An ecologist's guide to the animal model

1. Efforts to understand the links between evolutionary and ecological dynamics hinge on our ability to measure and understand how genes influence phenotypes, fitness and population dynamics. Quantitative genetics provides a range of theoretical and empirical tools with which to achieve this when the relatedness between individuals within a population is known.
2. A number of recent studies have used a type of mixed-effects model, known as the animal model, to estimate the genetic component of phenotypic variation using data collected in the field. Here, we provide a practical guide for ecologists interested in exploring the potential to apply this quantitative genetic method in their research.
3. We begin by outlining, in simple terms, key concepts in quantitative genetics and how an animal model estimates relevant quantitative genetic parameters, such as heritabilities or genetic correlations.
4. We then provide three detailed example tutorials, for implementation in a variety of software packages, for some basic applications of the animal model. We discuss several important statistical issues relating to best practice when fitting different kinds of mixed models.
5. We conclude by briefly summarizing more complex applications of the animal model, and by highlighting key pitfalls and dangers for the researcher wanting to begin using quantitative genetic tools to address ecological and evolutionary questions.     

数量遗传学理论框架下的进化生态学研究：以动物模型的运用为例

目前,生态学家越来越关注深入的生物学问题,例如,1)理解生态和进化过程的互作和关系;2)种群中一个重要的表型特征,受遗传基因影响多大?即其可遗传程度,表示该性状的进化潜能;3)基因是怎样影响表型性状,及其对应的个体适合度以及种群动态?4)决定多个重要表型性状的基因之间关系和互作如何?随着生物统计软件尤其是线性混合模型的发展,结合经典数量遗传学的理论,发展出了针对上述问题的动物模型(Animal Model),使得我们可以对野外种群进行上述研究。本文首先介绍了经典数量遗传学的重要概念,随后在其理论框架下,举例介绍了动物模型的操作和使用,最后探讨和展望了利用数量遗传学方法进行进化生态学研究的前景。     

A Bayesian framework for comparative quantitative genetics

Bayesian approaches have been extensively used in animal breeding sciences, but similar approaches in the context of evolutionary quantitative genetics have been rare. We compared the performance of Bayesian and frequentist approaches in estimation of quantitative genetic parameters (viz. matrices of additive and dominance variances) in datasets typical of evolutionary studies and traits differing in their genetic architecture. Our results illustrate that it is difficult to disentangle the relative roles of different genetic components from small datasets, and that ignoring, e.g. dominance is likely to lead to biased estimates of additive variance. We suggest that a natural summary statistic for G-matrix comparisons can be obtained by examining how different the underlying multinormal probability distributions are, and illustrate our approach with data on the common frog (Rana temporaria). Furthermore, we derive a simple Monte Carlo method for computation of fraternity coefficients needed for the estimation of dominance variance, and use the pedigree of a natural Siberian jay (Perisoreus infaustus) population to illustrate that the commonly used approximate values can be substantially biased.     

Combined linkage disequilibrium and linkage mapping: Bayesian multilocus approach

Quantitative trait loci (QTL) affecting the phenotype of interest can be detected using linkage analysis (LA), linkage disequilibrium (LD) mapping or a combination of both (LDLA). The LA approach uses information from recombination events within the observed pedigree and LD mapping from the historical recombinations within the unobserved pedigree. We propose the Bayesian variable selection approach for combined LDLA analysis for single-nucleotide polymorphism (SNP) data. The novel approach uses both sources of information simultaneously as is commonly done in plant and animal genetics, but it makes fewer assumptions about population demography than previous LDLA methods. This differs from approaches in human genetics, where LDLA methods use LA information conditional on LD information or the other way round. We argue that the multilocus LDLA model is more powerful for the detection of phenotype–genotype associations than single-locus LDLA analysis. To illustrate the performance of the Bayesian multilocus LDLA method, we analyzed simulation replicates based on real SNP genotype data from small three-generational CEPH families and compared the results with commonly used quantitative transmission disequilibrium test (QTDT). This paper is intended to be conceptual in the sense that it is not meant to be a practical method for analyzing high-density SNP data, which is more common. Our aim was to test whether this approach can function in principle.     

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.     

A quantitative genetic method for estimating developmental instability

The concept of developmental instability (DI) is frequently used in evolutionary biology, and a range of definitions has been proposed. Moreover, numerous different statistical methods have been used for estimation of DI. The common basis for all methods is that measures need to be obtained from repeated structures within organisms. In the case of fluctuating asymmetry, mirror images could be interpreted as the repeats of each other. All repeats of a trait on one organism should, from a quantitative perspective, have the same genetic foundation. Most previous methods have not accounted for the genetics of the underlying trait. It is here shown how a statistical method from quantitative genetics (the repeated records animal model) can be used for assessment of DI, based on estimation of the variance due to the permanent environment. Moreover, Gibbs sampling is used for inference of the parameters, which provides a Bayesian framework where posterior distributions easily can be calculated from any functions of the variance components. The method is applied to a real dataset from two populations of the plant Scabiosa canescens, and results shows that it works well under realistic situations.     

