Development of genetic differentiation and postzygotic isolation in experimental metapopulations of spider mites

We studied the development of genetic differentiation and postzygotic isolation in experimental metapopulations of the two-spotted spider mite, Tetranychus urticae Koch. A genetically diverse starter population was made by allowing six inbred sublines to interbreed. Then three migration patterns were tested: no migration, or one or three immigrants per subpopulation per generation. Variations in four traits were investigated: allozymes, acaricide resistance, diapause, and hatchability. In the allozymes, acaricide resistance, and diapause, genetic variation among subpopulations became high in metapopulations with no migration, but not in the others, which showed that one immigrant is enough to prevent genetic differentiation. Hatchability, which was decreased by interbreeding among the six sublines, gradually recovered in succeeding generations. In metapopulations with no migration, hatchability was reduced again after in-migration at the 15th generation. Different karyotypes or coadapted gene complexes can survive in different subpopulations by genetic drift, and both Wolbachia-infected and -noninfected subpopulations may be selected, which would lead to postzygotic isolation between isolated subpopulations. Our results indicate that sampling effects such as genetic drift or stochastic loss of Wolbachia produce postzygotic isolation in laboratory populations of spider mite.     

A microsatellite analysis of natterjack toad, Bufo calamita, metapopulations

Although it is widely recognised that spatial subdivision of populations is common in nature, there is no consensus as to how metapopulation dynamics affect genetic diversity. We investigated the genetic differentiation of natterjack toads, Bufo calamita , in three regions of Britain where habitat continuity indicated the likely occurrence of extensive metapopulations. Our intention was to determine whether genetic analysis supported the existence of metapopulation structures, if so of what type, and to identify barriers to migration between subpopulations. Allele frequencies were determined across eight polymorphic microsatellite loci for a total of 24 toad subpopulations at three separate sites. Genetic differentiation was assessed using five measures of genetic distance, notably F _ST , R _ST , Nei's standard distance D _s , Δμ² and the Cavalli-Sforza chord distance D _c . B. calamita exhibited small but significant levels of genetic differentiation between subpopulations in all three study areas, and genetic and geographic distance correlations indicated isolation-by-distance effects in all three cases. The effects on correlation strengths of compensation for positive (sea, rivers, urban development) and negative (pond clusters) barriers to toad migration between the subpopulations in each area were also determined. D _c , a measure which assumes that differentiation is caused by drift with negligible mutation effect, yielded the most plausible interpretation of metapopulation structures. Overall the patterns of genetic variation suggested the existence of a mixed metapopulation model for this species, with high levels of gene flow compatible with one version of the classical model but often supported by particularly stable subpopulations as in the mainland-island model.     

The Island Model of Population Differentiation: A General Solution

The island model deals with a species which is subdivided into a number of discrete finite populations, races or subspecies, between which some migration occurs. If the number of populations is small, an assumption of equal rates of migration between each pair of populations may be reasonable approximation. Mutation at a constant rate to novel alleles may also be assumed.-A general solution is given for the process of population divergence under this model following subdivision of a single parental population, expressed in terms of the observed average frequency of heterozygotes within and between subpopulations at a randomly chosen set of independently segregating loci. No restriction is imposed on the magnitude of the migration or mutation rates involved, nor on the number of populations exchanging migrants.-The properties of two fundamental measures of genetic divergence are deduced from the theory. One is a parameter related to varphi, the coefficient of kinship, and the other, gamma, measures the rate of mutational divergence between the sub-populations.     

Inferring Patterns of Migration from Gene Frequencies under Equilibrium Conditions

A new maximum likelihood method to simultaneously estimate the parameters of any migration pattern from gene frequencies in stochastic equilibrium is developed, based on a model of multivariate genetic drift in a subdivided population. Motivated by simulations of this process in the simplified case of two subpopulations, problems related to the nuisance parameter q, the equilibrium gene frequency, are eliminated by conditioning on the observed mean gene frequency. The covariance matrix of this conditional distribution is calculated by constructing an abstract process that mimics the behavior of the original process in the subspace of interest. The approximation holds as long as there is limited differentiation between subpopulations. The bias and variance of estimates of long-range and short-range migration in a finite stepping stone model are evaluated by fitting the model to simulated data with known values of the parameters. Possible ecological extensions of the model are discussed.     

