Complex trait architecture: the pleiotropic model revisited.

There is currently much debate about how much the genetic heritability of complex traits is due to very rare alleles. This issue is important because it determines sampling strategies for genetic association studies. Several recent theoretical papers based on a pleiotropic model for trait evolution suggest that it is possible that a large proportion of the genetic variance could be explained by rare alleles. This model assumes that mutations with a large effect on fitness also tend to have large positive or negative effects on phenotypic traits. We show that conclusions based on standard diffusion results are generally applicable to simulations of whole genomes with overlapping generations in a finite population, although the variance contribution of rare alleles is somewhat smaller than theoretical predictions. We show that under many scenarios the pleiotropic model predicts trait distributions that are unrealistically leptokurtic. We argue that this imposes a limit on the relationship between fitness and trait effects.

Coestimation of recombination, substitution and molecular adaptation rates by approximate Bayesian computation.

The estimation of parameters in molecular evolution may be biased when some processes are not considered. For example, the estimation of selection at the molecular level using codon-substitution models can have an upward bias when recombination is ignored. Here we address the joint estimation of recombination, molecular adaptation and substitution rates from coding sequences using approximate Bayesian computation (ABC). We describe the implementation of a regression-based strategy for choosing subsets of summary statistics for coding data, and show that this approach can accurately infer recombination allowing for intracodon recombination breakpoints, molecular adaptation and codon substitution rates. We demonstrate that our ABC approach can outperform other analytical methods under a variety of evolutionary scenarios. We also show that although the choice of the codon-substitution model is important, our inferences are robust to a moderate degree of model misspecification. In addition, we demonstrate that our approach can accurately choose the evolutionary model that best fits the data, providing an alternative for when the use of full-likelihood methods is impracticable. Finally, we applied our ABC method to co-estimate recombination, substitution and molecular adaptation rates from 24 published human immunodeficiency virus 1 coding data sets.

Approximate Bayesian computation for modular inference problems with many parameters: the example of migration rates.

We propose a two-step procedure for estimating multiple migration rates in an approximate Bayesian computation (ABC) framework, accounting for global nuisance parameters. The approach is not limited to migration, but generally of interest for inference problems with multiple parameters and a modular structure (e.g. independent sets of demes or loci). We condition on a known, but complex demographic model of a spatially subdivided population, motivated by the reintroduction of Alpine ibex (Capra ibex) into Switzerland. In the first step, the global parameters ancestral mutation rate and male mating skew have been estimated for the whole population in Aeschbacher et al. (Genetics 2012; 192: 1027). In the second step, we estimate in this study the migration rates independently for clusters of demes putatively connected by migration. For large clusters (many migration rates), ABC faces the problem of too many summary statistics. We therefore assess by simulation if estimation per pair of demes is a valid alternative. We find that the trade-off between reduced dimensionality for the pairwise estimation on the one hand and lower accuracy due to the assumption of pairwise independence on the other depends on the number of migration rates to be inferred: the accuracy of the pairwise approach increases with the number of parameters, relative to the joint estimation approach. To distinguish between low and zero migration, we perform ABC-type model comparison between a model with migration and one without. Applying the approach to microsatellite data from Alpine ibex, we find no evidence for substantial gene flow via migration, except for one pair of demes in one direction.

Challenges and pitfalls in the characterization of anonymous outlier AFLP markers in non-model species: lessons from an ocellated lizard genome scan.

In the last few years, dozens of studies have documented the detection of loci influenced by selection from genome scans in a wide range of non-model species. Many of those studies used amplified fragment length polymorphism (AFLP) markers, which became popular for being easily applicable to any organism. However, because they are anonymous markers, AFLPs impose many challenges for their isolation and identification. Most recent AFLP genome scans used capillary electrophoresis (CE), which adds even more obstacles to the isolation of bands with a specific size for sequencing. These caveats might explain the extremely low number of studies that moved from the detection of outlier AFLP markers to their actual isolation and characterization. We document our efforts to characterize a set of outlier AFLP markers from a previous genome scan with CE in ocellated lizards (Lacerta lepida). Seven outliers were successfully isolated, cloned and sequenced. Their sequences are noncoding and show internal indels or polymorphic repetitive elements (microsatellites). Three outliers were converted into codominant markers by using specific internal primers to sequence and screen population variability from undigested DNA. Amplification in closely related lizard species was also achieved, revealing remarkable interspecific conservation in outlier loci sequences. We stress the importance of following up AFLP genome scans to validate selection signatures of outlier loci, but also report the main challenges and pitfalls that may be faced during the process.

