Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission.

Genetic manipulations of insect populations for pest control have been advocated for some time, but there are few cases where manipulated individuals have been released in the field and no cases where they have successfully invaded target populations. Population transformation using the intracellular bacterium Wolbachia is particularly attractive because this maternally-inherited agent provides a powerful mechanism to invade natural populations through cytoplasmic incompatibility. When Wolbachia are introduced into mosquitoes, they interfere with pathogen transmission and influence key life history traits such as lifespan. Here we describe how the wMel Wolbachia infection, introduced into the dengue vector Aedes aegypti from Drosophila melanogaster, successfully invaded two natural A. aegypti populations in Australia, reaching near-fixation in a few months following releases of wMel-infected A. aegypti adults. Models with plausible parameter values indicate that Wolbachia-infected mosquitoes suffered relatively small fitness costs, leading to an unstable equilibrium frequency <30% that must be exceeded for invasion. These findings demonstrate that Wolbachia-based strategies can be deployed as a practical approach to dengue suppression with potential for area-wide implementation.

Effects of pleiotropy on predictions concerning mutation-selection balance for polygenic traits.

Previous mathematical analyses of mutation-selection balance for metric traits assume that selection acts on the relevant loci only through the character(s) under study. Thus, they implicitly assume that all of the relevant mutation and selection parameters are estimable. A more realistic analysis must recognize that many of the pleiotropic effects of loci contributing variation to a given character are not known. To explore the consequences of these hidden effects, I analyze models of two pleiotropically connected polygenic traits, denoted P1 and P2. The actual equilibrium genetic variance for P1, based on complete knowledge of all mutation and selection parameters for both P1 and P2, can be compared to a prediction based solely on observations of P1. This extrapolation mimics empirically obtainable predictions because of the inevitability of unknown pleiotropic effects. The mutation parameters relevant to P1 are assumed to be known, but selection intensity is estimated from the within-generation reduction of phenotypic variance for P1. The extrapolated prediction is obtained by substituting these parameters into formulas based on single-character analyses. Approximate analytical and numerical results show that the level of agreement between these univariate extrapolations and the actual equilibrium variance depends critically on both the genetic model assumed and the relative magnitudes of the mutation and selection parameters. Unless per locus mutation rates are extremely high, i.e., generally greater than 10(-4), the widely used gaussian approximation for genetic effects at individual loci is not applicable. Nevertheless, the gaussian approximations predict that the true and extrapolated equilibria are in reasonable agreement, i.e., within a factor of two, over a wide range of parameter values. In contrast, an alternative approximation that applies for moderate and low per locus mutation rates predicts that the extrapolation will generally overestimate the true equilibrium variance unless there is little selection associated with hidden effects. The tendency to overestimate is understandable because selection acts on all of the pleiotropic manifestations of a new mutation, but equilibrium covariances among the characters affected may not reveal all of this selection. This casts doubt on the proposal that much of the additive polygenic variance observed in natural populations can be explained by mutation-selection balance. It also indicates the difficulty of critically evaluating this hypothesis.

Cis-trans effects induced by linkage disequilibrium.

This note concerns theoretical and experimental studies of multifactorial traits, especially fitness and its components, in which (1) the loci studied are only a subset of those relevant to the character of interest and (2) the genotypes at the loci studied are in nonrandom association (linkage disequilibrium) with genotypes at the loci ignored. In these cases, phenotypic differences between cis and trans double heterozygotes can occur even though no linkage phase effects are inherent in the genetic determination of the trait. Examples are drawn from both theoretical and experimental work, and implications in both areas are discussed.

Laboratory estimates of heritabilities and genetic correlations in nature.

A lower bound on heritability in a natural environment can be determined from the regression of offspring raised in the laboratory on parents raised in nature. An estimate of additive genetic variance in the laboratory is also required. The estimated lower bounds on heritabilities can sometimes be used to demonstrate a significant genetic correlation between two traits in nature, if their genetic and phenotypic correlations in nature have the same sign, and if sample sizes are large, and heritabilities and phenotypic and genetic correlations are high.

Genotype-environment interactions and the maintenance of polygenic variation.

Genotype-environment interactions may be a potent force maintaining genetic variation in quantitative traits in natural populations. This is shown by a simple model of additive polygenic inheritance in which the additive contributions of alleles vary with the environment. Under simplifying symmetry assumptions, the model implies that the variance of the phenotypes produced across environments by a multilocus genotype decreases as the number of heterozygous loci increases. In the region of an optimal phenotype, the mapping from the quantitative trait into fitness is concave, and the mean fitness of a genotype will increase with the number of heterozygous loci. This leads to balancing selection, polymorphism, and potentially high levels of additive genetic variance, even though all allelic effects remain additive within each specific environment. An important implication of the model is that the variation maintained by genotype-environment interactions is difficult to study with the restricted range of environments represented in typical experiments. In particular, if fluctuations in allelic effects are pervasive, as suggested by the extensive literature on genotype-environment interactions, efforts to estimate genetic parameters in a single environment may be of limited value.

Unidirectional incompatibility in Drosophila simulans: inheritance, geographic variation and fitness effects.

In California, Drosophila simulans females from some populations (type W) produce relatively few adult progeny when crossed to males from some other populations (type R), but the productivity of the reciprocal cross is comparable to within-population controls. These two incompatibility types are widespread in North America and are also present elsewhere. Both types sometimes occur in the same population. Type R females always produce type R progeny irrespective of the father's type. However, matings between R males and females from stocks classified as type W produce type R progeny at low frequency. This suggests rare paternal transmission of the R incompatibility type, as we have found no evidence for segregation of incompatibility types in the W stocks. There is quantitative variation among type R lines for compatibility with W females, but not vice versa. Population cage studies and productivity tests suggest that deleterious side effects are associated with the type R cytoplasm.

