Reconstruction of a beech population bottleneck using archival demographic information and Bayesian analysis of genetic data

Range expansion and contraction has occurred in the history of most species and can seriously impact patterns of genetic diversity. Historical data about range change are rare and generally appropriate for studies at large scales, whereas the individual pollen and seed dispersal events that form the basis of geneflow and colonization generally occur at a local scale. In this study, we investigated range change in Fagus sylvatica on Mont Ventoux, France, using historical data from 1838 to the present and approximate Bayesian computation (ABC) analyses of genetic data. From the historical data, we identified a population minimum in 1845 and located remnant populations at least 200 years old. The ABC analysis selected a demographic scenario with three populations, corresponding to two remnant populations and one area of recent expansion. It also identified expansion from a smaller ancestral population but did not find that this expansion followed a population bottleneck, as suggested by the historical data. Despite a strong support to the selected scenario for our data set, the ABC approach showed a low power to discriminate among scenarios on average and a low ability to accurately estimate effective population sizes and divergence dates, probably due to the temporal scale of the study. This study provides an unusual opportunity to test ABC analysis in a system with a well-documented demographic history and identify discrepancies between the results of historical, classical population genetic and ABC analyses. The results also provide valuable insights into genetic processes at work at a fine spatial and temporal scale in range change and colonization.     

Monitoring the effective population size of a brown bear (Ursus arctos) population using new single-sample approaches

The effective population size (N(e) ) could be the ideal parameter for monitoring populations of conservation concern as it conveniently summarizes both the evolutionary potential of the population and its sensitivity to genetic stochasticity. However, tracing its change through time is difficult in natural populations. We applied four new methods for estimating N(e) from a single sample of genotypes to trace temporal change in N(e) for bears in the Northern Dinaric Mountains. We genotyped 510 bears using 20 microsatellite loci and determined their age. The samples were organized into cohorts with regard to the year when the animals were born and yearly samples with age categories for every year when they were alive. We used the Estimator by Parentage Assignment (EPA) to directly estimate both N(e) and generation interval for each yearly sample. For cohorts, we estimated the effective number of breeders (N(b) ) using linkage disequilibrium, sibship assignment and approximate Bayesian computation methods and extrapolated these estimates to N(e) using the generation interval. The N(e) estimate by EPA is 276 (183-350 95% CI), meeting the inbreeding-avoidance criterion of N(e) > 50 but short of the long-term minimum viable population goal of N(e) > 500. The results obtained by the other methods are highly consistent with this result, and all indicate a rapid increase in N(e) probably in the late 1990s and early 2000s. The new single-sample approaches to the estimation of N(e) provide efficient means for including N(e) in monitoring frameworks and will be of great importance for future management and conservation.     

Disentangling the impact of demographic factors on population differentiation of an endangered freshwater crayfish (Austropotamobius pallipes) using population density and microsatellite data

1. Habitat fragmentation of stream ecosystems often results in decreased connectivity between populations and lower population sizes. Hence, understanding how habitat fragmentation affects genetic erosion is important for the preservation of freshwater biodiversity, in particular, as small populations suffer from loss of genetic diversity through genetic drift and loss of fitness because of inbreeding, increasing the risk of extinction. 2. Here, we assess the impact of demographic factors on population differentiation in the endangered freshwater crayfish Austropotamobius pallipes by analysing population genetic structure, estimating effective population sizes and comparing levels of polymorphism at five microsatellite loci with density estimates of 10 populations within a small French catchment that has become progressively confined to headwaters over the last six decades. 3. Levels of expected heterozygosity and allelic richness per population were relatively low (0.214–0.396 and 1.6–2.6, respectively). We found strong genetic differentiation between these geographically close populations (F_ST = 0.283), with weak statistical evidence for a pattern of isolation by distance. Estimates of effective population size were low (<150) in most populations, but potentially reached several thousands in three populations. 4. Population density and allelic richness were strongly positively correlated. A robust relationship between population density and heterozygosity values was also noted, but only after discarding two populations for which significant genetic signatures of a recent bottleneck were found; these two populations displayed high expected heterozygosity compared with a very low density. Populations with the highest densities of individuals had the highest effective population size estimates and vice versa. 5. Our results clearly show the importance of demographic factors and genetic drift on A. pallipes populations. Furthermore, analysis of genetic and population density data is a pragmatic and efficient approach to corroborate inferences from genetic data and can be particularly useful in the identification of populations experiencing a bottleneck and therefore in conservation genetics studies aiming at identifying priority populations for conservation.     

