ABCtoolbox: a versatile toolkit for approximate Bayesian computations

Background The estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations. Results Here we present ABCtoolbox, a series of open source programs to perform Approximate Bayesian Computations (ABC). It implements various ABC algorithms including rejection sampling, MCMC without likelihood, a Particle-based sampler and ABC-GLM. ABCtoolbox is bundled with, but not limited to, a program that allows parameter inference in a population genetics context and the simultaneous use of different types of markers with different ploidy levels. In addition, ABCtoolbox can also interact with most simulation and summary statistics computation programs. The usability of the ABCtoolbox is demonstrated by inferring the evolutionary history of two evolutionary lineages of Microtus arvalis. Using nuclear microsatellites and mitochondrial sequence data in the same estimation procedure enabled us to infer sex-specific population sizes and migration rates and to find that males show smaller population sizes but much higher levels of migration than females. Conclusion ABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results.

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.

Diversification in the South American Pampas: the genetic and morphological variation of the widespread Petunia axillaris complex (Solanaceae)

Understanding the spatiotemporal distribution of genetic variation and the ways in which this distribution is connected to the ecological context of natural populations is fundamental for understanding the nature and mode of intraspecific and, ultimately, interspecific differentiation. The Petunia axillaris complex is endemic to the grasslands of southern South America and includes three subspecies: P.a.axillaris, P.a.parodii and P.a.subandina. These subspecies are traditionally delimited based on both geography and floral morphology, although the latter is highly variable. Here, we determined the patterns of genetic (nuclear and cpDNA), morphological and ecological (bioclimatic) variation of a large number of P.axillaris populations and found that they are mostly coincident with subspecies delimitation. The nuclear data suggest that the subspecies are likely independent evolutionary units, and their morphological differences may be associated with local adaptations to diverse climatic and/or edaphic conditions and population isolation. The demographic dynamics over time estimated by skyline plot analyses showed different patterns for each subspecies in the last 100000years, which is compatible with a divergence time between 35000 and 107000years ago between P.a.axillaris and P.a.parodii, as estimated with the IMa program. Coalescent simulation tests using Approximate Bayesian Computation do not support previous suggestions of extensive gene flow between P.a.axillaris and P.a.parodii in their contact zone.

Chapter Six – Individual Trait Variation and Diversity in Food Webs

In recent years, there has been a renewed interest in the ecological consequences of individual trait variation within populations. Given that individual variability arises from evolutionary dynamics, to fully understand eco-evolutionary feedback loops, we need to pay special attention to how standing trait variability affects ecological dynamics. There is mounting empirical evidence that intra-specific phenotypic variation can exceed species-level means, but theoretical models of multi-trophic species coexistence typically neglect individual-level trait variability. What is needed are multispecies datasets that are resolved at the individual level that can be used to discriminate among alternative models of resource selection and species coexistence in food webs. Here, using one the largest individual-based datasets of a food web compiled to date, along with an individual trait-based stochastic model that incorporates Approximate Bayesian computation methods, we document intra-population variation in the strength of prey selection by different classes or predator phenotypes which could potentially alter the diversity and coexistence patterns of food webs. In particular, we found that strongly connected individual predators preferentially consumed common prey, whereas weakly connected predators preferentially selected rare prey. Such patterns suggest that food web diversity may be governed by the distribution of predator connectivity and individual trait variation in prey selection. We discuss the consequences of intra-specific variation in prey selection to assess fitness differences among predator classes (or phenotypes) and track longer term food web patterns of coexistence accounting for several phenotypes within each prey and predator species.

Divergent evolutionary processes associated with colonization of offshore islands

Oceanic islands have been a test ground for evolutionary theory, but here, we focus on the possibilities for evolutionary study created by offshore islands. These can be colonized through various means and by a wide range of species, including those with low dispersal capabilities. We use morphology, modern and ancient sequences of cytochrome b (cytb) and microsatellite genotypes to examine colonization history and evolutionary change associated with occupation of the Orkney archipelago by the common vole (Microtus arvalis), a species found in continental Europe but not in Britain. Among possible colonization scenarios, our results are most consistent with human introduction at least 5100 bp (confirmed by radiocarbon dating). We used approximate Bayesian computation of population history to infer the coast of Belgium as the possible source and estimated the evolutionary timescale using a Bayesian coalescent approach. We showed substantial morphological divergence of the island populations, including a size increase presumably driven by selection and reduced microsatellite variation likely reflecting founder events and genetic drift. More surprisingly, our results suggest that a recent and widespread cytb replacement event in the continental source area purged cytb variation there, whereas the ancestral diversity is largely retained in the colonized islands as a genetic ‘ark’. The replacement event in the continental M. arvalis was probably triggered by anthropogenic causes (land-use change). Our studies illustrate that small offshore islands can act as field laboratories for studying various evolutionary processes over relatively short timescales, informing about the mainland source area as well as the island.

Evaluation of a Bayesian MCMC Random Effects Inference Methodology for Capture-Mark-Recapture Data

Monte Carlo simulation was used to evaluate properties of a simple Bayesian MCMC analysis of the random effects model for single group Cormack-Jolly-Seber capture-recapture data. The MCMC method is applied to the model via a logit link, so parameters p, S are on a logit scale, where logit(S) is assumed to have, and is generated from, a normal distribution with mean μ and variance σ2 . Marginal prior distributions on logit(p) and μ were independent normal with mean zero and standard deviation 1.75 for logit(p) and 100 for μ ; hence minimally informative. Marginal prior distribution on σ2 was placed on τ2=1/σ2 as a gamma distribution with α=β=0.001 . The study design has 432 points spread over 5 factors: occasions (t) , new releases per occasion (u), p, μ , and σ . At each design point 100 independent trials were completed (hence 43,200 trials in total), each with sample size n=10,000 from the parameter posterior distribution. At 128 of these design points comparisons are made to previously reported results from a method of moments procedure. We looked at properties of point and interval inference on μ , and σ based on the posterior mean, median, and mode and equal-tailed 95% credibility interval. Bayesian inference did very well for the parameter μ , but under the conditions used here, MCMC inference performance for σ was mixed: poor for sparse data (i.e., only 7 occasions) or σ=0 , but good when there were sufficient data and not small σ .

Twenty questions with noise: Bayes optimal policies for entropy loss

We consider the problem of twenty questions with noisy answers, in which we seek to find a target by repeatedly choosing a set, asking an oracle whether the target lies in this set, and obtaining an answer corrupted by noise. Starting with a prior distribution on the target's location, we seek to minimize the expected entropy of the posterior distribution. We formulate this problem as a dynamic program and show that any policy optimizing the one-step expected reduction in entropy is also optimal over the full horizon. Two such Bayes optimal policies are presented: one generalizes the probabilistic bisection policy due to Horstein and the other asks a deterministic set of questions. We study the structural properties of the latter, and illustrate its use in a computer vision application.