Effect of unsampled populations on the estimation of population sizes and migration rates between sampled populations

Current estimators of gene flow come in two methods; those that estimate parameters assuming that the populations investigated are a small random sample of a large number of populations and those that assume that all populations were sampled. Maximum likelihood or Bayesian approaches that estimate the migration rates and population sizes directly using coalescent theory can easily accommodate datasets that contain a population that has no data, a so-called 'ghost' population. This manipulation allows us to explore the effects of missing populations on the estimation of population sizes and migration rates between two specific populations. The biases of the inferred population parameters depend on the magnitude of the migration rate from the unknown populations. The effects on the population sizes are larger than the effects on the migration rates. The more immigrants from the unknown populations that are arriving in the sample populations the larger the estimated population sizes. Taking into account a ghost population improves or at least does not harm the estimation of population sizes. Estimates of the scaled migration rate M (migration rate per generation divided by the mutation rate per generation) are fairly robust as long as migration rates from the unknown populations are not huge. The inclusion of a ghost population does not improve the estimation of the migration rate M; when the migration rates are estimated as the number of immigrants Nm then a ghost population improves the estimates because of its effect on population size estimation. It seems that for 'real world' analyses one should carefully choose which populations to sample, but there is no need to sample every population in the neighbourhood of a population of interest.     

Effective population size,genetic diversity,and coalescence time in subdivided populations

A formula for the effective population size for the finite island model of subdivided populations is derived. The formula indicates that the effective size can be substantially greater than the actual number of individuals in the entire population when the migration rate among subpopulations is small. It is shown that the mean nucleotide diversity, coalescence time, and heterozygosity for genes sampled from the entire population can be predicted fairly well from the theory for randomly mating populations if the effective population size for the finite island model is used.     

Convergence to the island-model coalescent process in populations with restricted migration

In this article we apply some graph-theoretic results to the study of coalescence in a structured population with migration. The graph is the pattern of migration among subpopulations, or demes, and we use the theory of random walks on graphs to characterize the ease with which ancestral lineages can traverse the habitat in a series of migration events. We identify conditions under which the coalescent process in populations with restricted migration, such that individuals cannot traverse the habitat freely in a single migration event, nonetheless becomes identical to the coalescent process in the island migration model in the limit as the number of demes tends to infinity. Specifically, we first note that a sequence of symmetric graphs with Diaconis-Stroock constant bounded above has an unstructured Kingman-type coalescent in the limit for a sample of size two from two different demes. We then show that circular and toroidal models with long-range but restricted migration have an upper bound on this constant and so have an unstructured-migration coalescent in the limit. We investigate the rate of convergence to this limit using simulations.     

A review of extinction in experimental populations

1. Population extinction is a fundamental ecological process. Recent experimental work has begun to test the large body of theory that predicts how demographic, genetic and environmental factors influence extinction risk. We review empirical studies of extinction conducted under controlled laboratory conditions. Our synthesis highlights four findings. First, extinction theory largely considers individual, isolated populations. However, species interactions frequently altered or even reversed the influence of environmental factors on population extinction as compared to single-species conditions, highlighting the need to integrate community ecology into population theory. 2. While most single-species studies qualitatively agree with theoretical predictions, studies are needed that quantitatively compare observed and predicted extinction rates. A quantitative understanding of extinction processes is needed to further advance theory and to predict population extinction resulting from human activities. 3. Many stresses leading to population extinction can be assuaged by migration between subpopulations. However, too much migration increases synchrony between subpopulations and thus increases extinction risk. Research is needed to determine how to strike a balance that maximizes the benefit of migration. 4. Results from laboratory experiments often conflict with field studies. Understanding these inconsistencies is crucial for extending extinction theory to natural populations.     

Management of subdivided populations in conservation programs: development of a novel dynamic system

Within the context of a conservation program the management of subdivided populations implies a compromise between the control of the global genetic diversity, the avoidance of high inbreeding levels, and, sometimes, the maintenance of a certain degree of differentiation between subpopulations. We present a dynamic and flexible methodology, based on genealogical information, for the maximization of the genetic diversity (measured through the global population coancestry) in captive subdivided populations while controlling/restricting the levels of inbreeding. The method is able to implement specific restrictions on the desired relative levels of coancestry between and within subpopulations. By accounting for the particular genetic population structure, the method determines the optimal contributions (i.e., number of offspring) of each individual, the number of migrants, and the particular subpopulations involved in the exchange of individuals. Computer simulations are used to illustrate the procedure and its performance in a range of reasonable scenarios. The method performs well in most situations and is shown to be more efficient than the commonly accepted one-migrant-per-generation strategy.     

