Recombination, gene conversion, and identity-by-descent at three loci

We investigate the probabilities of identity-by-descent at three loci in order to find a signature which differentiates between the two types of crossing over events: recombination and gene conversion. We use a Markov chain to model coalescence, recombination, gene conversion and mutation in a sample of size two. Using numerical analysis, we calculate the total probability of identity-by-descent at the three loci, and partition these probabilities based on a partial ordering of coalescent events at the three loci. We use these results to compute the probabilities of four different patterns of conditional identity and non-identity at the three loci under recombination and gene conversion. Although recombination and gene conversion do make different predictions, the differences are not likely to be useful in distinguishing between them using three locus patterns between pairs of DNA sequences. This implies that measures of genetic identity in larger samples will be needed to distinguish between gene conversion and recombination.     

One- and multi-locus multi-allele selection models in a random environment

Summary We deduce conditions for stochastic local stability of general perturbed linear stochastic difference equations widely applicable in population genetics. The findings are adapted to evaluate the stability properties of equilibria in classical one- and multi-locus multi-allele selection models influenced by random temporal variation in selection intensities. As an example of some conclusions and biological interpretations we analyse a special one-locus multi-allele model in more detail.This work was supported in part by Stiftung Volkswagenwerk.     

A multi-locus analysis of phylogenetic relationships within cheilostome bryozoans supports multiple origins of ascophoran frontal shields

Phylogenetic relationships within the bryozoan order Cheilostomata are currently uncertain, with many morphological hypotheses proposed but scarcely tested by independent means of molecular analysis. This research uses DNA sequence data across five loci of both mitochondrial and nuclear origin from 91 species of cheilostome Bryozoa (34 species newly sequenced). This vastly improved the taxonomic coverage and number of loci used in a molecular analysis of this order and allowed a more in-depth look into the evolutionary history of Cheilostomata. Maximum likelihood and Bayesian analyses of individual loci were carried out along with a partitioned multi-locus approach, plus a range of topology tests based on morphological hypotheses. Together, these provide a comprehensive set of phylogenetic analyses of the order Cheilostomata. From these results inferences are made about the evolutionary history of this order and proposed morphological hypotheses are discussed in light of the independent evidence gained from the molecular data.Infraorder Ascophorina was demonstrated to be non-monophyletic, and there appears to be multiple origins of the ascus and associated structures involved in lophophore extension. This was further supported by the lack of monophyly within each of the four ascophoran grades (acanthostegomorph/spinocystal, hippothoomorph/gymnocystal, umbonulomorph/umbonuloid, lepraliomorph/lepralioid) defined by frontal-shield morphology. Chorizopora, currently classified in the ascophoran grade Hippothoomorpha, is phylogenetically distinct from Hippothoidae, providing strong evidence for multiple origins of the gymnocystal frontal shield type. Further evidence is produced to support the morphological hypothesis of multiple umbonuloid origins of lepralioid frontal shields, using a step-wise set of topological hypothesis tests combined with examination of multi-locus phylogenies.     

Multi-site adaptation in the presence of infrequent recombination

The adverse effect of co-inheritance linkage of a large number of sites on adaptation has been studied extensively for asexual populations. However, it is insufficiently understood for multi-site populations in the presence of recombination. In the present work, motivated by our studies of HIV evolution in infected patients, we consider a model of haploid populations with infrequent recombination. We assume that small quantities of beneficial alleles preexist at a large number of sites and neglect new mutation. Using a generalized form of the traveling wave method, we show that the effectiveness of recombination is impeded and the adaptation rate is decreased by inter-sequence correlations, arising due to the fact that some pairs of homologous sites have common ancestors existing after the onset of adaptation. As the recombination rate per individual becomes smaller, site pairs with common ancestors become more frequent, making recombination even less effective. In addition, an increasing number of sites become identical by descent across large samples of sequences, causing reversion of the direction of evolution and the loss of beneficial alleles at these sites. As a result, within a 10-fold range of the recombination rate, the average adaptation rate falls from 90% of the infinite-recombination value down to 10%. The entire transition from almost maximum to almost zero may occur at very small recombination rates. Interestingly, the strong effect of linkage on the adaptation rate is predicted in the absence of average linkage disequilibrium (Lewontin’s measure).     