贝叶斯统计在QTL作图中的应用研究进展

在许多复杂情况下, 贝叶斯统计方法比经典数理统计方法能更直接解决问题, 且可有效整合部分先验信息, 但其需要高强度计算的特性曾限制了其广泛应用。近几十年来, 随着高速计算机的发展以及MCMC算法的不断提出, 贝叶斯方法已被用于群体遗传学、分子进化、连锁作图和数量遗传学等研究领域, 文章综述了数量遗传学中QTL作图的贝叶斯方法从简单到复杂的发展历程。     

Evolution of phenotypic plasticity: where are we going now?

The study of phenotypic plasticity has progressed significantly over the past few decades. We have moved from variation for plasticity being considered as a nuisance in evolutionary studies to it being the primary target of investigations that use an array of methods, including quantitative and molecular genetics, as well as of several approaches that model the evolution of plastic responses. Here, I consider some of the major aspects of research on phenotypic plasticity, assessing where progress has been made and where additional effort is required. I suggest that some areas of research, such the study of the quantitative genetic underpinning of plasticity, have been either settled in broad outline or superseded by new approaches and questions. Other issues, such as the costs of plasticity are currently at the forefront of research in this field, and are likely to be areas of major future development.     

Inclusive heritability: combining genetic and non‐genetic information to study animal behavior and culture

Phenotypic variance results from variation in biological information possessed by individuals. Quantitative geneticists often strive to partition out all environmental variance to measure heritability. Behavioral biologists and ecologists however, require methods to integrate genetic and environmental components of inherited phenotypic variance in order to estimate the evolutionary potential of traits, which encompasses any form of information that is inherited. To help develop this integration, we build on the tools of quantitative genetics and offer the concept of ‘inclusive heritability’ which identifies and unifies the various mechanisms of information transmission across generations. A controversial component of non‐genetic information is animal culture, which is the part of phenotypic variance inherited through social learning. Culture has the unique property of being transmitted horizontally and obliquely, as well as vertically. Accounting for cultural variation would allow us to examine a broader range of evolutionary mechanisms. Culture may, for instance, produce behavioral isolating mechanisms leading to speciation. To advance the study of animal culture, we offer a definition of culture that is rooted in quantitative genetics. We also offer four testable criteria to determine whether a trait is culturally inherited. These criteria may constitute a conceptual tool to study animal culture. We briefly discuss methods to partition out cultural variance. Several authors have recently called for ‘modernizing the modern synthesis’ by including non‐genetic factors such as epigenetics and phenotypic plasticity in order to more fully explain phenotypic evolution. Here, we further propose to broaden the concept of inheritance by incorporating the cultural component of behavior. Applying the concept of inclusive heritability may advance the integration of multiple forms of inheritance into the study of evolution.     

Reconstructing routes of invasion using genetic data: why,how and so what?

Detailed knowledge about the geographical pathways followed by propagules from their source to the invading populations—referred to here as routes of invasion—provides information about the history of the invasion process and the origin and genetic composition of the invading populations. The reconstruction of invasion routes is required for defining and testing different hypotheses concerning the environmental and evolutionary factors responsible for biological invasions. In practical terms, it facilitates the design of strategies for controlling or preventing invasions. Most of our knowledge about the introduction routes of invasive species is derived from historical and observational data, which are often sparse, incomplete and, sometimes, misleading. In this context, population genetics has proved a useful approach for reconstructing routes of introduction, highlighting the complexity and the often counterintuitive nature of the true story. This approach has proved particularly useful since the recent development of new model‐based methods, such as approximate Bayesian computation, making it possible to make quantitative inferences in the complex evolutionary scenarios typically encountered in invasive species. In this review, we summarize some of the fundamental aspects of routes of invasion, explain why the reconstruction of these routes is useful for addressing both practical and theoretical questions, and comment on the various reconstruction methods available. Finally, we consider the main insights obtained to date from studies of invasion routes.     

