Abstract: Altruistic behaviors occur when an individual decreases its personal fitness to help another individual. Such behaviors occur across a range of species and environments, and they take different forms. The diversity of altruistic behaviors is also characterized by various group living features, including group structure and social interactions. In this thesis, I develop models to study how the specificities of group living can influence the evolution of altruistic behaviors. I use inclusive fitness models to understand how the social environment the group creates, the ecological factors, and the benefits of altruistic behaviors impact the evolution of social behaviors. In the first model, I study the evolution of delayed dispersal with group size benefits. Dispersal tends to be delayed when breeding opportunities are scarce, i.e., when the habitat is saturated. I find that habitat saturation is not always associated with a high level of dispersal. This finding challenges previous results and highlights the need to model environmental feedback explicitly. In a second model, I measure how redirected help can emerge when individuals disperse near their relatives. Redirected help happens when an individual whose entire brood fails reallocates the effort it would have expended on parental care to help a related neighbor. The adaptive significance of this strategy may look straightforward, but if the population is viscous, the helper also competes with its relatives. This population viscosity creates additional costs and benefits that can restrain the evolution of altruism. To investigate the evolution of redirected help in a viscous population, I use an infinite-island model where redirected help can provide survival or fecundity benefits to the recipients. I find that the survival benefits associated with redirected help sometimes promote the emergence of help better than fecundity benefits, which contradicts previous findings. In a third model, I delve more deeply into the evolution of redirected help by explicitly accounting for spatial structuring within the population. I find that switching to a spatially explicit model has repercussions for the evolution of redirected help. For instance, the influence of offspring dispersal on the evolution of redirected help is reversed between the two models. My findings highlight the impact of spatial structure on the evolution of social behaviors. Overall, my thesis shows that different group living features can challenge predictions on the evolution of social behaviors.

Abstract: Let $M$ be a smooth manifold. Let $k$, $r$ be positive integers. A $k$-plectic (multisymplectic) form on $M$ is a closed non-degenerate $(k+1)$-form on $M$. Let's define a polysymplectic form on $M$ as an ${\mathbb{R}}^r$-valued closed non-degenerate 2-form on $M$. I will discuss the Darboux theorem and the Poisson bracket.