Population divergence with or without admixture: selecting models using an ABC approach.

Genetic data have been widely used to reconstruct the demographic history of populations, including the estimation of migration rates, divergence times and relative admixture contribution from different populations. Recently, increasing interest has been given to the ability of genetic data to distinguish alternative models. One of the issues that has plagued this kind of inference is that ancestral shared polymorphism is often difficult to separate from admixture or gene flow. Here, we applied an approximate Bayesian computation (ABC) approach to select the model that best fits microsatellite data among alternative splitting and admixture models. We performed a simulation study and showed that with reasonably large data sets (20 loci) it is possible to identify with a high level of accuracy the model that generated the data. This suggests that it is possible to distinguish genetic patterns due to past admixture events from those due to shared polymorphism (population split without admixture). We then apply this approach to microsatellite data from an endangered and endemic Iberian freshwater fish species, in which a clustering analysis suggested that one of the populations could be admixed. In contrast, our results suggest that the observed genetic patterns are better explained by a population split model without admixture.

Association of Mc1r variants with ecologically relevant phenotypes in the European ocellated lizard, Lacerta lepida.

A comprehensive knowledge on the genetic basis of coloration is crucial to understand how new colour phenotypes arise and how they contribute to the emergence of new species. Variation in melanocortin-1 receptor (Mc1r), a gene that has been reported as a target for repeated evolution in a wide range of vertebrate taxa, was assessed in European ocellated lizards (Lacerta lepida) to search for associations with melanin-based colour phenotypes. Lacerta lepida subspecies' distribution is associated with the three major bio-climatic regions in the Iberian Peninsula. A nonconserved and derived substitution (T162I) was associated with the L. l. nevadensis phenotype (prevalence of brown scales). Another substitution (S172C) was associated with the presence of black scales in both L. l. lepida and L. l. iberica, but no mutations were found to be associated with the higher proportion of black in L. l. iberica. Extensive genotyping of Mc1r along the contact zone between L. l. nevadensis and L. l. lepida revealed low gene flow (only two hybrids detected). The implications of these findings are discussed in the context of previous knowledge about the evolutionary history of ocellated lizards.

Adaptive divergence and speciation among sexual and pseudoviviparous populations of Festuca.

Pseudovivipary is an environmentally induced flowering abnormality in which vegetative shoots replace seminiferous (sexual) inflorescences. Pseudovivipary is usually retained in transplantation experiments, indicating that the trait is not solely induced by the growing environment. Pseudovivipary is the defining characteristic of Festuca vivipara, and arguably the only feature separating this species from its closest seminiferous relative, Festuca ovina. We performed phylogenetic and population genetic analysis on sympatric F. ovina and F. vivipara samples to establish whether pseudovivipary is an adaptive trait that accurately defines the separation of genetically distinct Festuca species. Chloroplast and nuclear marker-based analyses revealed that variation at a geographical level can exceed that between F. vivipara and F. ovina. We deduced that F. vivipara is a recent species that frequently arises independently within F. ovina populations and has not accumulated significant genetic differentiation from its progenitor. We inferred local gene flow between the species. We identified one amplified fragment length polymorphism marker that may be linked to a pseudovivipary-related region of the genome, and several other markers provide evidence of regional local adaptation in Festuca populations. We conclude that F. vivipara can only be appropriately recognized as a morphologically and ecologically distinct species; it lacks genetic differentiation from its relatives. This is the first report of a 'failure in normal flowering development' that repeatedly appears to be adaptive, such that the trait responsible for species recognition constantly reappears on a local basis.

