Significance: Evolution by Darwinian natural selection can not only shape how organisms survive and reproduce, but also affect transmission of genetic and other information between generations. Modifier-gene models for the evolution of information transmission have revealed a universal tendency for more faithful transmission to evolve in populations at equilibrium where natural selection is balanced by errors in information transmission. This is shown to be a very general property of models that include mutation and migration under selection and recombination under selection on diploids. The breadth of this reduction principle focuses attention on the departures from its mathematical assumptions, which may explain those biological phenomena of information transmission between generations for which the reduction principle fails.

The spectral bound, s ( αA + βV ), of a combination of a resolvent positive linear operator A and an operator of multiplication V , was shown by Kato to be convex in . Kato's result is shown here to imply, through an elementary “dual convexity” lemma, that s ( αA + βV ) is also convex in α > 0, and notably, ∂ s ( αA + βV )/∂ α ≤ s ( A ). Diffusions typically have s ( A ) ≤ 0, so that for diffusions with spatially heterogeneous growth or decay rates, greater mixing reduces growth . Models of the evolution of dispersal in particular have found this result when A is a Laplacian or second-order elliptic operator, or a nonlocal diffusion operator, implying selection for reduced dispersal. These cases are shown here to be part of a single, broadly general, “reduction” phenomenon.

— The choice of how to represent the search space for a genetic algorithm (GA) is critical to the GA's per- formance. Representations are usually engineered by hand and fixedfor the duration of the GA run. Here a new method is described in which the degrees of free- dom of the representation — i.e. the genes - are in- creased incrementally. The phenotypic effects of the new genes are randomly drawn from a space of differ- ent functional effects. Only those genes that initially increase fitnessare kept. The genotype-phenotype map that results from this selection during the construction of the genome allows better adaptation. This effect is illustrated with the NK landscape model. The resulting genotype-phenotype maps are much less epistatic than unselected maps would be, having extremely low values of "K" — the number of fitnesscomponents affected by each gene. Moreover, these maps are exquisitely tuned to the specifics of the epistatic fitness function, creat- ing adaptive landscapes that are much smoother than generic NK landscapes with the same genotype-pheno- type maps, with fitnesspeaks many standard deviations higher. Thus a caveat should be made when making ar- guments about the applicability of generic properties of complex systems to evolved systems. This method may help to solve the problem of choice of representations in genetic algorithms.

Estimates of measures of niche overlap are often reported without any indication of sampling variance or an accompanying confidence interval. We have investigated the delta, jackknife, and bootstrap methods for making statistical inferences on four measures of niche overlap: the coefficient of community, Morisita's index, Horn's index, and the Euclidian distance. Our qualitative conclusions are: (1) The bias of these estimators was usually @<10% of the mean unless the sample size was small and the number of resource categories large. The jackknife and bootstrap can significantly reduce this bias. (2) The variance of the bootstrap and jackknife estimators was usually greater than that of the “standard” estimator. (3) Under a variety of circumstances, the population sampled may actually represent several unrecognized subpopulations. In such cases confidence intervals generated by the jackknife and delta techniques can be quite inaccurate, while the nonparametric confidence intervals derived from the bootstrap are highly accurate.