Recent trends in population genetics: more data! More math! Simple models?

Sweepstakes reproduction facilitates rapid adaptation in highly fecund populations

Adaptation enables natural populations to survive in a changing environment. Understanding the mechanics of adaptation is therefore crucial for learning about the evolution and ecology of natural populations. We focus on the impact of random sweepstakes on selection in highly fecund haploid and diploid populations partitioned into two genetic types, with one type conferring selective advantage. For the diploid populations, we incorporate various dominance mechanisms. We assume that the populations may experience recurrent bottlenecks. In random sweepstakes, the distribution of individual recruitment success is highly skewed, resulting in a huge variance in the number of offspring contributed by the individuals present in any given generation. Using computer simulations, we investigate the joint effects of random sweepstakes, recurrent bottlenecks and dominance mechanisms on selection. In our framework, bottlenecks allow random sweepstakes to have an effect on the time to fixation, and in diploid populations, the effect of random sweepstakes depends on the dominance mechanism. We describe selective sweepstakes that are approximated by recurrent sweeps of strongly beneficial allelic types arising by mutation. We demonstrate that both types of sweepstakes reproduction may facilitate rapid adaptation (as defined based on the average time to fixation of a type conferring selective advantage conditioned on fixation of the type). However, whether random sweepstakes cause rapid adaptation depends also on their interactions with bottlenecks and dominance mechanisms. Finally, we review a case study in which a model of recurrent sweeps is shown to essentially explain population genomic data from Atlantic cod.

Open problems in mathematical biology

Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life- and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.

Population genomics reveals moderate genetic differentiation between populations of endangered Forest Musk Deer located in Shaanxi and Sichuan

BACKGROUND

Many endangered species exist in small, genetically depauperate, or inbred populations, hence promoting genetic differentiation and reducing long-term population viability. Forest Musk Deer (Moschus berezovskii) has been subject to illegal hunting for hundreds of years due to the medical and commercial values of musk, resulting in a significant decline in population size. However, it is still unclear to what extent the genetic exchange and inbreeding levels are between geographically isolated populations. By using whole-genome data, we reconstructed the demographic history, evaluated genetic diversity, and characterized the population genetic structure of Forest Musk Deer from one wild population in Sichuan Province and two captive populations from two ex-situ centers in Shaanxi Province.

RESULTS

SNP calling by GATK resulted in a total of 44,008,662 SNPs. Principal component analysis (PCA), phylogenetic tree (NJ tree), ancestral component analysis (ADMIXTURE) and the ABBA-BABA test separated Sichuan and Shaanxi Forest Musk Deer as two genetic clusters, but no obvious genetic differentiation was observed between the two captive populations. The average pairwise FST value between the populations in Sichuan and Shaanxi ranged from 0.05-0.07, suggesting a low to moderate genetic differentiation. The mean heterozygous SNPs rate was 0.14% (0.11%-0.15%) for Forest Musk Deer at the genomic scale, and varied significantly among three populations (Chi-square = 1.22, p < 0.05, Kruskal-Wallis Test), with the Sichuan population having the lowest (0.11%). The nucleotide diversity of three populations varied significantly (p < 0.05, Kruskal-Wallis Test), with the Sichuan population having the lowest genetic θπ (1.69 × 10-3).

CONCLUSIONS

Genetic diversity of Forest Musk Deer was moderate at the genomic scale compared with other endangered species. Genetic differentiation between populations in Sichuan and Shaanxi may not only result from historical biogeographical factors but also be associated with contemporary human disturbances. Our findings provide scientific aid for the conservation and management of Forest Musk Deer. They can extend the proposed measures at the genomic level to apply to other musk deer species worldwide.

Graph-structured populations and the Hill-Robertson effect

The Hill-Robertson effect describes how, in a finite panmictic diploid population, selection at one diallelic locus reduces the fixation probability of a selectively favoured allele at a second, linked diallelic locus. Here we investigate the influence of population structure on the Hill-Robertson effect in a population of size N. We model population structure as a network by assuming that individuals occupy nodes on a graph connected by edges that link members who can reproduce with each other. Three regular networks (fully connected, ring and torus), two forms of scale-free network and a star are examined. We find that (i) the effect of population structure on the probability of fixation of the favourable allele is invariant for regular structures, but on some scale-free networks and a star, this probability is greatly reduced; (ii) compared to a panmictic population, the mean time to fixation of the favoured allele is much greater on a ring, torus and linear scale-free network, but much less on power-2 scale-free and star networks; (iii) the likelihood with which each of the four possible haplotypes eventually fix is similar across regular networks, but scale-free populations and the star are consistently less likely and much faster to fix the optimal haplotype; (iv) increasing recombination increases the likelihood of fixing the favoured haplotype across all structures, whereas the time to fixation of that haplotype usually increased, and (v) star-like structures were overwhelmingly likely to fix the least fit haplotype and did so significantly more rapidly than other populations. Last, we find that small (N < 64) panmictic populations do not exhibit the scaling property expected from Hill & Robertson (1966 Genet. Res. 8, 269-294. (doi:10.1017/S0016672300010156)).

Approximating the Coalescent Under Facultative Sex

Genome studies of facultative sexual species, which can either reproduce sexually or asexually, are providing insight into the evolutionary consequences of mixed reproductive modes. It is currently unclear to what extent the evolutionary history of facultative sexuals' genomes can be approximated by the standard coalescent, and if a coalescent effective population size Ne exists. Here, I determine if and when these approximations can be made. When sex is frequent (occurring at a frequency much greater than 1/N per reproduction per generation, for N the actual population size), the underlying genealogy can be approximated by the standard coalescent, with a coalescent Ne≈N. When sex is very rare (at frequency much lower than 1/N), approximations for the pairwise coalescent time can be obtained, which is strongly influenced by the frequencies of sex and mitotic gene conversion, rather than N. However, these terms do not translate into a coalescent Ne. These results are used to discuss the best sampling strategies for investigating the evolutionary history of facultative sexual species.

A coalescent sampler successfully detects biologically meaningful population structure overlooked by F-statistics

Assessing the geographic structure of populations has relied heavily on Sewell Wright's F-statistics and their numerous analogues for many decades. However, it is well appreciated that, due to their nonlinear relationship with gene flow, F-statistics frequently fail to reject the null model of panmixia in species with relatively high levels of gene flow and large population sizes. Coalescent genealogy samplers instead allow a model-selection approach to the characterization of population structure, thereby providing the opportunity for stronger inference. Here, we validate the use of coalescent samplers in a high gene flow context using simulations of a stepping-stone model. In an example case study, we then re-analyze genetic datasets from 41 marine species sampled from throughout the Hawaiian archipelago using coalescent model selection. Due to the archipelago's linear nature, it is expected that most species will conform to some sort of stepping-stone model (leading to an expected pattern of isolation by distance), but F-statistics have only supported this inference in ~10% of these datasets. Our simulation analysis shows that a coalescent sampler can make a correct inference of stepping-stone gene flow in nearly 100% of cases where gene flow is ≤100 migrants per generation (equivalent to F ST = 0.002), while F-statistics had mixed results. Our re-analysis of empirical datasets found that nearly 70% of datasets with an unambiguous result fit a stepping-stone model with varying population sizes and rates of gene flow, although 37% of datasets yielded ambiguous results. Together, our results demonstrate that coalescent samplers hold great promise for detecting weak but meaningful population structure, and defining appropriate management units.

Recombination-Driven Genome Evolution and Stability of Bacterial Species

While bacteria divide clonally, horizontal gene transfer followed by homologous recombination is now recognized as an important contributor to their evolution. However, the details of how the competition between clonality and recombination shapes genome diversity remains poorly understood. Using a computational model, we find two principal regimes in bacterial evolution and identify two composite parameters that dictate the evolutionary fate of bacterial species. In the divergent regime, characterized by either a low recombination frequency or strict barriers to recombination, cohesion due to recombination is not sufficient to overcome the mutational drift. As a consequence, the divergence between pairs of genomes in the population steadily increases in the course of their evolution. The species lacks genetic coherence with sexually isolated clonal subpopulations continuously formed and dissolved. In contrast, in the metastable regime, characterized by a high recombination frequency combined with low barriers to recombination, genomes continuously recombine with the rest of the population. The population remains genetically cohesive and temporally stable. Notably, the transition between these two regimes can be affected by relatively small changes in evolutionary parameters. Using the Multi Locus Sequence Typing (MLST) data, we classify a number of bacterial species to be either the divergent or the metastable type. Generalizations of our framework to include selection, ecologically structured populations, and horizontal gene transfer of nonhomologous regions are discussed as well.

Forward-in-Time, Spatially Explicit Modeling Software to Simulate Genetic Lineages Under Selection

SELECTOR is a software package for studying the evolution of multiallelic genes under balancing or positive selection while simulating complex evolutionary scenarios that integrate demographic growth and migration in a spatially explicit population framework. Parameters can be varied both in space and time to account for geographical, environmental, and cultural heterogeneity. SELECTOR can be used within an approximate Bayesian computation estimation framework. We first describe the principles of SELECTOR and validate the algorithms by comparing its outputs for simple models with theoretical expectations. Then, we show how it can be used to investigate genetic differentiation of loci under balancing selection in interconnected demes with spatially heterogeneous gene flow. We identify situations in which balancing selection reduces genetic differentiation between population groups compared with neutrality and explain conflicting outcomes observed for human leukocyte antigen loci. These results and three previously published applications demonstrate that SELECTOR is efficient and robust for building insight into human settlement history and evolution.

Selective whole genome amplification for resequencing target microbial species from complex natural samples

Population genomic analyses have demonstrated power to address major questions in evolutionary and molecular microbiology. Collecting populations of genomes is hindered in many microbial species by the absence of a cost effective and practical method to collect ample quantities of sufficiently pure genomic DNA for next-generation sequencing. Here we present a simple method to amplify genomes of a target microbial species present in a complex, natural sample. The selective whole genome amplification (SWGA) technique amplifies target genomes using nucleotide sequence motifs that are common in the target microbe genome, but rare in the background genomes, to prime the highly processive phi29 polymerase. SWGA thus selectively amplifies the target genome from samples in which it originally represented a minor fraction of the total DNA. The post-SWGA samples are enriched in target genomic DNA, which are ideal for population resequencing. We demonstrate the efficacy of SWGA using both laboratory-prepared mixtures of cultured microbes as well as a natural host-microbe association. Targeted amplification of Borrelia burgdorferi mixed with Escherichia coli at genome ratios of 1:2000 resulted in >10(5)-fold amplification of the target genomes with <6.7-fold amplification of the background. SWGA-treated genomic extracts from Wolbachia pipientis-infected Drosophila melanogaster resulted in up to 70% of high-throughput resequencing reads mapping to the W. pipientis genome. By contrast, 2-9% of sequencing reads were derived from W. pipientis without prior amplification. The SWGA technique results in high sequencing coverage at a fraction of the sequencing effort, thus allowing population genomic studies at affordable costs.

Selection and adaptation in the human genome

An enduring goal of evolutionary biology is to understand how natural selection has shaped patterns of polymorphism and divergence within and between species and to map the genetic basis of adaptations. The rapid maturation of next-generation sequencing technology has generated a deluge of genomics data from nonhuman primates, extinct hominins, and diverse human populations. These emerging genome data sets have simultaneously broadened our understanding of human evolution and sharply defined existing gaps in knowledge about the mechanistic basis of evolutionary change. In this review, we summarize recent insights into how natural selection has influenced the human genome across different timescales. Although the path to a more comprehensive understanding of selection and adaptation in humans remains arduous, some general insights are beginning to emerge, such as the importance of adaptive regulatory evolution, the absence of pervasive classic selective sweeps, and the potential roles that selection from standing variation and polygenic adaptation have likely played in recent human evolutionary history.