Fine-scale population structure in a desert amphibian: landscape genetics of the black toad (Bufo exsul)

Environmental variables can strongly influence a variety of intra- and inter-population processes, including demography, population structure and gene flow. When environmental conditions are particularly harsh for a certain species, investigating these effects is important to understanding how populations persist under difficult conditions. Furthermore, species inhabiting challenging environments present excellent opportunities to examine the effects of complex landscapes on population processes because these effects will often be more pronounced. In this study, I use 16 microsatellite loci to examine population structure, gene flow and demographic history in the black toad, Bufo exsul , which has one of the most restricted natural ranges of any amphibian. Bufo exsul inhabits four springs in the Deep Springs Valley high desert basin and has never been observed more than several meters from any source of water. My results reveal limited gene flow and moderately high levels of population structure ( F _ST = 0.051–0.063) between all but the two closest springs. I found that the geographic distance across the arid scrub habitat between springs is significantly correlated with genetic structure when distance accounts for topography and barriers to dispersal. I also found very low effective population sizes ( N _e = 7–30) and substantial evidence for historical population bottlenecks in all four populations. Together, these results suggest that the desert landscape and B.   exsul 's high habitat specificity contribute significantly to population structure and demography in this species and emphasize the importance of considering behavioural and landscape data in conservation genetic studies of natural systems.     

Interpreting scratch assays using pair density dynamics and approximate Bayesian computation

Quantifying the impact of biochemical compounds on collective cell spreading is an essential element of drug design, with various applications including developing treatments for chronic wounds and cancer. Scratch assays are a technically simple and inexpensive method used to study collective cell spreading; however, most previous interpretations of scratch assays are qualitative and do not provide estimates of the cell diffusivity, D, or the cell proliferation rate, λ. Estimating D and λ is important for investigating the efficacy of a potential treatment and provides insight into the mechanism through which the potential treatment acts. While a few methods for estimating D and λ have been proposed, these previous methods lead to point estimates of D and λ, and provide no insight into the uncertainty in these estimates. Here, we compare various types of information that can be extracted from images of a scratch assay, and quantify D and λ using discrete computational simulations and approximate Bayesian computation. We show that it is possible to robustly recover estimates of D and λ from synthetic data, as well as a new set of experimental data. For the first time, our approach also provides a method to estimate the uncertainty in our estimates of D and λ. We anticipate that our approach can be generalized to deal with more realistic experimental scenarios in which we are interested in estimating D and λ, as well as additional relevant parameters such as the strength of cell-to-cell adhesion or the strength of cell-to-substrate adhesion.     

Monte Carlo integration over stepping stone models for spatial genetic inference using approximate Bayesian computation

Approximate Bayesian computation (ABC) substitutes simulation for analytic models in Bayesian inference. Simulating evolutionary scenarios under Kimura’s stepping stone model (KSS) might therefore allow inference over spatial genetic process where analytical results are difficult to obtain. ABC first creates a reference set of simulations and would proceed by comparing summary statistics over KSS simulations to summary statistics from localities sampled in the field, but: comparison of which localities and stepping stones? Identical stepping stones can be arranged so two localities fall in the same stepping stone, nearest or diagonal neighbours, or without contact. None is intrinsically correct, yet some choice must be made and this affects inference. We explore a Bayesian strategy for mapping field observations onto discrete stepping stones. We make Sundial, for projecting field data onto the plane, available. We generalize KSS over regular tilings of the plane. We show Bayesian averaging over the mapping between a continuous field area and discrete stepping stones improves the fit between KSS and isolation by distance expectations. We make Tiler Durden available for carrying out this Bayesian averaging. We describe a novel parameterization of KSS based on Wright’s neighbourhood size, placing an upper bound on the geographic area represented by a stepping stone and make it available as m Vector. We generalize spatial coalescence recursions to continuous and discrete space cases and use these to numerically solve for KSS coalescence previously examined only using simulation. We thus provide applied and analytical resources for comparison of stepping stone simulations with field observations.     

Reconstructing demographic events from population genetic data: the introduction of bumblebees to New Zealand

Four British bumblebee species (Bombus terrestris, Bombus hortorum, Bombus ruderatus and Bombus subterraneus) became established in New Zealand following their introduction at the turn of the last century. Of these, two remain common in the United Kingdom (B. terrestris and B. hortorum), whilst two (B. ruderatus and B. subterraneus) have undergone marked declines, the latter being declared extinct in 2000. The presence of these bumblebees in New Zealand provides an unique system in which four related species have been isolated from their source population for over 100 years, providing a rare opportunity to examine the impacts of an initial bottleneck and introduction to a novel environment on their population genetics. We used microsatellite markers to compare modern populations of B. terrestris, B. hortorum and B. ruderatus in the United Kingdom and New Zealand and to compare museum specimens of British B. subterraneus with the current New Zealand population. We used approximate Bayesian computation to estimate demographic parameters of the introduction history, notably to estimate the number of founders involved in the initial introduction. Species-specific patterns derived from genetic analysis were consistent with the predictions based on the presumed history of these populations; demographic events have left a marked genetic signature on all four species. Approximate Bayesian analyses suggest that the New Zealand population of B. subterraneus may have been founded by as few as two individuals, giving rise to low genetic diversity and marked genetic divergence from the (now extinct) UK population.     

