Importance sampling on coalescent histories. I

Genetic diversity and structure related to expansion history and habitat isolation: stone marten populating rural-urban habitats

Background

Population genetic diversity and structure are determined by past and current evolutionary processes, among which spatially limited dispersal, genetic drift, and shifts in species distribution boundaries have major effects. In most wildlife species, environmental modifications by humans often lead to contraction of species’ ranges and/or limit their dispersal by acting as environmental barriers. However, in species well adapted to anthropogenic habitat or open landscapes, human induced environmental changes may facilitate dispersal and range expansions. In this study, we analysed whether isolation by distance and deforestation, among other environmental features, promotes or restricts dispersal and expansion in stone marten (Martes foina) populations.

Results

We genotyped 298 martens from eight sites at twenty-two microsatellite loci to characterize the genetic variability, population structure and demographic history of stone martens in Poland. At the landscape scale, limited genetic differentiation between sites in a mosaic of urban, rural and forest habitats was mostly influenced by isolation by distance. Statistical clustering and multivariate analyses showed weak genetic structuring with two to four clusters and a high rate of gene flow between them. Stronger genetic differentiation was detected for one stone marten population (NE1) located inside a large forest complex. Genetic differentiation between this site and all others was 20% higher than between other sites separated by similar distances. The genetic uniqueness index of NE1 was also twofold higher than in other sites. Past demographic history analyses showed recent expansion of this species in north-eastern Poland. A decrease in genetic diversity from south to north, and MIGRAINE analyses indicated the direction of expansion of stone marten.

Conclusions

Our results showed that two processes, changes in species distribution boundaries and limited dispersal associated with landscape barriers, affect genetic diversity and structure in stone marten. Analysis of local barriers that reduced dispersal and large scale analyses of genetic structure and demographic history highlight the importance of isolation by distance and forest cover for the past colonization of central Europe by stone marten. This confirmed the hypothesis that human-landscape changes (deforestation) accelerated stone marten expansion, to which climate warming probably has also been contributing over the last few decades.

Electronic supplementary material

The online version of this article (10.1186/s12898-017-0156-6) contains supplementary material, which is available to authorized users.

Importance sampling on coalescent histories. II: Subdivided population models

De Iorio and Griffiths (2004) developed a new method of constructing sequential importance-sampling proposal distributions on coalescent histories of a sample of genes for computing the likelihood of a type configuration of genes in the sample by simulation. The method is based on approximating the diffusion-process generator describing the distribution of population gene frequencies, leading to an approximate sample distribution and finally to importance-sampling proposal distributions. This paper applies that method to construct an importance-sampling algorithm for computing the likelihood of samples of genes in subdivided population models. The importance-sampling technique of Stephens and Donnelly (2000) is thus extended to models with a Markov chain mutation mechanism between gene types and migration of genes between subpopulations. An algorithm for computing the likelihood of a sample configuration of genes from a subdivided population in an infinitely-many-alleles model of mutation is derived, extending Ewens's (1972) sampling formula in a single population. Likelihood calculation and ancestral inference in gene trees constructed from DNA sequences under the infinitely-many-sites model are also studied. The Griffiths-Tavaré method of likelihood calculation in gene trees of Bahlo and Griffiths (2000) is improved for subdivided populations.

Maximum-likelihood inference of population size contractions from microsatellite data

Understanding the demographic history of populations and species is a central issue in evolutionary biology and molecular ecology. In this work, we develop a maximum-likelihood method for the inference of past changes in population size from microsatellite allelic data. Our method is based on importance sampling of gene genealogies, extended for new mutation models, notably the generalized stepwise mutation model (GSM). Using simulations, we test its performance to detect and characterize past reductions in population size. First, we test the estimation precision and confidence intervals coverage properties under ideal conditions, then we compare the accuracy of the estimation with another available method (MSVAR) and we finally test its robustness to misspecification of the mutational model and population structure. We show that our method is very competitive compared with alternative ones. Moreover, our implementation of a GSM allows more accurate analysis of microsatellite data, as we show that the violations of a single step mutation assumption induce very high bias toward false contraction detection rates. However, our simulation tests also showed some limits, which most importantly are large computation times for strong disequilibrium scenarios and a strong influence of some form of unaccounted population structure. This inference method is available in the latest implementation of the MIGRAINE software package.

Blockwise HMM computation for large-scale population genomic inference

MOTIVATION

A promising class of methods for large-scale population genomic inference use the conditional sampling distribution (CSD), which approximates the probability of sampling an individual with a particular DNA sequence, given that a collection of sequences from the population has already been observed. The CSD has a wide range of applications, including imputing missing sequence data, estimating recombination rates, inferring human colonization history and identifying tracts of distinct ancestry in admixed populations. Most well-used CSDs are based on hidden Markov models (HMMs). Although computationally efficient in principle, methods resulting from the common implementation of the relevant HMM techniques remain intractable for large genomic datasets.

RESULTS

To address this issue, a set of algorithmic improvements for performing the exact HMM computation is introduced here, by exploiting the particular structure of the CSD and typical characteristics of genomic data. It is empirically demonstrated that these improvements result in a speedup of several orders of magnitude for large datasets and that the speedup continues to increase with the number of sequences. The optimized algorithms can be adopted in methods for various applications, including the ones mentioned above and make previously impracticable analyses possible.

AVAILABILITY

Software available upon request.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

CONTACT

yss@eecs.berkeley.edu.

Likelihood-based inferences under isolation by distance: two-dimensional habitats and confidence intervals

Likelihood-based methods of inference of population parameters from genetic data in structured populations have been implemented but still little tested in large networks of populations. In this work, a previous software implementation of inference in linear habitats is extended to two-dimensional habitats, and the coverage properties of confidence intervals are analyzed in both cases. Both standard likelihood and an efficient approximation are considered. The effects of misspecification of mutation model and dispersal distribution, and of spatial binning of samples, are considered. In the absence of model misspecification, the estimators have low bias, low mean square error, and the coverage properties of confidence intervals are consistent with theoretical expectations. Inferences of dispersal parameters and of the mutation rate are sensitive to misspecification or to approximations inherent to the coalescent algorithms used. In particular, coalescent approximations are not appropriate to infer the shape of the dispersal distribution. However, inferences of the neighborhood parameter (or of the product of population density and mean square dispersal rate) are generally robust with respect to complicating factors, such as misspecification of the mutation process and of the shape of the dispersal distribution, and with respect to spatial binning of samples. Likelihood inferences appear feasible in moderately sized networks of populations (up to 400 populations in this work), and they are more efficient than previous moment-based spatial regression method in realistic conditions.

IMPORTANCE SAMPLING AND THE TWO-LOCUS MODEL WITH SUBDIVIDED POPULATION STRUCTURE

The diffusion-generator approximation technique developed by De Iorio and Griffiths (2004a) is a very useful method of constructing importance sampling proposal distributions. Being based on general mathematical principles, the method can be applied to various models in population genetics. In this paper we extend the technique to the neutral coalescent model with recombination, thus obtaining novel sampling distributions for the two-locus model. We consider the case with subdivided population structure, as well as the classic case with only a single population. In the latter case we also consider the importance sampling proposal distributions suggested by Fearnhead and Donnelly (2001), and show that their two-locus distributions generally differ from ours. In the case of the infinitely-many-alleles model, our approximate sampling distributions are shown to be generally closer to the true distributions than are Fearnhead and Donnelly's.