the past years I have been working on different aspects of population
dynamics. Some of my main works on this area were developed using
individual based simulations, focusing on processes of speciation and
their relation with physical space. In particular, we try to understand
the role of partial geographical barriers and natural selection in
speciation. Recently, we have applied these models to the study of ring
species (see below), where we were able to directly compare the results
of the simulations with empirical data. The results obtained by these
models also motivated the development of a series of theoretical
studies, where we write down equations that capture the features
explored by the numerical models and that clarify the role of the many
model parameters, such as the mutation rate, the size of the
population, the number of genes, etc.
Parallel to my work in evolutionary biology I also have interest in
chaotic and complex dynamical systems, including topics in statistical
mechanics, networks and semiclassical limit. Most of these projects
have been developed with the help of graduate students and
collaborators, particularly Yaneer
Bar-Yam and, until very recently, with Michel Baranger.
In Memorian: Michel Baranger (1927-2014)
Evolution and Stability of Ring Species
Ayana B. Martins, M.A.M. de Aguiar and Y. Bar-Yam,
PNAS 110(13) (2013) 5080.