ldne: a program for estimating effective population size from data on linkage disequilibrium

ldne is a program with a Visual Basic interface that implements a recently developed bias correction for estimates of effective population size (N(e) ) based on linkage disequilibrium data. The program reads genotypic data in standard formats and can accommodate an arbitrary number of samples, individuals, loci, and alleles, as well as two mating systems: random and lifetime monogamy. ldne calculates separate estimates using different criteria for excluding rare alleles, which facilitates evaluation of data for highly polymorphic markers such as microsatellites. The program also introduces a jackknife method for obtaining confidence intervals that appears to perform better than parametric methods currently in use.     

Coalescent process with fluctuating population size and its effective size

We consider a Wright-Fisher model whose population size is a finite Markov chain. We introduce a sequence of two-dimensional discrete time Markov chains whose components describe the coalescent process and the fluctuation of population size. For the limiting process of the sequence of Markov chains, the relationship of the expectation of coalescence time to the harmonic and the arithmetic means of population sizes is shown, and the Laplace transform of the distribution of coalescence time is calculated. We define the coalescence effective population size (cEPS) by the expectation of coalescence time. We show that cEPS is strictly larger (resp. smaller) than the harmonic (resp. arithmetic) mean. As the population size fluctuates more quickly (resp. slowly), cEPS is closer to the harmonic (resp. arithmetic) mean. For the case of a two-valued Markov chain, we show the explicit expression of cEPS and its dependency on the sample size.     

ABC as a flexible framework to estimate demography over space and time: some cons,many pros

The analysis of genetic variation to estimate demographic and historical parameters and to quantitatively compare alternative scenarios recently gained a powerful and flexible approach: the Approximate Bayesian Computation (ABC). The likelihood functions does not need to be theoretically specified, but posterior distributions can be approximated by simulation even assuming very complex population models including both natural and human‐induced processes. Prior information can be easily incorporated and the quality of the results can be analysed with rather limited additional effort. ABC is not a statistical analysis per se, but rather a statistical framework and any specific application is a sort of hybrid between a simulation and a data‐analysis study. Complete software packages performing the necessary steps under a set of models and for specific genetic markers are already available, but the flexibility of the method is better exploited combining different programs. Many questions relevant in ecology can be addressed using ABC, but adequate amount of time should be dedicated to decide among alternative options and to evaluate the results. In this paper we will describe and critically comment on the different steps of an ABC analysis, analyse some of the published applications of ABC and provide user guidelines.     

Small effective population sizes in a widespread selfing species, Lymnaea truncatula (Gastropoda: Pulmonata)

We present here a spatial and temporal population genetic survey of a common freshwater snail, also a predominantly selfing species, Lymnaea truncatula. The rate of genetic diversity loss was quantified by estimating the effective size (Ne) of the snail populations, using two different methods. A temporal survey allowed estimation of a variance effective size of the populations, and a spatial survey allowed the estimation of an inbreeding effective size, from two-locus identity disequilibria estimates. Both methods were consistent and provided low Ne values. Drift due to (i) high amounts of selfing and (ii) fluctuations in population sizes because of temporary habitats, and also selection coupled to genome-wide linkage disequilibria, could explain such reductions in Ne. The loss of genetic diversity appears to be counterbalanced only very partially by low apparent rates of gene flow.     

Inbreeding effective population size under some artificial selection schemes

Summary It is well known that truncation selection is the most efficient form of directional selection in terms of changing gene frequency. In this paper we show circumstances where truncation selection followed by a balanced mating generates inbreeding effective population size smaller than that generated by a selection that assigns mating frequencies to individuals according to their breeding values, where both selection schemes give the same expected performance of selected individuals (selection differential). Breeding values of selected individuals and the weight used to determine mating frequencies are assumed to be linearly distributed on a performance scales, x. To assign mating frequencies to the individuals in the weighting system, the selected individuals are grouped using a constant , and ith group in the interval x_i, x_i + . With small number of groups, say 2 or 3, the weighting system in general generates inbreeding effective population size that is larger than that generated by a truncation selection. As the number of the groups increases, truncation selection generates larger effective numbers.     