Heterozygote excess in small populations and the heterozygote-excess effective population size

It has been proposed that effective size could be estimated in small dioecious population by considering the heterozygote excess observed at neutral markers. When the number of breeders is small, allelic frequencies in males and females will slightly differ due to binomial sampling error. However, this excess of heterozygotes is not generated by dioecy but by the absence of individuals produced through selfing. Consequently, the approach can also be applied to self-incompatible monoecious species. Some inaccuracies in earlier equations expressing effective size as function of the heterozygote excess are also corrected in this paper. The approach is then extended to subdivided populations, where time of sampling becomes crucial. When adults are sampled, the effective size of the entire population can be estimated, whereas when juveniles are sampled, the average effective number of breeders per subpopulations can be estimated. The main limitation of the heterozygote excess method is that it will only perform satisfactorily for populations with a small number of reproducing individuals. While this situation is unlikely to happen frequently at the scale of the entire population, structured populations with small subpopulations are likely to be common. The estimation of the average number of breeders per subpopulations is thus expected to be applicable to many natural populations. The approach is straightforward to compute and independent of equilibrium assumptions. Applications to simulated data suggest the estimation of the number of breeders to be robust to mutation and migration rates, and to specificities of the mating system.     

Genetic structure among remnant populations of a migratory passerine,the Northern Wheatear Oenanthe oenanthe

Continuous animal populations often become fragmented due to anthropogenic habitat alterations. These small, fragmented populations are fragile due to demographic and genetic factors, whereas immigration can enhance their long‐term viability. Previously, we showed that high philopatry affected the local dynamics of three small and remnant subpopulations of Northern Wheatears in The Netherlands. Here, we show that these three populations together with an additional larger population in the European lowlands are highly genetically differentiated based on 22 microsatellite markers. In contrast, we found no evidence for differentiation using two mitochondrial DNA markers. An IMa2 analysis indicates that gene flow has occurred regularly among our sampled populations. As immigration of colour‐ringed birds among our sampled populations is rare at best, our results suggest that the populations have recently become isolated from one another. Low dispersal rates in highly mobile birds may occur when suitable habitat becomes highly fragmented, and will accentuate stochastic demographic processes and inbreeding, both reducing population viability. As dispersal rates are low among populations of Northern Wheatears in The Netherlands, there is only a small probability of recolonization of habitat patches where populations have become locally extinct.     

Relationship between Migration and DNA Polymorphism in a Local Population

The expected amount of DNA polymorphism, measured in terms of the number of nucleotide differences between the two DNA sequences randomly sampled from subpopulations, was studied by using the stepping-stone model and the finite island model, under the assumption that the migration rate is not the same among different subpopulations. The results obtained indicate that the expected amount of DNA polymorphism in the subpopulation with lower migration rate is smaller than that of higher migration rate. This suggests that marginal populations tend to have lower level of DNA polymorphism than central populations if the migration rate in the marginal populations is lower than that of the central populations.     

Variance and covariance of homozygosity in a structured population

The variance of homozygosity for a K-allele model with n partially isolated subpopulations is derived numerically using identity coefficients. The variance of homozygosity within a subpopulation is shown to depend strongly upon the migration rates between subpopulations but is not strongly influenced by the number of alleles possible at a locus. The variance of homozygosity within a subpopulation, given the value of expected homozygosity, is approximately equal to the value of the variance of homozygosity given by Stewart's formula for a single population. If the population is presumed to be panmictic, but is actually subdivided, and the gametes are sampled at random from the total population, the apparent variance of homozygosity depends on the number of alleles possible. With small migration rates and K large, the apparent variance of homozygosity is much smaller than in a single population with the same expected homozygosity. However, when K is small, the variance of homozygosity is approximately given by Stewart's formula. The transient behavior of the variance of homozygosity shows that a large number of generations may be required to approach equilibrium values.     

