MultiRNAflow: integrated analysis of temporal RNA-seq data with multiple biological conditions.

Motivation: The dynamic transcriptional mechanisms that govern eukaryotic cell function can now be analyzed by RNA sequencing. However, the packages currently available for the analysis of raw sequencing data do not provide automatic analysis of complex experimental designs with multiple biological conditions and multiple analysis time-points.

Results: The MultiRNAflow suite combines several packages in a unified framework allowing exploratory and supervised statistical analyses of temporal data for multiple biological conditions.

Local adaptation, dispersal evolution, and the spatial eco-evolutionary dynamics of invasion.

Local adaptation and dispersal evolution are key evolutionary processes shaping the invasion dynamics of populations colonizing new environments. Yet their interaction is largely unresolved. Using a single-species population model along a one-dimensional environmental gradient, we show how local competition and dispersal jointly shape the eco-evolutionary dynamics and speed of invasion.

Links between deterministic and stochastic approaches for invasion in growth-fragmentation-death models.

We present two approaches to study invasion in growth-fragmentation-death models. The first one is based on a stochastic individual based model, which is a piecewise deterministic branching process with a continuum of types, and the second one is based on an integro-differential model. The invasion of the population is described by the survival probability for the former model and by an eigenproblem for the latter one.

Invasion and adaptive evolution for individual-based spatially structured populations.

The interplay between space and evolution is an important issue in population dynamics, that is particularly crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution are closely related. Here, we model the interplay between space and evolution starting with an individual-based approach and show the important role of parameter scalings on clustering and invasion.

Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models.

A distinctive signature of living systems is Darwinian evolution, that is, a propensity to generate as well as self-select individual diversity. To capture this essential feature of life while describing the dynamics of populations, mathematical models must be rooted in the microscopic, stochastic description of discrete individuals characterized by one or several adaptive traits and interacting with each other. The simplest models assume asexual reproduction and haploid genetics: an offspring usually inherits the trait values of her progenitor, except when a mutation causes the offspring to take a mutation step to new trait values; selection follows from ecological interactions among individuals.