Coalescent and biophysical models of stepping-stone gene flow in neritid snails

Marine species in the Indo-Pacific have ranges that can span thousands of kilometres, yet studies increasingly suggest that mean larval dispersal distances are less than historically assumed. Gene flow across these ranges must therefore rely to some extent on larval dispersal among intermediate 'stepping-stone' populations in combination with long-distance dispersal far beyond the mean of the dispersal kernel. We evaluate the strength of stepping-stone dynamics by employing a spatially explicit biophysical model of larval dispersal in the tropical Pacific to construct hypotheses for dispersal pathways. We evaluate these hypotheses with coalescent models of gene flow among high-island archipelagos in four neritid gastropod species. Two of the species live in the marine intertidal, while the other two are amphidromous, living in fresh water but retaining pelagic dispersal. Dispersal pathways predicted by the biophysical model were strongly favoured in 16 of 18 tests against alternate hypotheses. In regions where connectivity among high-island archipelagos was predicted as direct, there was no difference in gene flow between marine and amphidromous species. In regions where connectivity was predicted through stepping-stone atolls only accessible to marine species, gene flow estimates between high-island archipelagos were significantly higher in marine species. Moreover, one of the marine species showed a significant pattern of isolation by distance consistent with stepping-stone dynamics. While our results support stepping-stone dynamics in Indo-Pacific species, we also see evidence for nonequilibrium processes such as range expansions or rare long-distance dispersal events. This study couples population genetic and biophysical models to help to shed light on larval dispersal pathways.

Recent colonization of the Galápagos by the tree Geoffroea spinosa Jacq. (Leguminosae)

This study puts together genetic data and an approximate bayesian computation (ABC) approach to infer the time at which the tree Geoffroea spinosa colonized the Galápagos Islands. The genetic diversity and differentiation between Peru and Galápagos population samples, estimated using three chloroplast spacers and six microsatellite loci, reveal significant differences between two mainland regions separated by the Andes mountains (Inter Andean vs. Pacific Coast) as well as a significant genetic differentiation of island populations. Microsatellites identify two distinct geographical clusters, the Galápagos and the mainland, and chloroplast markers show a private haplotype in the Galápagos. The nuclear distinctiveness of the Inter Andean populations suggests current restricted pollen flow, but chloroplast points to cross-Andean dispersals via seeds, indicating that the Andes might not be an effective biogeographical barrier. The ABC analyses clearly point to the colonization of the Galápagos within the last 160,000 years and possibly as recently as 4750 years ago (475 generations). Founder events associated with colonization of the two islands where the species occurs are detected, with Española having been colonized after Floreana. We discuss two nonmutually exclusive possibilities for the colonization of the Galápagos, recent natural dispersal vs. human introduction.

The evolution of HIV: inferences using phylogenetics

Molecular phylogenetics has revolutionized the study of not only evolution but also disparate fields such as genomics, bioinformatics, epidemiology, ecology, microbiology, molecular biology and biochemistry. Particularly significant are its achievements in population genetics as a result of the development of coalescent theory, which have contributed to more accurate model-based parameter estimation and explicit hypothesis testing. The study of the evolution of many microorganisms, and HIV in particular, have benefited from these new methodologies. HIV is well suited for such sophisticated population analyses because of its large population sizes, short generation times, high substitution rates and relatively small genomes. All these factors make HIV an ideal and fascinating model to study molecular evolution in real time. Here we review the significant advances made in HIV evolution through the application of phylogenetic approaches. We first examine the relative roles of mutation and recombination on the molecular evolution of HIV and its adaptive response to drug therapy and tissue allocation. We then review some of the fundamental questions in HIV evolution in relation to its origin and diversification and describe some of the insights gained using phylogenies. Finally, we show how phylogenetic analysis has advanced our knowledge of HIV dynamics (i.e., phylodynamics).

