Evolution of coadaptation in a subdivided population

The interplay between population subdivision and epistasis is investigated by studying the fixation probability of a coadapted haplotype in a subdivided population. Analytical and simulation models are developed to study the evolutionary fate of two conditionally neutral mutations that interact epistatically to enhance fitness. We find that the fixation probability of a coadapted haplotype shows a marked increase when the population is genetically subdivided and subpopulations are loosely connected by migration. Moderate migration and isolation allow the propagation of the mutant alleles across subpopulations, while at the same time preserving the favorable allelic combination established within each subpopulation. Together they create the condition most favorable for the ultimate fixation of the coadapted haplotype. On the basis of the analytical and simulation results, we discuss the fundamental role of population subdivision and restricted gene flow in promoting the evolution of functionally integrated systems, with some implications for the shifting-balance theory of evolution.     

Variation after a selective sweep in a subdivided population

The effect of genetic hitchhiking on neutral variation is analyzed in subdivided populations with differentiated demes. After fixation of a favorable mutation, the consequences on particular subpopulations can be radically different. In the subpopulation where the mutation first appeared by mutation, variation at linked neutral loci is expected to be reduced, as predicted by the classical theory. However, the effect in the other subpopulations, where the mutation is introduced by migration, can be the opposite. This effect depends on the level of genetic differentiation of the subpopulations, the selective advantage of the mutation, the recombination frequency, and the population size, as stated by analytical derivations and computer simulations. The characteristic outcomes of the effect are three. First, the genomic region of reduced variation around the selected locus is smaller than that predicted in a panmictic population. Second, for more distant neutral loci, the amount of variation increases over the level they had before the hitchhiking event. Third, for these loci, the spectrum of gene frequencies is dominated by an excess of alleles at intermediate frequencies when compared with the neutral theory. At these loci, hitchhiking works like a system that takes variation from the between-subpopulation component and introduces it into the subpopulations. The mechanism can also operate in other systems in which the genetic variation is distributed in clusters with limited exchange of variation, such as chromosome arrangements or genomic regions closely linked to targets of balancing selection.     

Inference from gene trees in a subdivided population

This paper studies gene trees in subdivided populations which are constructed as perfect phylogenies from the pattern of mutations in a sample of DNA sequences and presents a new recursion for the probability distribution of such gene trees. The underlying evolutionary model is the coalescent process in a subdivided population. The infinitely-many-sites model of mutation is assumed. Ancestral inference questions that are discussed are maximum likelihood estimation of migration and mutation rates; detection of population growth by likelihood techniques; determining the distribution of the time to the most recent common ancestor of a sample of sequences; determining the distribution of the age of the mutations on the gene tree; determining in which subpopulation the most recent common ancestor of all the sequences was; determining subpopulation ancestors, where they were, and times to them; and determining in which subpopulations mutations occurred. A computational technique of Griffiths and Tavaré used is a computer intensive Markov chain simulation, which simulates gene trees conditional on their topology implied by the mutation pattern in the sample of DNA sequences. The software GENETREE, which implements these ancestral inference techniques, is available.     

Match probabilities in a finite, subdivided population

We generalize a recently introduced graphical framework to compute the probability that haplotypes or genotypes of two individuals drawn from a finite, subdivided population match. As in the previous work, we assume an infinite-alleles model. We focus on the case of a population divided into two subpopulations, but the underlying framework can be applied to a general model of population subdivision. We examine the effect of population subdivision on the match probabilities and the accuracy of the product rule which approximates multi-locus match probabilities as a product of one-locus match probabilities. We quantify the deviation from predictions of the product rule by R, the ratio of the multi-locus match probability to the product of the one-locus match probabilities. We carry out the computation for two loci and find that ignoring subdivision can lead to underestimation of the match probabilities if the population under consideration actually has subdivision structure and the individuals originate from the same subpopulation. On the other hand, under a given model of population subdivision, we find that the ratio R for two loci is only slightly greater than 1 for a large range of symmetric and asymmetric migration rates. Keeping in mind that the infinite-alleles model is not the appropriate mutation model for STR loci, we conclude that, for two loci and biologically reasonable parameter values, population subdivision may lead to results that disfavor innocent suspects because of an increase in identity-by-descent in finite populations. On the other hand, for the same range of parameters, population subdivision does not lead to a substantial increase in linkage disequilibrium between loci. Those results are consistent with established practice.     

