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.     

Estimation and interpretation of incidence rate difference for recurrent events when the estimation model is misspecified

Recurrent events data are common in experimental and observational studies. It is often of interest to estimate the effect of an intervention on the incidence rate of the recurrent events. The incidence rate difference is a useful measure of intervention effect. A weighted least squares estimator of the incidence rate difference for recurrent events was recently proposed for an additive rate model in which both the baseline incidence rate and the covariate effects were constant over time. In this article, we relax this model assumption and examine the properties of the estimator under the additive and multiplicative rate models assumption in which the baseline incidence rate and covariate effects may vary over time. We show analytically and numerically that the estimator gives an appropriate summary measure of the time‐varying covariate effects. In particular, when the underlying covariate effects are additive and time‐varying, the estimator consistently estimates the weighted average of the covariate effects over time. When the underlying covariate effects are multiplicative and time‐varying, and if there is only one binary covariate indicating the intervention status, the estimator consistently estimates the weighted average of the underlying incidence rate difference between the intervention and control groups over time. We illustrate the method with data from a randomized vaccine trial.     

Effect of mass selection on the within-family genetic variance in finite populations

Summary The adequacy of an expression for the withinfamily genetic variance under pure random drift in an additive infinitesimal model was tested via simulation in populations undergoing mass selection. Two hundred or one thousand unlinked loci with two alleles at initial frequencies of 1/2 were considered. The size of the population was 100 (50 males and 50 females). Full-sib matings were carried out for 15 generations with only one male and one female chosen as parents each generation, either randomly or on an individual phenotypic value. In the unselected population, results obtained from 200 replicates were in agreement with predictions. With mass selection, within-family genetic variance was overpredicted by theory from the 12th and 4th generations for the 1,000 and 200 loci cases, respectively. Taking into account the observed change in gene frequencies in the algorithm led to a much better agreement with observed values. Results for the distribution of gene frequencies and the withinlocus genetic covariance are presented. It is concluded that the expression for the within-family genetic variance derived for pure random drift holds well for mass selection within the limits of an additive infinitesimal model.     

Two Estimators of Mean Frequency in Products of Multinormal Probability Models

Two estimators, one additive the other multiplicative, are considered for mean frequencies in a complete three-way table. Using the mean square error criterion it is shown that preference for the additive estimator can be as high 7/8 in tables with row-column independence and in homogeneous tables. Extension to other estimators are discussed.     

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.     

Predicting cumulated response to directional selection in finite panmictic populations

Summary Accurate prediction of the cumulated genetic gain requires predicting genetic variance over time under the joint effects of selection and limited population size. An algorithm is proposed to quantify at each generation the effects of these factors on average coefficient of inbreeding, genetic variance, and genetic mean, under a purely additive polygenic model, with no mutation, and under the assumption of absence of inbreeding depression on viability affecting selection differentials. This algorithm is relevant to populations where mating is at random and generations do not overlap. It was tested via Monte Carlo simulation on a population of 3 males and 25 females mass selected out of 50 candidates of each sex, over 30 generations. For two values of the initial heritability of the selected trait, 0.5 and 0.9 (to represent high accuracy in index selection), predicted values of the genetic variance are in agreement with observed results up to the 12th and 19th generations, respectively. Beyond these generations, the variance is overestimated, due to an underestimation of the effect of selection on the rate of inbreeding. Finally, the algorithm provides predictions of the cumulated responses close to the observed values in both selected populations. It is concluded that, as regards the hypotheses of the study, the proposed algorithm is satisfactory, and could be used to optimize selection methods with respect to the cumulated genetic gain in the mid- or long-term. Possible extensions of the algorithm to more realistic situations are discussed.     

Joint effect of selection, linkage and partial inbreeding on additive genetic variance in an infinite population

Under the inifinitesimal model of gene effects, selection reduces the additive genetic variance by inducing negative linkage disequilibrium among selected genes. If the selected genes are linked, the decay of linkage disequilibrium is delayed, and the reduction of additive genetic variance is enhanced. Inbreeding in an infinite population also alters the additive genetic variance through the generation of positive association among genes within a locus. In the present study, the joint effect of selection, linkage and partial inbreeding (partial selfing or partial full-sib mating) on the additive genetic variance was modeled. The recurrence relations of the additive genetic variance between successive generations and the prediction equation of the asymptotic additive genetic variance were derived. Numerical computation showed that although partially inbred populations initially maintain larger genetic variances, the accumulated effect of selection overrides the effect of inbreeding. Stochastic simulation was carried out to check the precision of prediction, showing that the obtained equations give a satisfactory prediction during initial generations. However, the predicted values always overestimate the simulated values, especially in later generations. Based on these results, possible extensions and perspectives of the assumed model were discussed.     

The meaning of natural selection revisited at the molecular level

Various molecular interaction mechanisms cause biased transmission of genes. Meiotic drive is an example of strong bias, and compartmentalization of mammalian chromosomes reflects weak bias. Such biases are the results of interaction between DNA and proteins, and should be distinguished from natural selection. Separating the effects of molecular interaction from those of natural selection, however, is often very difficult. Natural selection and molecular mechanisms interact, and our understanding of how selection works requires revision.     