Perturbation analysis of a two-locus model with directional selection and recombination

A population genetic two-locus model with additive, directional selection and recombination is considered. It is assumed that recombination is weaker than selection; i.e., the recombination parameter r is smaller than the selection coefficients. This assumption is appropriate for describing the effects of two-locus selection at the molecular level. The model is formulated in terms of ordinary differential equations (ODES) for the gamete frequencies x = (x ₁, x ₂, x ₃, x ₄), defined on the simplex S ₄. The ODEs are analyzed using first a regular pertubation technique. However, this approach yields satisfactory results only if r is very small relative to the selection coefficients and if the initial values x(0) are in the interior part of S ₄. To cope with this problem, a novel two-scale perturbation method is proposed which rests on the theory of averaging of vectorfields. It is demonstrated that the zeroth-order solution of this two-scale approach approximates the numerical solution of the model well, even if recombination rate is on the order of the selection coefficients.     

Highly fit ancestors of a partly sexual haploid population

Earlier, using the semi-deterministic solitary wave approach, we have investigated accumulation of pre-existing beneficial alleles in genomes consisting of a large number of simultaneously evolving sites in the presence of selection and infrequent recombination with small rate r per genome. Our previous results for the dynamics of the fitness distribution of genomes are now interpreted in terms of the life cycle of recombinant clones. We show that, at sufficiently small r, the clones dominating fitness classes, at the moment of their birth, are nearly the best fit in a population. New progeny clones are mostly generated by parental genomes whose fitness falls within a narrow interval in the middle of the high-fitness tail of fitness distribution. We also derive the fitness distribution for the distant ancestors of sites of a randomly sampled genome and show that its form is controlled by a single composite model parameter proportional to r. The ancestral fitness distribution differs dramatically from the fitness distribution of the entire ancient population: it is much broader and localized in the high-fitness tail of the ancient population. We generalize these results to the case of moderately small r to conclude that, regardless of fitness of an individual, all its distant ancestors are exceptionally well fit.     

On the relation between genetic and environmental variability in animals

Summary If a phenotypic character is under stabilizing selection, the selective disadvantage of a nonoptimal genotype will decrease exponentially to zero as the proportion of phenotypic variation that is environmental in origin -V _e /V _p - increases. Under the modified mutation-drift hypothesis of genetic polymorphism, the proportion of mutations that are effectively neutral and average heterozygosity should increase with this ratio. Invertebrates, because of their small size, fast development, and low degree of homeostasis (relative to vertebrates), are expected to show a larger environmental component of phenotypic variation than vertebrates. This may help explain why invertebrates are in general more genetically variable than vertebrates and why, when laboratory populations ofDrosophila are maintained in heterogeneous environments, genetic variability is lost less rapidly than when they are kept in constant conditions.     

Environmental variation, fluctuating selection and genetic drift in subdivided populations

Although there have many studies of the population genetical consequences of environmental variation, little is known about the combined effects of genetic drift and fluctuating selection in structured populations. Here we use diffusion theory to investigate the effects of temporally and spatially varying selection on a population of haploid individuals subdivided into a large number of demes. Using a perturbation method for processes with multiple time scales, we show that as the number of demes tends to infinity, the overall frequency converges to a diffusion process that is also the diffusion approximation for a finite, panmictic population subject to temporally fluctuating selection. We find that the coefficients of this process have a complicated dependence on deme size and migration rate, and that changes in these demographic parameters can determine both the balance between the dispersive and stabilizing effects of environmental variation and whether selection favors alleles with lower or higher fitness variance.     

Equilibrium structure and stability in a frequency-dependent,two-population diploid model

We investigate the equilibrium structure for an evolutionary genetic model in discrete time involving two monoecious populations subject to intraspecific and interspecific random pairwise interactions. A characterization for local stability of an equilibrium is found, related to the proximity of this equilibrium with evolutionarily stable strategies (ESS). This extends to a multi-population framework a principle initially proposed for single populations, which states that the mean population strategy at a locally stable equilibrium is as close as possible to an ESS.     

The two-locus model of Gaussian stabilizing selection

We study the equilibrium structure of a well-known two-locus model in which two diallelic loci contribute additively to a quantitative trait that is under Gaussian stabilizing selection. The population is assumed to be infinitely large, randomly mating, and having discrete generations. The two loci may have arbitrary effects on the trait, the strength of selection and the recombination rate may also be arbitrary. We find that 16 different equilibrium patterns exist, having up to 11 equilibria; up to seven interior equilibria may coexist, and up to four interior equilibria, three in negative and one in positive linkage disequilibrium, may be simultaneously stable. Also, two monomorphic and two fully polymorphic equilibria may be simultaneously stable. Therefore, the result of evolution may be highly sensitive to perturbations in the initial conditions or in the underlying genetic parameters. For the special case of equal effects, global stability results are proved. In the general case, we rely in part on numerical computations. The results are compared with previous analyses of the special case of extremely strong selection, of an approximate model that assumes linkage equilibrium, and of the much simpler quadratic optimum model.     

Variation in recombination rate across the genome: evidence and implications

Recent data from humans and other species provide convincing evidence of variation in recombination rate in different genomic regions. Comparison of physical and genetic maps reveals variation on a scale of megabases, with substantial differences between sexes. Recombination is often suppressed near centromeres and elevated near telomeres, but neither of these observations is true for all chromosomes. In humans, patterns of linkage disequilibrium and experimental measures of recombination from sperm-typing reveal dramatic hotspots of recombination on a scale of kilobases. Genome-wide variation in the amount of crossing-over may be due to variation in the density of hotspots, the intensity of hotspots, or both. Theoretical models of selection and linkage predict that genetic variation will be reduced in regions of low recombination, and this prediction is supported by data from several species. Heterogeneity in rates of crossing-over provides both an opportunity and a challenge for identifying disease genes: as associations occur in blocks, genomic regions containing disease loci may be identified with relatively few markers, yet identifying the causal mutations is unlikely to be achieved through associations alone.     

The number of equilibria in the diallelic Levene model with multiple demes

The Levene model is the simplest mathematical model to describe the evolution of gene frequencies in spatially subdivided populations. It provides insight into how locally varying selection promotes a population’s genetic diversity. Despite its simplicity, interesting problems have remained unsolved even in the diallelic case.In this paper we answer an open problem by establishing that for two alleles at one locus and J demes, up to 2J−1 polymorphic equilibria may coexist. We first present a proof for the case of stable monomorphisms and then show that the result also holds for protected alleles. These findings allow us to prove that any odd number (up to 2J−1) of equilibria is possible, before we extend the proof to even numbers. We conclude with some numerical results and show that for J>2, the proportion of parameter space affording this maximum is extremely small.     

The two-locus ancestral graph in a subdivided population: convergence as the number of demes grows in the island model

