Coalescent processes when the distribution of offspring number among individuals is highly skewed

We report a complex set of scaling relationships between mutation and reproduction in a simple model of a population. These follow from a consideration of patterns of genetic diversity in a sample of DNA sequences. Five different possible limit processes, each with a different scaled mutation parameter, can be used to describe genetic diversity in a large population. Only one of these corresponds to the usual population genetic model, and the others make drastically different predictions about genetic diversity. The complexity arises because individuals can potentially have very many offspring. To the extent that this occurs in a given species, our results imply that inferences from genetic data made under the usual assumptions are likely to be wrong. Our results also uncover a fundamental difference between populations in which generations are overlapping and those in which generations are discrete. We choose one of the five limit processes that appears to be appropriate for some marine organisms and use a sample of genetic data from a population of Pacific oysters to infer the parameters of the model. The data suggest the presence of rare reproduction events in which approximately 8% of the population is replaced by the offspring of a single individual.     

Time-dependent solutions of the spatially implicit neutral model of biodiversity

Previous research into the neutral theory of biodiversity has focused mainly on equilibrium solutions rather than time-dependent solutions. Understanding the time-dependent solutions is essential for applying neutral theory to ecosystems in which time-dependent processes, such as succession and invasion, are driving the dynamics. Time-dependent solutions also facilitate tests against data that are stronger than those based on static equilibrium patterns. Here I investigate the time-dependent solutions of the classic spatially implicit neutral model, in which a small local community is coupled to a much larger metacommunity through immigration. I present explicit general formulas for the eigenvalues, left eigenvectors and right eigenvectors of the models’s transition matrix. The time-dependent solutions can then be expressed in terms of these eigenvalues and eigenvectors. Some of these results are translated directly from existing results for the classic Moran model of population genetics (the Moran model is equivalent to the spatially implicit neutral model after a reparameterization); others of the results are new. I demonstrate that the asymptotic time-dependent solution corresponding to just these first two eigenvectors can be a good approximation to the full time-dependent solution. I also demonstrate the feasibility of a partial eigendecomposition of the transition matrix, which facilitates direct application of the results to a biologically relevant example in which a newly invading species is initially present in the metacommunity but absent from the local community.     

Contrasting genetic structures of two parasitic nematodes,determined on the basis of neutral microsatellite markers and selected anthelmintic resistance markers

For the first time, the neutral genetic relatedness of natural populations of Trichostrongylid nematodes was investigated in relation to polymorphism of the β‐tubulin gene, which is selected for anthelminthic treatments. The aim of the study was to assess the contribution of several evolutionary processes: migration and genetic drift by neutral genetic markers and selection by anthelminthic treatments on the presence of resistance alleles at β‐tubulin. We studied two nematode species (Teladorsagia circumcincta and Haemonchus contortus) common in temperate climatic zones; these species are characterized by contrasting life history traits. We studied 10 isolated populations of goat nematode parasites: no infected adult goat had been exchanged after the herds were established. Beta‐tubulin polymorphism was similar in these two species. One and two β‐tubulin alleles from T. circumcincta and H. contortus respectively were shared by several populations. Most of the β‐tubulin alleles were ‘private’ alleles. No recombination between alleles was detected in BZ‐resistant alleles from T. circumcincta and H. contortus. The T. circumcincta populations have not diverged much since their isolation (F_ST <0.08), whereas H. contortus displayed marked local genetic differentiation (F_ST ranging from 0.08 to 0.18). These findings suggest that there are severe bottlenecks in the H. contortus populations, possibly because of their reduced abundance during unfavourable periods and their high reproductive rate, which allows the species to persist even after severe population reduction. Overall, the data reported contradict the hypothesis of the origin of β‐tubulin resistance alleles in these populations from a single mutational event, but two other hypotheses (recurrent mutation generating new alleles in isolated populations and the introduction of existing alleles) emerge as equally likely.     