Adaptive migratory divergence among sympatric brook charr populations

Ecological processes clearly contribute to population divergence, yet how they interact over complex life cycles remains poorly understood. Notably, the evolutionary consequences of migration between breeding and non-breeding areas have received limited attention. We provide evidence for a negative association between interpopulation differences in migration (between breeding and feeding areas, as well as within each) and the amount of gene flow (m) among three brook charr (Salvelinus fontinalis) populations inhabiting Mistassini Lake, Quebec, Canada. Individuals (n = 1166) captured throughout lake feeding areas over two consecutive sampling years were genotyped (10 microsatellites) and assigned to one of the three populations. Interpopulation differences in migration were compared based on spatial distribution overlap, habitat selection, migration distance within feeding areas, and morphology. We observed a temporally stable, heterogeneous spatial distribution within feeding areas among populations, with the extent of spatial segregation related to differential habitat selection (represented by littoral zone substrate). Spatial segregation was lowest and gene flow highest (m = 0.015) between two populations breeding in separate lake inflows. Segregation was highest and gene flow was lowest (mean m = 0.007) between inflow populations and a third population breeding in the outflow. Compared to outflow migrants, inflow migrants showed longer migration distances within feeding areas (64-70 km vs. 22 km). After entering natal rivers to breed, inflow migrants also migrated longer distances (35-75 km) and at greater elevations (50-150 m) to breeding areas than outflow migrants (0-15 km; -10-0 m). Accordingly, inflow migrants were more streamlined with longer caudal regions, traits known to improve swimming efficiency. There was no association between the geographic distance separating population pairs and the amount of gene flow they exchanged. Collectively, our results are consistent with the hypothesis that reduced gene flow between these brook charr populations results from divergent natural selection leading to interpopulation differences in migration. They also illustrate how phenotypic and genetic differentiation may arise over complex migratory life cycles.     

Patterns of gene flow and source‐sink dynamics in high altitude populations of the common toad Bufo bufo (Anura: Bufonidae)

Understanding patterns of genetic structure is fundamental for developing successful management programmes for deme‐structured organisms, such as amphibians. We used five microsatellite loci and DNA sequences of the mitochondrial control region to assess the relative influences of landscape (geographic distance, altitude and rivers as corridors for dispersal) and historical factors on patterns of gene flow in populations of the toad Bufo bufo in Central Spain. We sampled 175 individuals from eight populations distributed along two major river drainages and used maximum‐likelihood and Bayesian approaches to infer patterns of gene flow and population structure. The mitochondrial DNA data show closely‐related haplotypes distributed across the Iberian Peninsula with no geographic structuring, suggesting recent differentiation of haplotypes and extensive gene flow between populations. On the other hand, microsatellites provide finer resolution, showing that high altitude populations (> 2000 m) exchange lower numbers of migrants with other populations. The results of Bayesian estimates for recent migration rates in high altitude populations suggest source‐sink dynamics between ponds that are consistent with independent data from monitoring over the past 20 years. © 2008 The Linnean Society of London, Biological Journal of the Linnean Society, 2008, 95 , 824–839.     

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.     

Pairwise differences under a general model of population subdivision

A number of different migration and isolation models of population subdivision have been studied. In this paper I analyse a general model of two populations derived from a common ancestral population at some time in the past. The two populations may exchange migrants, but they may also be completely isolated from each other. I derive the expectation and variance of the number of differences between two sequences sampled from the two populations. These are then compared to the corresponding results from two other much-used models: equilibrium migration and complete isolation.     

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.     

Winter Fidelity and Apparent Survival of Lesser Snow Goose Populations in the Pacific Flyway

Abstract The Beringia region of the Arctic contains 2 colonies of lesser snow geese (Chen caerulescens caerulescens) breeding on Wrangel Island, Russia, and Banks Island, Canada, and wintering in North America. The Wrangel Island population is composed of 2 subpopulations from a sympatric breeding colony but separate wintering areas, whereas the Banks Island population shares a sympatric wintering area in California, USA, with one of the Wrangel Island subpopulations. The Wrangel Island colony represents the last major snow goose population in Russia and has fluctuated considerably since 1970, whereas the Banks Island population has more than doubled. The reasons for these changes are unclear, but hypotheses include independent population demographics (survival and recruitment) and immigration and emigration among breeding or wintering populations. These demographic and movement patterns have important ecological and management implications for understanding goose population structure, harvest of admixed populations, and gene flow among populations with separate breeding or wintering areas. From 1993 to 1996, we neckbanded molting birds at their breeding colonies and resighted birds on the wintering grounds. We used multistate mark-recapture models to evaluate apparent survival rates, resighting rates, winter fidelity, and potential exchange among these populations. We also compared the utility of face stain in Wrangel Island breeding geese as a predictor of their wintering area. Our results showed similar apparent survival rates between subpopulations of Wrangel Island snow geese and lower apparent survival, but higher emigration, for the Banks Island birds. Males had lower apparent survival than females, most likely due to differences in neckband loss. Transition between wintering areas was low (<3%), with equal movement between northern and southern wintering areas for Wrangel Island birds and little evidence of exchange between the Banks and northern Wrangel Island populations. Face staining was an unreliable indicator of wintering area. Our findings suggest that northern and southern Wrangel Island subpopulations should be considered a metapopulation in better understanding and managing Pacific Flyway lesser snow geese. Yet the absence of a strong population connection between Banks Island and Wrangel Island geese suggests that these breeding colonies can be managed as separate but overlapping populations. Additionally, winter population fidelity may be more important in lesser snow geese than in other species, and both breeding and wintering areas are important components of population management for sympatric wintering populations.     