On the meaning of density dependence

Summary Despite a long history, the term density dependence lacks a generally accepted definition. A definition is offered that seems consistent with most other definitions and general usage, that is, a density-dependent factor is any component of the environment whose intensity is correlated with population density and whose action affects survival and reproduction. This definition is used in evaluating the role of territorial behavior, the availability of nest sites, and competition in determining the size of a population. Because neither territory size nor the number of nest sites is correlated with either density or with changes in the birth and death rates of these populations, these cannot be considered density-dependent factors. Competition determines who does breed and who does not rather than the number of breeders, and thus it is not a density-dependent factor determining a population's size.     

On Model-Choice in Discrimination with Categorical Variables

An algorithm for model selection in discrimination with categorical variables is presented. It is based on four models applied hierarchically and linked with a build-up procedure of feature-selection. The choice of models and features is ensured by a consequent cross-validation. Results of an application in medical diagnostics are described.     

Antler size in red deer: heritability and selection but no evolution

We present estimates of the selection on and the heritability of a male secondary sexual weapon in a wild population: antler size in red deer. Male red deer with large antlers had increased lifetime breeding success, both before and after correcting for body size, generating a standardized selection gradient of 0.44 (+/- 0.18 SE). Despite substantial age- and environment-related variation, antler size was also heritable (heritability of antler mass = 0.33 +/- 0.12). However the observed selection did not generate an evolutionary response in antler size over the study period of nearly 30 years, and there was no evidence of a positive genetic correlation between antler size and fitness nor of a positive association between breeding values for antler size and fitness. Our results are consistent with the hypothesis that a heritable trait under directional selection will not evolve if associations between the measured trait and fitness are determined by environmental covariances: In red deer males, for example, both antler size and success in the fights for mates may be heavily dependent on an individual's nutritional state.     

On the Methodology of Nematode Extraction from Field Samples: Density Flotation Techniques

Density flotation has been frequently used for the extraction of nematodes from field samples. Density flotation curves for four nematode species and five solutes have been prepared. The curves confirm that flotation was governed by several factors: solute density, solute osmotic activity, and physiological properties of the nematode species. Nematode viability and function can be adversely affected by improper selection of solute for density extraction of nematodes; nevertheless, some nematode species can be enriched from mixtures by density and solute selection.     

Stabilizing selection on sperm number revealed by artificial selection and experimental evolution

Sperm competition is taxonomically widespread in animals and is usually associated with large sperm production, being the number of sperm in the competing pool the prime predictor of fertilization success. Despite the strong postcopulatory selection acting directionally on sperm production, its genetic variance is often very high. This can be explained by trade‐offs between sperm production and traits associated with mate acquisition or survival, that may contribute to generate an overall stabilizing selection. To investigate this hypothesis, we first artificially selected male guppies (Poecilia reticulata) for high and low sperm production for three generations, while simultaneously removing sexual selection. Then, we interrupted artificial selection and restored sexual selection. Sperm production responded to divergent selection in one generation, and when we restored sexual selection, both high and low lines converged back to the mean sperm production of the original population within two generations, indicating that sperm number is subject to strong stabilizing total sexual selection (i.e., selection acting simultaneously on all traits associated with reproductive success). We discuss the possible mechanisms responsible for the maintenance of high genetic variability in sperm production despite strong selection acting on it.     

Global convergence properties in multilocus viability selection models: the additive model and the Hardy-Weinberg law

A natural coordinate system is introduced for the analysis of the global stability of the Hardy-Weinberg (HW) polymorphism under the general multilocus additive viability model. A global convergence criterion is developed and used to prove that the HW polymorphism is globally stable when each of the loci is diallelic, provided the loci are overdominant and the multilocus recombination is positive. As a corollary the multilocus Hardy-Weinberg law for neutral selection is derived.Research supported in part by NIH grants GM 39907-01, GM 10452-26 and NSF Grant DMS 86-06244Research supported in part by a US-Israel Binational Science Foundation grant 85-00021 and NIH grant GM 28016     

Darwinian balancing selection: Predation counters sexual selection in a wild insect

The potential viability costs of sexually selected traits are central to hypotheses about the evolution of exaggerated traits. Estimates of these costs in nature can come from selection analyses using multiple components of fitness during the same time frame. For a population of tree crickets (Oecanthus nigricornis: Gryllidae), we analyzed viability and sexual selection on male traits by comparing Oecanthus prey of a solitary wasp to those that survived, and comparing mating individuals to solitary males. We measured forewing width (sexually size dimorphic and used for singing), head width, pronotum length, and size of hind jumping legs as potential targets of selection. Supporting the hypothesis that sexually selected traits have viability costs, we found that significant directional sexual selection for wider heads was opposed by significant viability selection for narrower heads. Nonlinear selection revealed that individuals with wide heads and small legs were most attractive, but individuals with narrow heads, large legs, and intermediate pronotum length were most likely to survive. Successful mating may put males at greater risk of predation, especially if copulation per se is risky. Such balancing selection in tree crickets may have constrained the evolution of sexual dimorphism in head size—a condition seen in other gryllids and orthopterans.