Single-Crossover Dynamics: Finite versus Infinite Populations

Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarize and adapt a deterministic approach, as valid for infinite populations, which assumes continuous time and single crossover events. The corresponding nonlinear system of differential equations permits a closed solution, both in terms of the type frequencies and via linkage disequilibria of all orders. To include stochastic effects, we then consider the corresponding finite-population model, the Moran model with single crossovers, and examine it both analytically and by means of simulations. Particular emphasis is on the connection with the deterministic solution. If there is only recombination and every pair of recombined offspring replaces their pair of parents (i.e., there is no resampling), then the expected type frequencies in the finite population, of arbitrary size, equal the type frequencies in the infinite population. If resampling is included, the stochastic process converges, in the infinite-population limit, to the deterministic dynamics, which turns out to be a good approximation already for populations of moderate size.     

Dynamics of neutral biodiversity

Hubbell's neutral model has become a major paradigm in ecology. Whereas the steady-state structure is well understood, results about the dynamical aspects of the model are scarce. Here we derive dynamical equations for the Simpson diversity index. Both mean and variance of the diversity are proven to satisfy stable linear system dynamics. We show that in the stationary limit we indeed recover previous results, and we supplement this with numerical simulations to validate the dynamical part of our analytical computations. These findings are especially relevant for experiments in microbial ecology, where the Simpson diversity index can be accurately measured as a function of time.     

Dynamics of Horizontal Gene Transfer and the Ecological Risk Assessment of Genetically Engineered Organisms

The extensive published discussion of potential ecological impacts of introduced genetic sequences and genetically engineered organisms has lacked a quantified delineation of the critical questions for the estimation of risk. Ultimately, the ecological risk assessment of introduced gene sequences is the application of evolution, population genetics, and ecology to risk estimation and decision making. This paper provides a framework for the estimation of risk due to introduced sequences in bacteria, and the principles should also hold for many diploid species. Horizontal genetic exchange poses new challenges for ecological risk assessment. Plasmid transfer can occur without any impacts, although the sequence can become ubiquitous in the population. Conversely, the introduction of a plasmid can change the dynamics of the host population, potentially altering the population minimum and maximum characteristics of its dynamics. Because of genetic exchange, new genetic information is unlikely to be constrained among one type of prokaryote. An example of the use of the model is given using genetic exchange data from a series of published soil microcosm experiments. The model demonstrates the increase in plasmid frequency when using experimentally derived conjugation frequencies. Application of these results to ongoing discussion of the risks of genetically engineered organisms is presented. Particular attention is paid to the transfer of genetic material and the resultant changes in host population dynamics.     

Extensive polymorphism and geographical variation at a positively selected MHC class II B gene of the lesser kestrel (Falco naumanni)

Understanding the selective forces that shape genetic variation in natural populations remains a high priority in evolutionary biology. Genes at the major histocompatibility complex (MHC) have become excellent models for the investigation of adaptive variation and natural selection because of their crucial role in fighting off pathogens. Here we present one of the first data sets examining patterns of MHC variation in wild populations of a bird of prey, the lesser kestrel, Falco naumanni . We report extensive polymorphism at the second exon of a putatively functional MHC class II gene, Fana- DAB*1. Overall, 103 alleles were isolated from 121 individuals sampled from Spain to Kazakhstan. Bayesian inference of diversifying selection suggests that several amino acid sites may have experienced strong positive selection (ω = 4.02 per codon). The analysis also suggests a prominent role of recombination in generating and maintaining MHC diversity (ρ = 4 Nc  = 0.389 per codon, θ = 0.017 per codon). Both the Fana -DAB*1 locus and a set of eight polymorphic microsatellite markers revealed an isolation-by-distance pattern across the Western Palaearctic ( r  = 0.67; P  = 0.01 and r  = 0.50; P  = 0.04, respectively). Nonetheless, geographical variation at the MHC contrasts with relatively uniform distributions in the frequencies of microsatellite alleles. In addition, we found lower fixation rates in the MHC than those predicted by genetic drift after controlling for neutral mitochondrial sequences. Our results therefore underscore the role of balancing selection as well as spatial variations in parasite-mediated selection regimes in shaping MHC diversity when gene flow is limited.     