Inferring introduction routes of invasive species using approximate Bayesian computation on microsatellite data.

Determining the routes of introduction provides not only information about the history of an invasion process, but also information about the origin and construction of the genetic composition of the invading population. It remains difficult, however, to infer introduction routes from molecular data because of a lack of appropriate methods. We evaluate here the use of an approximate Bayesian computation (ABC) method for estimating the probabilities of introduction routes of invasive populations based on microsatellite data. We considered the crucial case of a single source population from which two invasive populations originated either serially from a single introduction event or from two independent introduction events. Using simulated datasets, we found that the method gave correct inferences and was robust to many erroneous beliefs. The method was also more efficient than traditional methods based on raw values of statistics such as assignment likelihood or pairwise F(ST). We illustrate some of the features of our ABC method, using real microsatellite datasets obtained for invasive populations of the western corn rootworm, Diabrotica virgifera virgifera. Most computations were performed with the DIYABC program (http://www1.montpellier.inra.fr/CBGP/diyabc/).

ABC: a useful Bayesian tool for the analysis of population data.

Approximate Bayesian computation (ABC) is a recently developed technique for solving problems in Bayesian inference. Although typically less accurate than, for example, the frequently used Markov Chain Monte Carlo (MCMC) methods, they have greater flexibility because they do not require the specification of a likelihood function. For this reason considerable amounts of data can be analysed and more complex models can be used providing, thereby, a potential better fit of the model to the data. Since its first applications in the late 1990s its usage has been steadily increasing. The framework was originally developed to solve problems in population genetics. However, as its efficiency was recognized its popularity increased and, consequently, it started to be used in fields as diverse as phylogenetics, ecology, conservation, molecular evolution and epidemiology. While the ABC algorithm is still being greatly studied and alterations to it are being proposed, the statistical approach has already reached a level of maturity well demonstrated by the number of related computer packages that are being developed. As improved ABC algorithms are proposed, the expansion of the use of this method can only increase. In this paper we are going to depict the context that led to the development of ABC focusing on the field of infectious disease epidemiology. We are then going to describe its current usage in such field and present its most recent developments.

A note on the accuracy of PAC-likelihood inference with microsatellite data.

Stephens and Donnelly have introduced a simple yet powerful importance sampling scheme for computing the likelihood in population genetic models. Fundamental to the method is an approximation to the conditional probability of the allelic type of an additional gene, given those currently in the sample. As noted by Li and Stephens, the product of these conditional probabilities for a sequence of draws that gives the frequency of allelic types in a sample is an approximation to the likelihood, and can be used directly in inference. The aim of this note is to demonstrate the high level of accuracy of "product of approximate conditionals" (PAC) likelihood when used with microsatellite data. Results obtained on simulated microsatellite data show that this strategy leads to a negligible bias over a wide range of the scaled mutation parameter theta. Furthermore, the sampling variance of likelihood estimates as well as the computation time are lower than that obtained with importance sampling on the whole range of theta. It follows that this approach represents an efficient substitute to IS algorithms in computer intensive (e.g. MCMC) inference methods in population genetics.

Inference on microsatellite mutation processes in the invasive mite, Varroa destructor, using reversible jump Markov chain Monte Carlo.

Varroa destructor is a parasitic mite of the Eastern honeybee Apis cerana. Fifty years ago, two distinct evolutionary lineages (Korean and Japanese) invaded the Western honeybee Apis mellifera. This haplo-diploid parasite species reproduces mainly through brother-sister matings, a system which largely favors the fixation of new mutations. In a worldwide sample of 225 individuals from 21 locations collected on Western honeybees and analyzed at 19 microsatellite loci, a series of de novo mutations was observed. Using historical data concerning the invasion, this original biological system has been exploited to compare three mutation models with allele size constraints for microsatellite markers: stepwise (SMM) and generalized (GSM) mutation models, and a model with mutation rate increasing exponentially with microsatellite length (ESM). Posterior probabilities of the three models have been estimated for each locus individually using reversible jump Markov Chain Monte Carlo. The relative support of each model varies widely among loci, but the GSM is the only model that always receives at least 9% support, whatever the locus. The analysis also provides robust estimates of mutation parameters for each locus and of the divergence time of the two invasive lineages (67,000 generations with a 90% credibility interval of 35,000-174,000). With an average of 10 generations per year, this divergence time fits with the last post-glacial Korea-Japan land separation.