Measuring the degree of starshape in genealogies--summary statistics and demographic inference

The degree of starshape of a genealogy is readily detectable using summary statistics and can be taken as a surrogate for the effect of past demography and other non-neutral forces. Summary statistics such as Tajima's D and related measures are commonly used for this. However, it is well known that because of their neglect of the genealogy underlying a sample such neutrality tests are far from ideal. Here, we investigate the properties of two types of summary statistics that are derived by considering the genealogy: (i) genealogical ratios based on the number of mutations on the rootward branches, which can be inferred from sequence data using a simple algorithm and (ii) summary statistics that use properties of a perfectly star-shaped genealogy. The power of these measures to detect a history of exponential growth is compared with that of standard summary statistics and a likelihood method for the single and multi-locus case. Statistics that depend on pairwise measures such as Tajima's D have comparatively low power, being sensitive to the random topology of the underlying genealogy. When analysing multi-locus data, we find that the genealogical measures are most powerful. Provided reliable outgroup information is available they may constitute a useful alternative to full likelihood estimation and standard tests of neutrality.

A structured coalescent process for seasonally fluctuating populations

Many short-lived organisms pass through several generations during favorable growing seasons, separated by inhospitable periods during which only small hibernating or estivating refugia remain. This induces pronounced seasonal fluctuations in population size and metapopulation structure. The first generations in the growing season will be characterized by small, relatively isolated demes whereas the later generations will experience larger deme sizes with more extensive gene flow. Fluctuations of this sort can induce changes in the amount of genetic variation in early season samples compared to late season samples, a classical example being the observations of seasonal variation in allelism in New England Drosophila populations by P.T. Ives. In this article, we study the properties of a structured coalescent process under seasonal fluctuations using numerical analysis of exact state equations, analytical approximations that rely on a separation of timescales between intrademic versus interdemic processes, and individual-based simulations. We show that although an increase in genetic variation during each favorable growing season is observed, it is not as pronounced as in the empirical observations. This suggests that some of the temporal patterns of variation seen by Ives may be due to selection against deleterious lethals rather than neutral processes.

Constructing genomic maps of positive selection in humans: where do we go from here?

Identifying targets of positive selection in humans has, until recently, been frustratingly slow, relying on the analysis of individual candidate genes. Genomics, however, has provided the necessary resources to systematically interrogate the entire genome for signatures of natural selection. To date, 21 genome-wide scans for recent or ongoing positive selection have been performed in humans. A key challenge is to begin synthesizing these newly constructed maps of positive selection into a coherent narrative of human evolutionary history and derive a deeper mechanistic understanding of how natural populations evolve. Here, I chronicle the recent history of the burgeoning field of human population genomics, critically assess genome-wide scans for positive selection in humans, identify important gaps in knowledge, and discuss both short- and long-term strategies for traversing the path from the low-resolution, incomplete, and error-prone maps of selection today to the ultimate goal of a detailed molecular, mechanistic, phenotypic, and population genetics characterization of adaptive alleles.

A landscape genetics approach for quantifying the relative influence of historic and contemporary habitat heterogeneity on the genetic connectivity of a rainforest bird

