Marjorie A. Asmussen

The likelihood of homoploid hybrid speciation.

New species may be formed through hybridization and without an increase in ploidy. The challenge is for hybrid derivatives to escape the homogenizing effects of gene flow from parental species. The mechanisms hypothesized to underlie this process were modelled using a computer simulation. The model is of recombinational speciation, in which chromosomal rearrangements between parental species result in poor fertility of F1 hybrids, but through recombination, novel homozygous types are formed that have restored fertility. In simulations, stable populations bearing the recombinant karyotypes originated frequently and were maintained when the fertility of F1 hybrids was high. However, this high rate of origination was offset by low genetic isolation, and lower F1 hybrid fertility increased the evolutionary independence of derived populations. In addition, simulations showed that ecological and spatial isolation were required to achieve substantial reproductive isolation of incipient species. In the model, the opportunity for ecological isolation arose as a result of adaptation to extreme habitats not occupied by parental species, and any form of spatial isolation (e.g. founder events) contributed to genetic isolation. Our results confirmed the importance of the combination of factors that had been emphasized in verbal models and illustrate the trade-off between the frequency at which hybrid species arise and the genetic integrity of incipient species.

The use of incompletely linked markers in genetic counseling: accuracy versus linkage.

The utility of incompletely linked, selectively neutral, multiallelic markers for tracing the transmission of associated genes is examined theoretically for all genetic counseling situations in which the diagnosis of deleterious progeny is in question. The analysis focuses on the fraction of progeny from each two locus mating which can be diagnosed with minimal accuracy A solely on the basis of the marker alleles transmitted, as a function of A, the recombination fraction between the loci, and the gametic frequency distribution in the population. Together the results allow a quantitative assessment of the diagnostic value of a given marker-target locus association to the total population of at-risk individuals.

Constraints and normalized measures for cytonuclear disequilibria

The full bounds are derived for cytonuclear disequilibria in two-locus systems with an arbitrary number of alleles at the cytoplasmic and nuclear markers. The associated marginal frequencies constrain the nonrandom associations between cytoplasmic alleles and nuclear genotypes in the same way that the allele frequencies constrain the linkage disequilibrium between two nuclear loci. Additional constraints are imposed on the nonrandom associations between cytoplasmic and nuclear alleles, however, by the marginal frequencies of nuclear genotypes carrying either two or no copies of the associated nuclear allele. These bounds are analysed and used to define normalized measures of cytonuclear disequilibria, whose practical utility is illustrated through applications to two sets of recent nuclear-mitochondrial data.

Regular and chaotic cycling in models of ecological genetics

Abstract A model of density-dependent selection is investigated for the cyclical behavior associated with the analogous nonlinear models of population growth. If the population size regulating mechanism reacts too sharply to perturbations in population size, regular and chaotic limit cycles may result. It is established analytically that the population may converge to fixation or an invariant polymorphic gene frequency while the population size undergoes regular or chaotic oscillations. The possibility of joint limit cycles in both the population size and gene frequency is demonstrated and investigated numerically. Such cycles may occur even though one or both fixation equilibria are locally stable. In the context of equilibrium cycles it is found that overdominance in carrying capacity is not necessary for the maintenance of genetic variation in the population. Furthermore, the genetic system appears able to exert a stabilizing influence on the overall system.

CYTONUCLEAR THEORY FOR HAPLODIPLOID SPECIES AND X-LINKED GENES. II. STEPPING-STONE MODELS OF GENE FLOW AND APPLICATION TO A FIRE ANT HYBRID ZONE

We develop cytonuclear, hybrid zone models for haplodiploid species or X‐linked genes in diploid species using a stepping‐stone framework of migration, in which migration rates vary with both direction and sex. The equilibrium clines for the allele frequencies, cytonuclear disequilibria, and frequencies of pure parental types are examined for species with diagnostic markers, under four important migration schemes: uniform migration of both sexes in both directions, greater migration of both sexes from one direction, greater migration of females, and greater migration of males. Of the three cytonuclear variables examined, the allele frequency clines are the most informative in differentiating among the various migration patterns. The cytonuclear disequilibria and the frequency of the pure parental types tend to be useful only in revealing directional asymmetries in migration. The extent of hybrid zone subdivision has quantitative but not qualitative effects on the distribution of cytonuclear variables, in that the allele frequency clines become more gradual, the cytonuclear disequilibria decrease in magnitude, and the frequencies of pure parentals decline with increasing subpopulation number. Also, the only major difference between the X‐linked and haplodiploid frameworks is that a higher frequency of pure parentals is found when considering haplodiploids, in which male production does not require mating. The final important theoretical result is that censusing after migration yields greater disequilibria and parental frequencies than censusing after mating. We analyzed cytonuclear data from two transects from a naturally occurring hybrid zone between two haplodiploid fire ant species, Solenopsis invicta and S. richteri, using our stepping‐stone framework. The frequency of S. invicta mtDNA exceeds the frequency of the S. invicta nuclear markers through much of this hybrid zone, indicating that sex differences in migration or selection may be occurring. Maximum‐likelihood estimates for the migration rates are very high, due to an unexpectedly large number of pure parental types in the hybrid zone, and differ substantially between the two transects. Overall, our model does not provide a good fit, in part because the S. invicta–S. richteri hybrid zone has not yet reached equilibrium.

