A branching process, its application in biology: Influence of demographic parameters on the social structure in mammal groups

Branching processes are widely used in biology. This theoretical tool is used in cell dynamics, epidemics and population dynamics. In population dynamics, branching processes are mainly used to access extinction probabilities of populations, groups or families, with the Galton–Watson branching process. Many mammal species live in socially-structured groups, and the smallest units of these groups are lineages (or families) of kin-related individuals. In many primate species, these lineages are matrilines, as females remain in their natal groups most of the time, whereas males generally disperse. Lineage parameters, such as numbers of matrilines, size of each matriline and average degree of relatedness, could strongly influence the genetic composition of groups. Evidence indicates that division along matrilines could induce substantial differentiation among fission groups. Here, we develop a novel mathematical model based on the branching process theory describing demographic dynamics of groups. The main result of this model is an explicit analytical expression of the joint distribution of numbers of lineages and sizes of socially-structured groups. We investigated the influence of parameters such as natality and mortality on the outcome of the process, including extinction probability. Finally, we discuss this theoretical result with respect to biological significance.