Bernoulli and binomial proliferation on evolutionary graphs.

In this paper we introduce random proliferation models on graphs. We consider two types of particles: type-1/mutant/invader/red particles proliferates on a population of type-2/wild-type/resident/blue particles. Unlike the well-known Moran model on graphs -as introduced in Lieberman et al.

Evolutionary regime transitions in structured populations.

The evolutionary dynamics of a finite population where resident individuals are replaced by mutant ones depends on its spatial structure. Usually, the population adopts the form of an undirected graph where the place occupied by each individual is represented by a vertex and it is bidirectionally linked to the places that can be occupied by its offspring. There are undirected graph structures that act as amplifiers of selection increasing the probability that the offspring of an advantageous mutant spreads through the graph reaching any vertex.

A method for validating Rent's rule for technological and biological networks.

Rent's rule is empirical power law introduced in an effort to describe and optimize the wiring complexity of computer logic graphs. It is known that brain and neuronal networks also obey Rent's rule, which is consistent with the idea that wiring costs play a fundamental role in brain evolution and development. Here we propose a method to validate this power law for a certain range of network partitions.

Suppressors of selection.

Inspired by recent works on evolutionary graph theory, an area of growing interest in mathematical and computational biology, we present examples of undirected structures acting as suppressors of selection for any fitness value r > 1. This means that the average fixation probability of an advantageous mutant or invader individual placed at some node is strictly less than that of this individual placed in a well-mixed population. This leads the way to study more robust structures less prone to invasion, contrary to what happens with the amplifiers of selection where the fixation probability is increased on average for advantageous invader individuals.

Exploring the topological sources of robustness against invasion in biological and technological networks.

For a network, the accomplishment of its functions despite perturbations is called robustness. Although this property has been extensively studied, in most cases, the network is modified by removing nodes. In our approach, it is no longer perturbed by site percolation, but evolves after site invasion.