Haldane's rule and X-chromosome size in Drosophila.

The "dominance theory" of HALDANE'S rule postulates that hybrids of the heterogametic sex are more likely to be inviable or sterile than the homogametic sex because some of the epistatic incompatibilities contributing to postzygotic isolation behave as X-linked partial recessives. When this is true, pairs of taxa with relatively large X chromosomes should require less divergence time, on average, to produce HALDANE'S rule than pairs with smaller Xs. Similarly, if the dominance theory is correct and if the X chromosome evolves at a similar rate to the autosomes, the size of the X should not influence the rate at which homogametic hybrids become inviable or sterile. We use Drosophila data to examine both of these predictions. As expected under the dominance theory, pairs of taxa with large X chromosomes (approximately 40% of the nuclear genome) show HALDANE's rule for sterility at significantly smaller genetic distances than pairs with smaller X chromosomes (approximately 20% of the genome). As also predicted, the genetic distances between taxa that exhibit female inviability/sterility show no differences between "large X" vs. "small X" pairs. We present some simple mathematical models to relate these data to the dominance theory and alternative hypotheses involving faster evolution of the X vs. the autosomes and/or faster evolution of incompatibilities that produce male-specific vs. female-specific sterility. Although the data agree qualitatively with the predictions of the dominance theory, they depart significantly from the quantitative predictions of simple models of the dominance theory and the other hypotheses considered. These departures probably stem from the many simplifying assumptions needed to tractably model epistatic incompatibilities and to analyze heterogeneous data from many taxa.

Should individual fitness increase with heterozygosity?

Natural selection influences not only gamete frequencies in populations but also the multilocus fitness structures associated with segregating gametes. In particular, only certain patterns of multilocus fitnesses are consistent with the maintenance of stable multilocus polymorphisms. This paper offers support for the proposition that, at stable, viability-maintained, multilocus polymorphisms, the fitness of a genotype tends to increase with the number of heterozygous loci it contains. Average fitness always increases with heterozygosity at stable product equilibria (i.e., those without linkage disequilibrium) maintained by either additive or multiplicative fitness schemes. Simulations suggest that it "generally" increases for arbitrary fitness schemes. The empirical literature correlating allozyme heterozygosity with fitness-correlated traits is discussed in the light of these and other theoretical results.

Deleterious mutations, apparent stabilizing selection and the maintenance of quantitative variation.

Apparent stabilizing selection on a quantitative trait that is not causally connected to fitness can result from the pleiotropic effects of unconditionally deleterious mutations, because as N. Barton noted, "...individuals with extreme values of the trait will tend to carry more deleterious alleles...." We use a simple model to investigate the dependence of this apparent selection on the genomic deleterious mutation rate, U; the equilibrium distribution of K, the number of deleterious mutations per genome; and the parameters describing directional selection against deleterious mutations. Unlike previous analyses, we allow for epistatic selection against deleterious alleles. For various selection functions and realistic parameter values, the distribution of K, the distribution of breeding values for a pleiotropically affected trait, and the apparent stabilizing selection function are all nearly Gaussian. The additive genetic variance for the quantitative trait is kQa2, where k is the average number of deleterious mutations per genome, Q is the proportion of deleterious mutations that affect the trait, and a2 is the variance of pleiotropic effects for individual mutations that do affect the trait. In contrast, when the trait is measured in units of its additive standard deviation, the apparent fitness function is essentially independent of Q and a2; and beta, the intensity of selection, measured as the ratio of additive genetic variance to the "variance" of the fitness curve, is very close to s = U/k, the selection coefficient against individual deleterious mutations at equilibrium. Therefore, this model predicts appreciable apparent stabilizing selection if s exceeds about 0.03, which is consistent with various data. However, the model also predicts that beta must equal Vm/VG, the ratio of new additive variance for the trait introduced each generation by mutation to the standing additive variance. Most, although not all, estimates of this ratio imply apparent stabilizing selection weaker than generally observed. A qualitative argument suggests that even when direct selection is responsible for most of the selection observed on a character, it may be essentially irrelevant to the maintenance of variation for the character by mutation-selection balance. Simple experiments can indicate the fraction of observed stabilizing selection attributable to the pleiotropic effects of deleterious mutations.

The dominance theory of Haldane's rule.

"HALDANE's rule" states that, if species hybrids of one sex only are inviable or sterile, the afflicted sex is much more likely to be heterogametic (XY) than homogametic (XX). We show that most or all of the phenomena associated with HALDANE's rule can be explained by the simple hypothesis that alleles decreasing hybrid fitness are partially recessive. Under this hypothesis, the XY sex suffers more than the XX because X-linked alleles causing postzygotic isolation tend to have greater cumulative effects when hemizygous than when heterozygous, even though the XX sex carries twice as many such alleles. The dominance hypothesis can also account for the "large X effect," the disproportionate effect of the X chromosome on hybrid inviability/sterility. In addition, the dominance theory is consistent with: the long temporal lag between the evolution of heterogametic and homogametic postzygotic isolation, the frequency of exceptions to HALDANE's rule, puzzling Drosophila experiments in which "unbalanced" hybrid females, who carry two X chromosomes from the same species, remain fertile whereas F1 hybrid males are sterile, and the absence of cases of HALDANE's rule for hybrid inviability in mammals. We discuss several novel predictions that could lead to rejection of the dominance theory.