Landscape genetics is an important framework for investigating the influence of spatial pattern on ecological process. Nevertheless, the standard analytic frameworks in landscape genetics have difficulty evaluating hypotheses about spatial processes in dynamic landscapes. We use a predictive hypothesis-driven approach to quantify the relative contribution of historic and contemporary processes to genetic connectivity. By confronting genetic data with models of historic and contemporary landscapes, we identify dispersal processes operating in naturally heterogeneous and human-altered systems. We demonstrate the approach using a case study of microsatellite polymorphism and indirect estimates of gene flow for a rainforest bird, the logrunner (Orthonyx temminckii). Of particular interest was how much information in the genetic data was attributable to processes occurring in the reconstructed historic landscape and contemporary human-modified landscape. A linear mixed model was used to estimate appropriate sampling variance from nonindependent data and information-theoretic model selection provided strength of evidence for alternative hypotheses. The contemporary landscape explained slightly more information in the genetic differentiation data than the historic landscape, and there was considerable evidence for a temporal shift in dispersal pattern. In contrast, migration rates estimated from genealogical information were primarily influenced by contemporary landscape change. We discovered that landscape heterogeneity facilitated gene flow before European settlement, but contemporary deforestation is rapidly becoming the most important barrier to logrunner dispersal.

Testing comparative phylogeographic models of marine vicariance and dispersal using a hierarchical Bayesian approach

BACKGROUND

Marine allopatric speciation is an enigma because pelagic larval dispersal can potentially connect disjunct populations thereby preventing reproductive and morphological divergence. Here we present a new hierarchical approximate Bayesian computation model (HABC) that tests two hypotheses of marine allopatric speciation: 1.) "soft vicariance", where a speciation involves fragmentation of a large widespread ancestral species range that was previously connected by long distance gene flow; and 2.) peripatric colonization, where speciations in peripheral archipelagos emerge from sweepstakes colonizations from central source regions. The HABC approach analyzes all the phylogeographic datasets at once in order to make across taxon-pair inferences about biogeographic processes while explicitly allowing for uncertainty in the demographic differences within each taxon-pair. Our method uses comparative phylogeographic data that consists of single locus mtDNA sequences from multiple co-distributed taxa containing pairs of central and peripheral populations. We use the method on two comparative phylogeographic data sets consisting of cowrie gastropod endemics co-distributed in the Hawaiian (11 taxon-pairs) and Marquesan archipelagos (7 taxon-pairs).

RESULTS

Given the Marquesan data, we find strong evidence of simultaneous colonization across all seven cowrie gastropod endemics co-distributed in the Marquesas. In contrast, the lower sample sizes in the Hawaiian data lead to greater uncertainty associated with the Hawaiian estimates. Although, the hyper-parameter estimates point to soft vicariance in a subset of the 11 Hawaiian taxon-pairs, the hyper-prior and hyper-posterior are too similar to make a definitive conclusion. Both results are not inconsistent with what is known about the geologic history of the archipelagos. Simulations verify that our method can successfully distinguish these two histories across a wide range of conditions given sufficient sampling.

CONCLUSION

Although soft vicariance and colonization are likely to produce similar genetic patterns when a single taxon-pair is used, our hierarchical Bayesian model can potentially detect if either history is a dominant process across co-distributed taxon-pairs. As comparative phylogeographic datasets grow to include > 100 co-distributed taxon-pairs, the HABC approach will be well suited to dissect temporal patterns in community assembly and evolution, thereby providing a bridge linking comparative phylogeography with community ecology.

The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population

We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the biological process. We focus on the growth of fixation times with the number of subpopulations, and variation of fixation probabilities and times with initial distributions of mutants. A general formula for the fixation probability for arbitrary initial condition is derived by extending a duality relation between forwards- and backwards-time properties of the model from a panmictic to a subdivided population. From this we obtain new formulae(formally exact in the limit of extremely weak migration) for the mean fixation time from an arbitrary initial condition for Wright's island model, presenting two cases as examples. For more general models of population subdivision, formulae are introduced for an arbitrary number of mutants that are randomly located, and a single mutant whose position is known. These formulae contain parameters that typically have to be obtained numerically, a procedure we follow for two contrasting clustered models. These data suggest that variation of fixation time with the initial condition is slight, but depends strongly on the nature of subdivision. In particular, we demonstrate conditions under which the fixation time remains finite even in the limit of an infinite number of demes. In many cases-except this last where fixation in a finite time is seen--the time to fixation is shown to be in precise agreement with predictions from formulae for the asymptotic effective population size.

