R. B. Campbell

The interdependence of mating structure and inbreeding depression

The level of inbreeding depression depends on the genetic structure and composition of a population, and is not a meaningful concept in its own right. Models are presented for the dynamics of alleles governing mating strategy when viability is determined by generalized heterosis or lethal recessive alleles. It is shown that a protected polymorphism for mating strategy may ensue from generalized heterosis, while lethal recessive alleles may favor the common mating strategy. Further, neither model provides the conditions allowing spread of an allele when rare (protection) which are obtained by assuming as constant the level of inbreeding depression associated with the equilibrium genetic structure dictated by the common mating strategy.

THE EXISTENCE OF A PROTECTED POLYMORPHISM UNDER CONDITIONS OF SOFT AS OPPOSED TO HARD SELECTION IN A MULTIDEME POPULATION SYSTEM

The role for maintaining polymorphism of the time of occurrence during the life history of selection in subdivided populations (which has also been interpreted as reflecting density- and frequency-dependent selection) is studied by contrasting hard and soft selection. The case of total panmixia (Levene migration) and other well-studied migration patterns (Deakin, circular stepping-stone, clines) provide a protected polymorphism more readily under soft selection than under hard selection (hard protection implies soft protection) for fixed migration and selection parameters. There are selection-migration regimes which will maintain a polymorphism under hard selection although not under soft selection, but at least three habitats are necessary for such a circumstance and the known examples involve unnatural migration and rather extreme selection parameters. The analyses are also relevant for studying some concepts of more migration and averaged environments with respect to polymorphism.

John Graunt, John Arbuthnott, and the Human Sex Ratio

John Graunt was the first person to compile data that showed an excess of male births over female births. He also noticed spatial and temporal variation in the sex ratio, but the variation in his data is not significant. John Arbuthnott was the first person to demonstrate that the excess of male births is statistically significant. He erroneously concluded that there is less variation in the sex ratio than would occur by chance, and asserted without a basis that the sex ratio would be uniform over all time and space.

A Logistic Branching Process For Population Genetics

A logistic (regulated population size) branching process population genetic model is presented. It is a modification of both the Wright-Fisher and (unconstrained) branching process models, and shares several properties including the coalescent time and shape, and structure of the coalescent process with those models. An important feature of the model is that population size fluctuation and regulation are intrinsic to the model rather than externally imposed. A consequence of this model is that the fluctuation in population size enhances the prospects for fixation of a beneficial mutation with constant relative viability, which is contrary to a result for the Wright-Fisher model with fluctuating population size. Explanation of this result follows from distinguishing between expected and realized viabilities, in addition to the contrast between absolute and relative viabilities.

Polymorphism in subdivided populations characterised by a major and subordinate demes.

SummarySubdivided populations where one deme plays a major role and the other demes play subordinate roles are studied. The models are appropriate for socially structured and age structured populations (including plant species with seed pools) as well as spatially subdivided populations. Concise sufficient criteria as well as tractable necessary and sufficient criteria assuring the maintenance of a polymorphism are given. The incorporation of temporal variation is included, and appropriate concepts of environmental heterogeneity are discussed.

Polymorphic equilibria with assortative mating and selection in subdivided populations

Abstract Two modes of assortative mating, partial selfing and assorting by phenotypic classes, are studied in a subdivided population. Differential viability is allowed and the selection intensities and assorting tendencies are permitted to vary among the habitats. There exists a symmetric polymorphism; we delimit its level of heterozygosity and stability nature (dependent on the selection intensities and assorting propensities). This complements studies of the fixation states and thereby provides further insight into the global equilibrium structure in subdivided populations. Circumstances are given where the fixation states and symmetric polymorphism comprise the global equilibrium structure. Examples are also given where migration engenders stable polymorphic equilibria and stable polymorphic equilibrium cycles which are absent in single demes without migration.

Hard selection in haploid species

Abstract The formulation of hard selection is reviwed in the context of haploid viabilities and the criteria for stability of the fixation states are given. In contrast to soft selection, both fixation states can be simultaneously stable. However, this is not possible if the migration matrix is positive definite. In the case of only two demes there is at most one polymorphic equilibrium as occurs under soft selection, but the internal equilibrium may be unstable in contrast to the soft selection case. The question of hard versus soft protection is posed in the context of haploid viabilities and the principle hard protection implies soft protection holds with a similar degree of generality as in the diploid case.

Regular systems of inbreeding with mutation.

Probability of identity by type is studied for regular systems of inbreeding in the presence of mutation. Analytic results are presented for half-sib mating, first cousin mating, and half nth cousin mating under both infinite allele and two allele (back mutation) models. Reasonable rates of mutation do not provide significantly different results from probability of identity by descent in the absence of mutation. Homozygosity is higher under half-sib mating than under first cousin mating, but the expected number of copies of a gene in the population is higher under first cousin mating than under half-sib mating.

Dimension reduction projection and our perception of evolution

The evolution of a species can be viewed as a trajectory in multidimensional space. What we perceive is only a low dimensional projection from the total dimensionality necessary to fully describe a species. Motivated by the phenomenon of punctuated equilibria, it is shown that there are projections of gradualistic evolution which will have a punctuated character. However, whether our eyes and minds would choose such a projection of the total phenotype is not resolved.

Some circumstances assuring monomorphism in subdivided populations

Abstract It is well known that in a subdivided population subject to soft selection with two alleles at one locus, instability of both fixation states (a “protected polymorphism”) entails at least one stable polymorphic equilibrium. Although stable polymorphic and monomorphic equilibria can coexist in general, a stable fixation state (monomorphic equilibrium) precludes the existence of any polymorphic equilibrium under the circumstances of haploid or submultiplicative diploid viabilities. This provides that a stable monomorphism is robust against random fluctuations in allele frequencies. It also increases the known circumstances where there is a unique globally attracting stable equilibrium, i.e., where allele frequencies are determined by the selection-migration structure independent of the history of the system.