Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptation in a stochastic multi-resources chemostat model   We are interested in modeling the Darwinian evolution resulting from the
interplay of phenotypic variation and natural selection through ecological
interactions, in the specific scales of the biological framework of adaptive
dynamics. Adaptive dynamics so far has been put on a rigorous footing only for
direct competition models (Lotka-Volterra models) involving a competition
kernel which describes the competition pressure from one individual to another
one. We extend this to a multi-resources chemostat model, where the competition
between individuals results from the sharing of several resources which have
their own dynamics. Starting from a stochastic birth and death process model,
we prove that, when advantageous mutations are rare, the population behaves on
the mutational time scale as a jump process moving between equilibrium states
(the polymorphic evolution sequence of the adaptive dynamics literature). An
essential technical ingredient is the study of the long time behavior of a
chemostat multi-resources dynamical system. In the small mutational steps limit
this process in turn gives rise to a differential equation in phenotype space
called canonical equation of adaptive dynamics. From this canonical equation
and still assuming small mutation steps, we prove a rigorous characterization
of the evolutionary branching points.

26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex