Natural Selection for within-Generation Variance in Offspring Number II. Discrete Haploid Models

In the classical model of genetic drift in population genetics theory, use is made of a hypothetical "infinite-gametic pool". If, instead, the gametic pool is determined by the random number of offspring per individual, a new form of natural selection acting on the variance in offspring number occurs. A diffusion model of this selection process is derived and some of its properties are explored. It is shown that, independent of the sampling scheme used, the diffusion equation has the drift coefficient M(p) = p(1-p) (mul--mu2 + sigma2e2--sigma2el) and the diffusion coefficient v(p) equals p(1-p) [psigma2e2 + (l--p)sigma2el]. It is also pointed out that the Direct Product Branching process model of genetic drift introduces a non-biological interaction between individuals and is thus inappropriate for modeling natural selection.     

The Role of Life Cycle and Migration in Selection for Variance in Offspring Number

For two genotypes that have the same mean number of offspring but differ in the variance in offspring number, naturalselection will favor the genotype with lower variance. In such cases, the average growth rate is not sufficient as a measure of fitness or as a predictor of fixation probability. However, the effect of variance in offspring number on the fixationprobability of mutant strategies has been calculated under several scenarios with the general conclusion that variance in offspring number reduces fitness in proportion to the inverse of the population size [Gillespie, J., Genetics 76:601–606, 1974; Proulx, S.R., Theor. Popul. Biol. 58:33–47, 2000]. This relationship becomes more complicated under a metapopulation scenario where the “effective” population size depends on migration rate, population structure, and lifecycle. It is shown that in a life cycle where reproduction and migration (the birth-migration-regulation life cycle, or BMR)occur prior to density regulation within every deme, the fitness of a strategy depends on migration rate. When migration rates are near zero, the fitness of the strategy is determined by the size of individual demes, so that the strategy favoredin small populations tends to be fixed. As migration rate increases and approaches panmixis between demes, the fitness ofa reproductive strategy approaches what its value would be in a single, panmictic deme with a population size correspondingtothe census size of the metapopulation. Interestingly, when the life cycle is characterized by having density regulation in each deme prior to migration (the BRM life cycle) the fixation probability of a strategy is independent of migration rate. These results are found to be qualitatively consistent with the individual-based simulation results in Shpak [Theor. Biosci.124:65–85, 2005]. An erratum to this article can be found at     

Dominance Genetic Variance for Traits Under Directional Selection in Drosophila serrata

In contrast to our growing understanding of patterns of additive genetic variance in single- and multi-trait combinations, the relative contribution of nonadditive genetic variance, particularly dominance variance, to multivariate phenotypes is largely unknown. While mechanisms for the evolution of dominance genetic variance have been, and to some degree remain, subject to debate, the pervasiveness of dominance is widely recognized and may play a key role in several evolutionary processes. Theoretical and empirical evidence suggests that the contribution of dominance variance to phenotypic variance may increase with the correlation between a trait and fitness; however, direct tests of this hypothesis are few. Using a multigenerational breeding design in an unmanipulated population of Drosophila serrata, we estimated additive and dominance genetic covariance matrices for multivariate wing-shape phenotypes, together with a comprehensive measure of fitness, to determine whether there is an association between directional selection and dominance variance. Fitness, a trait unequivocally under directional selection, had no detectable additive genetic variance, but significant dominance genetic variance contributing 32% of the phenotypic variance. For single and multivariate morphological traits, however, no relationship was observed between trait–fitness correlations and dominance variance. A similar proportion of additive and dominance variance was found to contribute to phenotypic variance for single traits, and double the amount of additive compared to dominance variance was found for the multivariate trait combination under directional selection. These data suggest that for many fitness components a positive association between directional selection and dominance genetic variance may not be expected.     

Interaction between Natural Selection for Heterozygotes and Directional Selection

Significant correlations between allelic frequencies and environmental variables in a number of insect species have been demonstrated by multivariate techniques. Since many environmental variables show a strong relationship to geographic location and since gene flow between populations can also produce patterns of gene frequencies which are related to the geographic location, both selection and gene-flow hypotheses are consistent with the observed correlations. The genetic variables can be corrected for geographic location and so for linear gene-flow patterns. If, after correction, the genetic variables still show significant correlations with similarly corrected environmental variables, then these correlations are consistent with hypotheses of selection but not of gene flow. The data of Johnson and Schaffer (1973) have been reanalyzed using the method of canonical correlation after correction for geographical location by means of multiple regression. Five of the nine loci studied exhibit significant canonical correlations. These results, under the assumption of linear gene flow, support hypotheses of selective action of environmental variables in the genotype-environment relationships observed.     