METAPOP—A software for the management and analysis of subdivided populations in conservation programs

We introduce a computer program for the dynamic and flexible management of conserved subdivided populations. Using molecular marker data or pedigree information, the software determines the optimal contributions (i.e., number of offspring) of each individual, the number of migrants, and the particular subpopulations involved in the exchange of individuals in order to maintain the largest level of gene diversity in the whole population with a desired control in the rate of inbreeding. Restrictions can be introduced for the total number of migrants, and the mating of particular pairs and their contribution. A full genetic diversity analysis of the population is carried out. The optimal contribution from each subpopulation to a pool of maximal gene diversity is also provided by the program.     

Amplified fragment length polymorphism analysis of Mythimna separata (Lepidoptera: Noctuidae) geographic and melanic laboratory populations in China

Genetic diversity within and among three wild-type natural populations and one melanic laboratory population of Mythimna separata (Walker) (Lepidoptera: Noctuidae) were evaluated using amplified fragment length polymorphism (AFLP) analysis. Although extensive genetic diversity occurs among individuals from different geographic populations (P = 54.5%, h = 0.209, I = 0.305), the majority of the genetic diversity is within populations and not between populations (G(ST) = 0.172), indicating high gene flow (N(M) = 2.403) and suggesting that M. separata in northern China are a part of a single large metapopulation. Genetic diversity in the natural populations was significantly higher than that in the melanic laboratory population (with P = 43.4% versus P = 25.9%, h = 0.173 versus h = 0.086, and I = 0.251 versus I = 0.127), suggesting that the melanic laboratory population is narrowly genetic-based and genetically uniform. Genetic similarities based on AFLP data were calculated, and cluster analysis was preformed to graphically display groupings between individuals and populations. Individuals from the same region were not grouped together in cluster analysis of three natural populations, whereas melanic individuals from laboratory population were grouped together very well. Four subpopulations were clustered into two broad groups. Melanic laboratory population became a single group, which had apparent differentiation from the other group in which three natural subpopulations were included. These results indicated that although high genetic variability existed among the individuals of natural populations, there was little genetic differentiation among three geographic populations that could be explained by the effects of the long distance migration of the oriental armyworm in China enhanced the level of gene flow. Influences of migration on the genetic polymorphism and differentiations that make a significant contribution to evolution in this insect are reviewed.     

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.     

Genetic differentiation among five populations of the South African ghost frog,Heleophryne natalensis

Allozyme electrophoresis was used to analyse genetic heterogeneity in five ghost frog populations (Heleophryne natalensis) (Hewitt, 1913) from different localities in South Africa. A population of the congeneric H. purcelli, was used as a reference group. A total of 25 loci were resolved from 14 enzymes and an unspecified protein. Of the 25 loci resolved, eight were variable within or across populations, revealing an overall polymorphism of 32% but not more than 8% in any individual population. Four of the H. natalensis populations sampled were monoallelic, whereas the fifth population displayed an average heterozygosity of 2.97%. However, there was considerable variation among H. natalensis populations, including monomorphic populations, with fixed allelic differences at three loci. Gene flow among H. natalensis populations was 0.156–0.915 migrants per generation for four pairwise comparisons but zero for the remaining six pairs; the latter is unusual for conspecific populations. The overall intraspecific fixation index value for H. natalensis was 0.876, not much lower than the interspecific F_ST value of 0.912 calculated when data for H. natalensis and H. purcelli was pooled for comparison. This confirms low gene flow and tight selection within microhabitats. Genetic distances ranged from 0.008 to 0.128 between conspecific populations, increasing to 0.182–0.284 between the H. natalensis populations sampled, and H. purcelli. The results are discussed with reference to the relationship between low genetic heterogeneity, response to selection and habitat tolerance of frogs.