A FORMAL ASSESSMENT OF GENE FLOW AND SELECTION IN THE FIRE ANT SOLENOPSIS INVICTA

Abstract.— Recent studies of the introduced fire ant Solenopsis invicta suggest that introduced polygyne (with multiple queens per nest) populations are strongly influenced by male‐mediated gene flow from neighboring monogyne (single queen per nest) populations and selection acting on a single locus, general protein‐9 (Gp‐9). This investigation formally tests this hypothesis and determines if these processes can account for the genotypic structure of polygyne S. invicta. To increase the statistical power of this test, we considered the genotypes of polygyne queens and workers at both Gp‐9 and the closely linked, selectively neutral locus Pgm‐3. We then constructed and analyzed a novel mathematical model to delimit the effects of monogyne male gene flow and selection on the joint genotypes at the Pgm‐3/Gp‐9 superlocus. Using this framework, a hierarchical maximum‐likelihood method was developed to estimate the best‐fitting gene flow and selection parameters based on the fit of our model to data from both the current study and an earlier one of the same population. In each case, selection on polygyne queens and workers alone, with no monogyne male gene flow, provides the most parsimonious explanation for the observed genotype frequencies. The apparent discrepancy between this result and the empirical evidence for monogyne male gene flow indicates that undocumented factors, such as other forms of selection in polygyne males or workers, are operating in introduced polygyne S. invicta.

Evolution of dispersal in density regulated populations: A haploid model

The evolution of dispersal is explored in a density-dependent framework. Attention is restricted to haploid populations in which the genotypic fitnesses at a single diallelic locus are decreasing functions of the changing number of individuals in the population. It is shown that migration between two populations in which the genotypic response to density is reversed can maintain both alleles when the intermigration rates are constant or nondecreasing functions of the population densities. There is always a unique symmetric interior equilibrium with equal numbers but opposite gene frequencies in the two populations, provided the system is not degenerate. Numerical examples with exponential and hyperbolic fitnesses suggest that this is the only stable equilibrium state under constant positive migration rates (m) less than 12. Practically speaking, however, there is only convergence after a reasonable number of generations for relatively small migration rates (m < 14). A migration-modifying mutant at a second, neutral locus, can successfully enter two populations at a stable migration-selection balance if and only if it reduces the intermigration rates of its carriers at the original equilibrium population size. Moreover, migration modification will always result in a higher equilibrium population size, provided the system approaches another symmetric interior equilibrium. The new equilibrium migration rate will be lower than that at the original equilibrium, even when the modified migration rate is a nondecreasing function of the population sizes. Therefore, as in constant viability models, evolution will lead to reduced dispersal.

Frequency-Dependent Selection With Dominance: A Window Onto the Behavior of the Mean Fitness

Selection in which fitnesses vary with the changing genetic composition of the population may facilitate the maintenance of genetic diversity in a wide range of organisms. Here, a detailed theoretical investigation is made of a frequency-dependent selection model, in which fitnesses are based on pairwise interactions between the two phenotypes at a diploid, diallelic, autosomal locus with complete dominance. The allele frequency dynamics are fully delimited analytically, along with all possible shapes of the mean fitness function in terms of where it increases or decreases as a function of the current allele frequency in the population. These results in turn allow possibly the first complete characterization of the dynamical behavior by the mean fitness through time under frequency-dependent selection. Here the mean fitness (i) monotonically increases, (ii) monotonically decreases, (iii) initially increases and then decreases, or (iv) initially decreases and then increases as equilibrium is approached. We analytically derive the exact initial and fitness conditions that produce each dynamic and how often each arises. Computer simulations with random initial conditions and fitnesses reveal that the potential decline in mean fitness is not negligible; on average a net decrease occurs 20% of the time and reduces the mean fitness by >17%.

Rates of decay of linkage disequilibrium under two-locus models of selection

AbstractThe effect of selection and linkage on the decay of linkage disequilibrium, D, is investigated for a hierarchy of two-locus models. The method of analysis rests upon a qualitative classification of the dynamic of D under selection relative to the neutral dynamic. To eliminate the confounding effects of gene frequency change, the behavior of D is first studied with gene frequencies fixed at their invariant values. Second, the results are extended to certain special situations where gene frequencies are changing simultaneously.A wide variety of selection regimes can cause an acceleration of the rate of decay of D relative to the neutral rate. Specifically, the asymptotic rate of decay is always faster than the neutral rate in the neighborhood of a stable equilibrium point, when viabilities are additive or only one locus is selected. This is not necessarily the case for models in which there is nonzero additive epistasis. With multiplicative viabilities, decay is always accelerated near a stable boundary equilibrium, but decay is only faster near the stable central equilibrium (with