On the maintenance of genetic variation: Global analysis of Kimura's continuum-of-alleles model

DOI10.1007/BF00275642zbMath0631.92009WikidataQ41474398 ScholiaQ41474398MaRDI QIDQ1095066

Reinhard Bürger

Publication date: 1986

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

zbMATH Keywords

global stabilitylowest eigenvalueRayleigh-Ritz techniquemutationgenetic variationmultiallele modelsstabilizing selectioncontinuum-of-alleles modelequilibrium distribution of allelic effectsestimates of the exact equilibrium varianceselection balance

Mathematics Subject Classification ID

Problems related to evolution (92D15) Integro-partial differential equations (45K05) Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) Genetics and epigenetics (92D10)

Related Items (15)

Mixed functional-differential equations ⋮ On the modelling of spatially heterogeneous nonlocal diffusion: deciding factors and preferential position of individuals ⋮ Non-equivalent loci and mutation-selection balance ⋮ Mutation-selection models in population genetics and evolutionary game theory ⋮ Kingman’s model with random mutation probabilities: convergence and condensation I ⋮ Kingman's model with random mutation probabilities: convergence and condensation. II ⋮ Confining integro-differential equations originating from evolutionary biology: ground states and long time dynamics ⋮ Study the genetic variation using eta functions ⋮ The two-locus model of Gaussian stabilizing selection ⋮ Density dependent replicator-mutator models in directed evolution ⋮ A white noise approach to evolutionary ecology ⋮ Mutation-selection balance and continuum-of-alleles models ⋮ Perturbations of positive semigroups and applications to population genetics ⋮ Open quasispecies models: stability, optimization, and distributed extension ⋮ Evolutionary branching via replicator-mutator equations

Cites Work

• Heritable genetic variation via mutation-selection balance: Lerch's zeta meets the abdominal bristle
• Global solutions of reaction-diffusion systems
• Geometric theory of semilinear parabolic equations
• Equilibrium Distributions of Continuous Polygenic Traits
• Global stability of genetic systems governed by mutation and selection
• On the properties of bilinear models for the balance between genetic mutation and selection
• A simple model for the balance between selection and mutation
• A stochastic model concerning the maintenance of genetic variability in quantitative characters.
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