Bayesian estimation of recent migration rates after a spatial expansion

Approximate Bayesian computation (ABC) is a highly flexible technique that allows the estimation of parameters under demographic models that are too complex to be handled by full-likelihood methods. We assess the utility of this method to estimate the parameters of range expansion in a two-dimensional stepping-stone model, using samples from either a single deme or multiple demes. A minor modification to the ABC procedure is introduced, which leads to an improvement in the accuracy of estimation. The method is then used to estimate the expansion time and migration rates for five natural common vole populations in Switzerland typed for a sex-linked marker and a nuclear marker. Estimates based on both markers suggest that expansion occurred < 10,000 years ago, after the most recent glaciation, and that migration rates are strongly male biased.

Bayesian parameter estimation for latent Markov random fields and social networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.

Colonization history of the Swiss Rhine basin by the bullhead (Cottus gobio): inference under a Bayesian spatially explicit framework

The present distribution of freshwater fish in the Alpine region has been strongly affected by colonization events occurring after the last glacial maximum (LGM), some 20,000 years ago. We use here a spatially explicit simulation framework to model and better understand their colonization dynamics in the Swiss Rhine basin. This approach is applied to the European bullhead (Cottus gobio), which is an ideal model organism to study fish past demographic processes since it has not been managed by humans. The molecular diversity of eight sampled populations is simulated and compared to observed data at six microsatellite loci under an approximate Bayesian computation framework to estimate the parameters of the colonization process. Our demographic estimates fit well with current knowledge about the biology of this species, but they suggest that the Swiss Rhine basin was colonized very recently, after the Younger Dryas some 6600 years ago. We discuss the implication of this result, as well as the strengths and limits of the spatially explicit approach coupled to the approximate Bayesian computation framework.

Exact and approximate Bayesian solutions for inference about variance components and multivariate inadmissibility : final report for period 1 May 1972-1 January 1976 /

Performing organization: Dept. of Statistics, University of Michigan.

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Sampling Methods for Exploring Between Subject Variability in Cardiac Electrophysiology Experiments

Between-subject and within-subject variability is ubiquitous in biology and physiology and understanding and dealing with this is one of the biggest challenges in medicine. At the same time it is difficult to investigate this variability by experiments alone. A recent modelling and simulation approach, known as population of models (POM), allows this exploration to take place by building a mathematical model consisting of multiple parameter sets calibrated against experimental data. However, finding such sets within a high-dimensional parameter space of complex electrophysiological models is computationally challenging. By placing the POM approach within a statistical framework, we develop a novel and efficient algorithm based on sequential Monte Carlo (SMC). We compare the SMC approach with Latin hypercube sampling (LHS), a method commonly adopted in the literature for obtaining the POM, in terms of efficiency and output variability in the presence of a drug block through an in-depth investigation via the Beeler-Reuter cardiac electrophysiological model. We show improved efficiency via SMC and that it produces similar responses to LHS when making out-of-sample predictions in the presence of a simulated drug block.

Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

Approximate Bayesian computation (ABC) is a popular technique for analysing data for complex models where the likelihood function is intractable. It involves using simulation from the model to approximate the likelihood, with this approximate likelihood then being used to construct an approximate posterior. In this paper, we consider methods that estimate the parameters by maximizing the approximate likelihood used in ABC. We give a theoretical analysis of the asymptotic properties of the resulting estimator. In particular, we derive results analogous to those of consistency and asymptotic normality for standard maximum likelihood estimation. We also discuss how sequential Monte Carlo methods provide a natural method for implementing our likelihood-based ABC procedures.

Patterns of genetic variation in the endangered European mink (Mustela lutreola L., 1761)

Background: The European mink (Mustela lutreola, L. 1761) is a critically endangered mustelid, which inhabits several main river drainages in Europe. Here, we assess the genetic variation of existing populations of this species, including new sampling sites and additional molecular markers (newly developed microsatellite loci specific to European mink) as compared to previous studies. Probabilistic analyses were used to examine genetic structure within and between existing populations, and to infer phylogeographic processes and past demography. Results: According to both mitochondrial and nuclear microsatellite markers, Northeastern (Russia, Estonia and Belarus) and Southeastern (Romania) European populations showed the highest intraspecific diversity. In contrast, Western European (France and Spain) populations were the least polymorphic, featuring a unique mitochondrial DNA haplotype. The high differentiation values detected between Eastern and Western European populations could be the result of genetic drift in the latter due to population isolation and reduction. Genetic differences among populations were further supported by Bayesian clustering and two main groups were confirmed (Eastern vs. Western Europe) along with two contained subgroups at a more local scale (Northeastern vs. Southeastern Europe; France vs. Spain). Conclusions: Genetic data and performed analyses support a historical scenario of stable European mink populations, not affected by Quaternary climate oscillations in the Late Pleistocene, and posterior expansion events following river connections in both North-and Southeastern European populations. This suggests an eastern refuge during glacial maxima (as already proposed for boreal and continental species). In contrast, Western Europe was colonised more recently following either natural expansions or putative human introductions. Low levels of genetic diversity observed within each studied population suggest recent bottleneck events and stress the urgent need for conservation measures to counteract the demographic decline experienced by the European mink.

