Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of dirac concentrations in the evolution of quantitative
  alleles with sexual reproduction   A proper understanding of the links between varying gene expression levels
and complex trait adaptation is still lacking, despite recent advances in
sequencing techniques leading to new insights on their importance in some
evolutionary processes. This calls for extensions of the continuum-of-alleles
framework first introduced by Kimura (1965) that bypass the classical Gaussian
approximation. Here, we propose a novel mathematical framework to study the
evolutionary dynamics of quantitative alleles for sexually reproducing
populations under natural selection and competition through an
integro-differential equation. It involves a new reproduction operator which
allows to use techniques based on the maximum principle, unlike the
infinitesimal model operator used in other studies with sexual reproduction. In
an asymptotic regime where initially the population has a small phenotypic
variance, we analyse the long-term dynamics of the phenotypic distributions
according to the methodology of small variance (Diekmann et al. 2005). Under
some assumptions on the limit equation, we show that the population remains
monomorphic, that is the phenotypic distribution remains concentrated as a
moving Dirac mass. Moreover, in the case of a monomorphic distribution we
derive a canonical equation describing the dynamics of the dominant alleles.

16
The categories of this paper are: stat
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th