-valued traits

In genetic studies, many interesting traits, including growth curves and skeletal shape, have temporal or spatial structure. They are better treated as curves or function-valued traits. Identification of genetic loci contributing to such traits is facilitated by specialized methods that explicitly address the function-valued nature of the data. Current methods for mapping function-valued traits are mostly likelihood-based, requiring specification of the distribution and error structure. However, such specification is difficult or impractical in many scenarios. We propose a general functional regression approach based on estimating equations that is robust to misspecification of the covariance structure. Estimation is based on a two-step least-squares algorithm, which is fast and applicable even when the number of time points exceeds the number of samples. It is also flexible due to a general linear functional model; changing the number of covariates does not necessitate a new set of formulas and programs. In addition, many meaningful extensions are straightforward. For example, we can accommodate incomplete genotype data, and the algorithm can be trivially parallelized. The framework is an attractive alternative to likelihood-based methods when the covariance structure of the data is not known. It provides a good compromise between model simplicity, statistical efficiency, and computational speed. We illustrate our method and its advantages using circadian mouse behavioral data.     

Genetic analysis of female preference functions as function-valued traits

The genetic analysis of female preferences has been seen as a particularly challenging empirical endeavor because of difficulties in generating suitable preference metrics in experiments large enough to adequately characterize variation. In this article, we take an alternative approach, treating female preference as a function-valued trait and exploiting random-coefficient models to characterize the genetic basis of female preference without measuring preference functions in each individual. Applying this approach to Drosophila bunnanda, in which females assess males through a multivariate contact pheromone system, we gain three valuable insights into the genetic basis of female preference functions. First, most genetic variation was attributable to one eigenfunction, suggesting shared genetic control of preferences for nine male pheromones. Second, genetic variance in female preference functions was not associated with genetic variance in the pheromones, implying that genetic variation in female preference did not maintain genetic variation in male traits. Finally, breeding values for female preference functions were skewed away from the direction of selection on the male traits, suggesting directional selection on female preferences. The genetic analysis of female preference functions as function-valued traits offers a robust statistical framework for investigations of female preference, in addition to alleviating some experimental difficulties associated with estimating variation in preference functions.     

Phylogenetic inference of reciprocal effects between geographic range evolution and diversification

Geographic characters--traits describing the spatial distribution of a species-may both affect and be affected by processes associated with lineage birth and death. This is potentially confounding to comparative analyses of species distributions because current models do not allow reciprocal interactions between the evolution of ranges and the growth of phylogenetic trees. Here, we introduce a likelihood-based approach to estimating region-dependent rates of speciation, extinction, and range evolution from a phylogeny, using a new model in which these processes are interdependent. We demonstrate the method with simulation tests that accurately recover parameters relating to the mode of speciation and source-sink dynamics. We then apply it to the evolution of habitat occupancy in Californian plant communities, where we find higher rates of speciation in chaparral than in forests and evidence for expanding habitat tolerances.     

Hypothesis testing in comparative and experimental studies of function-valued traits

Many traits of evolutionary interest, when placed in their developmental, physiological, or environmental contexts, are function-valued. For instance, gene expression during development is typically a function of the age of an organism and physiological processes are often a function of environment. In comparative and experimental studies, a fundamental question is whether the function-valued trait of one group is different from another. To address this question, evolutionary biologists have several statistical methods available. These methods can be classified into one of two types: multivariate and functional. Multivariate methods, including univariate repeated-measures analysis of variance (ANOVA), treat each trait as a finite list of data. Functional methods, such as repeated-measures regression, view the data as a sample of points drawn from an underlying function. A key difference between multivariate and functional methods is that functional methods retain information about the ordering and spacing of a set of data values, information that is discarded by multivariate methods. In this study, we evaluated the importance of that discarded information in statistical analyses of function-valued traits. Our results indicate that functional methods tend to have substantially greater statistical power than multivariate approaches to detect differences in a function-valued trait between groups.     

Multivariate character process models for the analysis of two or more correlated function-valued traits

Various methods, including random regression, structured antedependence models, and character process models, have been proposed for the genetic analysis of longitudinal data and other function-valued traits. For univariate problems, the character process models have been shown to perform well in comparison to alternative methods. The aim of this article is to present an extension of these models to the simultaneous analysis of two or more correlated function-valued traits. Analytical forms for stationary and nonstationary cross-covariance functions are studied. Comparisons with the other approaches are presented in a simulation study and in an example of a bivariate analysis of genetic covariance in age-specific fecundity and mortality in Drosophila. As in the univariate case, bivariate character process models with an exponential correlation were found to be quite close to first-order structured antedependence models. The simulation study showed that the choice of the most appropriate methodology is highly dependent on the covariance structure of the data. The bivariate character process approach proved to be able to deal with quite complex nonstationary and nonsymmetric cross-correlation structures and was found to be the most appropriate for the real data example of the fruit fly Drosophila melanogaster.     

