Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Hamilton-Jacobi approach to characterize the evolutionary equilibria
  in heterogeneous environments   In this work, we characterize the solution of a system of elliptic
integro-differential equations describing a phenotypically structured
population subject to mutation, selection and migration between two habitats.
Assuming that the effects of the mutations are small but nonzero, we show that
the population's distribution has at most two peaks and we give explicit
conditions under which the population will be monomorphic (unimodal
distribution) or dimorphic (bimodal distribution). More importantly, we provide
a general method to determine the dominant terms of the population's
distribution in each case. Our work, which is based on Hamilton-Jacobi
equations with constraint, goes further than previous works where such tools
were used, for different problems from evolutionary biology, to identify the
asymptotic solutions, while the mutations vanish, as a sum of Dirac masses. In
order to extend such results to the case with non-vanishing effects of
mutations, the main elements are a uniqueness property and the computation of
the correctors. This method allows indeed to go further than the Gaussian
approximation commonly used by biologists and makes a connection between the
theories of adaptive dynamics and quantitative genetics. Our work being
motivated by biological questions, the objective of this article is to provide
the mathematical details which are necessary for our biological results [16].

23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg