The diffusion model for migration and selection in a dioecious population

The diffusion approximation is derived for migration and selection at a multiallelic locus in a dioecious population subdivided into a lattice of panmictic colonies. Generations are discrete and nonoverlapping; autosomal and X-linked loci are analyzed. The relation between juvenile and adult subpopulation numbers is very general and includes both soft and hard selection; the zygotic sex ratio is the same in every colony. All the results hold for both adult and juvenile migration. If ploidy-weighted average selection, drift, and diffusion coefficients are used, then the ploidy-weighted average allelic frequencies satisfy the corresponding partial differential equation for a monoecious population. The boundary conditions and the unidimensional transition conditions for coincident discontinuities in the carrying capacity and migration rate extend identically. The previous unidimensional formulation and analysis of symmetric, nearest-neighbor migration of a monoecious population across a geographical barrier is generalized to symmetric migration of arbitrary finite range, and the transition conditions are shown to hold for a dioecious population. Thus, the entire theory of clines and of the wave of advance of favorable alleles is applicable to dioecious populations.This work was supported by National Science Foundation grant BSR-9006285     

Genetic variability due to geographical inhomogeneity

The frequency of one of two alleles is studied as a function of position and time in a one, two, or three dimensional region. A nonlinear diffusion equation is employed. Each allele is assumed to have a selective advantage in some part of the region. An asymptotic solution is constructed for the case when the selection coefficient is large compared to the diffusion coefficient, i.e. when selection acts more rapidly than diffusion. Then as time increases, the solution tends to a cline, i.e. an equilibrium distribution in which both alleles are present everywhere, each predominating where it has the advantage. In a narrow region around the boundary where the selective advantage switches from one allele to the other, both alleles are present with comparable frequencies. Along a line normal to this boundary, the frequency varies as in a one dimensional habitat with a simple variation in selective advantage. The asymptotic solution is compared with the numerical solution for a special two dimensional case, and the agreement is found to be good.Research supported by the National Science Foundation.     

A SIMULATION STUDY OF MULTILOCUS CLINES

Fisher's method of junctions is used to investigate the degree of association between selected alleles in a cline, in the limit where there is divergence between very many genes. A computer model is used to simulate one of a pair of infinite demes that exchange individuals each generation. Selection is on haploids; it is additive and is equivalent to heterozygote disadvantage. Recombination is uniform over a single chromosome. A “critical value” of selection exists at equilibrium, below which loci act independently and above which they act in association (Barton 1983). Starting with secondary contact, simulation results contrast markedly with the equilibrium solution. The “critical value” is not apparent in the simulated clines, even after many generations. Rather, loci remain associated to some extent under all degrees of selection. The simulation is consistent with the equilibrium analysis in all other respects, and therefore indicates that under weak selection the approach to equilibrium is very slow. This is borne out by further numerical calculations. The slow approach to equilibrium enables us to estimate the time since contact between two demes under idealized conditions. Extending this work toward natural hybrid zones is discussed.     

Stability of displacement clines arising in allospecies competition

Summary A stability analysis for geographic displacement clines between competing allospecies is presented. The competition model incorporates the effects of annual dispersal and of selective recruitment determined by geographically varying conditions at the breeding sites. It is assumed that a species gains a local competitive advantage wherever it attains sufficient numerical predominance. This assumption is valid when the species crosspair but the hybrids produced are not recruited into the adult population, because the minority species loses proportionately more of its reproductive potential. It is shown that no stable equilibria occur when the competitive balance is independent of location, but that even a slight geographic variation in the competitive balance allows stable equilibria. The greater the length of the combined breeding ranges of the two species, the smaller the geographic shift in competitive balance needed to produce stability.     