Phylogenetic inference from platyhelminth life-cycle stages

Studies of the life cycle stages of digeneans and oncophoreans (= monogeneans and cestodes) indicate that these two groups had separate origins from free-living rhabdocoel-like ancestors and that the original single-host life cycles became 2-host cycles through accidental ingestion, in digeneans by free-swimming adults being ingested by vertebrates, and in cestodes by eggs being ingested by invertebrates. In both lines a third host was incorporated as a means of increasing the efficiency of transfer between hosts, in digeneans between the primary mollusc and the secondary vertebrate, and in cestodes between the secondary (“first intermediate”) host and the primary vertebrate host.     

Phylogenetic inference via sequential Monte Carlo

Bayesian inference provides an appealing general framework for phylogenetic analysis, able to incorporate a wide variety of modeling assumptions and to provide a coherent treatment of uncertainty. Existing computational approaches to bayesian inference based on Markov chain Monte Carlo (MCMC) have not, however, kept pace with the scale of the data analysis problems in phylogenetics, and this has hindered the adoption of bayesian methods. In this paper, we present an alternative to MCMC based on Sequential Monte Carlo (SMC). We develop an extension of classical SMC based on partially ordered sets and show how to apply this framework--which we refer to as PosetSMC--to phylogenetic analysis. We provide a theoretical treatment of PosetSMC and also present experimental evaluation of PosetSMC on both synthetic and real data. The empirical results demonstrate that PosetSMC is a very promising alternative to MCMC, providing up to two orders of magnitude faster convergence. We discuss other factors favorable to the adoption of PosetSMC in phylogenetics, including its ability to estimate marginal likelihoods, its ready implementability on parallel and distributed computing platforms, and the possibility of combining with MCMC in hybrid MCMC-SMC schemes. Software for PosetSMC is available at http://www.stat.ubc.ca/ bouchard/PosetSMC.     

Phylogenetic inference and comparative evolution of a complex microsatellite and its flanking regions in carnivores

We sequenced locus Mel 08, with complex short repetitive motifs, in 24 carnivore species belonging to five different families in order to explore mutational changes in the region in the context of locus and species evolution. This non-coding locus includes up to four different parts or repetitive motifs showing size variability. The variability consists of repeat additions and deletions; substitutions, insertions and/or deletions creating interruptions in the repeat; and substitutions, insertions and deletions in the flanking regions. The locus has different repeat expansions in different carnivore subfamilies. We hypothesize that the complexity of this locus is due to a high mutation rate at an ancestral DNA sequence and, thus, prompts the emergence of repeats at mutational hotspots. High levels of homoplasy were evident, with nine electromorphs representing 28 haplotypes never shared across species. The variability in flanking regions was informative for phylogenetic inference and their evolutionary content. Tree topologies were congruent with relevant hypotheses on current conflicts in carnivore phylogenies, such as: (i) the monophyly of Lutrinae, (ii) the paraphyly of Mustelinae, (iii) the basal position of the Eurasian badger, Meles meles , in the Mustelidae, (iv) the classification of skunks as a separate family, Mephitidae, and (v) the placement of the red panda, Ailurus fulgens , as a monotypic family, Ailuridae, at a basal position in the Musteloidea.     

Phylogenetic reconstruction of key traits in the evolution of ivies (Hedera L.)

The Mediterranean harbours the highest number of Hedera (Araliaceae) species, lineages, ploidy levels, and trichome morphologies of any area where the genus occurs. Previous molecular and cytogenetic studies identified two main centres of diversity for Hedera (Araliaceae), the eastern and western parts of the Mediterranean region. An explicit analysis of key traits was performed to investigate geographical patterns and ancestral character states of ivy lineages. Interestingly, the greatest diversity of Hedera was found in the western Mediterranean, including the three species of Macaronesia (H. azorica in the Azores, H. maderensis in Madeira and H. canariensis in the Canary Islands). Phylogenetic and phylogeographical analyses of the nrITS and plastid trnT-L sequences revealed multiple connections between the Mediterranean region and Asia, and suggest recurrent colonization between these two areas. Reconstruction of three important characters long used to distinguish members of the genus (trichome types, ploidy levels, and geographical areas) suggests that a diploid species with scale-like trichomes from the Mediterranean basin was the most recent common ancestor of the extant species of Hedera.     

Phylogenetic inference under the pure drift model

When pairwise genetic distances are used for phylogenetic reconstruction, it is usually assumed that the genetic distance between two taxa contains information about the time after the two taxa diverged. As a result, upon an appropriate transformation if necessary, the distance usually can be fitted to a linear model such that it is expressed as the sum of lengths of all branches that connect the two taxa in a given phylogeny. This kind of distance is referred to as "additive distance." For a phylogenetic tree exclusively driven by random genetic drift, genetic distances related to coancestry coefficients (theta XY) between any two taxa are more suitable. However, these distances are fundamentally different from the additive distance in that coancestry does not contain any information about the time after two taxa split from a common ancestral population; instead, it reflects the time before the two taxa diverged. In other words, the magnitude of theta XY provides information about how long the two taxa share the same evolutionary pathways. The fundamental difference between the two kinds of distances has led to a different algorithm of evaluating phylogenetic trees when theta XY and related distance measures are used. Here we present the new algorithm using the ordinary- least-squares approach but fitting to a different linear model. This treatment allows genetic variation within a taxon to be included in the model. Monte Carlo simulation for a rooted phylogeny of four taxa has verified the efficacy and consistency of the new method. Application of the method to human population was demonstrated.      

Phylogenetic inference from conserved sites alignments.

Molecular sequences provide a rich source of data for inferring the phylogenetic relationships among species. However, recent work indicates that even an accurate multiple alignment of a large sequence set may yield an incorrect phylogeny and that the quality of the phylogenetic tree improves when the input consists only of the highly conserved, motif regions of the alignment. This work introduces two methods of producing multiple alignments that include only the conserved regions of the initial alignment. The first method retains conserved motifs, whereas the second retains individual conserved sites in the initial alignment. Using parsimony analysis on a mitochondrial data set containing 19 species among which the phylogenetic relationships are widely accepted, both conserved alignment methods produce better phylogenetic trees than the complete alignment. Unlike any of the 19 inference methods used before to analyze this data, both methods produce trees that are completely consistent with the known phylogeny. The motif-based method employs far fewer alignment sites for comparable error rates. For a larger data set containing mitochondrial sequences from 39 species, the site-based method produces a phylogenetic tree that is largely consistent with known phylogenetic relationships and suggests several novel placements. J. Exp. Zool. ( Mol. Dev. Evol.) 285:128-139, 1999.     

Phylogenetic inference and peristome evolution in haplolepideous mosses,focusing on Pseudoditrichaceae and Ditrichaceae s. l.

Pseudoditrichum mirabile, the only species of Pseudoditrichaceae, has been known for a long time from a single collection from the Canadian Arctic. Its systematic position remained enigmatic due to similarity in gametophyte structure with Ditrichaceae, a family that has simple peristomes, whereas the peristome in Pseudoditrichum is double. Due to this difference, Pseudoditrichum was classified in either Funariales or Bryales. A recent discovery of this species in the Anabar Plateau in northern Siberia has allowed its phylogenetic position to be tested based on plastid rps4 and rbcL and mitochondrial nad5 sequences. The results of this research reject the earlier hypotheses. Instead, the molecular analysis resolves Pseudoditrichum in a clade with Chrysoblastella chilensis (formerly Ditrichaceae) in the haplolepideous lineage. The peristome of Pseudoditrichum is of a previously unknown type with a fully developed exostome and hyaline endostome elements opposite the exostome teeth, based not on the 4:2:4 peristomial formula, but on 4:2:3. Double peristomes of the same type, albeit rather strongly reduced, occur in Catoscopium, Chrysoblastella, Distichium and Ditrichum flexicaule. The polyphyly of Ditrichaceae is confirmed by molecular phylogenetic analysis, and Ditrichum flexicaule and D. gracile are segregated into the new genus Flexitrichum and family Flexitrichaceae. An independent status of the recently resurrected family Distichiaceae is supported, and segregation of Chrysoblastella and Saelania into new monospecific families is proposed.     

Early rodent incisor enamel evolution: Phylogenetic implications

Incisor enamel microstructure proved to be a very effective tool for assessment of phylogenetic relationships among the Rodentia. Pauciserial and multiserial Schmelzmuster are clearly distinct by structural characters such as orientation of interprismatic matrix, presence or absence of transition zones between Hunter-Schreger bands (HSB), inclination of HSB, enamel thickness, and others. Pauciserial HSB are structurally very close to the earliest known mammalian HSB found in Paleocene arctocyonids. Biomechanical arguments and outgroup comparison with mixodontians indicate that the pauciserial Schmelzmuster is a symplesiomorphy of the Rodentia. Transitional stages from pauciserial to multiserial Schmelzmuster were observed in middle Eocene ctenodactyloids and from pauciserial to uniserial in middle to late Eocene anomalurids. The multiserial Schmelzmuster is considered a synapomorphy of the Hystricognathi, ctenodactylids, and pedetids. Schmelzmuster evolution reflects the early dichotomy of the Rodentia: In the Asian ctenodactyloid lineage a multiserial Schmelzmuster evolved once and in the North American/European ischyromyoid lineage a uniserial Schmelzmuster developed several times convergently. The pauci- to uniserial Schmelzmuster of the anomalurids excludes a close relationship to the phiomyids, because the ctenodactyloid-phiomyid lineage is characterized by the development of a multiserial Schmelzmuster.     

Bayesian inference of character evolution

Much recent progress in evolutionary biology is based on the inference of ancestral states and past transformations in important traits on phylogenetic trees. These exercises often assume that the tree is known without error and that ancestral states and character change can be mapped onto it exactly. In reality, there is often considerable uncertainty about both the tree and the character mapping. Recently introduced Bayesian statistical methods enable the study of character evolution while simultaneously accounting for both phylogenetic and mapping uncertainty, adding much needed credibility to the reconstruction of evolutionary history.