We study the ancestral recombination graph for a pair of sites in a geographically structured population. In particular, we consider the limiting behavior of the graph, under Wrights island model, as the number of subpopulations, or demes, goes to infinity. After an instantaneous sample-size adjustment, the graph becomes identical to the two-locus graph in an unstructured population, but with a time scale that depends on the migration rate and the deme size. Interestingly, when migration is gametic, this rescaling of time increases the population mutation rate but does not affect the population recombination rate. We compare this to the case of a partially-selfing population, in which both mutation and recombination depend on the selfing rate. Our result for gametic migration holds both for finite-sized demes, and in the limit as the deme size goes to infinity. However, when migration occurs during the diploid phase of the life cycle and demes are finite in size, the population recombination rate does depend on the migration rate, in a way that is reminiscent of partial selfing. Simulations imply that convergence to a rescaled panmictic ancestral recombination graph occurs for any number of sites as the number of demes approaches infinity.Send offprint request to: Sabin LessardS. Lessard was supported by grants from the Natural Sciences and Research Council of Canada, the Fonds Québécois de la Recherche sur la Nature et les Technologies, and the Université de Montréal.J. Wakeley was supported by a Career Award (DEB-0133760) and by a grant (DEB-9815367) from the National Science Foundation.     

MtArt: a new model of amino acid replacement for Arthropoda

A statistical approach was applied to select those models that best fit each individual mitochondrial (mt) protein at different taxonomic levels of metazoans. The existing mitochondrial replacement matrices, MtREV and MtMam, were found to be the best-fit models for the mt-proteins of vertebrates, with the exception of Nd6, at different taxonomic levels. Remarkably, existing mitochondrial matrices generally failed to best-fit invertebrate mt-proteins. In an attempt to better model the evolution of invertebrate mt-proteins, a new replacement matrix, named MtArt, was constructed based on arthropod mt-proteomes. The new model was found to best fit almost all analyzed invertebrate mt-protein data sets. The observed pattern of model fit across the different data sets indicates that no single replacement matrix is able to describe the general evolutionary properties of mt-proteins but rather that taxonomical biases and/or the existence of different mt-genetic codes have great influence on which model is selected.     

Evolutionary model selection with a genetic algorithm: a case study using stem RNA

The choice of a probabilistic model to describe sequence evolution can and should be justified. Underfitting the data through the use of overly simplistic models may miss out on interesting phenomena and lead to incorrect inferences. Overfitting the data with models that are too complex may ascribe biological meaning to statistical artifacts and result in falsely significant findings. We describe a likelihood-based approach for evolutionary model selection. The procedure employs a genetic algorithm (GA) to quickly explore a combinatorially large set of all possible time-reversible Markov models with a fixed number of substitution rates. When applied to stem RNA data subject to well-understood evolutionary forces, the models found by the GA 1) capture the expected overall rate patterns a priori; 2) fit the data better than the best available models based on a priori assumptions, suggesting subtle substitution patterns not previously recognized; 3) cannot be rejected in favor of the general reversible model, implying that the evolution of stem RNA sequences can be explained well with only a few substitution rate parameters; and 4) perform well on simulated data, both in terms of goodness of fit and the ability to estimate evolutionary rates. We also investigate the utility of several distance measures for comparing and contrasting inferred evolutionary models. Using widely available small computer clusters, our approach allows, for the first time, to evaluate the performance of existing RNA evolutionary models by comparing them with a large pool of candidate models and to validate common modeling assumptions. In addition, the new method provides the foundation for rigorous selection and comparison of substitution models for other types of sequence data.     

Shaping the phylogenetic tree of influenza by cross-immunity

Cross-immunity among related strains can account for the selection producing the slender phylogenetic tree of influenza A and B in humans. Using a model of seasonal influenza epidemics with drift (Andreasen, 2003. Dynamics of annual influenza A epidemics with immuno-selection. J. Math. Biol. 46, 504-536), and assuming that two mutants arrive in the host population sequentially, we determine the threshold condition for the establishment of the second mutant in the presence of partial cross-protection caused by the first mutant and their common ancestors. For fixed levels of cross-protection, the chance that the second mutant establishes increases with rho the basic reproduction ratio and some temporary immunity may be necessary to explain the slenderness of flu's phylogenetic tree. In the presence of moderate levels of temporary immunity, an asymmetric situation can arise in the season after the two mutants were introduced and established: if the offspring of the new mutant arrives before the offspring of the resident type, then the mutant-line may produce a massive epidemic suppressing the original lineage. However, if the original lineage arrives first then both strains may establish and the phylogenetic tree may bifurcate.     

