This program is part of the thematic year on Mathematics of Planet Earth (MPE2013). Its purpose is to bring together researchers from different fields with common interests in biodiversity and evolution to exchange new ideas on these subjects and think about future directions of research. This semester aims to understand the phenomenal variability among species, from their apparition on Earth to their extinction, through their intricate interactions with one another and with the physical world. Tentative answers will be sought through a wide range of mathematical, statistical and computational approaches : stochastic modeling, branching processes, ancestral processes, evolutionary dynamics and games, optimization, phylogenetic inference, maximum-likelihood methods.