Extending coalescent theory to autotetraploids.

We develop coalescent models for autotetraploid species with tetrasomic inheritance. We show that the ancestral genetic process in a large population without recombination may be approximated using Kingman's standard coalescent, with a coalescent effective population size 4N. Numerical results suggest that this approximation is accurate for population sizes on the order of hundreds of individuals. Therefore, existing coalescent simulation programs can be adapted to study population history in autotetraploids simply by interpreting the timescale in units of 4N generations. We also consider the possibility of double reduction, a phenomenon unique to polysomic inheritance, and show that its effects on gene genealogies are similar to partial self-fertilization.

Expected coalescence times and segregating sites in a model of glacial cycles.

The climatic fluctuations of the Quaternary have influenced the distribution of numerous plant and animal species. Several species suffer population reduction and fragmentation, becoming restricted to refugia during glacial periods and expanding again during interglacials. The reduction in population size may reduce the effective population size, mean coalescence time and genetic variation, whereas an increased subdivision may have the opposite effect. To investigate these two opposing forces, we proposed a model in which a panmictic and a structured phase alternate, corresponding to interglacial and glacial periods. From this model, we derived an expression for the expected coalescence time and number of segregating sites for a pair of genes. We observed that increasing the number of demes or the duration of the structured phases causes an increase in coalescence time and expected levels of genetic variation. We compared numerical results with the ones expected for a panmictic population of constant size, and showed that the mean number of segregating sites can be greater in our model even when population size is much smaller in the structured phases. This points to the importance of population structure in the history of species subject to climatic fluctuations, and helps explain the long gene genealogies observed in several organisms.

Effects of intra-gene fitness interactions on the benefit of sexual recombination.

Whereas spontaneous point mutation operates on nucleotides individually, sexual recombination manipulates the set of nucleotides within an allele as an essentially particulate unit. In principle, these two different scales of variation enable selection to follow fitness gradients in two different spaces: in nucleotide sequence space and allele sequence space respectively. Epistasis for fitness at these two scales, between nucleotides and between genes, may be qualitatively different and may significantly influence the advantage of mutation-based and recombination-based evolutionary trajectories respectively. We examine scenarios where the genetic sequence within a gene strongly influences the fitness effect of a mutation in that gene, whereas epistatic interactions between sites in different genes are weak or absent. We find that, in cases where beneficial alleles of a gene differ from one another at several nucleotide sites, sexual populations can exhibit enormous benefit compared with asexual populations: not only discovering fit genotypes faster than asexual populations, but also discovering high-fitness genotypes that are effectively not evolvable in asexual populations.

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

Recent developments in population genetics are reviewed and placed in a historical context. Current and future challenges, both in computational methodology and in analytical theory, are to develop models and techniques to extract the most information possible from multilocus DNA datasets. As an example of the theoretical issues, five limiting forms of the island model of population subdivision with migration are presented in a unified framework. These approximations illustrate the interplay between migration and drift in structuring gene genealogies, and some of them make connections between the fairly complicated island-model genealogical process and the much simpler, unstructured neutral coalescent process which underlies most inferential techniques in population genetics.

A robust measure of HIV-1 population turnover within chronically infected individuals.

A simple nonparameteric test for population structure was applied to temporally spaced samples of HIV-1 sequences from the gag-pol region within two chronically infected individuals. The results show that temporal structure can be detected for samples separated by about 22 months or more. The performance of the method, which was originally proposed to detect geographic structure, was tested for temporally spaced samples using neutral coalescent simulations. Simulations showed that the method is robust to variation in samples sizes and mutation rates, to the presence/absence of recombination, and that the power to detect temporal structure is high. By comparing levels of temporal structure in simulations to the levels observed in real data, we estimate the effective intra-individual population size of HIV-1 to be between 10(3) and 10(4) viruses, which is in agreement with some previous estimates. Using this estimate and a simple measure of sequence diversity, we estimate an effective neutral mutation rate of about 5 x 10(-6) per site per generation in the gag-pol region. The definition and interpretation of estimates of such "effective" population parameters are discussed.

Effects of beta-adrenoceptor blockade on components of human decision-making.

