Jody Hey

Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics

In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically. The result is an approximation to the full joint posterior density of the model parameters. For many purposes, this function can be treated as a likelihood, thereby permitting likelihood-based analyses, including likelihood ratio tests of nested models. Several examples, including an application to the divergence of chimpanzee subspecies, are provided.

The limits of selection during maize domestication

The domestication of all major crop plants occurred during a brief period in human history about 10,000 years ago. During this time, ancient agriculturalists selected seed of preferred forms and culled out seed of undesirable types to produce each subsequent generation. Consequently, favoured alleles at genes controlling traits of interest increased in frequency, ultimately reaching fixation. When selection is strong, domestication has the potential to drastically reduce genetic diversity in a crop. To understand the impact of selection during maize domestication, we examined nucleotide polymorphism in teosinte branched1, a gene involved in maize evolution. Here we show that the effects of selection were limited to the genes regulatory region and cannot be detected in the protein-coding region. Although selection was apparently strong, high rates of recombination and a prolonged domestication period probably limited its effects. Our results help to explain why maize is such a variable crop. They also suggest that maize domestication required hundreds of years, and confirm previous evidence that maize was domesticated from Balsas teosinte of southwestern Mexico.

Isolation with Migration Models for More Than Two Populations

A method for studying the divergence of multiple closely related populations is described and assessed. The approach of Hey and Nielsen (2007, Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics. Proc Natl Acad Sci USA. 104:2785-2790) for fitting an isolation-with-migration model was extended to the case of multiple populations with a known phylogeny. Analysis of simulated data sets reveals the kinds of history that are accessible with a multipopulation analysis. Necessarily, processes associated with older time periods in a phylogeny are more difficult to estimate; and histories with high levels of gene flow are particularly difficult with more than two populations. However, for histories with modest levels of gene flow, or for very large data sets, it is possible to study large complex divergence problems that involve multiple closely related populations or species.

On the Number of New World Founders: A Population Genetic Portrait of the Peopling of the Americas

The founding of New World populations by Asian peoples is the focus of considerable archaeological and genetic research, and there persist important questions on when and how these events occurred. Genetic data offer great potential for the study of human population history, but there are significant challenges in discerning distinct demographic processes. A new method for the study of diverging populations was applied to questions on the founding and history of Amerind-speaking Native American populations. The model permits estimation of founding population sizes, changes in population size, time of population formation, and gene flow. Analyses of data from nine loci are consistent with the general portrait that has emerged from archaeological and other kinds of evidence. The estimated effective size of the founding population for the New World is fewer than 80 individuals, approximately 1% of the effective size of the estimated ancestral Asian population. By adding a splitting parameter to population divergence models it becomes possible to develop detailed portraits of human demographic history. Analyses of Asian and New World data support a model of a recent founding of the New World by a population of quite small effective size.

THE STUDY OF STRUCTURED POPULATIONS — NEW HOPE FOR A DIFFICULT AND DIVIDED SCIENCE

Natural populations, including those of humans, have complex geographies and histories. Studying how they evolve is difficult, but it is possible with population-based DNA sequence data. However, the study of structured populations is divided by two distinct schools of thought and analysis. The phylogeographic approach is fundamentally graphical and begins with a gene-tree estimate. By contrast, the more traditional approach of using summary statistics is fundamentally mathematical. Both approaches have limitations, but there is promise in newer probabilistic methods that offer the flexibility and data exploitation of the phylogeographic approach in an explicitly model-based mathematical framework.