Fixation probability for a beneficial allele and a mutant strategy in a linear game under weak selection in a finite island model

The effect of population structure on the probability of fixation of a newly introduced mutant under weak selection is studied using a coalescent approach. Wright's island model in a framework of a finite number of demes is assumed and two selection regimes are considered: a beneficial allele model and a linear game among offspring. A first-order approximation of the fixation probability for a single mutant with respect to the intensity of selection is deduced. The approximation requires the calculation of expected coalescence times, under neutrality, for lineages starting from two or three sampled individuals. The results are obtained in a general setting without assumptions on the number of demes, the deme size or the migration rate, which allows for simultaneous coalescence or migration events in the genealogy of the sampled individuals. Comparisons are made with limit cases as the deme size or the number of demes goes to infinity or the migration rate goes to zero for which a diffusion approximation approach is possible. Conditions for selection to favor a mutant strategy replacing a resident strategy in the context of a linear game in a finite island population are addressed.

How to compute the effective size of spatiotemporally structured populations using separation of time scales

Calculations to derive effective population size become highly complicated when complex population structure is considered. We provide an easy method of computing the effective size of a subdivided population with overlapping generations (a spatiotemporally structured population) using an approximation based on separation of time scales. We also numerically compute the effective size to verify the accuracy of the derived formula. Various interesting quantities, including moments of coalescent time, are readily derived using this approach.

Gene sampling strategies for multi-locus population estimates of genetic diversity (theta)

Background

Theoretical work suggests that data from multiple nuclear loci provide better estimates of population genetic parameters than do single loci, but just how many loci are needed and how much sequence is required from each has been little explored.

Methodology/Principle Findings

To investigate how much data is required to estimate the population genetic parameter θ (4N_eμ) accurately under ideal circumstances, we simulated datasets of DNA sequences under three values of θ per site (0.1, 0.01, 0.001), varying in both the total number of base pairs sequenced per individual and the number of equal-length loci. From these datasets we estimated θ using the maximum likelihood coalescent framework implemented in the computer program Migrate. Our results corroborated the theoretical expectation that increasing the number of loci impacted the accuracy of the estimate more than increasing the sequence length at single loci. However, when the value of θ was low (0.001), the per-locus sequence length was also important for estimating θ accurately, something that has not been emphasized in previous work.

Conclusions/Significance

Accurate estimation of θ required data from at least 25 independently evolving loci. Beyond this, there was little added benefit in terms of decreasing the squared coefficient of variation of the coalescent estimates relative to the extra effort required to sample more loci.

Comparative phylogeographic summary statistics for testing simultaneous vicariance

Testing for simultaneous vicariance across comparative phylogeographic data sets is a notoriously difficult problem hindered by mutational variance, the coalescent variance, and variability across pairs of sister taxa in parameters that affect genetic divergence. We simulate vicariance to characterize the behaviour of several commonly used summary statistics across a range of divergence times, and to characterize this behaviour in comparative phylogeographic datasets having multiple taxon-pairs. We found Tajima's D to be relatively uncorrelated with other summary statistics across divergence times, and using simple hypothesis testing of simultaneous vicariance given variable population sizes, we counter-intuitively found that the variance across taxon pairs in Nei and Li's net nucleotide divergence (pi(net)), a common measure of population divergence, is often inferior to using the variance in Tajima's D across taxon pairs as a test statistic to distinguish ancient simultaneous vicariance from variable vicariance histories. The opposite and more intuitive pattern is found for testing more recent simultaneous vicariance, and overall we found that depending on the timing of vicariance, one of these two test statistics can achieve high statistical power for rejecting simultaneous vicariance, given a reasonable number of intron loci (> 5 loci, 400 bp) and a range of conditions. These results suggest that components of these two composite summary statistics should be used in future simulation-based methods which can simultaneously use a pool of summary statistics to test comparative the phylogeographic hypotheses we consider here.