The evolution of social communication systems in a subdivided population

Evolution of social communication systems is modeled with a quantitative genetic model. The mathematical model describes the coevolutionary process of a social signal (a social character) and responsiveness (a social preference) to the signal. The responsiveness is postulated to influence fitness of senders of the signal. Considerations are extended to subdivided population structure by combining the social selection model with a group selection model. The numerical results derived from the models indicate that the evolutionary rate of social communication systems depends largely on genetic correlation between the signal and the responsiveness. Group selection can reinforce the evolutionary rate and relax its dependence on genetic correlation. The origin of genetic correlation is discussed in relation to group selection.     

Selection in a subdivided population with local extinction and recolonization

In a subdivided population, local extinction and subsequent recolonization affect the fate of alleles. Of particular interest is the interaction of this force with natural selection. The effect of selection can be weakened by this additional source of stochastic change in allele frequency. The behavior of a selected allele in such a population is shown to be equivalent to that of an allele with a different selection coefficient in an unstructured population with a different size. This equivalence allows use of established results for panmictic populations to predict such quantities as fixation probabilities and mean times to fixation. The magnitude of the quantity N(e)s(e), which determines fixation probability, is decreased by extinction and recolonization. Thus deleterious alleles are more likely to fix, and advantageous alleles less likely to do so, in the presence of extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.     

Single versus subdivided population strategies in breeding against an adverse genetic correlation

In advanced conifer breeding programmes, the simultaneous genetic improvement of adversely correlated traits constitutes a major challenge. Population subdivision strategies have been proposed to deal with breeding objective uncertainty, to reduce inbreeding depression in production populations and to reduce genetic correlation adversity. We used Monte Carlo simulations based on a finite locus model to study the effect of a two-breeding-population strategy applying selection for each trait in each breeding population on the genetic correlation and on genetic gains in breeding populations (BP) and the production population (PP) within a time frame of ten generations. A single-BP and a two-subline strategy both applying multitrait index selection with equal trait weights were used as references. Two BP strategy simulations indicated that simultaneous genetic gain for the two traits could be achieved in the PP despite adverse pleiotropy. The adversity of the genetic correlations decreased in BPs of the two-BP strategy, in contrast to single-BP and subline strategies, but the adversity reduction came at the cost of a lower rate of aggregated (summed) genetic gain in the PP for the two-BP strategy compared to the single-BP or subline strategies. The subline strategy exhibited increased genetic gain in the PP at equal levels of inbreeding as intended. Two BP strategies could be useful to develop breeds specialised on different traits and to simultaneously reduce adverse genetic correlations. However, if the aggregated genetic gain should be maximised, the single-BP strategy appears a better choice.     

Coalescence time for two genes from a subdivided population

In this paper a new form of the solution for the Laplace transform and moments of the distribution of the waiting time for two genes to coalescence is presented. The two genes are sampled from a subdivided population where migration rates between populations are constant in time. Equal subpopulation size is not assumed. For the special case of an island model with equal migration rates between islands, the Laplace transform of the coalescence time and the first and second moments are found explicitly. The new form of the solutions allows numerical calculation. The connection of how the results relate to a panmictic population when migration rates are large is illustrated using strong-migration-limit theory. Received: 19 April 1999 / Revised version: 22 March 2001 / Published online: 19 September 2001     

The expected number of heterozygous sites in a subdivided population.

A simple, exact formula is derived for the expected number of heterozygous sites per individual at equilibrium in a subdivided population. The model of infinitely many neutral sites is posited; the linkage map is arbitrary. The monoecious, diploid population is subdivided into a finite number of panmictic colonies that exchange gametes. The backward migration matrix is arbitrary, but time independent and ergodic (i.e., irreducible and aperiodic). With suitable weighting, the expected number of heterozygous sites is 4Neu, where Ne denotes the migration effective population number and u designates the total mutation rate per gene (or DNA sequence). For diploid migration, this formula is a good approximation if Ne >> 1.     

Selection in a subdivided population with dominance or local frequency dependence

The interplay between population structure and natural selection is an area of great interest. It is known that certain types of population subdivision do not alter fixation probabilities of selected alleles under genic, frequency-independent selection. In the presence of dominance for fitness or frequency-dependent selection these same types of subdivision can have large effects on fixation probabilities. For example, the barrier to fixation of a fitter allele due to underdominance is reduced by subdivision. Analytic results presented here relate a subdivided population that conforms to a finite island model to an approximately equivalent panmictic population. The size of this equivalent population is different from (larger than) the actual size of the subdivided population. Selection parameters are also different in the hypothetical equivalent population. As expected, the degree of dominance is lower in the equivalent population. The results are not limited to dominance but cover any form of polynomial frequency dependence.     

