In computational biology, and more specifically in population genetics, spatial branching processes with competitive selection and migration mechanisms can also be represented by mean field genetic type population dynamics models. The first moments of the occupation measures of a spatial branching process are given by Feynman-Kac distribution flows. The mean field genetic type approximation of these flows offers a fixed population size interpretation of these branching processes. Extinction probabilities can be interpreted as absorption probabilities of some Markov process evolving in some absorbing environment. These absorption models are represented by Feynman-Kac models. The long time behavior of these processes conditioned on non-extinction can be expressed in an equivalent way by quasi-invariant measures, Yaglom limits, or invariant measures of nonlinear normalized Feynman-Kac flows.