Applying a quantitative genetics framework to behavioural syndrome research

Current interest in behavioural syndromes, or 'animal personalities', reinforces a need for behavioural ecologists to adopt a multivariate view of phenotypes. Fortunately, many of the methodological and theoretical issues currently being dealt with by behavioural ecologists within the context of behavioural syndromes have previously been investigated by researchers in other areas of evolutionary ecology. As a result of these previous efforts, behavioural syndrome researchers have considerable theory and a wide range of tools already available to them. Here, we discuss aspects of quantitative genetics useful for understanding the multivariate phenotype as well as the relevance of quantitative genetics to behavioural syndrome research. These methods not only allow the proper characterization of the multivariate behavioural phenotype and genotype-including behaviours within, among and independent of behavioural syndrome structures-but also allow predictions as to how populations may respond to selection on behaviours within syndromes. An application of a quantitative genetics framework to behavioural syndrome research also clarifies and refines the questions that should be asked.     

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.     

A hierarchical Bayesian model for next-generation population genomics

The demography of populations and natural selection shape genetic variation across the genome and understanding the genomic consequences of these evolutionary processes is a fundamental aim of population genetics. We have developed a hierarchical Bayesian model to quantify genome-wide population structure and identify candidate genetic regions affected by selection. This model improves on existing methods by accounting for stochastic sampling of sequences inherent in next-generation sequencing (with pooled or indexed individual samples) and by incorporating genetic distances among haplotypes in measures of genetic differentiation. Using simulations we demonstrate that this model has a low false-positive rate for classifying neutral genetic regions as selected genes (i.e., Φ(ST) outliers), but can detect recent selective sweeps, particularly when genetic regions in multiple populations are affected by selection. Nonetheless, selection affecting just a single population was difficult to detect and resulted in a high false-negative rate under certain conditions. We applied the Bayesian model to two large sets of human population genetic data. We found evidence of widespread positive and balancing selection among worldwide human populations, including many genetic regions previously thought to be under selection. Additionally, we identified novel candidate genes for selection, several of which have been linked to human diseases. This model will facilitate the population genetic analysis of a wide range of organisms on the basis of next-generation sequence data.     

Extending eco-evolutionary theory with oligomorphic dynamics

Understanding the interplay between ecological processes and the evolutionary dynamics of quantitative traits in natural systems remains a major challenge. Two main theoretical frameworks are used to address this question, adaptive dynamics and quantitative genetics, both of which have strengths and limitations and are often used by distinct research communities to address different questions. In order to make progress, new theoretical developments are needed that integrate these approaches and strengthen the link to empirical data. Here, we discuss a novel theoretical framework that bridges the gap between quantitative genetics and adaptive dynamics approaches. ‘Oligomorphic dynamics’ can be used to analyse eco-evolutionary dynamics across different time scales and extends quantitative genetics theory to account for multimodal trait distributions, the dynamical nature of genetic variance, the potential for disruptive selection due to ecological feedbacks, and the non-normal or skewed trait distributions encountered in nature. Oligomorphic dynamics explicitly takes into account the effect of environmental feedback, such as frequency- and density-dependent selection, on the dynamics of multi-modal trait distributions and we argue it has the potential to facilitate a much tighter integration between eco-evolutionary theory and empirical data.     

Selection for increased body length in Subantarctic fur seals on Amsterdam Island

The traditional distinction between ecological and evolutionary times is eroding, calling for tighter links between ecology and evolution. An example of such a brigde between the two disciplines is the so-called 'animal model', a methodology initially developed by animal breeders, which has become very popular among ecologists studying contemporary microevolution. Using a Bayesian multi-trait 'animal model', we investigated the quantitative genetics of body size, a fitness-related trait, in Subantarctic fur seals (Arctocephalus tropicalis) breeding on Amsterdam Island, Southern Ocean. Our approach jointly modelled the growth and selection processes at work in this population. Body length is heritable for both sexes, and females are under selection for increased body length in this population. We strongly suspect the peculiar ecological context of impoverished, suitable prey availability exacerbated by density-dependence phenomena to be an important selective agent on females breeding on Amsterdam Island.     

The use of approximate Bayesian computation in conservation genetics and its application in a case study on yellow-eyed penguins

The inference of demographic parameters from genetic data has become an integral part of conservation studies. A group of Bayesian methods developed originally in population genetics, known as approximate Bayesian computation (ABC), has been shown to be particularly useful for the estimation of such parameters. These methods do not need to evaluate likelihood functions analytically and can therefore be used even while assuming complex models. In this paper we describe the ABC approach and identify specific parts of its algorithm that are being the subject of intensive studies in order to further expand its usability. Furthermore, we discuss applications of this Bayesian algorithm in conservation studies, providing insights on the potentialities of these tools. Finally, we present a case study in which we use a simple Isolation-Migration model to estimate a number of demographic parameters of two populations of yellow-eyed penguins (Megadyptes antipodes) in New Zealand. The resulting estimates confirm our current understanding of M. antipodes dynamic, demographic history and provide new insights into the expansion this species has undergone during the last centuries.     