Tumor micro-ecology and competitive interactions

Three nested models describing the growth of individual subpopulations in a heterogeneous environment are described. The models represent the dynamics of two populations which compete, to varying degrees, for common resources. The first model describes growth in a totally non-competitive micro-environment, the second model describes an ecology in which competition is proportional to competitor population size, and the third model ecology extends the model described by Jansson & Revesz (1974), which allows one population to emerge from the other. The critical points for each model are defined using the isoclines derived from the Ordinary Differential Equations (ODE's) describing competitive growth. The critical points for each model are characterized by the signs of the eigenvalues of the variational matrix at each point. The theoretical results of the analysis show that a competitive model ecology with Verhulstian logistics allows four critical points: the origin which is a repeller, two competitive exclusion points, and an equilibrium state (Waltman, 1983). The extended model ecology of Jansson & Revesz (1974), allows three critical points: the origin which is a repeller, competitive exclusion of the first population, and an equilibrium point. Data from a human adenocarcinoma of the colon and murine mammary tumors are used as qualitative measures of the dynamics of the three micro-ecologies. Issues such as stochastic extension to model small populations either for clonal extinction or heterogeneous emergence are discussed.     

Dynamics of extinction in coupled populations of the flour beetle Tribolium castaneum.

In this study we analyzed the effect of migration on the persistence time of coupled local populations of Tribolium in different environments. Four treatments were set up to compare different levels of environmental heterogeneity. We established high, low, moderate, and no heterogeneity. These levels were estimated by the different amounts of food offered to each population. To investigate how risk spreading works, a stochastic model for two subpopulations was employed. The high heterogeneity treatment resulted in the longest persistence, even though survival analysis revealed no significant difference among treatments. The magnitude of differences in growth rates among subpopulations is probably associated with persistence.     

Insight into the Peopling of Mainland Southeast Asia from Thai Population Genetic Structure

There is considerable ethno-linguistic and genetic variation among human populations in Asia, although tracing the origins of this diversity is complicated by migration events. Thailand is at the center of Mainland Southeast Asia (MSEA), a region within Asia that has not been extensively studied. Genetic substructure may exist in the Thai population, since waves of migration from southern China throughout its recent history may have contributed to substantial gene flow. Autosomal SNP data were collated for 438,503 markers from 992 Thai individuals. Using the available self-reported regional origin, four Thai subpopulations genetically distinct from each other and from other Asian populations were resolved by Neighbor-Joining analysis using a 41,569 marker subset. Using an independent Principal Components-based unsupervised clustering approach, four major MSEA subpopulations were resolved in which regional bias was apparent. A major ancestry component was common to these MSEA subpopulations and distinguishes them from other Asian subpopulations. On the other hand, these MSEA subpopulations were admixed with other ancestries, in particular one shared with Chinese. Subpopulation clustering using only Thai individuals and the complete marker set resolved four subpopulations, which are distributed differently across Thailand. A Sino-Thai subpopulation was concentrated in the Central region of Thailand, although this constituted a minority in an otherwise diverse region. Among the most highly differentiated markers which distinguish the Thai subpopulations, several map to regions known to affect phenotypic traits such as skin pigmentation and susceptibility to common diseases. The subpopulation patterns elucidated have important implications for evolutionary and medical genetics. The subpopulation structure within Thailand may reflect the contributions of different migrants throughout the history of MSEA. The information will also be important for genetic association studies to account for population-structure confounding effects.     

The rule of "one migrant per generation" and genetic differentiation in subdivided populations

The genetic differentiation in population with migration according island and two-dimensional stepping stone models was studied with simulation methods. It is shown that migration of one or few individuals per generation is insufficient for leveling differences between subpopulations in allele frequencies. Even if migration is estimated as m = 0.5 (exchange of 50 and 500 individuals per generation) statistically significant differences remain at least in the half of populations with insular structure. Spatial heterogeneity disappears completely only if m = 0.7-0.8. In case of two-dimensional step model the level of genetic differentiation is higher and statistically significant heterogeneity remains at all levels of genetic exchange including that which was estimated as m = 1.     

Life not lived due to disequilibrium in heterogeneous age-structured populations

Three models of age-structured populations with demographically heterogeneous subpopulations are analyzed. In the first model, each subpopulation has its own age-specific vital rates which are fixed in time. In the second model, the vital rates of each subpopulation are uniformly inhibited by increasing total numbers of individuals. In the third, the vital rates of groups of subpopulations are inhibited by the total numbers of individuals in other groups of subpopulations with an intensity that depends on the interacting pair of groups. Three functions are defined to measure disequilibrium in the subpopulation frequencies, subpopulation age structures, and total population size. For the first model, we show that disequilibrium will shift the trajectory of the total numbers of individuals forward or backward in time by an asymptotic constant that is proportional to the sum of the disequilibrium measures. For the second model, we establish sufficient conditions for the existence of a globally stable equilibrium and we show that disequilibrium will result in a finite loss or gain in life which is proportional to the sum of the disequilibrium measures. For the last model, we show that the loss or gain in life for each group of subpopulations is a linear combination over all groups of the sums of the three disequilibrium measures. We illustrate these results with numerical examples and give possible biological interpretations of the models. We relate these new results to previous work on the cost of natural selection and measures of demographic disequilibrium.     

Extremely Rare Interbreeding Events Can Explain Neanderthal DNA in Living Humans

Considering the recent experimental discovery of Green et al that present-day non-Africans have 1 to of their nuclear DNA of Neanderthal origin, we propose here a model which is able to quantify the genetic interbreeding between two subpopulations with equal fitness, living in the same geographic region. The model consists of a solvable system of deterministic ordinary differential equations containing as a stochastic ingredient a realization of the neutral Wright-Fisher process. By simulating the stochastic part of the model we are able to apply it to the interbreeding ofthe African ancestors of Eurasians and Middle Eastern Neanderthal subpopulations and estimate the only parameter of the model, which is the number of individuals per generation exchanged between subpopulations. Our results indicate that the amount of Neanderthal DNA in living non-Africans can be explained with maximum probability by the exchange of a single pair of individuals between the subpopulations at each 77 generations, but larger exchange frequencies are also allowed with sizeable probability. The results are compatible with a long coexistence time of 130,000 years, a total interbreeding population of order individuals, and with all living humans being descendants of Africans both for mitochondrial DNA and Y chromosome.     

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model

Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect directly to the rich predictive mathematics of information theory; (3) Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4) Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information (“Shannon differentiation”) between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (Sturnus vulgaris) in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.     

A statistical test for detecting geographic subdivision.

A statistical test for detecting genetic differentiation of subpopulations is described that uses molecular variation in samples of DNA sequences from two or more localities. The statistical significance of the test is determined with Monte Carlo simulations. The power of the test to detect genetic differentiation in a selectively neutral Wright-Fisher island model depends on both sample size and the rates of migration, mutation, and recombination. It is found that the power of the test is substantial with samples of size 50, when 4Nm less than 10, where N is the subpopulation size and m is the fraction of migrants in each subpopulation each generation. More powerful tests are obtained with genes with recombination than with genes without recombination.     

Evolution of migration under kin selection and local adaptation

We present here a stochastic two-locus, two-habitat model for the evolution of migration with local adaptation and kin selection. One locus determines the migration rate while the other causes local adaptation. We show that the opposing forces of kin competition and local adaptation can lead to the existence of one or two convergence stable migration rates, notably depending on the recombination rate between the two loci. We show that linkage between migration and local adaptation loci has two antagonist effects: when linkage is tight, cost of local adaptation increases, leading to smaller equilibrium migration rates. However, when linkage is tighter, the population structure at the migration locus tends to be very high because of the indirect selection, and thus equilibrium migration rates increases. This result, qualitatively different from results obtained with other models of migration evolution, indicates that ignoring drift or the detail of the genetic architecture may lead to incorrect conclusions.     

Quantitative genetic variation in an ecological setting

The machinery was developed to investigate the behavior of quantitative genetic variation in an ecological model of a finite number of islands of finite size, with migration rate m and extinction rate e, for a quantitative genetic model general for numbers of alleles and loci and additive, dominance, and additive by additive epistatic effects. It was necessary to reckon with seven quadratic genetic components, whose coefficients in the genotypic variance components within demes, sigma Gw2, between demes within populations, sigma s2, and between replicate populations, sigma r2, are given by descent measures. The descent measures at any time are calculated with the use of transition equations which are determined by the parameters of the ecological model. Numerical results were obtained for the coefficients of the quadratic genetic components in each of the three genotypic variance components in the early phase of differentiation. The general effect of extinction is to speed up the time course leading to fixation, to increase sigma r2, and to decrease sigma s2 (with a few exceptions) in comparison with no extinction. The general effect of migration is to slow down the time course leading to fixation, to increase sigma Gw2, at least in the later generations, and to decrease sigma s2 (with a few exceptions) in comparison with no migration. Except for these, the effects of migration and extinction on the variance components are complex, depending on the genetic model, and sometimes involve interaction of migration and extinction. Sufficient details are given for an investigator to evaluate numerically the results for variations in the quantitative genetic and ecological models.     

Genetic load in subdivided populations: interactions between the migration rate, the size and the number of subpopulations

We assess the relative importance of migration rate, size and number of subpopulations on the genetic load of subdivided populations. Using diffusion approximations, we show that in most cases subdivision has detrimental effects on fitness. Moreover, our results suggest that fitness increases with subpopulation size, so that for the same total population size, genetic load is relatively lower when there are a small number of large subpopulations. Using elasticity analysis, we show that the size of the subpopulations appears to be the parameter that most strongly determines genetic load. interconnecting subpopulations via migration would also be of importance for population fitness when subpopulations are small and gene flow is low. Interestingly, the number of subpopulations has minor influence on genetic load except for the case of both very slightly deleterious mutations and small subpopulations. Elasticities decrease as the magnitude of deleterious effects increases. In other words, population structure does not matter for very deleterious alleles, but strongly affects fitness for slightly deleterious alleles.     

Geographic and genetic boundaries of brown bear (Ursus arctos) population in the Caucasus

The taxonomic status of brown bears in the Caucasus remains unclear. Several morphs or subspecies have been identified from the morphological (craniological) data, but the status of each of these subspecies has never been verified by molecular genetic methods. We analysed mitochondrial DNA sequences (control region) to reveal phylogenetic relationships and infer divergence time between brown bear subpopulations in the Caucasus. We estimated migration and gene flow from both mitochondrial DNA and microsatellite allele frequencies, and identified possible barriers to gene flow among the subpopulations. Our suggestion is that all Caucasian bears belong to the nominal subspecies of Ursus arctos. Our results revealed two genetically and geographically distinct maternal haplogroups: one from the Lesser Caucasus and the other one from the Greater Caucasus. The genetic divergence between these haplogroups dates as far back as the beginning of human colonization of the Caucasus. Our analysis of the least‐cost distances between the subpopulations suggests humans as a major barrier to gene flow. The low genetic differentiation inferred from microsatellite allele frequencies indicates that gene flow between the two populations in the Caucasus is maintained through the movements of male brown bears. The Likhi Ridge that connects the Greater and Lesser Caucasus mountains is the most likely corridor for this migration.     

Evolution of intrahost HIV-1 genetic diversity during chronic infection

HIV-1 is one of the fastest evolving entities known. Given that census population sizes of HIV-1 within individuals are much greater than the inverse mutation rate, every possible single point mutation in the viral genome occurs each generation. This enormous capability to generate genetic variation allows for escape from immune surveillance and antiviral therapy. However, compared to this potential, populations of HIV-1 within individuals exhibit little genetic variation. This discrepancy between the known mutation rate of HIV-1 and the average level of genetic variation in the env gene observed in vivo is reflected in comparisons of the actual numbers of productively infected cells, estimated as 10(7), and the effective population size, estimated as 10(3). Using approximate Bayesian computation, we evaluated several hypotheses based on a variety of selective and demographic processes to explain the low effective population size of HIV-1. Of the models we examined, the metapopulation model, in which HIV-1 evolves within an individual as a large collection of small subpopulations subject to frequent migration, extinction, and recolonization, was most consistent with the observed levels of genetic variation and the average frequencies of those variants. The metapopulation model links previous studies of viral dynamics and population genetics.     

Effect of the landscape matrix on gene flow in a coastal amphibian metapopulation

Functional connectivity is crucial for the persistence of a metapopulation, because migration among subpopulations enables recolonization and counteracts genetic drift, which is especially important in small subpopulations. We studied the degree and drivers of connectivity among occupied patches of a coastal dune metapopulation of the Natterjack Toad (Epidalea calamita Laurenti), on the basis of microsatellite variation. As spatial landscape heterogeneity is expected to influence dispersal and genetic structure, we analyzed which landscape features affect functional connectivity and to what extent. Sixty different landscape resistance scenarios as well as the isolation-by-distance model were compared using two landscape genetics approaches. We identified three subpopulations with unidirectional levels of gene flow among the two most geographically separated subpopulations, while inferred gene flow into the geographically intermediate subpopulation was limited. Urbanization and vegetation height negatively affected connectivity. Low estimates of genetic diversity and effective population size indicate that conservation measures in the smallest and most isolated subpopulation are required.