EPISTASIS AND THE INCREASE IN ADDITIVE GENETIC VARIANCE: IMPLICATIONS FOR PHASE 1 OF WRIGHT'S SHIFTING-BALANCE PROCESS

Central to Wright's shifting-balance theory is the idea that genetic drift and selection in systems with gene interaction can lead to the formation of “adaptive gene complexes.” The theory of genetic drift has been well developed over the last 60 years; however, nearly all of this theory is based on the assumption that only additive gene effects are acting. Wright's theory was developed recognizing that there was a “universality of interaction effects,” which implies that additive theory may not be adequate to describe the process of differentiation that Wright was considering. The concept of an adaptive gene complex implies that an allele that is favored by individual selection in one deme may be removed by selection in another deme. In quantitative genetic terms, the average effects of an allele relative to other alleles changes from deme to deme. The model presented here examines the variance in local breeding values (LBVs) of a single individual and the covariance in the LBVs of a pair of individuals mated in the same deme relative to when they are mated in different demes. Local breeding value is a measure of the average effects of the alleles that make up that individual in a particular deme. I show that when there are only additive effects the covariance between the LBVs of individuals equals the variance in the LBV of an individual. As the amount of epistasis in the ancestral population increases, the variance in the LBV of an individual increases and the covariance between the LBVs of a pair of individuals decreases. The divergence in these two values is a measure of the extent to which the LBV of an individual varies independently of the LBVs of other individuals. When this value is large, it means that the relative ordering of the average effects of alleles will change from deme to deme. These results confirm an important component of Wright's shifting-balance theory: When there is gene interaction, genetic drift can lead to the reordering of the average effects of alleles and when coupled with selection this will lead to the formation of the adaptive gene complexes.     

PEAK SHIFTS AND POLYMORPHISM DURING PHASE THREE OF WRIGHT'S SHIFTING-BALANCE PROCESS

The third phase of Wright's shifting-balance theory involves the export of adaptive gene combinations from one subpopulation to another. Previous results have demonstrated that this can occur at very low migration rates, but it has been argued that this simply reflects the ability of migration to overcome selection and fix any (even deleterious) alleles. Here, previous analyses are extended by concentrating on the critical balance between forward and reverse migration rates that still allows phase III to proceed. It is shown that selective advantage, dominance, recombination rate, and the number of loci all affect the ability of a genotype to invade and become fixed in a new subpopulation, but it is unlikely that phase III will occur in the absence of differential migration unless the invading genotype consists of a few dominant loci with a large selection advantage, spreading into a few populations of lower fitness. Therefore, as was envisioned by Wright, differential migration from more to less fit populations will be necessary for phase III to occur under most circumstances.     

A SIMULATION OF WRIGHT'S SHIFTING-BALANCE PROCESS: MIGRATION AND THE THREE PHASES

Wright partitioned the shifting-balance process into three phases. Phase one is the shift of a deme within a population to the domain of a higher adaptive peak from that of the historical peak. Phase two is mass selection within a deme towards that higher peak. Phase three is the conversion of additional demes to the higher peak. The migration rate between demes is critical for the existence of phases one and three. Phase one requires small effective population sizes, hence low migration rates. Phase three is optimal under high migration rates that spread the most-fit genotype from deme to deme. Thus, a population-wide peak shift requires intermediate levels of migration. By altering the rates of phases one and three, migration affects the predominant direction of mass selection within a population. This study examines the degree to which migration, through its effects on phases one and three, determines the probability of a simulated population arriving at its genotypic optimum after 12,000 generations. These simulations reveal that there is a range of migration rates for which an entire population might be expected to shift to a higher peak. Below m = 0.001 peak shifts occur frequently (phases I and II) but are not successfully exported out of subpopulations (phase III), and above 0.01 peak shifts within demes (phase I and II), required to initiate phase III, become increasingly uncommon. Because it is unlikely that real populations will have uniform migration rates from generation to generation, the probable effects of varying migration rates on broadening the range of conditions producing peak shifts are discussed.     

NEUTRAL THEORY OF QUANTITATIVE GENETIC VARIANCE IN AN ISLAND MODEL WITH LOCAL EXTINCTION AND COLONIZATION

Additive genetic variance maintained by mutation in a selectively neutral quantitative character is analyzed for an ideal population distributed on n islands, each with local effective size N, that exchange migrants at a small rate, m. In a stable population structure, the expected genetic variance maintained within islands is identical to that in a panmictic population of the same total size, regardless of the migration rate (m > 0). This result contrasts with Wright's classical conclusion, based on inbreeding coefficients, that at least one immigrant per island every other generation (Nm > ½) is necessary for the genetic variance within local populations to approach that under panmixia. The expected genetic variance maintained among islands is inversely proportional to m and increases with the number of islands, but is independent of N. Local extinction and colonization diminish the genetic variance maintained within islands by reducing the effective size of island populations through the founder effect, although the expected genetic variance within islands is nearly as large as that in a panmictic population of the same total effective size. If the founders of new colonies originate from more than one island, rates of local extinction and colonization larger than about twice the migration rate will substantially reduce the genetic variance maintained among islands. These results indicate the importance of mutation and migration in maintaining quantitative genetic variance within small local populations.     

THE ROLE OF DEME SIZE,REPRODUCTIVE PATTERNS,AND DISPERSAL IN THE DYNAMICS OF t-LETHAL HAPLOTYPES

The t-lethal haplotypes (t) found in house mouse (Mus musculus) populations are recessive lethals favored by gametic selection whereby male heterozygotes exhibit a non-Mendelian transmission ratio of about 95% t. The expected equilibrium frequency is 0.385; however, empirical values are lower, averaging close to 0.13. We examined the hypothesis that interdemic selection is the cause of the low empirical values by using a deme-structured simulation model that included overlapping generations, a realistic breeding system, differential deme productivity, and a large total population. We found that under some conditions interdemic selection could lower t frequency below 0.13 in the face of immigration rates up to 5%. Low frequencies were correlated with effective deme size (n_e), regardless of whether n_e was changed through changing deme size (n) or through changing the proportion of breeding adults. Earlier workers showed how the first two phases of interdemic selection (random genetic differentiation and mass selection) interacted to reduce the haplotype frequency, but here we show the importance of the third phase (differential productivity of demes) once demes are linked by dispersal. The effect of this phase is not due to the (negative) covariation between deme productivity and haplotype frequency, but occurs when differential deme productivity generates a difference in t frequency between the population of juveniles recruited into their natal deme and the population of juvenile dispersers. This difference was maximized when the average productivity of demes was low, either because few adult females bred at any one time and/or because fecundity was low. Contrary to an earlier prediction, male-biased dispersal also reduced haplotype frequency, and this probably stems from the relative excess of wild-type genotypes among dispersers compared to the deme residents. Another unexpected finding was that the randomly generated excess of heterozygotes (F_IS < 0) found in small demes favored t haplotypes; however, the effect was only seen when the more powerful influence of the third phase of interdemic selection was removed. Simulations of neutral polymorphisms showed that a deme structure giving F_ST ≤ 0.6 is inconsistent with a haplotype frequency below 0.13. Based on current empirical estimates of F_ST (about 0.2), we concluded that immigration rates in the field are too high for interdemic selection alone to cause the observed deficit of lethal haplotypes. One factor that could combine with population structure effects is the observation that the transmission ratio is lowered to around 0.6 in litters produced from postpartum estrus (PPE). Incorporating this factor, we showed that interdemic selection could be effective in lowering the frequency of t below 0.13 when F_ST was above 0.43 even when migration rates were up to 10%. These results suggest that if empirical haplotype and F_ST estimates are accurate, then additional factors such as a lowered fitness of heterozygotes may be involved.     

CORRELATION OF PAIRWISE GENETIC AND GEOGRAPHIC DISTANCE MEASURES: INFERRING THE RELATIVE INFLUENCES OF GENE FLOW AND DRIFT ON THE DISTRIBUTION OF GENETIC VARIABILITY

Attempts to relate estimates of regional F_ST to gene flow and drift via Wright's (1931) equation F_ST ≈ 1/ (4Nm + 1) are often inappropriate because most natural sets of populations probably are not at equilibrium (McCauley 1993), as assumed by the island model upon which the equation is based, or ineffective because the influences of gene flow and drift are confounded in the product Nm. Evaluations of the association between genetic (F_ST) and geographic distances separating all pairwise populations combinations in a region allows one to test for regional equilibrium, to evaluate the relative influences of gene flow and drift on population structure both within and between regions, and to visualize the behavior of the association across all degrees of geographic separation. Tests of the model using microsatellite data from 51 populations of eastern collared lizards (Crotaphytus collaris collaris) collected from four distinct geographical regions gave results highly consistent with predicted patterns of association based on regional differences in various historical and ecological factors that affect the amount of drift and gene flow. The model provides a prerequisite for and an alternative to regional F_ST analyses, which often simply assume regional equilibrium, thus potentially leading to erroneous and misleading inferences regarding regional population structure.     

HIERARCHICAL GENETIC STRUCTURE AND GENE FLOW IN MACROGEOGRAPHIC POPULATIONS OF THE EASTERN TENT CATERPILLAR (MALACOSOMA AMERICANUM)

Genetic structure and inferred rates of gene flow in macrogeographic populations of the eastern tent caterpillar Malacosoma americanum were analyzed at two hierarchical scales: local demes and regional subpopulations. Wright's F-statistics were used to estimate population genetic structure using multilocus genotypic data generated electrophoretically. Estimated values of F_ST and the distribution of private alleles were then used to obtain indirect estimates of gene flow. We found modest, though significant, genetic structure at both spatial scales, a pattern consistent with high rates of gene flow over the large distances involved. Modest values obtained for Nei's genetic distance also suggested high levels of gene flow across the range of this species, although some gene-flow restriction resulting from isolation by distance was suggested by a positive regression of genetic distance on geographic distance. The observed homogeneity at enzyme loci across the range of M. americanum parallels the reported uniformity in morphology, suggesting a general absence of local genetic differentiation in this widely distributed species. The genetic homogeneity observed in this wide-ranging insect is discussed in terms of organism-specific environmental experience at different spatial scales. Some organisms occupying apparently heterogeneous environments may ameliorate unsuitable local conditions through microhabitat selection or behavioral modification of their microenvironment. This may be accomplished in M. americanum through group shelter construction and behavioral thermoregulation, closely tying thermoregulation to social biology in this species. If in this way the tent helps produce an effectively homogeneous environment for this species across its extensive range, this system may provide a unique example of how social behavior can influence the distribution of genetic variation in a population.