Recent developments in genetic data analysis: what can they tell us about human demographic history?

Over the last decade, a number of new methods of population genetic analysis based on likelihood have been introduced. This review describes and explains the general statistical techniques that have recently been used, and discusses the underlying population genetic models. Experimental papers that use these methods to infer human demographic and phylogeographic history are reviewed. It appears that the use of likelihood has hitherto had little impact in the field of human population genetics, which is still primarily driven by more traditional approaches. However, with the current uncertainty about the effects of natural selection, population structure and ascertainment of single-nucleotide polymorphism markers, it is suggested that likelihood-based methods may have a greater impact in the future.

Estimation of admixture proportions: a likelihood-based approach using Markov chain Monte Carlo.

When populations are separated for long periods and then brought into contact for a brief episode in part of their range, this can result in genetic admixture. To analyze this type of event we considered a simple model under which two parental populations (P1 and P2) mix and create a hybrid population (H). After that event, the three populations evolve under pure drift without exchange during T generations. We developed a new method, which allows the simultaneous estimation of the time since the admixture event (scaled by the population size t(i) = T/N(i), where N(i) is the effective population size of population i) and the contribution of one of two parental populations (which we call p1). This method takes into account drift since the admixture event, variation caused by sampling, and uncertainty in the estimation of the ancestral allele frequencies. The method is tested on simulated data sets and then applied to a human data set. We find that (i) for single-locus data, point estimates are poor indicators of the real admixture proportions even when there are many alleles; (ii) biallelic loci provide little information about the admixture proportion and the time since admixture, even for very small amounts of drift, but can be powerful when many loci are used; (iii) the precision of the parameters' estimates increases with sample size n = 50 vs. n = 200 but this effect is larger for the t(i)'s than for p1; and (iv) the increase in precision provided by multiple loci is quite large, even when there is substantial drift (we found, for instance, that it is preferable to use five loci than one locus, even when drift is 100 times larger for the five loci). Our analysis of a previously studied human data set illustrates that the joint estimation of drift and p1 can provide additional insights into the data.

Immigration and the ephemerality of a natural population bottleneck: evidence from molecular markers.

Population bottlenecks are often invoked to explain low levels of genetic variation in natural populations, yet few studies have documented the direct genetic consequences of known bottlenecks in the wild. Empirical studies of natural population bottlenecks are therefore needed, because key assumptions of theoretical and laboratory studies of bottlenecks may not hold in the wild. Here we present microsatellite data from a severe bottleneck (95% mortality) in an insular population of song sparrows (Melospiza melodia). The major findings of our study are as follows: (i) The bottleneck reduced heterozygosity and allelic diversity nearly to neutral expectations, despite non-random survival of birds with respect to inbreeding and wing length. (ii) All measures of genetic diversity regained pre-bottleneck levels within two to three years of the crash. This rapid recovery was due to low levels of immigration. (iii) The rapid recovery occurred despite a coincident, strong increase in average inbreeding. These results show that immigration at levels that are hard to measure in most field studies can lead to qualitatively very different genetic outcomes from those expected from mutations only. We suggest that future theoretical and empirical work on bottlenecks and metapopulations should address the impact of immigration.

Detecting population expansion and decline using microsatellites.

