40 citations · 264 across the 35 of their papers we have counts for
6 papers · 2 filters
Confining integro-differential equations originating from evolutionary biology: ground states and long time dynamics
Matthieu Alfaro, Pierre Gabriel, Otared Kavian
We consider nonlinear mutation selection models, known as replicator-mutator equations in evolutionary biology. They involve a nonlocal mutation kernel and a confining fitness pote…
Lotka-Volterra competition-diffusion system: the critical competition case
Matthieu Alfaro, Dongyuan Xiao
We consider the reaction-diffusion competition system in the so-called {\it critical competition case}. The associated ODE system then admits infinitely many equilibria, which make…
On the modelling of spatially heterogeneous nonlocal diffusion: deciding factors and preferential position of individuals
Matthieu Alfaro, Thomas Giletti, Yong-Jung Kim +2
We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the…
Populations facing a nonlinear environmental gradient: steady states and pulsating fronts
Matthieu Alfaro, Gwenaël Peltier
We consider a population structured by a spacevariable and a phenotypical trait, submitted to dispersion,mutations, growth and nonlocal competition. This population is facing an {\…
The spatio-temporal dynamics of interacting genetic incompatibilities. Part I: The case of stacked underdominant clines
Matthieu Alfaro, Quentin Griette, Denis Roze +1
We explore the interaction between two genetic incompatibilities (underdominant loci in diploid organisms) in a population occupying a one-dimensional space. We derive a system of…
The emergence of a birth-dependent mutation rate: causes and consequences
Florian Patout, R Forien, M Alfaro +2
In unicellular organisms such as bacteria and in most viruses, mutations mainly occur during reproduction. Thus, genotypes with a high birth rate should have a higher mutation rate…