Contrasting microsatellite variation between subalpine and western larch, two closely related species with different distribution patterns

Subalpine larch (Larix lyallii Parl.) and western larch (Larix occidentalis Nutt.) represent two closely related species with contrasting abundance and distribution patterns in Western North America. Genetic diversity at seven informative microsatellite loci was determined for 19 populations of subalpine larch and nine populations of western larch. Contrasting genetic diversity and patterns of population differentiation were observed between the two species. The overall within-population genetic diversity parameters were lower in subalpine larch (A = 3.2; A(P) = 3.6; H(E) = 0.418) than in western larch (A(P) = 5.51; H(E) = 0.580), a pattern that is likely related to historical or demographic factors. No evidence of interspecific hybridization was observed. Significantly more population differentiation (theta = 0.15; R(ST) = 0.07), consistent with more restricted gene flow, was observed for subalpine larch as compared to western larch (theta = 0.05; R(ST) = 0.04). Under the assumption of an infinite allele mutation model, 12 of the 19 subalpine larch populations showed signs of deviation from the mutation-drift equilibrium, which suggests Holocene population bottlenecks and fluctuations in effective population size for this species. None of the western larch populations deviated significantly from the mutation-drift equilibrium. For both species, Mantel's test revealed a significant positive relationship between geographical and genetic distances indicative of isolation by distance. A similar geographical structure was detected in both species, suggesting at least two genetically distinct glacial populations in each species. The various implications for gene conservation are discussed.     

Habitat distribution influences dispersal and fine-scale genetic population structure of eastern foxsnakes (Mintonius gloydi) across a fragmented landscape

Dispersal is a fundamental attribute of species in nature and shapes population dynamics, evolutionary trajectories and genetic variation across spatial and temporal scales. It is increasingly clear that landscape features have large impacts on dispersal patterns. Thus, understanding how individuals and species move through landscapes is essential for predicting impacts of landscape alterations. Information on dispersal patterns, however, is lacking for many taxa, particularly reptiles. Eastern foxsnakes (Mintoinus gloydi) are marsh and prairie specialists that avoid agricultural fields, but they have persisted across a fragmented region in southwestern Ontario and northern Ohio. Here, we combined habitat suitability modelling with population genetic analyses to infer how foxsnakes disperse through a habitat mosaic of natural and altered landscape features. Boundary regions between the eight genetic clusters, identified through assignment tests, were comprised of low suitability habitat (e.g. agricultural fields). Island populations were grouped into a single genetic cluster, and comparatively low F(ST) values between island and mainland populations suggest open water presents less of a barrier than nonsuitable terrestrial habitat. Isolation by resistance and least-cost path analysis produced similar results with matrices of pairwise individual genetic distance significantly more correlated to matrices of resistance values derived from habitat suitability than models with an undifferentiated landscape. Spatial autocorrelation results matched better with assignment results when incorporating resistance values rather than straight-line distances. All analyses used in our study produced similar results suggesting that habitat degradation limits dispersal for foxsnakes, which has had a strong effect on the genetic population structure across this region.     

The sampling theory of neutral alleles and an urn model in population genetics

The behaviour of a Pólya-like urn which generates Ewens' sampling formula in population genetics is investigated. Connections are made with work of Watterson and Kingman and to the Poisson-Dirichlet distribution. The order in which novel types occur in the urn is shown to parallel the age distribution of the infinitely many alleles diffusion model and consequences of this property are explored. Finally the urn process is related to Kingman's coalescent with mutation to provide a rigorous basis for this parallel.This research was partially supported by the Sloan Foundation under Grant 85-6-14 and by the National Science Foundation     

Comparative studies of quantitative trait and neutral marker divergence: a meta-analysis

