TY - JOUR
T1 - Non-local effects in an integro-PDE model from population genetics
AU - Li, F.
AU - Nakashima, K.
AU - Ni, W. M.
N1 - Publisher Copyright:
© Cambridge University Press 2015.
PY - 2017/2/1
Y1 - 2017/2/1
N2 - In this paper, we study the following non-local problem: This model, proposed by T. Nagylaki, describes the evolution of two alleles under the joint action of selection, migration, and partial panmixia - a non-local term, for the complete dominance case, where g(x) is assumed to change sign at least once to reflect the diversity of the environment. First, properties for general non-local problems are studied. Then, existence of non-trivial steady states, in terms of the diffusion coefficient d and the partial panmixia rate b, is obtained under different signs of the integral ∫Ω g(x)dx. Furthermore, stability and instability properties for non-trivial steady states, as well as the trivial steady states u ≡ 0 and u ≡ 1 are investigated. Our results illustrate how the non-local term - namely, the partial panmixia - helps the migration in this model.
AB - In this paper, we study the following non-local problem: This model, proposed by T. Nagylaki, describes the evolution of two alleles under the joint action of selection, migration, and partial panmixia - a non-local term, for the complete dominance case, where g(x) is assumed to change sign at least once to reflect the diversity of the environment. First, properties for general non-local problems are studied. Then, existence of non-trivial steady states, in terms of the diffusion coefficient d and the partial panmixia rate b, is obtained under different signs of the integral ∫Ω g(x)dx. Furthermore, stability and instability properties for non-trivial steady states, as well as the trivial steady states u ≡ 0 and u ≡ 1 are investigated. Our results illustrate how the non-local term - namely, the partial panmixia - helps the migration in this model.
KW - non-local effects
KW - non-trivial steady states
KW - partial panmixia
KW - stability
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U2 - 10.1017/S0956792515000601
DO - 10.1017/S0956792515000601
M3 - Article
AN - SCOPUS:84947711563
SN - 0956-7925
VL - 28
SP - 1
EP - 41
JO - European Journal of Applied Mathematics
JF - European Journal of Applied Mathematics
IS - 1
ER -