TY - JOUR
T1 - The evolutionary limit for models of populations interacting competitively via several resources
AU - Champagnat, Nicolas
AU - Jabin, Pierre Emmanuel
PY - 2011/7/1
Y1 - 2011/7/1
N2 - We consider an integro-differential nonlinear model that describes the evolution of a population structured by a quantitative trait. The interactions between individuals occur by way of competition for resources whose concentrations depend on the current state of the population. Following the formalism of Diekmann et al. (2005) [16], we study a concentration phenomenon arising in the limit of strong selection and small mutations. We prove that the population density converges to a sum of Dirac masses characterized by the solution φ of a Hamilton-Jacobi equation which depends on resource concentrations that we fully characterize in terms of the function φ.
AB - We consider an integro-differential nonlinear model that describes the evolution of a population structured by a quantitative trait. The interactions between individuals occur by way of competition for resources whose concentrations depend on the current state of the population. Following the formalism of Diekmann et al. (2005) [16], we study a concentration phenomenon arising in the limit of strong selection and small mutations. We prove that the population density converges to a sum of Dirac masses characterized by the solution φ of a Hamilton-Jacobi equation which depends on resource concentrations that we fully characterize in terms of the function φ.
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U2 - 10.1016/j.jde.2011.03.007
DO - 10.1016/j.jde.2011.03.007
M3 - Article
AN - SCOPUS:79954882361
SN - 0022-0396
VL - 251
SP - 176
EP - 195
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 1
ER -