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Age-abundance relationships for neutral communities

Neutral models for the dynamics of a system of competing species are used, nowadays, to describe a wide variety of empirical communities. These models are used in many situations, ranging from population genetics and ecological biodiversity to macroevolution and cancer tumors. One of the main issues discussed within this framework is the relationships between the abundance of a species and its age. Here we provide a comprehensive analysis of the age-abundance relationships for fixed-size and growing communities. Explicit formulas for the average and the most likely age of a species with abundance $n$ are given, together with the full probability distribution function. We further discuss the universality of these results and their applicability to the tropical forest community.