Comparative studies of quantitative genetic and neutral marker differentiation have provided means for assessing the relative roles of natural selection and random genetic drift in explaining among-population divergence. This information can be useful for our fundamental understanding of population differentiation, as well as for identifying management units in conservation biology. Here, we provide comprehensive review and meta-analysis of the empirical studies that have compared quantitative genetic (Q(ST)) and neutral marker (F(ST)) differentiation among natural populations. Our analyses confirm the conclusion from previous reviews - based on ca. 100% more data - that the Q(ST) values are on average higher than F(ST) values [mean difference 0.12 (SD 0.27)] suggesting a predominant role for natural selection as a cause of differentiation in quantitative traits. However, although the influence of trait (life history, morphological and behavioural) and marker type (e.g. microsatellites and allozymes) on the variance of the difference between Q(ST) and F(ST) is small, there is much heterogeneity in the data attributable to variation between specific studies and traits. The latter is understandable as there is no reason to expect that natural selection would be acting in similar fashion on all populations and traits (except for fitness itself). We also found evidence to suggest that Q(ST) and F(ST) values across studies are positively correlated, but the significance of this finding remains unclear. We discuss these results in the context of utility of the Q(ST)-F(ST) comparisons as a tool for inferring natural selection, as well as associated methodological and interpretational problems involved with individual and meta-analytic studies.     

The balance between pleiotropic mutation and selection,when alleles have discrete effects

The theory of pleiotropic mutation and selection is investigated and developed for a large population of asexual organisms. Members of the population are subject to stabilising selection on Omega phenotypic characters, which each independently affect fitness. Pleiotropy is incorporated into the model by allowing each mutation to simultaneously affect all characters. To expose differences with continuous-allele models, the characters are taken to originate from discrete-effect alleles and thus have discrete genotypic effects. Each character can take the values nxDelta where n=0,+/-1,+/-2, em leader, and the splitting in character effects, Delta, is a parameter of the model. When the distribution of mutant effects is normally distributed around the parental value, and Delta is large, a "stepwise" model of mutation arises, where only adjacent trait effects are accessible from a single mutation. The present work is primarily concerned with the opposite limit, where Delta is small and many different trait effects are accessible from a single mutation.In contrast to what has been established for continuous-effect models, discrete-effect models do not yield a singular equilibrium distribution of genotypic effects for any value of Omega. Instead, for different values of Omega, the equilibrium frequencies of trait values have very different dependencies on Delta. For Omega=1 and 2, decreasing Delta broadens the width of the frequency distribution and hence increases the equilibrium level of polymorphism. For all sufficiently large values of Omega, however, decreasing Delta decreases the width of the frequency distribution and the equilibrium level of polymorphism. The connection with continuous trait models follows when the limit Delta-->0 is considered, and a singular probability density of trait values is obtained for all sufficiently large Omega.     

The onion model, a simple neutral model for the evolution of diversity in bacterial biofilms

Bacterial biofilms are particularly resistant to a wide variety of antimicrobial compounds. Their persistence in the face of antibiotic therapies causes significant problems in the treatment of infectious diseases. Seldom have evolutionary processes like genetic drift and mutation been invoked to explain how resistance to antibiotics emerges in biofilms, and we lack a simple and tractable model for the genetic and phenotypic diversification that occurs in bacterial biofilms. Here, we introduce the 'onion model', a simple neutral evolutionary model for phenotypic diversification in biofilms. We explore its properties and show that the model produces patterns of diversity that are qualitatively similar to observed patterns of phenotypic diversity in biofilms. We suggest that models like our onion model, which explicitly invoke evolutionary process, are key to understanding biofilm resistance to bactericidal and bacteriostatic agents. Elevated phenotypic variance provides an insurance effect that increases the likelihood that some proportion of the population will be resistant to imposed selective agents and may thus enhance persistence of the biofilm. Accounting for evolutionary change in biofilms will improve our ability to understand and counter diseases that are caused by biofilm persistence.     

Birth-death symmetry in the evolution of a social trait

Studies of the evolution of a social trait often make ecological assumptions (of population structure, life history), and thus a trait can be studied many different times with different assumptions. Here, I consider a Moran model of continuous reproduction and use an inclusive fitness analysis to investigate the relationships between fecundity or survival selection and birth-death (BD) or death-birth (DB) demography on the evolution of a social trait. A simple symmetry obtains: fecundity (respectively survival) effects under BD behave the same as survival (respectively fecundity) effects under DB. When these results are specialized to a homogeneous population, greatly simplified conditions for a positive inclusive fitness effect are obtained in both a finite and an infinite population. The results are established using the elegant formalism of mathematical group theory and are illustrated with an example of a finite population arranged in a cycle with asymmetric offspring dispersal.