RATIONALE: Converging evidence from studies with neurological patients and brain imaging studies with healthy volunteers suggests that the capacity to make choices between actions associated with probabilistic rewards and punishments depends upon a network of cortico-limbic systems including the orbitofrontal cortex, cingulate cortex, amygdala and striatum. The involvement of such structures highlights the emotional aspects of decision-making and suggests that decision-making may be sensitive to manipulations of the catecholamine systems that innervate these structures. In this study, we investigated the possible role of noradrenaline (NA). OBJECTIVE: We examined the effects of a single oral 80 mg dose of the beta-adrenoceptor blocker, propranolol, on the decision-making of healthy volunteers in a double-blind, placebo-controlled, between-subjects design. METHODS: Seventeen volunteers ingested a placebo while 15 volunteers ingested propranolol. Visual analogue scales, and self-reported positive and negative ratings, were used to assess subjective changes and mood. Vital signs were also monitored. Seventy-five minutes after treatment, volunteers were asked to make a series of choices between two simultaneously presented gambles, differing in the magnitude of possible gains (i.e. reward), the magnitude of possible losses (i.e. punishment), and the probabilities with which these outcomes were delivered. Volunteers also chose between gambles probing identified non-cognitive biases in human decision-making, namely, risk-aversion when choosing between gains and risk-seeking when choosing between losses. RESULTS: Propranolol treatment did not result in gross changes in subjective state or mood in comparison to placebo, but did slow heart rate significantly. Propranolol produced a selective change in volunteers' decision-making; namely, it significantly reduced the discrimination between large and small possible losses when the probability of winning was relatively low and the probability of losing was high. CONCLUSIONS: These results suggest that NA modulates the processing of punishment signals when choosing between probabilistic rewards and punishments under conditions of increased arousal.

The discovery of single-nucleotide polymorphisms--and inferences about human demographic history.

A method of historical inference that accounts for ascertainment bias is developed and applied to single-nucleotide polymorphism (SNP) data in humans. The data consist of 84 short fragments of the genome that were selected, from three recent SNP surveys, to contain at least two polymorphisms in their respective ascertainment samples and that were then fully resequenced in 47 globally distributed individuals. Ascertainment bias is the deviation, from what would be observed in a random sample, caused either by discovery of polymorphisms in small samples or by locus selection based on levels or patterns of polymorphism. The three SNP surveys from which the present data were derived differ both in their protocols for ascertainment and in the size of the samples used for discovery. We implemented a Monte Carlo maximum-likelihood method to fit a subdivided-population model that includes a possible change in effective size at some time in the past. Incorrectly assuming that ascertainment bias does not exist causes errors in inference, affecting both estimates of migration rates and historical changes in size. Migration rates are overestimated when ascertainment bias is ignored. However, the direction of error in inferences about changes in effective population size (whether the population is inferred to be shrinking or growing) depends on whether either the numbers of SNPs per fragment or the SNP-allele frequencies are analyzed. We use the abbreviation "SDL," for "SNP-discovered locus," in recognition of the genomic-discovery context of SNPs. When ascertainment bias is modeled fully, both the number of SNPs per SDL and their allele frequencies support a scenario of growth in effective size in the context of a subdivided population. If subdivision is ignored, however, the hypothesis of constant effective population size cannot be rejected. An important conclusion of this work is that, in demographic or other studies, SNP data are useful only to the extent that their ascertainment can be modeled.

Gene genealogies in a metapopulation.

A simple genealogical process is found for samples from a metapopulation, which is a population that is subdivided into a large number of demes, each of which is subject to extinction and recolonization and receives migrants from other demes. As in the migration-only models studied previously, the genealogy of any sample includes two phases: a brief sample-size adjustment followed by a coalescent process that dominates the history. This result will hold for metapopulations that are composed of a large number of demes. It is robust to the details of population structure, as long as the number of possible source demes of migrants and colonists for each deme is large. Analytic predictions about levels of genetic variation are possible, and results for average numbers of pairwise differences within and between demes are given. Further analysis of the expected number of segregating sites in a sample from a single deme illustrates some previously known differences between migration and extinction/recolonization. The ancestral process is also amenable to computer simulation. Simulation results show that migration and extinction/recolonization have very different effects on the site-frequency distribution in a sample from a single deme. Migration can cause a U-shaped site-frequency distribution, which is qualitatively similar to the pattern reported recently for positive selection. Extinction and recolonization, in contrast, can produce a mode in the site-frequency distribution at intermediate frequencies, even in a sample from a single deme.

Distinguishing migration from isolation: a Markov chain Monte Carlo approach.

A Markov chain Monte Carlo method for estimating the relative effects of migration and isolation on genetic diversity in a pair of populations from DNA sequence data is developed and tested using simulations. The two populations are assumed to be descended from a panmictic ancestral population at some time in the past and may (or may not) after that be connected by migration. The use of a Markov chain Monte Carlo method allows the joint estimation of multiple demographic parameters in either a Bayesian or a likelihood framework. The parameters estimated include the migration rate for each population, the time since the two populations diverged from a common ancestral population, and the relative size of each of the two current populations and of the common ancestral population. The results show that even a single nonrecombining genetic locus can provide substantial power to test the hypothesis of no ongoing migration and/or to test models of symmetric migration between the two populations. The use of the method is illustrated in an application to mitochondrial DNA sequence data from a fish species: the threespine stickleback (Gasterosteus aculeatus).

The coalescent in an island model of population subdivision with variation among demes.

A simple genealogical structure is found for a general finite island model of population subdivision. The model allows for variation in the sizes of demes, in contributions to the migrant pool, and in the fraction of each deme that is replaced by migrants every generation. The ancestry of a sample of non-recombining DNA sequences has a simple structure when the sample size is much smaller than the total number of demes in the population. This allows an expression for the probability distribution of the number of segregating sites in the sample to be derived under the infinite-sites mutation model. It also yields easily computed estimators of the migration parameter for each deme in a multi-deme sample. The genealogical process is such that the lineages ancestral to the sample tend to accumulate in demes with low migration rates and/or which contribute disproportionately to the migrant pool. In addition, common ancestor or coalescent events tend to occur in demes of small size. This provides a framework for understanding the determinants of the effective size of the population, and leads to an expression for the probability that the root of a genealogy occurs in a particular geographic region, or among a particular set of demes.

Directional selection and the site-frequency spectrum.

In this article we explore statistical properties of the maximum-likelihood estimates (MLEs) of the selection and mutation parameters in a Poisson random field population genetics model of directional selection at DNA sites. We derive the asymptotic variances and covariance of the MLEs and explore the power of the likelihood ratio tests (LRT) of neutrality for varying levels of mutation and selection as well as the robustness of the LRT to deviations from the assumption of free recombination among sites. We also discuss the coverage of confidence intervals on the basis of two standard-likelihood methods. We find that the LRT has high power to detect deviations from neutrality and that the maximum-likelihood estimation performs very well when the ancestral states of all mutations in the sample are known. When the ancestral states are not known, the test has high power to detect deviations from neutrality for negative selection but not for positive selection. We also find that the LRT is not robust to deviations from the assumption of independence among sites.

The population genetics of the origin and divergence of the Drosophila simulans complex species.

The origins and divergence of Drosophila simulans and close relatives D. mauritiana and D. sechellia were examined using the patterns of DNA sequence variation found within and between species at 14 different genes. D. sechellia consistently revealed low levels of polymorphism, and genes from D. sechellia have accumulated mutations at a rate that is approximately 50% higher than the same genes from D. simulans. At synonymous sites, D. sechellia has experienced a significant excess of unpreferred codon substitutions. Together these observations suggest that D. sechellia has had a reduced effective population size for some time, and that it is accumulating slightly deleterious mutations as a result. D. simulans and D. mauritiana are both highly polymorphic and the two species share many polymorphisms, probably since the time of common ancestry. A simple isolation speciation model, with zero gene flow following incipient species separation, was fitted to both the simulans/mauritiana divergence and the simulans/sechellia divergence. In both cases the model fit the data quite well, and the analyses revealed little evidence of gene flow between the species. The exception is one gene copy at one locus in D. sechellia, which closely resembled other D. simulans sequences. The overall picture is of two allopatric speciation events that occurred quite near one another in time.

