We consider a model with two types of genes (alleles) A1 A2. The population lives in a bounded habitat R, contained in r-dimensional space (r= 1, 2, 3). Let u (t, x) denote the frequency of A 1 at time t and place x ɛ R. Then u (t, x) is assumed to obey a nonlinear parabolic partial differential equation, describing the effects of population dispersal within R and selective advantages among the three possible genotypes A 1 A 1, A 1 A 2, A 2 A 2. It is assumed that the selection coefficients vary over R, so that a selective advantage at some points x becomes a disadvantage at others. The results concern the existence, stability properties, and bifurcation phenomena for equilibrium solutions.
%0 Journal Article
%1 fleming1975selectionmigration
%A Fleming, W. H.
%D 1975
%J J. Math. Biol.
%K existence_and_uniqueness fishers_diffusion selection spatial_structure
%N 3
%P 219--233
%T A selection-migration model in population genetics
%U http://www.ams.org/mathscinet-getitem?mr=403720
%V 2
%X We consider a model with two types of genes (alleles) A1 A2. The population lives in a bounded habitat R, contained in r-dimensional space (r= 1, 2, 3). Let u (t, x) denote the frequency of A 1 at time t and place x ɛ R. Then u (t, x) is assumed to obey a nonlinear parabolic partial differential equation, describing the effects of population dispersal within R and selective advantages among the three possible genotypes A 1 A 1, A 1 A 2, A 2 A 2. It is assumed that the selection coefficients vary over R, so that a selective advantage at some points x becomes a disadvantage at others. The results concern the existence, stability properties, and bifurcation phenomena for equilibrium solutions.
@article{fleming1975selectionmigration,
abstract = {We consider a model with two types of genes (alleles) A1 A2. The population lives in a bounded habitat R, contained in r-dimensional space (r= 1, 2, 3). Let u (t, x) denote the frequency of A 1 at time t and place x ɛ R. Then u (t, x) is assumed to obey a nonlinear parabolic partial differential equation, describing the effects of population dispersal within R and selective advantages among the three possible genotypes A 1 A 1, A 1 A 2, A 2 A 2. It is assumed that the selection coefficients vary over R, so that a selective advantage at some points x becomes a disadvantage at others. The results concern the existence, stability properties, and bifurcation phenomena for equilibrium solutions.},
added-at = {2013-03-13T12:23:05.000+0100},
author = {Fleming, W. H.},
biburl = {https://www.bibsonomy.org/bibtex/2c2ee473152b7defd57c89de57df4360e/peter.ralph},
fjournal = {Journal of Mathematical Biology},
interhash = {466bf03f6c30684d093de03cb57f0121},
intrahash = {c2ee473152b7defd57c89de57df4360e},
issn = {0303-6812},
journal = {J. Math. Biol.},
keywords = {existence_and_uniqueness fishers_diffusion selection spatial_structure},
mrclass = {92A10 (35K20)},
mrnumber = {0403720 (53 \#7531)},
mrreviewer = {D. Ludwig},
number = 3,
pages = {219--233},
timestamp = {2013-03-13T12:25:30.000+0100},
title = {A selection-migration model in population genetics},
url = {http://www.ams.org/mathscinet-getitem?mr=403720},
volume = 2,
year = 1975
}