Existence and nonexistence of steady-state solutions for a selection-migration model in population genetics

K. J. Brown; S. S. Lin; A. Tertikas

doi:10.1007/BF00276083

Existence and nonexistence of steady-state solutions for a selection-migration model in population genetics

K. J. Brown, S. S. Lin, A. Tertikas

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Abstract

We discuss a selection-migration model in population genetics, involving two alleles A₁ and A₂ such that A₁ is at an advantage over A₂ in certain subregions and at a disadvantage in others. It is shown that if A₁ is at an overall disadvantage to A₂ and the rate of gene flow is sufficiently large than A₁ must die out; on the other hand, if the two alleles are in some sense equally advantaged overall, then A₁ and A₂ can coexist no matter how great the rate of gene flow. © 1989 Springer-Verlag.

Original language	English
Pages (from-to)	91-104
Number of pages	14
Journal	Journal of Mathematical Biology
Volume	27
Issue number	1
DOIs	https://doi.org/10.1007/BF00276083
Publication status	Published - Feb 1989

Keywords

Bifurcation theory
Indefinite weight functions
Population genetics
Sub- and supersolutions

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10.1007/BF00276083

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title = "Existence and nonexistence of steady-state solutions for a selection-migration model in population genetics",

abstract = "We discuss a selection-migration model in population genetics, involving two alleles A1 and A2 such that A1 is at an advantage over A2 in certain subregions and at a disadvantage in others. It is shown that if A1 is at an overall disadvantage to A2 and the rate of gene flow is sufficiently large than A1 must die out; on the other hand, if the two alleles are in some sense equally advantaged overall, then A1 and A2 can coexist no matter how great the rate of gene flow. {\textcopyright} 1989 Springer-Verlag.",

keywords = "Bifurcation theory, Indefinite weight functions, Population genetics, Sub- and supersolutions",

author = "Brown, \{K. J.\} and Lin, \{S. S.\} and A. Tertikas",

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AU - Brown, K. J.

AU - Lin, S. S.

AU - Tertikas, A.

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N2 - We discuss a selection-migration model in population genetics, involving two alleles A1 and A2 such that A1 is at an advantage over A2 in certain subregions and at a disadvantage in others. It is shown that if A1 is at an overall disadvantage to A2 and the rate of gene flow is sufficiently large than A1 must die out; on the other hand, if the two alleles are in some sense equally advantaged overall, then A1 and A2 can coexist no matter how great the rate of gene flow. © 1989 Springer-Verlag.

AB - We discuss a selection-migration model in population genetics, involving two alleles A1 and A2 such that A1 is at an advantage over A2 in certain subregions and at a disadvantage in others. It is shown that if A1 is at an overall disadvantage to A2 and the rate of gene flow is sufficiently large than A1 must die out; on the other hand, if the two alleles are in some sense equally advantaged overall, then A1 and A2 can coexist no matter how great the rate of gene flow. © 1989 Springer-Verlag.

KW - Bifurcation theory

KW - Indefinite weight functions

KW - Population genetics

KW - Sub- and supersolutions

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EP - 104

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

IS - 1

ER -

Existence and nonexistence of steady-state solutions for a selection-migration model in population genetics

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Keywords

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