Exploratory Bayesian model selection for serial genetics data

Characterizing the process by which molecular and cellular level changes occur over time will have broad implications for clinical decision making and help further our knowledge of disease etiology across many complex diseases. However, this presents an analytic challenge due to the large number of potentially relevant biomarkers and the complex, uncharacterized relationships among them. We propose an exploratory Bayesian model selection procedure that searches for model simplicity through independence testing of multiple discrete biomarkers measured over time. Bayes factor calculations are used to identify and compare models that are best supported by the data. For large model spaces, i.e., a large number of multi-leveled biomarkers, we propose a Markov chain Monte Carlo (MCMC) stochastic search algorithm for finding promising models. We apply our procedure to explore the extent to which HIV-1 genetic changes occur independently over time.     

A population genetics model for multiple quantitative traits exhibiting pleiotropy and epistasis

We study a population genetics model of an organism with a genome of L(tot)loci that determine the values of T quantitative traits. Each trait is controlled by a subset of L loci assigned randomly from the genome. There is an optimum value for each trait, and stabilizing selection acts on the phenotype as a whole to maintain actual trait values close to their optima. The model contains pleiotropic effects (loci can affect more than one trait) and epistasis in fitness. We use adaptive walk simulations to find high-fitness genotypes and to study the way these genotypes are distributed in sequence space. We then simulate the evolution of haploid and diploid populations on these fitness landscapes and show that the genotypes of populations are able to drift through sequence space despite stabilizing selection on the phenotype. We study the way the rate of drift and the extent of the accessible region of sequence space is affected by mutation rate, selection strength, population size, recombination rate, and the parameters L and T that control the landscape shape. There are three regimes of the model. If LTL(tot), there are many small peaks that can be spread over a wide region of sequence space. Compensatory neutral mutations are important in the population dynamics in this case.     

A symmetric two locus model with viability and fertility selection

A two locus deterministic population genetic model is analysed. One locus is under viability selection, the other under fertility selection with both forms of selection completely symmetric. It is shown that linkage equilibrium may occur at two different equilibrium points. For a two-locus polymorphism to be stable, it is necessary that the viability locus be overdominant but not necessary that the fertility locus, considered separately, be able to support a stable polymorphism. The overlaps in stability are not as complex as under two locus symmetric fertilities, but considerably more complex than with symmetric viabilities. Extensions of the analysis for the central linkage equilibrium point with multiple viability and fertility loci are indicated.Research supported in part by NIH grants GM 28106 and GM 10452     

A Bayesian framework for comparative quantitative genetics

Bayesian approaches have been extensively used in animal breeding sciences, but similar approaches in the context of evolutionary quantitative genetics have been rare. We compared the performance of Bayesian and frequentist approaches in estimation of quantitative genetic parameters (viz. matrices of additive and dominance variances) in datasets typical of evolutionary studies and traits differing in their genetic architecture. Our results illustrate that it is difficult to disentangle the relative roles of different genetic components from small datasets, and that ignoring, e.g. dominance is likely to lead to biased estimates of additive variance. We suggest that a natural summary statistic for G-matrix comparisons can be obtained by examining how different the underlying multinormal probability distributions are, and illustrate our approach with data on the common frog (Rana temporaria). Furthermore, we derive a simple Monte Carlo method for computation of fraternity coefficients needed for the estimation of dominance variance, and use the pedigree of a natural Siberian jay (Perisoreus infaustus) population to illustrate that the commonly used approximate values can be substantially biased.     

The generalized multiplicative model for viability selection at multiple loci

Selection due to differential viability is studied in an n-locus two-allele model using a set indexation that allows the simplicity of the one-locus two-allele model to be carried to multi-locus models. The existence condition is analyzed for polymorphic equilibria with linkage equilibrium: Robbins' equilibria. The local stability condition is given for the Robbins' equilibria on the boundaries in the generalized non-epistatic selection regimes of Karlin and Liberman (1979). These generalized non-epistatic regimes include the additive selection model, the multiplicative selection model and the multiplicative interaction model, and their symmetric versions cover all the symmetric viability models.Research supported by grant no. 11-7805 from the Danish Natural Science Research Council, by NIH grant GM 28016, by a fellowship from the Research Foundation of Aarhus University, and by a visiting fellowship from the University of New England, N.S.W.     

A model of quantitative traits under frequency-dependent balancing selection

We describe a computer model that stimulates a combination of stabilizing and frequency-dependent selection acting on a quantitative character determined by several loci. The results correspond to many features of natural variations at both the phenotypic and genotypic levels. The model is robust, and its results are not strongly dependent either on the nature and shape of the function describing the stabilizing selection, or on the precise form of frequency dependence, except near the extrema. It suggests a mechanism for the maintenance of large amounts of variability, and shows a relation between population size and heterozygosity roughly corresponding to that found in nature. In this respect it is unlike the purely neutral model.     