General quantitative genetic methods for comparative biology: phylogenies,taxonomies and multi‐trait models for continuous and categorical characters

Although many of the statistical techniques used in comparative biology were originally developed in quantitative genetics, subsequent development of comparative techniques has progressed in relative isolation. Consequently, many of the new and planned developments in comparative analysis already have well‐tested solutions in quantitative genetics. In this paper, we take three recent publications that develop phylogenetic meta‐analysis, either implicitly or explicitly, and show how they can be considered as quantitative genetic models. We highlight some of the difficulties with the proposed solutions, and demonstrate that standard quantitative genetic theory and software offer solutions. We also show how results from Bayesian quantitative genetics can be used to create efficient Markov chain Monte Carlo algorithms for phylogenetic mixed models, thereby extending their generality to non‐Gaussian data. Of particular utility is the development of multinomial models for analysing the evolution of discrete traits, and the development of multi‐trait models in which traits can follow different distributions. Meta‐analyses often include a nonrandom collection of species for which the full phylogenetic tree has only been partly resolved. Using missing data theory, we show how the presented models can be used to correct for nonrandom sampling and show how taxonomies and phylogenies can be combined to give a flexible framework with which to model dependence.     

Bayesian mapping of quantitative trait loci for complex binary traits

A complex binary trait is a character that has a dichotomous expression but with a polygenic genetic background. Mapping quantitative trait loci (QTL) for such traits is difficult because of the discrete nature and the reduced variation in the phenotypic distribution. Bayesian statistics are proved to be a powerful tool for solving complicated genetic problems, such as multiple QTL with nonadditive effects, and have been successfully applied to QTL mapping for continuous traits. In this study, we show that Bayesian statistics are particularly useful for mapping QTL for complex binary traits. We model the binary trait under the classical threshold model of quantitative genetics. The Bayesian mapping statistics are developed on the basis of the idea of data augmentation. This treatment allows an easy way to generate the value of a hypothetical underlying variable (called the liability) and a threshold, which in turn allow the use of existing Bayesian statistics. The reversible jump Markov chain Monte Carlo algorithm is used to simulate the posterior samples of all unknowns, including the number of QTL, the locations and effects of identified QTL, genotypes of each individual at both the QTL and markers, and eventually the liability of each individual. The Bayesian mapping ends with an estimation of the joint posterior distribution of the number of QTL and the locations and effects of the identified QTL. Utilities of the method are demonstrated using a simulated outbred full-sib family. A computer program written in FORTRAN language is freely available on request.     

Bayesian phylogenetic analysis of combined data

The recent development of Bayesian phylogenetic inference using Markov chain Monte Carlo (MCMC) techniques has facilitated the exploration of parameter-rich evolutionary models. At the same time, stochastic models have become more realistic (and complex) and have been extended to new types of data, such as morphology. Based on this foundation, we developed a Bayesian MCMC approach to the analysis of combined data sets and explored its utility in inferring relationships among gall wasps based on data from morphology and four genes (nuclear and mitochondrial, ribosomal and protein coding). Examined models range in complexity from those recognizing only a morphological and a molecular partition to those having complex substitution models with independent parameters for each gene. Bayesian MCMC analysis deals efficiently with complex models: convergence occurs faster and more predictably for complex models, mixing is adequate for all parameters even under very complex models, and the parameter update cycle is virtually unaffected by model partitioning across sites. Morphology contributed only 5% of the characters in the data set but nevertheless influenced the combined-data tree, supporting the utility of morphological data in multigene analyses. We used Bayesian criteria (Bayes factors) to show that process heterogeneity across data partitions is a significant model component, although not as important as among-site rate variation. More complex evolutionary models are associated with more topological uncertainty and less conflict between morphology and molecules. Bayes factors sometimes favor simpler models over considerably more parameter-rich models, but the best model overall is also the most complex and Bayes factors do not support exclusion of apparently weak parameters from this model. Thus, Bayes factors appear to be useful for selecting among complex models, but it is still unclear whether their use strikes a reasonable balance between model complexity and error in parameter estimates.     

Population genetics of fungal diseases of plants

Although parasitism is one of the most common lifestyles among eukaryotes, population genetics on parasites lag for behind those on free-living organisms. Yet, the advent of molecular markers offers great tools for studying important processes, such as dispersal, mating systems, adaptation to host and speciation. Here we highlight some studies that used molecular markers to address questions about the population genetics of fungal (including oomycetes) plant pathogens. We conclude that population genetics approaches have provided tremendous insights into the biology of a few fungal parasites and warrant more wide use in phytopathology. However, theoretical advances are badly needed to best apply the existing methods. Fungi are of prime interest not only because they are major parasites of plants and animals, but they also constitute tractable and highly useful models for understanding evolutionary processes. We hope that the emerging field of fungal evolution will attract more evolutionary biologists in the near future.