A fine-scale spatial analysis of the mosaic hybrid zone between Gryllus firmus and Gryllus pennsylvanicus

Abstract.— The pattern of character variation within a hybrid zone, the hybrid zone structure, has been used to infer the processes that maintain hybrid zones. Unfortunately it is difficult to infer process from structure alone because many different processes can produce the same pattern of character variation. Mosaic hybrid zones may be maintained by exogenous selection in a heterogeneous environment and/or endogenous selection against hybrid individuals; habitat preference, premating isolating barriers and/or fertility selection can also contribute. The spatial scale at which a hybrid zone is sampled affects its apparent structure; a hybrid zone may appear clinal at one scale and mosaic at another. Here, we sample the mosaic hybrid zone between two field crickets, Gryllus firmus and G. pennsylvanicus , at a scale that spans the boundaries between individual soil-habitat patches. From our analysis, we find that at fine scales, the mosaic hybrid zone resolves into a set of steep clines across patch boundaries. Both morphological and molecular traits exhibit sharp and generally concordant clines. However, clines for mitochondrial DNA and one anonymous nuclear marker are clearly displaced as a result of current hybridization or past introgression (the "ghost of hybridization past"). Thus, scale is important for the structure of this and probably other hybrid zones. The extremely sharp, concordant clines across patch boundaries indicate that the cricket hybrid zone is undoubtedly structured by selection. However, the detailed mechanisms responsible for the maintenance of the hybrid zone–whether endogenous selection against hybrids, exogenous selection by the environment, and/or behavioral preferences for mates or habitats– remain to be elucidated. Determining these mechanisms will depend on closer inspection of the organisms themselves and their interactions, as is the case for all hybrid zones.     

Geographical variation of some taxonomically important characters in fishes: the case of the bitterlingRhodeus sericeus

Synopsis Geographical variation of three meristic characters, the number of pored scales in lateral line (LL), the number of branchial spines on the first gill arch (SPBR) and the number of transverse scale rows (SQU), were studied in the cyprinid fishRhodeus sericeus and their validity for subspecific discrimination was tested. Counts investigated were taken from population samples at 23 localities covering an area of about 68° geographical longitude (2°40 W – 49°30 E and 128°00 E – 143°00 E), and about 15° geographical latitude (37°30 N – 52°00 N). All three characters manifested a distinct clinal variation. LL, SQU and SPBR closely followed the species' essentially longitudinal distribution. The number of segments was also related to latitude, elevation, mean annual air temperature and fish size. Bergmann's rule was fully demonstrated for fishes and at the species level. Local regional differences were found within particular regions, indicating the existence ofsubclines. Variation of truly isolated populations seems to be predictable and dependent on the clines found in adjacent populations. None of the counts investigated, including a key character (number of pored scales in LL), can be used to distinguishamarus fromsericeus. Owing to sufficient evidence that meristic and morphometric characters used to distinguish fish subspecies succumb to the clinal variation controlled by various factors, the concept of subspecies and trinomial nomenclature is inefficient, superfluous and misleading, and should be excluded from taxonomy, nomenclature and ecology.     

GENETIC MODELS OF ADAPTATION AND GENE FLOW IN PERIPHERAL POPULATIONS

We investigate the interplay between gene flow and adaptation in peripheral populations of a widespread species. Models are developed for the evolution of a quantitative trait under clinally varying selection in a species whose density decreases from the center of the range to its periphery. Two major results emerge. First, gene flow from populations at the range center can be a strong force that inhibits peripheral populations from evolving to their local ecological optima. As a result, peripheral populations experience persistent directional selection. Second, response to local selection pressures can cause rapid and substantial evolution when a peripheral population is isolated from gene flow. The amount of evolutionary change depends on gene flow, selection, the ecological gradient, and the trait's heritability. Rapid divergence can also occur between the two halves of a formerly continuous population that is divided by a vicariant event. A general conclusion is that disruption of gene flow can cause evolutionary divergence, perhaps leading to speciation, in the absence of contributions from random genetic drift.     

Spatial scale and divergent patterns of variation in adapted traits in the ocean

The geography of adaptive genetic variation is crucial to species conservation yet poorly understood in marine systems. We analyse the spatial scale of genetic variation in traits that broadly display adaptation throughout the range of a highly dispersive marine species. We conducted common garden experiments on the Atlantic silverside, Menidia menidia, from 39 locations along its 3000 km range thereby mapping genetic variation for growth rate, vertebral number and sex determination. Each trait displayed unique clinal patterns, with significant differences (adaptive or not) occurring over very small distances. Breakpoints in the cline differed among traits, corresponding only partially with presumed eco-geographical boundaries. Because clinal patterns are unique to each selected character, neutral genes or those coding for a single character cannot serve as proxies for the genetic structure as a whole. Conservation plans designed to protect essential genetic subunits of a species will need to account for such complex spatial structures.