Bayesian model selection for genome-wide epistatic quantitative trait loci analysis

The problem of identifying complex epistatic quantitative trait loci (QTL) across the entire genome continues to be a formidable challenge for geneticists. The complexity of genome-wide epistatic analysis results mainly from the number of QTL being unknown and the number of possible epistatic effects being huge. In this article, we use a composite model space approach to develop a Bayesian model selection framework for identifying epistatic QTL for complex traits in experimental crosses from two inbred lines. By placing a liberal constraint on the upper bound of the number of detectable QTL we restrict attention to models of fixed dimension, greatly simplifying calculations. Indicators specify which main and epistatic effects of putative QTL are included. We detail how to use prior knowledge to bound the number of detectable QTL and to specify prior distributions for indicators of genetic effects. We develop a computationally efficient Markov chain Monte Carlo (MCMC) algorithm using the Gibbs sampler and Metropolis-Hastings algorithm to explore the posterior distribution. We illustrate the proposed method by detecting new epistatic QTL for obesity in a backcross of CAST/Ei mice onto M16i.     

Frequency-dependent viability selection (a single-locus, multi-phenotype model)

Frequency-dependent natural selection models are examined where the viability of an individual in the diploid population is determined by its phenotype and the frequency of other phenotypes present. The equilibria of the multi-phenotypic system are characterized through local mean fitness functions. It is shown that stability can best be analyzed by combining the principles of maximization of population mean fitness with the evolutionary stability conditions that apply when phenotypic fitnesses relative to the genetic constraints are equal.     

A spatial statistical model for landscape genetics

Landscape genetics is a new discipline that aims to provide information on how landscape and environmental features influence population genetic structure. The first key step of landscape genetics is the spatial detection and location of genetic discontinuities between populations. However, efficient methods for achieving this task are lacking. In this article, we first clarify what is conceptually involved in the spatial modeling of genetic data. Then we describe a Bayesian model implemented in a Markov chain Monte Carlo scheme that allows inference of the location of such genetic discontinuities from individual geo-referenced multilocus genotypes, without a priori knowledge on populational units and limits. In this method, the global set of sampled individuals is modeled as a spatial mixture of panmictic populations, and the spatial organization of populations is modeled through the colored Voronoi tessellation. In addition to spatially locating genetic discontinuities, the method quantifies the amount of spatial dependence in the data set, estimates the number of populations in the studied area, assigns individuals to their population of origin, and detects individual migrants between populations, while taking into account uncertainty on the location of sampled individuals. The performance of the method is evaluated through the analysis of simulated data sets. Results show good performances for standard data sets (e.g., 100 individuals genotyped at 10 loci with 10 alleles per locus), with high but also low levels of population differentiation (e.g., F_ST < 0.05). The method is then applied to a set of 88 individuals of wolverines (Gulo gulo) sampled in the northwestern United States and genotyped at 10 microsatellites.     

A new model system for tomato genetics

The purpose of this study was to develop a model system for studying tomato genetics. Agronomic, genetic, and molecular data are presented which show that the miniature Lycopersicon esculentum cultivar, Micro-Tom (Micro tomato), fulfills the requirements for such a model. It grows at high density (up to 1357 plants/m⁻²); it has a short life cycle (70–90 days from sowing to fruit ripening); and it can be transformed at frequencies of up to 80% through Agrobacterium -mediated transformation of cotyledons. Moreover, it differs from standard tomato cultivars by only two major genes. Therefore, any mutation or transgene can be conveniently studied in Micro-Tom's background and, when needed, transferred into a standard background. We took advantage of Micro-Tom's features to improve the infrastructure for mutagenesis in tomato. A screening of 9000 M1 and 20 000 M2 EMS mutagenized plants is described. Mutants with altered pigmentation or modified shape of leaves, flowers and fruits were found. In addition, an enhancer trapping and a gene trapping system, based on the Ac/Ds maize transposable elements, were transformed into Micro-Tom and found to be active. In summary, Micro-Tom opens new prospects to achieve saturated mutagenesis in tomato, and facilitates the application of transposon-based technologies such as gene tagging, trapping and knockout.     

Domesticated birds as a model for the genetics of speciation by sexual selection

In theory, even populations occupying identical environments can diverge in sexually selected traits, as a consequence of different mutational input. I evaluate the potential of this process by comparing the genetics of breeds of domesticated birds to what is known about the genetics of differences among species. Within domesticated species there is a strong correlation of time since domestication with the number of breeds. Descendants of the rock dove, Columba livia (the oldest domesticate) show differences in courtship, vocalizations, body shape, feather ornaments (crests and tails) and colors and color patterns. When nine other domesticated species are included there is a striking hierarchy, with more recent domesticates having a nested subset of these traits: the youngest domesticated species have breeds distinguished only by color. This suggests that selection of new, visible, mutations is driving the process of breed diversification, with mutations that appeal to the breeder happening the most frequently in color. In crosses among related species, color, feather ornaments and many vocalizations and displays show both intermediate dominance and pure dominance. Although the number of loci affecting each of these traits is typically unknown, limited evidence of the genetics of species differences suggests that some differences are due to the substitution of single genes of major effect. While neither the genetics of breeds nor the genetics of species provide a perfect model for the genetics of speciation, similarities between the two are sufficiently striking to infer that major, visible, mutations can provide the impetus underlying new directions of sexual selection.     

Equilibria in an epistatic viability model under arbitrary strength of selection

A class of viability models that generalize the standard additive model for the case of pairwise additive by additive epistatic interactions is considered. Conditions for existence and stability of steady states in the corresponding two-locus model are analyzed. Using regular perturbation techniques, the case when selection is weaker than recombination and the case when selection is stronger than recombination are investigated. The results derived are used to make conclusions on the dependence of population characteristics on the relation between the strength of selection and the recombination rate.