This article considers a demographic model where a population varies in size either linearly or exponentially. The genealogical history of microsatellite data sampled from this population can be described using coalescent theory. A method is presented whereby the posterior probability distribution of the genealogical and demographic parameters can be estimated using Markov chain Monte Carlo simulations. The likelihood surface for the demographic parameters is complicated and its general features are described. The method is then applied to published microsatellite data from two populations. Data from the northern hairy-nosed wombat show strong evidence of decline. Data from European humans show weak evidence of expansion.

Minisatellite mutational processes reduce F(st) estimates.

We have used a new method for binning minisatellite alleles (semi-automated allele aggregation) and report the extent of population diversity detectable by eleven minisatellite loci in 2,689 individuals from 19 human populations distributed widely throughout the world. Whereas population relationships are consistent with those found in other studies, our estimate of genetic differentiation (F(st)) between populations is less than 8%, which is lower than comparative estimates of between 10%-15% obtained by using other sources of polymorphism data. We infer that mutational processes are involved in reducing F(st) estimates from minisatellite data because, first, the lowest F(st) estimates are found at loci showing autocorrelated frequencies among alleles of similar size and, second, F(st) declines with heterozygosity but by more than predicted assuming simple models of mutation. These conclusions are consistent with the view that minisatellites are subject to selective or mutational constraints in addition to those expected under simple step-wise mutation models.

Evolution of optimal behaviour in networks of Boolean automata.

This paper describes the response to selection for optimal behaviour in networks of Boolean automata. The networks considered are "open" in the sense that they receive an input and produce an output. The task that the nets are selected to solve is to maximize the mean "height" attained in a fixed number of iterations in "landscapes" that vary in their ruggedness. This is analogous to an organism with a fixed time budget that attempts to maximize its food intake in an environment where the food concentration varies in space. The results suggest that it is possible to select simple Boolean nets to respond adaptively to their inputs. Selection on simple environments produces a near "optimal" response. The response to complex environments is worse. The results suggest that nets selected on complex environments perform better on environments of different degrees of complexity than those selected on simple environments. Although nets with larger numbers of automata do not respond markedly better to selection, the variability in the response to selection is reduced. It appears to be difficult to predict the movements of nets from a study of the attractors of net with sensory units clamped at particular values. The cycle of bits in clamped nets can vary greatly with small changes in the inputs to the nets. The actual movement of nets does not, however, reflect this instability. It is concluded that networks of Boolean automata may be useful models with which to investigate different genetic algorithms. Furthermore, perturbations in such systems may give insights into the nature of pleiotropy and epistasis.

Stabilizing selection and metabolism.

This paper attempts to provide a biochemical explanation for selection against extreme phenotypes. From current ideas on the analysis of metabolic control, it is argued that, on average, most mutations will reduce flux through metabolic pathways and change substrate pool concentrations in an arbitrary direction. Currently available experimental data suggests that there may be a positive relationship between flux and fitness. It is also argued that there may be a relationship between phenotypic traits and substrate pool concentrations. Given these premises, it is shown that intrinsic selective constraints occur against the production of extreme phenotypic variants.

The effect of lanthanum on nerve terminals in goldfish muscle after paralysis with tetanus toxin.

Lanthanum (1.9 mM) has previously been shown to produce a massive increase in the frequency of spontaneous miniature junction potentials at the neuromuscular junctions of goldfish fin muscles. In fins where transmission has been blocked by previous injection of tetanus toxin and where there are few (if any) spontaneous miniature potentials, lanthanum treatment is able to restore a modest frequency. The results of parallel experiments in which the ultrastructure of the nerve endings has been investigated by electron microscopy are reported. In normal goldfish muscles, the lanthanum-induced increase in frequency is accompanied by depletion of synaptic vesicles. In contrast, there is no depletion in tetanus toxin-paralysed nerve endings subjected to lanthanum treatment, which parallels the relative insensitivity of the endings to activation by lanthanum. Of particular interest is the finding that the lanthanum treatment of the toxin muscles apparently causes accumulation of vesicles in a row just inside the terminal membrane, both at synaptic and non-synaptic positions. The results are discussed with respect to the mechanisms of transmitter release and to the actions of tetanus toxin and lanthanum.