The Divergence of Chimpanzee Species and Subspecies as Revealed in Multipopulation Isolation-with-Migration Analyses

The divergence of bonobos and three subspecies of the common chimpanzee was examined under a multipopulation isolation-with-migration (IM) model with data from 73 loci drawn from the literature. A benefit of having a full multipopulation model, relative to conducting multiple pairwise analyses between sampled populations, is that a full model can reveal historical gene flow involving ancestral populations. An example of this was found in which gene flow is indicated between the western common chimpanzee subspecies and the ancestor of the central and the eastern common chimpanzee subspecies. The results of a full analysis on all four populations are strongly consistent with analyses on pairs of populations and generally similar to results from previous studies. The basal split between bonobos and common chimpanzees was estimated at 0.93 Ma (0.68-1.54 Ma, 95% highest posterior density interval), with the split among the ancestor of three common chimpanzee populations at 0.46 Ma (0.35-0.65), and the most recent split between central and eastern common chimpanzee populations at 0.093 Ma (0.041-0.157). Population size estimates mostly fell in the range from 5,000 to 10,000 individuals. The exceptions are the size of the ancestor of the common chimpanzee and the bonobo, at 17,000 (8,000-28,000) individuals, and the central common chimpanzee and its immediate ancestor with the eastern common chimpanzee, which have effective size estimates at 27,000 (16,000-44,000) and 32,000 (19,000-54,000) individuals, respectively.

The causes of phylogenetic conflict in a classic Drosophila species group

Bifurcating phylogenies are frequently used to describe the evolutionary history of groups of related species. However, simple bifurcating models may poorly represent the evolutionary history of species that have been exchanging genes. Here, we show that the history of three well–known closely related species, Drosophila pseudoobscura, D. persimilis and D. p. bogotana, is not well represented by a bifurcating phylogenetic tree. The phylogenetic relationships among these species vary widely between different genomic regions. Much of this phylogenetic variation can be explained by the potential of different genomic regions to introgress between species, as measured in laboratory studies. We argue that the utility of multiple markers in species–level phylogenetic studies can be greatly enhanced by knowledge of genomic location and, in the case of hybridizing species, by knowledge of the functional or linkage relationships among the markers and regions of the genome that reduce hybrid fitness.

Using phylogenetic trees to study speciation and extinction

One tool in the study of the forces that determine species diversity is the null, or simple, model. The fit of predictions to observations, good or bad, leads to a useful paradigm or to knowledge of forces not accounted for, respectively. It is shown how simple models of speciation and extinction lead directly to predictions of the structure of phylogenetic trees. These predictions include both essential attributes of phylogenetic trees: lengths, in the form of internode distances; and topology, in the form of internode links. These models also lead directly to statistical tests which can be used to compare predictions with phylogenetic trees that are estimated from data. Two different models and eight data sets are considered. A model without species extinction consistently yielded predictions closer to observations than did a model that included extinction. It is proposed that it may be useful to think of the diversification of recently formed monophyletic groups as a random speciation process without extinction.

In defence of model-based inference in phylogeography

Recent papers have promoted the view that model‐based methods in general, and those based on Approximate Bayesian Computation (ABC) in particular, are flawed in a number of ways, and are therefore inappropriate for the analysis of phylogeographic data. These papers further argue that Nested Clade Phylogeographic Analysis (NCPA) offers the best approach in statistical phylogeography. In order to remove the confusion and misconceptions introduced by these papers, we justify and explain the reasoning behind model‐based inference. We argue that ABC is a statistically valid approach, alongside other computational statistical techniques that have been successfully used to infer parameters and compare models in population genetics. We also examine the NCPA method and highlight numerous deficiencies, either when used with single or multiple loci. We further show that the ages of clades are carelessly used to infer ages of demographic events, that these ages are estimated under a simple model of panmixia and population stationarity but are then used under different and unspecified models to test hypotheses, a usage the invalidates these testing procedures. We conclude by encouraging researchers to study and use model‐based inference in population genetics.

Understanding the origin of species with genome-scale data: modelling gene flow

As it becomes easier to sequence multiple genomes from closely related species, evolutionary biologists working on speciation are struggling to get the most out of very large population genomic data sets. Such data hold the potential to resolve long-standing questions in evolutionary biology about the role of gene exchange in species formation. In principle, the new population genomic data can be used to disentangle the conflicting roles of natural selection and gene flow during the divergence process. However, there are great challenges in taking full advantage of such data, especially with regard to including recombination in genetic models of the divergence process. Current data, models, methods and the potential pitfalls in using them will be considered here.