The effects of subdivision on the genetic divergence of populations and species.

An island model of migration is used to study the effects of subdivision within populations and species on sample genealogies and on between-population or between-species measures of genetic variation. The model assumes that the number of demes within each population or species is large. When populations (or species), connected either by gene flow or historical association, are themselves subdivided into demes, changes in the migration rate among demes alter both the structure of genealogies and the time scale of the coalescent process. The time scale of the coalescent is related to the effective size of the population, which depends on the migration rate among demes. When the migration rate among demes within populations is low, isolation (or speciation) events seem more recent and migration rates among populations seem higher because the effective size of each population is increased. This affects the probability of reciprocal monophyly of two samples, the chance that a gene tree of a sample matches the species tree, and relative likelihoods of different types of polymorphic sites. It can also have a profound effect on the estimation of divergence times.

Nonequilibrium migration in human history.

A nonequilibrium migration model is proposed and applied to genetic data from humans. The model assumes symmetric migration among all possible pairs of demes and that the number of demes is large. With these assumptions it is straightforward to allow for changes in demography, and here a single abrupt change is considered. Under the model this change is identical to a change in the ancestral effective population size and might be caused by changes in deme size, in the number of demes, or in the migration rate. Expressions for the expected numbers of sites segregating at particular frequencies in a multideme sample are derived. A maximum-likelihood analysis of independent polymorphic restriction sites in humans reveals a decrease in effective size. This is consistent with a change in the rates of migration among human subpopulations from ancient low levels to present high ones.

Segregating sites in Wright's island model.

Expressions for the expectation and variance of the number of segregating sites in samples from an island model of population subdivision are derived. For small samples, an arbitrary number of demes can be accommodated. Results for larger samples are derived under the assumption of an infinite number of demes. However, simulations indicate that the latter results will hold quite well for the finite-island model in many cases. A new estimator of the population migration rate is proposed and is shown to outperform the widely used pairwise method.

A coalescent estimator of the population recombination rate.

Population genetic models often use a population recombination parameter 4Nc, where N is the effective population size and c is the recombination rate per generation. In many ways 4Nc is comparable to 4Nu, the population mutation rate. Both combine genome level and population level processes, and together they describe the rate of production of genetic variation in a population. However, 4Nc is more difficult to estimate. For a population sample of DNA sequences, historical recombination can only be detected if polymorphisms exist, and even then most recombination events are not detectable. This paper describes an estimator of 4Nc, hereafter designated gamma (gamma), that was developed using a coalescent model for a sample of four DNA sequences with recombination. The reliability of gamma was assessed using multiple coalescent simulations. In general gamma has low to moderate bias, and the reliability of gamma is comparable, though less, than that for a widely used estimator of 4Nu. If there exists an independent estimate of the recombination rate (per generation, per base pair), gamma can be used to estimate the effective population size or the neutral mutation rate.

Estimating ancestral population parameters.

The expected numbers of different categories of polymorphic sites are derived for two related models of population history the isolation model, in which an ancestral population splits into two descendents, and the size-change model, in which a single population undergoes an instantaneous change in size. For the isolation model, the observed numbers of shared, fixed, and exclusive polymorphic sites are used to estimate the relative sizes of the three populations, ancestral plus two descendent, as well as the time of the split. For the size change model, the numbers of sites segregating at particular frequencies in the sample are used to estimate the relative sizes of the ancestral and descendent populations plus the time the change took place. Parameters are estimated by choosing values that most closely equate expectations with observations. Computer simulations show that current and historical population parameters can be estimated accurately. The methods are applied to DNA data from two species of Drosophila and to some human mitochondrial DNA sequences.

Using the variance of pairwise differences to estimate the recombination rate.

A new estimator is proposed for the parameter C = 4Nc, where N is the population size and c is the recombination rate in a finite population model without selection. The estimator is an improved version of Hudson's (1987) estimator, which takes advantage of some recent theoretical developments. The improvement is slight, but the smaller bias and standard error of the new estimator support its use. The variance of the average number of pairwise differences is also derived, and is important in the formulation of the new estimator.