Genealogical Reinforcement in Branching Processes

Abstract

Within many ecological populations, survival and reproduction exhibit a dependence on social interactions with relatives. As one example, resource excess is often shared according to genealogical proximity. When viewed as a branching system, an individual's offspring distribution acquires an effective dependence on genealogical structure. In the specific case that a large, local family structure leads to a large set of offspring, this can be viewed as a form of genealogical reinforcement. To capture this mechanism, we introduce a branching model of finite-depth genealogical dependence. Given partial observations of this reproducing population and its genealogy, we would like to reject the hypothesis of independent branching and estimate the strength of dependence. We present a statistical framework for detection and estimation, combining analytical results with simulation-based validation. We then identify our branching model with a tree-valued multitype branching process on a finite type space, providing a rigorous characterization of the expected structural reinforcement. Finally, we discuss how these tree-valued interactions can be accommodated within a broader class of stochastic processes.