Genetic Variance for Body Size in a Natural Population of Drosophila Buzzatii

Previous work has shown thorax length to be under directional selection in the Drosophila buzzatii population of Carboneras. In order to predict the genetic consequences of natural selection, genetic variation for this trait was investigated in two ways. First, narrow sense heritability was estimated in the laboratory F2 generation of a sample of wild flies by means of the offspring-parent regression. A relatively high value, 0.59, was obtained. Because the phenotypic variance of wild flies was 7-9 times that of the flies raised in the laboratory, "natural" heritability may be estimated as one-seventh to one-ninth that value. Second, the contribution of the second and fourth chromosomes, which are polymorphic for paracentric inversions, to the genetic variance of thorax length was estimated in the field and in the laboratory. This was done with the assistance of a simple genetic model which shows that the variance among chromosome arrangements and the variance among karyotypes provide minimum estimates of the chromosome's contribution to the additive and genetic variances of the trait, respectively. In males raised under optimal conditions in the laboratory, the variance among second-chromosome karyotypes accounted for 11.43% of the total phenotypic variance and most of this variance was additive; by contrast, the contribution of the fourth chromosome was nonsignificant. The variance among second-chromosome karyotypes accounted for 1.56-1.78% of the total phenotypic variance in wild males and was nonsignificant in wild females. The variance among fourth chromosome karyotypes accounted for 0.14-3.48% of the total phenotypic variance in wild flies. At both chromosomes, the proportion of additive variance was higher in mating flies than in nonmating flies.     

Turbulence Model Selection for Low Reynolds Number Flows

One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil’s surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Re_θ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail.     

Change in Genetic Variance under Selection in a Self-Fertilizing Population

In this study we show how the genetic variance of a quantitative trait changes in a self-fertilizing population under repeated cycles of truncation selection, with the analysis based on the infinitesimal model in which it is assumed that the trait is determined by an infinite number of unlinked loci without epistasis. The genetic variance is reduced not as a consequence of the genotypic frequency change but due to the build-up of linkage disequilibrium under truncation selection in this model. We assume that the order of the genotypic contribution from each locus is n(-1/2), where n is the number of loci involved, and investigate the change in linkage disequilibrium resulting from selection and self-fertilization using genotypic frequency dynamics in order to analyze the change in the genetic variance. Our analysis gives recurrence relations of genetic variance among the succeeding generations for the three cases of gene action, i.e., purely additive action, pure dominance without additive effect and the presence of both additive effect and dominance, respectively. Numerical examples are also given as a check on the recurrence formulas.     

The Effect of Selection on the Phenotypic Variance

We consider the within-generation changes of phenotypic variance caused by selection w(x) which acts on a quantitative trait x. If before selection the trait has Gaussian distribution, its variance decreases if the second derivative of the logarithm of w(x) is negative for all x, while if it is positive for all x, the variance increases.     

Variance of Gene Frequencies from Recurrent Selection in Finite Populations

An equation was derived for estimation of the variance of gene frequencies due to drift in the presence of recurrent selection. The equation assumes knowledge of gene frequencies in successive generations. These can be approximated in at least three ways. Simulation data demonstrated that when satisfactory approximations are used, the variances supplied by the derived formula agree well with observed variances.     

Teleosemantics Without Natural Selection

Ruth Millikan and others advocate theories which attempt to naturalize wide mental content (e.g. beliefs’ truth conditions) in terms of function in the teleological sense, where a function is constituted in part by facts concerning past natural selection involving ancestors of a current entity. I argue that it is a mistake to base content on selection. Content should instead be based on functions which though historical, do not involve selection. I sketch an account of such functions.     

Infanticide and Maternal Offspring Defence in European Rabbits under Natural Breeding Conditions

Infanticide is an important source of mortality of dependent offspring in several mammal species, whereas female conspecifics are often the perpetrators. This has led to maternal counter‐strategies, such as the defence of the nests. However, cases of infanticide are hard to detect in the field, and studies on maternal offspring defence behaviour under natural breeding conditions are scarce. We conducted such a study on the European rabbit (Oryctolagus cuniculus), which is usually considered to show low maternal care. The study was carried out over 5 yr on a field enclosure population. We (1) studied infanticide rates and the impact of potential determinants: the group density and age structure of the females’ rank hierarchy within the groups; we used the latter as an estimator of social group stability. We (2) studied if mothers defend their breeding burrow against approaching, potentially infanticidal females. Overall, we recorded infanticide in 5% of all litters; infanticide was the cause in 12% of cases of litter mortality. The proportion of infanticide was 7% higher in groups where same‐age females occupied successive rank positions than in groups where the females’ rank hierarchy had a more heterogeneous and linear age structure. We hypothesize that social instability in the former groups was the reason for the increased infanticide risk. Infanticide rates were not correlated with group density and did not differ among mothers with different social ranks. Infanticide occurred exclusively during the first 10 d after parturition. During this time, mothers stayed closer to their breeding burrows than shortly before parturition or during later lactation. Moreover, mothers were more aggressive against other females in proximity to their breeding burrow than in more distant areas. We suggest that the pattern of spacing behaviour and intrasexual aggression of rabbit mothers are an adaptive response to the occurrence of female infanticidal behaviour.