The many-demes limit for selection and drift in a subdivided population

A diffusion approximation is obtained for the frequency of a selected allele in a population comprised of many subpopulations or demes. The form of the diffusion is equivalent to that for an unstructured population, except that it occurs on a longer time scale when migration among demes is restricted. This many-demes diffusion limit relies on the collection of demes always being in statistical equilibrium with respect to migration and drift for a given allele frequency in the total population. Selection is assumed to be weak, in inverse proportion to the number of demes, and the results hold for any deme sizes and migration rates greater than zero. The distribution of allele frequencies among demes is also described.     

A diffusion approximation for selection and drift in a subdivided population

The population-genetic consequences of population structure are of great interest and have been studied extensively. An area of particular interest is the interaction among population structure, natural selection, and genetic drift. At first glance, different results in this area give very different impressions of the effect of population subdivision on effective population size (N(e)), suggesting that no single value of N(e) can completely characterize a structured population. Results presented here show that a population conforming to Wright's island model of subdivision with genic selection can be related to an idealized panmictic population (a Wright-Fisher population). This equivalent panmictic population has a larger size than the actual population; i.e., N(e) is larger than the actual population size, as expected from many results for this type of population structure. The selection coefficient in the equivalent panmictic population, referred to here as the effective selection coefficient (s(e)), is smaller than the actual selection coefficient (s). This explains how the fixation probability of a selected allele can be unaffected by population subdivision despite the fact that subdivision increases N(e), for the product N(e)s(e) is not altered by subdivision.     

Bacterial population genomics and infectious disease diagnostics

New sequencing technologies have made the production of bacterial genome sequences increasingly easy, and it can be confidently forecasted that vast genomic databases will be generated in the next few years. Here, we detail how collections of bacterial genomes from a particular species (population genomics libraries) have already been used to improve the design of several diagnostic assays for bacterial pathogens. Genome sequencing itself is also becoming more commonly used for epidemiological, forensic and clinical investigations. There is an opportunity for the further development of bioinformatic tools to bring even further value to bacterial diagnostic genomics.     

Two-locus identity probabilities and identity disequilibrium in a partially selfing subdivided population

Measures of association of genes at different loci (linkage disequilibrium) are widely used to determine whether the structure of natural populations is clonal or not, to map genes from population data, or to test for the homogeneity of response of molecular markers to background selection, for example. However, the usual definitions of parameters for gametic associations may not be suitable for all these purposes. In this paper, we derive the recursion equations for one- and two-locus identity probabilities in an infinite island model. We study the role of drift, gene flow, partial selfing and mutation model on the expected association of genes across loci. We define the 'within-subpopulation identity disequilibrium' as the difference between the joint two-locus probability of identity in state and the expected product of one-locus identity probabilities. We evaluate this parameter as a function of recombination rate, effective size, gene flow and selfing rate. Within-subpopulation identity disequilibrium attains maximum values for intermediate immigration rates, whatever the selfing rate. Moreover, identity disequilibrium may be very small, even for high selfing rates. We discuss the implications of these findings for the analysis of data from natural populations.     

Effect of dominance on heterozygosity and the fixation probability in a subdivided population

Under the assumptions of a subdivided population and the presence of dominance for fitness, the expected sum of heterozygosity in the total population during the lifetime of mutant was investigated. It was shown analytically and by computer simulations that in the island model the effect of dominance on the expected sum of heterozygosity decreases as the migration rate decreases and is lost almost completely when the migration rate is very low. In addition to the expected sum of heterozygosity, the fixation probability of mutant was also investigated. The effect of dominance on the fixation probability also decreases as the migration rate decreases but is not completely lost when the migration rate is very low.     

Gene frequency patterns in the levene subdivided population model

In the context of a multideme population structure subject to selection, migration, and mating forces, it is desired to ascertain the stable evolutionary outcomes for various classes of selection regimes. These include selection patterns as (i) a mosaic of local directed selection effects, (ii) overdominance throughout with varying intensities of the local heterozygote advantage, (iii) varying degrees of underdominance throughout, (iv) a mixed underdominant-overdominant regime. An accounting of the nature of the equilibrium configurations in the Levene population subdivision model was done with respect to the above classes of selection regimes. In particular, it is established that multiple polymorphic equilibria do not arise for selection structures (i) and (ii), while for the mixed underdominant-overdominant selection form (iv) with appropriate parameter ranges there can exist two stable internal equilibria. A surprising finding is that the number and/or character of the equilibria is not changed by increased population division beyond that of two habitats, while there is a significant difference in the equilibrium possibilities for a one- as against a two-deme population. These results appear to be a special limiting feature of the Levene population subdivision formulation.