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.

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.

Population genetic structure and demography analysis in palinurus elephas populations from atlantic and mediterranean waters

Report for the scientific sojourn at the University of Reading, United Kingdom, from January until May 2008. The main objectives have been firstly to infer population structure and parameters in demographic models using a total of 13 microsatellite loci for genotyping approximately 30 individuals per population in 10 Palinurus elephas populations both from Mediterranean and Atlantic waters. Secondly, developing statistical methods to identify discrepant loci, possibly under selection and implement those methods using the R software environment. It is important to consider that the calculation of the probability distribution of the demographic and mutational parameters for a full genetic data set is numerically difficult for complex demographic history (Stephens 2003). The Approximate Bayesian Computation (ABC), based on summary statistics to infer posterior distributions of variable parameters without explicit likelihood calculations, can surmount this difficulty. This would allow to gather information on different demographic prior values (i.e. effective population sizes, migration rate, microsatellite mutation rate, mutational processes) and assay the sensitivity of inferences to demographic priors by assuming different priors.

Indirect likelihood inference (revised)

Standard indirect Inference (II) estimators take a given finite-dimensional statistic, Z_{n} , and then estimate the parameters by matching the sample statistic with the model-implied population moment. We here propose a novel estimation method that utilizes all available information contained in the distribution of Z_{n} , not just its first moment. This is done by computing the likelihood of Z_{n}, and then estimating the parameters by either maximizing the likelihood or computing the posterior mean for a given prior of the parameters. These are referred to as the maximum indirect likelihood (MIL) and Bayesian Indirect Likelihood (BIL) estimators, respectively. We show that the IL estimators are first-order equivalent to the corresponding moment-based II estimator that employs the optimal weighting matrix. However, due to higher-order features of Z_{n} , the IL estimators are higher order efficient relative to the standard II estimator. The likelihood of Z_{n} will in general be unknown and so simulated versions of IL estimators are developed. Monte Carlo results for a structural auction model and a DSGE model show that the proposed estimators indeed have attractive finite sample properties.

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.

Estimação do índice de memória em processos estocásticos com memória longa: uma abordagem via ABC

Neste trabalho propomos o uso de um método Bayesiano para estimar o parâmetro de memória de um processo estocástico com memória longa quando sua função de verossimilhança é intratável ou não está disponível. Esta abordagem fornece uma aproximação para a distribuição a posteriori sobre a memória e outros parâmetros e é baseada numa aplicação simples do método conhecido como computação Bayesiana aproximada (ABC). Alguns estimadores populares para o parâmetro de memória serão revisados e comparados com esta abordagem. O emprego de nossa proposta viabiliza a solução de problemas complexos sob o ponto de vista Bayesiano e, embora aproximativa, possui um desempenho muito satisfatório quando comparada com métodos clássicos.

THE USE OF SIMULATIONS IN EVOLUTIONARY POPULATION GENETICS: APPLICATIONS ON HUMANS, OWLS AND VIRTUAL ORGANISMS

Summary (in English) Computer simulations provide a practical way to address scientific questions that would be otherwise intractable. In evolutionary biology, and in population genetics in particular, the investigation of evolutionary processes frequently involves the implementation of complex models, making simulations a particularly valuable tool in the area. In this thesis work, I explored three questions involving the geographical range expansion of populations, taking advantage of spatially explicit simulations coupled with approximate Bayesian computation. First, the neutral evolutionary history of the human spread around the world was investigated, leading to a surprisingly simple model: A straightforward diffusion process of migrations from east Africa throughout a world map with homogeneous landmasses replicated to very large extent the complex patterns observed in real human populations, suggesting a more continuous (as opposed to structured) view of the distribution of modern human genetic diversity, which may play a better role as a base model for further studies. Second, the postglacial evolution of the European barn owl, with the formation of a remarkable coat-color cline, was inspected with two rounds of simulations: (i) determine the demographic background history and (ii) test the probability of a phenotypic cline, like the one observed in the natural populations, to appear without natural selection. We verified that the modern barn owl population originated from a single Iberian refugium and that they formed their color cline, not due to neutral evolution, but with the necessary participation of selection. The third and last part of this thesis refers to a simulation-only study inspired by the barn owl case above. In this chapter, we showed that selection is, indeed, effective during range expansions and that it leaves a distinguished signature, which can then be used to detect and measure natural selection in range-expanding populations. Résumé (en français) Les simulations fournissent un moyen pratique pour répondre à des questions scientifiques qui seraient inabordable autrement. En génétique des populations, l'étude des processus évolutifs implique souvent la mise en oeuvre de modèles complexes, et les simulations sont un outil particulièrement précieux dans ce domaine. Dans cette thèse, j'ai exploré trois questions en utilisant des simulations spatialement explicites dans un cadre de calculs Bayésiens approximés (approximate Bayesian computation : ABC). Tout d'abord, l'histoire de la colonisation humaine mondiale et de l'évolution de parties neutres du génome a été étudiée grâce à un modèle étonnement simple. Un processus de diffusion des migrants de l'Afrique orientale à travers un monde avec des masses terrestres homogènes a reproduit, dans une très large mesure, les signatures génétiques complexes observées dans les populations humaines réelles. Un tel modèle continu (opposé à un modèle structuré en populations) pourrait être très utile comme modèle de base dans l'étude de génétique humaine à l'avenir. Deuxièmement, l'évolution postglaciaire d'un gradient de couleur chez l'Effraie des clocher (Tyto alba) Européenne, a été examiné avec deux séries de simulations pour : (i) déterminer l'histoire démographique de base et (ii) tester la probabilité qu'un gradient phénotypique, tel qu'observé dans les populations naturelles puisse apparaître sans sélection naturelle. Nous avons montré que la population actuelle des chouettes est sortie d'un unique refuge ibérique et que le gradient de couleur ne peux pas s'être formé de manière neutre (sans l'action de la sélection naturelle). La troisième partie de cette thèse se réfère à une étude par simulations inspirée par l'étude de l'Effraie. Dans ce dernier chapitre, nous avons montré que la sélection est, en effet, aussi efficace dans les cas d'expansion d'aire de distribution et qu'elle laisse une signature unique, qui peut être utilisée pour la détecter et estimer sa force.

