Michael G. B. Blum

Approximate Bayesian Computation (ABC) in practice

Understanding the forces that influence natural variation within and among populations has been a major objective of evolutionary biologists for decades. Motivated by the growth in computational power and data complexity, modern approaches to this question make intensive use of simulation methods. Approximate Bayesian Computation (ABC) is one of these methods. Here we review the foundations of ABC, its recent algorithmic developments, and its applications in evolutionary biology and ecology. We argue that the use of ABC should incorporate all aspects of Bayesian data analysis: formulation, fitting, and improvement of a model. ABC can be a powerful tool to make inferences with complex models if these principles are carefully applied.

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.

Genomic Variation in Seven Khoe-San Groups Reveals Adaptation and Complex African History

African Origins Humans originated in Africa and then spread across the globe. The high genetic diversity found in sub-Saharan Africa is consistent with this view, but the relationships among and within African populations have been less well explored. Schlebusch et al. (p. 374, published online 20 September) genotyped 220 individuals from 11 populations representing groups from Southern Africa to determine their relationships and history. The data suggest that modern-day human populations arose from a complex blend of mixing between groups and genetic stratification. Cutting-edge genomic approaches test hypotheses about the roots of human history in southern African indigenous populations. The history of click-speaking Khoe-San, and African populations in general, remains poorly understood. We genotyped ∼2.3 million single-nucleotide polymorphisms in 220 southern Africans and found that the Khoe-San diverged from other populations ≥100,000 years ago, but population structure within the Khoe-San dated back to about 35,000 years ago. Genetic variation in various sub-Saharan populations did not localize the origin of modern humans to a single geographic region within Africa; instead, it indicated a history of admixture and stratification. We found evidence of adaptation targeting muscle function and immune response; potential adaptive introgression of protection from ultraviolet light; and selection predating modern human diversification, involving skeletal and neurological development. These new findings illustrate the importance of African genomic diversity in understanding human evolutionary history.

Evolutionary history and global spread of the Mycobacterium tuberculosis Beijing lineage

Mycobacterium tuberculosis strains of the Beijing lineage are globally distributed and are associated with the massive spread of multidrug-resistant (MDR) tuberculosis in Eurasia. Here we reconstructed the biogeographical structure and evolutionary history of this lineage by genetic analysis of 4,987 isolates from 99 countries and whole-genome sequencing of 110 representative isolates. We show that this lineage initially originated in the Far East, from where it radiated worldwide in several waves. We detected successive increases in population size for this pathogen over the last 200 years, practically coinciding with the Industrial Revolution, the First World War and HIV epidemics. Two MDR clones of this lineage started to spread throughout central Asia and Russia concomitantly with the collapse of the public health system in the former Soviet Union. Mutations identified in genes putatively under positive selection and associated with virulence might have favored the expansion of the most successful branches of the lineage.

The goat domestication process inferred from large-scale mitochondrial DNA analysis of wild and domestic individuals

The emergence of farming during the Neolithic transition, including the domestication of livestock, was a critical point in the evolution of human kind. The goat (Capra hircus) was one of the first domesticated ungulates. In this study, we compared the genetic diversity of domestic goats to that of the modern representatives of their wild ancestor, the bezoar, by analyzing 473 samples collected over the whole distribution range of the latter species. This partly confirms and significantly clarifies the goat domestication scenario already proposed by archaeological evidence. All of the mitochondrial DNA haplogroups found in current domestic goats have also been found in the bezoar. The geographic distribution of these haplogroups in the wild ancestor allowed the localization of the main domestication centers. We found no haplotype that could have been domesticated in the eastern half of the Iranian Plateau, nor further to the east. A signature of population expansion in bezoars of the C haplogroup suggests an early domestication center on the Central Iranian Plateau (Yazd and Kerman Provinces) and in the Southern Zagros (Fars Province), possibly corresponding to the management of wild flocks. However, the contribution of this center to the current domestic goat population is rather low (1.4%). We also found a second domestication center covering a large area in Eastern Anatolia, and possibly in Northern and Central Zagros. This last domestication center is the likely origin of almost all domestic goats today. This finding is consistent with archaeological data identifying Eastern Anatolia as an important domestication center.

Demographic history of european populations of Arabidopsis thaliana.

The model plant species Arabidopsis thaliana is successful at colonizing land that has recently undergone human-mediated disturbance. To investigate the prehistoric spread of A. thaliana, we applied approximate Bayesian computation and explicit spatial modeling to 76 European accessions sequenced at 876 nuclear loci. We find evidence that a major migration wave occurred from east to west, affecting most of the sampled individuals. The longitudinal gradient appears to result from the plant having spread in Europe from the east ∼10,000 years ago, with a rate of westward spread of ∼0.9 km/year. This wave-of-advance model is consistent with a natural colonization from an eastern glacial refugium that overwhelmed ancient western lineages. However, the speed and time frame of the model also suggest that the migration of A. thaliana into Europe may have accompanied the spread of agriculture during the Neolithic transition.

A comparative review of dimension reduction methods in approximate Bayesian computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

Which Random Processes Describe the Tree of Life? A Large-Scale Study of Phylogenetic Tree Imbalance

The explosion of phylogenetic studies not only provides a clear snapshot of biodiversity, but also makes it possible to infer how the diversity has arisen (see for example, Purvis and Hector, 2000; Harvey et al., 1996; Nee et al., 1996; Mace et al., 2003). To this aim, variation in speciation and extinction rates have been investigated through their signatures in the shapes of phylogenetic trees (Mooers and Heard, 1997). This issue is of great importance, as fitting stochastic models to tree data would help to understand underlying macroevolutionary processes. Although the prevailing view is that it does not represent phylogenies so well, the most popular model of phylogenetic trees is a branching process introduced by Yule, in which lineages split at random (Yule, 1924). Here we report the study of one major database of published

Deep divergences of human gene trees and models of human origins

Two competing hypotheses are at the forefront of the debate on modern human origins. In the first scenario, known as the recent Out-of-Africa hypothesis, modern humans arose in Africa about 100,000-200,000 years ago and spread throughout the world by replacing the local archaic human populations. By contrast, the second hypothesis posits substantial gene flow between archaic and emerging modern humans. In the last two decades, the young time estimates--between 100,000 and 200,000 years--of the most recent common ancestors for the mitochondrion and the Y chromosome provided evidence in favor of a recent African origin of modern humans. However, the presence of very old lineages for autosomal and X-linked genes has often been claimed to be incompatible with a simple, single origin of modern humans. Through the analysis of a public DNA sequence database, we find, similar to previous estimates, that the common ancestors of autosomal and X-linked genes are indeed very old, living, on average, respectively, 1,500,000 and 1,000,000 years ago. However, contrary to previous conclusions, we find that these deep gene genealogies are consistent with the Out-of-Africa scenario provided that the ancestral effective population size was approximately 14,000 individuals. We show that an ancient bottleneck in the Middle Pleistocene, possibly arising from an ancestral structured population, can reconcile the contradictory findings from the mitochondrion on the one hand, with the autosomes and the X chromosome on the other hand.

The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance

For two decades, the Colless index has been the most frequently used statistic for assessing the balance of phylogenctic trees. In this article, this statistic is studied under the Yule and unif ...