Estimating effective population size from linkage disequilibrium: severe bias in small samples

Effective population size (N _e) is a central concept in evolutionary biology and conservation genetics. It predicts rates of loss of neutral genetic variation, fixation of deleterious and favourable alleles, and the increase of inbreeding experienced by a population. A method exists for the estimation of N _e from the observed linkage disequilibrium between unlinked loci in a population sample. While an increasing number of studies have applied this method in natural and managed populations, its reliability has not yet been evaluated. We developed a computer program to calculate this estimator of N _e using the most widely used linkage disequilibrium algorithm and used simulations to show that this estimator is strongly biased when the sample size is small (<‰100) and below the true N _e. This is probably due to the linkage disequilibrium generated by the sampling process itself and the inadequate correction for this phenomenon in the method. Results suggest that N _e estimates derived using this method should be regarded with caution in many cases. To improve the method’s reliability and usefulness we propose a way to determine whether a given sample size exceeds the population N _e and can therefore be used for the computation of an unbiased estimate.     

Generation time and effective population size in Polar Eskimos

North Greenland Polar Eskimos are the only hunter-gatherer population, to our knowledge, who can offer precise genealogical records spanning several generations. This is the first report from Eskimos on two key parameters in population genetics, namely, generation time (T) and effective population size (Ne). The average mother-daughter and father-son intervals were 27 and 32 years, respectively, roughly similar to the previously published generation times obtained from recent agricultural societies across the world. To gain an insight for the generation time in our distant ancestors, we calculated maternal generation time for two wild chimpanzee populations. We also provide the first comparison among three distinct approaches (genealogy, variance and life table methods) for calculating Ne, which resulted in slightly differing values for the Eskimos. The ratio of the effective to the census population size is estimated as 0.6-0.7 for autosomal and X-chromosomal DNA, 0.7-0.9 for mitochondrial DNA and 0.5 for Y-chromosomal DNA. A simulation of alleles along the genealogy suggested that Y-chromosomal DNA may drift a little faster than mitochondrial DNA in this population, in contrast to agricultural Icelanders. Our values will be useful not only in prehistoric population inference but also in understanding the shaping of our genome today.     

Population genetic structure and effective population size of ayu (Plecoglossus altivelis), an amphidromous fish

The temporal and spatial population genetic structure of ayu Plecoglossus altivelis (Salmoniformes: Plecoglossidae), an amphidromous fish, was examined using analysis of variation at six microsatellite DNA loci. Intracohort genetic diversities, as measured by the number of alleles and heterozygosity, were similar among six cohorts (2001–2006) within a population (Nezugaseki River), with the mean number of alleles per cohort ranging from 11·0 to 12·5 and the expected heterozygosity ranging from 0·74 to 0·77. Intrapopulational genetic diversities were also similar across the three studied populations along the 50 km coast, with the mean number of alleles and the expected heterozygosity ranging from 11·33 to 11·67 and from 0·75 to 0·76, respectively. The authors observed only one significant difference in pair-wise population differentiation ( F _ST-value) between the cohorts within a population and among three populations. Estimates of the effective population size ( N _e) based on maximum-likelihood method yielded small values (ranging from 94·8 to 135·5), whereas census population size ranged from c. 4800 to 24 000. As a result, the ratio of annual effective population sizes to census population size ( N _e/ N ) ranged from 0·004 to 0·023. These estimates of N _e/ N agree more closely with estimates for marine fishes than that of the larger estimates for freshwater fishes. The present study suggests that ayu which is highly fecund and shows low survival during the early life stages is also characterized by having low value of N _e/ N , similar to marine species with a pelagic life cycle.     

Effective population size of natural populations of Drosophila buzzatii, with a comparative evaluation of nine methods of estimation

Allozyme and microsatellite data from numerous populations of Drosophila buzzatii have been used (i) to determine to what degree N(e) varies among generations within populations, and among populations, and (ii) to evaluate the congruence of four temporal and five single-sample estimators of N(e) . Effective size of different populations varied over two orders of magnitude, most populations are not temporally stable in genetic composition, and N(e) showed large variation over generations in some populations. Short-term N(e) estimates from the temporal methods were highly correlated, but the smallest estimates were the most precise for all four methods, and the most consistent across methods. Except for one population, N(e) estimates were lower when assuming gene flow than when assuming populations that were closed. However, attempts to jointly estimate N(e) and immigration rate were of little value because the source of migrants was unknown. Correlations among the estimates from the single-sample methods generally were not significant although, as for the temporal methods, estimates were most consistent when they were small. These single-sample estimates of current N(e) are generally smaller than the short-term temporal estimates. Nevertheless, population genetic variation is not being depleted, presumably because of past or ongoing migration. A clearer picture of current and short-term effective population sizes will only follow with better knowledge of migration rates between populations. Different methods are not necessarily estimating the same N(e) , they are subject to different bias, and the biology, demography and history of the population(s) may affect different estimators differently.