Rapid radiation in spiny lobsters (Palinurus spp) as revealed by classic and ABC methods using mtDNA and microsatellite data

Background: Molecular tools may help to uncover closely related and still diverging species from a wide variety of taxa and provide insight into the mechanisms, pace and geography of marine speciation. There is a certain controversy on the phylogeography and speciation modes of species-groups with an Eastern Atlantic-Western Indian Ocean distribution, with previous studies suggesting that older events (Miocene) and/or more recent (Pleistocene) oceanographic processes could have influenced the phylogeny of marine taxa. The spiny lobster genus Palinurus allows for testing among speciation hypotheses, since it has a particular distribution with two groups of three species each in the Northeastern Atlantic (P. elephas, P. mauritanicus and P. charlestoni) and Southeastern Atlantic and Southwestern Indian Oceans (P. gilchristi, P. delagoae and P. barbarae). In the present study, we obtain a more complete understanding of the phylogenetic relationships among these species through a combined dataset with both nuclear and mitochondrial markers, by testing alternative hypotheses on both the mutation rate and tree topology under the recently developed approximate Bayesian computation (ABC) methods. Results Our analyses support a North-to-South speciation pattern in Palinurus with all the South-African species forming a monophyletic clade nested within the Northern Hemisphere species. Coalescent-based ABC methods allowed us to reject the previously proposed hypothesis of a Middle Miocene speciation event related with the closure of the Tethyan Seaway. Instead, divergence times obtained for Palinurus species using the combined mtDNA-microsatellite dataset and standard mutation rates for mtDNA agree with known glaciation-related processes occurring during the last 2 my. Conclusion The Palinurus speciation pattern is a typical example of a series of rapid speciation events occurring within a group, with very short branches separating different species. Our results support the hypothesis that recent climate change-related oceanographic processes have influenced the phylogeny of marine taxa, with most Palinurus species originating during the last two million years. The present study highlights the value of new coalescent-based statistical methods such as ABC for testing different speciation hypotheses using molecular data.

Rapid radiation in spiny lobsters (Palinurus spp) as revealed by classic and ABC methods using mtDNA and microsatellite data

Background: Molecular tools may help to uncover closely related and still diverging species from a wide variety of taxa and provide insight into the mechanisms, pace and geography of marine speciation. There is a certain controversy on the phylogeography and speciation modes of species-groups with an Eastern Atlantic-Western Indian Ocean distribution, with previous studies suggesting that older events (Miocene) and/or more recent (Pleistocene) oceanographic processes could have influenced the phylogeny of marine taxa. The spiny lobster genus Palinurus allows for testing among speciation hypotheses, since it has a particular distribution with two groups of three species each in the Northeastern Atlantic (P. elephas, P. mauritanicus and P. charlestoni) and Southeastern Atlantic and Southwestern Indian Oceans (P. gilchristi, P. delagoae and P. barbarae). In the present study, we obtain a more complete understanding of the phylogenetic relationships among these species through a combined dataset with both nuclear and mitochondrial markers, by testing alternative hypotheses on both the mutation rate and tree topology under the recently developed approximate Bayesian computation (ABC) methods. Results: Our analyses support a North-to-South speciation pattern in Palinurus with all the South-African species forming a monophyletic clade nested within the Northern Hemisphere species. Coalescent-based ABC methods allowed us to reject the previously proposed hypothesis of a Middle Miocene speciation event related with the closure of the Tethyan Seaway. Instead, divergence times obtained for Palinurus species using the combined mtDNA-microsatellite dataset and standard mutation rates for mtDNA agree with known glaciation-related processes occurring during the last 2 my. Conclusion: The Palinurus speciation pattern is a typical example of a series of rapid speciation events occurring within a group, with very short branches separating different species. Our results support the hypothesis that recent climate change-related oceanographic processes have influenced the phylogeny of marine taxa, with most Palinurus species originating during the last two million years. The present study highlights the value of new coalescent-based statistical methods such as ABC for testing different speciation hypotheses using molecular data.

Barriers, rather than refugia, underlie the origin of diversity in toads endemic to the Brazilian Atlantic Forest

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

BayGO: Bayesian analysis of ontology term enrichment in microarray data

Abstract Background The search for enriched (aka over-represented or enhanced) ontology terms in a list of genes obtained from microarray experiments is becoming a standard procedure for a system-level analysis. This procedure tries to summarize the information focussing on classification designs such as Gene Ontology, KEGG pathways, and so on, instead of focussing on individual genes. Although it is well known in statistics that association and significance are distinct concepts, only the former approach has been used to deal with the ontology term enrichment problem. Results BayGO implements a Bayesian approach to search for enriched terms from microarray data. The R source-code is freely available at http://blasto.iq.usp.br/~tkoide/BayGO in three versions: Linux, which can be easily incorporated into pre-existent pipelines; Windows, to be controlled interactively; and as a web-tool. The software was validated using a bacterial heat shock response dataset, since this stress triggers known system-level responses. Conclusion The Bayesian model accounts for the fact that, eventually, not all the genes from a given category are observable in microarray data due to low intensity signal, quality filters, genes that were not spotted and so on. Moreover, BayGO allows one to measure the statistical association between generic ontology terms and differential expression, instead of working only with the common significance analysis.

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.

Plant distribution and climate data across western North America

Using an extensive network of occurrence records for 293 plant species collected over the past 40 years across a climatically diverse geographic section of western North America, we find that plant species distributions were just as likely to shift upwards (i.e., towards higher elevations) as downward (i.e., towards lower elevations) - despite consistent warming across the study area. Although there was no clear directional response to climate warming across the entire study area, there was significant region-to region- variation in responses (i.e. from as many as 73% to as few as32% of species shifting upward or downward). To understand the factors that might be controlling region-specific distributional shifts, we explored the relationship between the direction of change in distribution limits and the nature of recent climate change. We found that the direction of distribution limit shifts was explained by an interaction between the rate of change in local summer temperatures and seasonal precipitation. Specifically, species shifted upward at their upper elevational limit when snowfall declined at slower rates and minimum temperatures increased. By contrast, species shifted upwards at their lower elevation limit when maximum temperatures increased or both temperature and precipitation decreased. Our results suggest that future species' elevational distribution shifts will be complex, depending on the interaction between seasonal temperature and precipitation change.

Genetic variation and inference of demographic histories in non-model species

Both long-term environmental changes such as those driven by the glacial cycles and more recent anthropogenic impacts have had major effects on the past demography in wild organisms. Within species, these changes are reflected in the amount and distribution of neutral genetic variation. In this thesis, mitochondrial and microsatellite DNA was analysed to investigate how environmental and anthropogenic factors have affected genetic diversity and structure in four ecologically different animal species. Paper I describes the post-glacial recolonisation history of the speckled-wood butterfly (Pararge aegeria) in Northern Europe. A decrease in genetic diversity with latitude and a marked population structure were uncovered, consistent with a hypothesis of repeated founder events during the postglacial recolonisation. Moreover, Approximate Bayesian Computation analyses indicate that the univoltine populations in Scandinavia and Finland originate from recolonisations along two routes, one on each side of the Baltic. Paper II aimed to investigate how past sea-level rises affected the population history of the convict surgeonfish (Acanthurus triostegus) in the Indo-Pacific. Assessment of the species’ demographic history suggested a population expansion that occurred approximately at the end of the last glaciation. Moreover, the results demonstrated an overall lack of phylogeographic structure, probably due to the high dispersal rates associated with the species’ pelagic larval stage. Populations at the species’ eastern range margin were significantly differentiated from other populations, which likely is a consequence of their geographic isolation. In Paper III, we assessed the effect of human impact on the genetic variation of European moose (Alces alces) in Sweden. Genetic analyses revealed a spatial structure with two genetic clusters, one in northern and one in southern Sweden, which were separated by a narrow transition zone. Moreover, demographic inference suggested a recent population bottleneck. The inferred timing of this bottleneck coincided with a known reduction in population size in the 19th and early 20th century due to high hunting pressure. In Paper IV, we examined the effect of an indirect but well-described human impact, via environmental toxic chemicals (PCBs), on the genetic variation of Eurasian otters (Lutra lutra) in Sweden. Genetic clustering assignment revealed differentiation between otters in northern and southern Sweden, but also in the Stockholm region. ABC analyses indicated a decrease in effective population size in both northern and southern Sweden. Moreover, comparative analyses of historical and contemporary samples demonstrated a more severe decline in genetic diversity in southern Sweden compared to northern Sweden, in agreement with the levels of PCBs found.