Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The continuous limit of the Moran process and the diffusion of mutant
  genes in infinite populations   We consider the so called Moran process with frequency dependent fitness
given by a certain pay-off matrix. For finite populations, we show that the
final state must be homogeneous, and show how to compute the fixation
probabilities. Next, we consider the infinite population limit, and discuss the
appropriate scalings for the drift-diffusion limit. In this case, a degenerated
parabolic PDE is formally obtained that, in the special case of frequency
independent fitness, recovers the celebrated Kimura equation in population
genetics. We then show that the corresponding initial value problem is well
posed and that the discrete model converges to the PDE model as the population
size goes to infinity. We also study some game-theoretic aspects of the
dynamics and characterize the best strategies, in an appropriate sense.

1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin