Linlin Su

Clines with partial panmixia in an environmental pocket

In geographically structured populations, global panmixia can be regarded as the limiting case of long-distance migration. The effect of incorporating partial panmixia into diallelic single-locus clines (i.e., asymptotically stable equilibria) maintained by migration and selection in an isotropic environmental pocket in n dimensions is investigated. The population density is uniform. Migration and selection are both weak; the former is homogeneous and isotropic; the latter is directional. If the scaled panmictic rate β≥1, then the allele favored in the pocket is ultimately lost. For β<1, a cline is maintained if and only if the scaled radius a of the pocket exceeds a critical value an. For a step-environment without dominance, simple, explicit formulas are derived for a1 and a3; an equation with a unique solution and simple, explicit approximations are deduced for a2. The ratio of the selection coefficients outside and inside the pocket is -α. As expected intuitively, the cline becomes more difficult to maintain; i.e., the critical radius an increases for n=1,2,3,… as α, β, or n increases.

Patterns for four-allele population genetics model

In this paper, we find and classify all existing patterns for a single-locus four-allele population genetics models in continuous time. An existing pattern for a k-allele model means a set of all coexisting asymptotically stable equilibria with respect to the flow defined by the system of equations ṗ(i)=p(i)(r(i)-r),i=1,…,k, where p(i) and r(i) are the frequency and marginal fitness of allele A(i), respectively, and r is the mean fitness of the population. It is well known that for the two-allele model there are only three existing patterns, depending on the relative fitness between the homozygotes and the heterozygote. For the three-allele model there are 14 existing patterns, and we shall show in this paper that for the four-allele model there are 117 existing patterns. We also describe the domains of attraction for coexisting asymptotically stable equilibria. The problem of finding existing patterns has been studied in the past, and it is an important problem because the results can be used to predict the long-term genetic makeup of a population. It should be pointed out that this continuous-time model is only an approximation to the corresponding discrete-time model. However, the set of equilibria and their stability properties are the same for the two models.

Global Stability of Spatially Homogeneous Equilibria in Migration-Selection Models

We investigate the evolution of the gene frequencies at a multiallelic locus under the joint action of migration and viability selection. The population is subdivided into finitely many panmictic colonies that exchange adult migrants independently of their genotype. If the selection pattern is the same in every colony and such that

Advance of advantageous genes for a multiple-allele population genetics model

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An indefinite nonlinear diffusion problem in population genetics, II: Stability and multiplicity

is a globally asymptotically stable equilibrium under pure selection, then can migration change the (global) stability of

An indefinite nonlinear diffusion problem in population genetics, I: Existence and limiting profiles

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An integro-PDE model from population genetics☆

? When

Clines with directional selection and partial panmixia in an unbounded unidimensional habitat

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Clines With Partial Panmixia In An Environmental Pocket

is a complete polymorphism, the answer is no, which means the ultimate state of the population is unaffected by geographical structure. However, if not every allele is present in

Global stability in diallelic migration–selection models

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