Abstract
A simple model of a biological community assembly is studied. Communities are assembled by successive migrations and extinctions of species. In the model, species are interacting with each other. The intensity of the interaction between each pair of species is denoted by an interaction coefficient. At each time step, a new species is introduced to the system with randomly assigned interaction coefficients. If the sum of the coefficients, which we call the fitness of a species, is negative, the species goes extinct. The species-lifetime distribution is found to be well characterized by a stretched exponential function with an exponent close to 1/2. This profile agrees not only with more realistic population dynamics models but also with fossil records. We also find that an age-independent and inversely diversity-dependent mortality, which is confirmed in the simulation, is a key mechanism accounting for the distribution.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. The lifetime of species estimated from fossil records is known to show a characteristic skewed profile; it is convex on a semi-log plot and concave on a log–log plot. Recently the authors have seen that such a skewed profile is universally obtained in a wide variety of models with many species and interactions among them, which suggests a simpler origin for the characteristic distribution.
Main results. In this article a simple dynamical graph model for biological community assembly is proposed. From a systematic simulation, it is shown that this very simple model reproduces the characteristic lifetime distribution. It is also found that an age-independent and diversity-inversely-dependent mortality of species is a key mechanism.
Wider implications. Since the model and the mechanism are simple, our result may be applied to various systems with complex interactions, such as social and economical systems.