New insights on postglacial colonization in western Europe: the phylogeography of the Leisler’s bat (Nyctalus leisleri)

Despite recent advances in the understanding of the interplay between a dynamic physical environment and phylogeography in Europe, the origins of contemporary Irish biota remain uncertain. Current thinking is that Ireland was colonized post-glacially from southern European refugia, following the end of the last glacial maximum(LGM), some 20 000 years BP. The Leisler’s bat (Nyctalus leisleri), one of the few native Irish mammal species, is widely distributed throughout Europe but, with the exception of Ireland, is generally rare and considered vulnerable. We investigate the origins and phylogeographic relationships of Irish populations in relation to those across Europe, including the closely related species N. azoreum. We use a combination of approaches, including mitochondrial and nuclear DNA markers, in addition to approximate Bayesian computation and palaeo-climatic species distribution modelling. Molecular analyses revealed two distinct and diverse European mitochondrialDNAlineages,which probably diverged in separate glacial refugia. Awestern lineage, restricted to Ireland, Britain and the Azores, comprises Irish and British N. leisleri and N. azoreum specimens; an eastern lineage is distributed throughout mainland Europe. Palaeo-climatic projections indicate suitable habitats during the LGM, including known glacial refugia, in addition to potential novel cryptic refugia along the western fringe of Europe. These results may be applicable to populations of many species.

Unique mitochondrial DNA lineages in Irish stickleback populations: cryptic refugium or rapid recolonization?

Repeated recolonization of freshwater environments following Pleistocene glaciations has played a major role in the evolution and adaptation of anadromous taxa. Located at the western fringe of Europe, Ireland and Britain were likely recolonized rapidly by anadromous fishes from the North Atlantic following the last glacial maximum (LGM). While the presence of unique mitochondrial haplotypes in Ireland suggests that a cryptic northern refugium may have played a role in recolonization, no explicit test of this hypothesis has been conducted. The three-spined stickleback is native and ubiquitous to aquatic ecosystems throughout Ireland, making it an excellent model species with which to examine the biogeographical history of anadromous fishes in the region. We used mitochondrial and microsatellite markers to examine the presence of divergent evolutionary lineages and to assess broad-scale patterns of geographical clustering among postglacially isolated populations. Our results confirm that Ireland is a region of secondary contact for divergent mitochondrial lineages and that endemic haplotypes occur in populations in Central and Southern Ireland. To test whether a putative Irish lineage arose from a cryptic Irish refugium, we used approximate Bayesian computation (ABC). However, we found no support for this hypothesis. Instead, the Irish lineage likely diverged from the European lineage as a result of postglacial isolation of freshwater populations by rising sea levels. These findings emphasize the need to rigorously test biogeographical hypothesis and contribute further evidence that postglacial processes may have shaped genetic diversity in temperate fauna.

The Origins of Lactase Persistence in Europe

Lactase persistence (LP) is common among people of European ancestry, but with the exception of some African, Middle Eastern and southern Asian groups, is rare or absent elsewhere in the world. Lactase gene haplotype conservation around a polymorphism strongly associated with LP in Europeans (-13,910 C/T) indicates that the derived allele is recent in origin and has been subject to strong positive selection. Furthermore, ancient DNA work has shown that the -13,910*T (derived) allele was very rare or absent in early Neolithic central Europeans. It is unlikely that LP would provide a selective advantage without a supply of fresh milk, and this has lead to a gene-culture coevolutionary model where lactase persistence is only favoured in cultures practicing dairying, and dairying is more favoured in lactase persistent populations. We have developed a flexible demic computer simulation model to explore the spread of lactase persistence, dairying, other subsistence practices and unlinked genetic markers in Europe and western Asia's geographic space. Using data on -13,910*T allele frequency and farming arrival dates across Europe, and approximate Bayesian computation to estimate parameters of interest, we infer that the -13,910*T allele first underwent selection among dairying farmers around 7,500 years ago in a region between the central Balkans and central Europe, possibly in association with the dissemination of the Neolithic Linearbandkeramik culture over Central Europe. Furthermore, our results suggest that natural selection favouring a lactase persistence allele was not higher in northern latitudes through an increased requirement for dietary vitamin D. Our results provide a coherent and spatially explicit picture of the coevolution of lactase persistence and dairying in Europe.

PopABC: a program to infer historical demographic parameters

PopABC is a computer package for inferring the pattern of demographic divergence of closely related populations and species. The software performs coalescent simulation in the framework of approximate Bayesian computation (ABC). PopABC can also be used to perform Bayesian model choice to discriminate between different demographic scenarios. The program can be used either for research or for education and teaching purposes.