Population structure of two beetle-associated yeasts: comparison of a New World asexual and an endemic Nearctic sexual species in the <Emphasis Type="Italic">Metschnikowia</Emphasis> clade

The genetic structure of two related yeast species, one sexual and one asexual, was compared using polymorphic DNA markers. Although both yeasts propagate by asexual budding of haploid cells, Metschnikowia borealis reproduces sexually when compatible strains come in contact. To what extent this has occurred in nature was not known. As Candida ipomoeae is a closely related, asexual species, the two yeasts provide an excellent model system to assess the role of sexual reproduction in a biogeographic context. Natural isolates of the two species were characterized using several polymorphic DNA markers. As predicted for an organism whose reproduction is strictly clonal, C. ipomoeae exhibited low haplotype diversity, high linkage disequilibrium, and high population differentiation. In contrast, M. borealis had unique haplotypes in most isolates, lower population differentiation, and little linkage disequilibrium, demonstrating that sexual recombination is prevalent. Geographic gradients were identified in both species, indicating that historical and climatic factors both play a role in shaping the populations. The spatial structure is also thought to be influenced by the ecology of the small floricolous beetles (family Nitidulidae) that vector the yeasts. For example, Hawaiian strains of C. ipomoeae show evidence of having undergone a genetic bottleneck, most likely when the vector was introduced to the islands. The two haplotypes found in Hawaii were nearly identical and were also found in North and Central America. M. borealis had a more continuous distribution where the genetic markers follow latitudinal and longitudinal gradients.     

The impact of homologous recombination on the generation of diversity in bacteria

The imprint of demographic and selective processes on bacterial population structure needs to be evaluated as deviation from the expectations of an appropriate null neutral model. We explore the impact of varying the population mutation and recombination rates theta and rho on ideal populations, using a recently developed model of neutral drift at multiple loci. This model may be fitted to experimental data to provide estimates of these parameters, and we do so for seven bacterial species (Neisseria meningitidis, Streptococcus pneumoniae, Streptococcus pyogenes, Staphylococcus aureus, Helicobacter pylori, Burkholderia pseudomallei and Bacillus cereus), illustrating that bacterial species vary extensively in these fundamental parameters. Historically, the influence of recombination has often been estimated through its influence on the Index of Association I(A). We show that this may be relatively insensitive to changes in either mutation or recombination rates. It is known that biased sampling can lead to artificially high estimates of I(A). We therefore provide a method of precisely separating the effects of such bias and true linkage between alleles. We also demonstrate that by fitting the neutral model to experimental data, more informative and precise estimates of the relative roles of recombination and mutation may be obtained.     

Model-Based Inference of Recombination Hotspots in a Highly,Variable Oncogene

An emergent problem in the study of pathogen evolution is our ability to determine the extent to which their rapidly evolving genomes recombine. Such information is necessary and essential for locating pathogenicity loci using association studies, and it also directs future screening, therapeutic and vaccination strategies. Recombination also complicates the use of phylogenetic approaches to infer evolutionary parameters including selection pressures. Reliable methods that identify the presence of regions of recombination are therefore vital. We illustrate the use of an integrated model-based approach to inferring recombination structure using all available sequences of the highly variable, transforming Kaposis sarcoma-associated herpesviral gene, ORF-K1. This technique learns the parameters of a statistical model that takes recombination hotspots, population genetic effects, and variable rates of mutation into account. As there are no known mechanisms to explain the high mutation rate in this DNA viral gene, recombination may account for some of the variability observed. We infer recombination hotspots in conserved sites such as the tyrosine kinase signaling motif, referred to here as recombination drift, as well as in nonconserved sites, a process described as recombination shift.This article contains online supplementary material.