Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Individual-based probabilistic models of adaptive evolution and various
  scaling approximations   We are interested in modelling Darwinian evolution, resulting from the
interplay of phenotypic variation and natural selection through ecological
interactions. Our models are rooted in the microscopic, stochastic description
of a population of discrete individuals characterized by one or several
adaptive traits. The population is modelled as a stochastic point process whose
generator captures the probabilistic dynamics over continuous time of birth,
mutation, and death, as influenced by each individual's trait values, and
interactions between individuals. An offspring usually inherits the trait
values of her progenitor, except when a mutation causes the offspring to take
an instantaneous mutation step at birth to new trait values. We look for
tractable large population approximations. By combining various scalings on
population size, birth and death rates, mutation rate, mutation step, or time,
a single microscopic model is shown to lead to contrasting macroscopic limits,
of different nature: deterministic, in the form of ordinary, integro-, or
partial differential equations, or probabilistic, like stochastic partial
differential equations or superprocesses. In the limit of rare mutations, we
show that a possible approximation is a jump process, justifying rigorously the
so-called trait substitution sequence. We thus unify different points of view
concerning mutation-selection evolutionary models.

18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat