Universal Power Laws Govern Intermittent Rarity in Communities of Interacting Species

The temporal dynamics of many natural populations involve intermittent rarity, that is, the alternation, over variable periods of time, of phases of extremely low abundance, and short outbreaks. In this paper we show that intermittent rarity can arise in simple community models as a result of competitive interactions within and between species. Intermittently rare species are typified as weak invaders in fluctuating communities. Although the dynamics of intermittent rarity are highly irregular, the distribution of time spent in phases of rarity (‘rarity times’) involves strong regularity. Specifically, intermittent rarity is governed by a well-defined power law. The scaling exponent ( − 3 2 ) is a universal feature of intermittent rarity: it does not depend on species demographic parameters; it is insensitive to environmental stochasticity; and the same exponent is found in very different models of nonstructured populations. The distribution of rarity times implies that the dynamics of rarity have no characteristic timescale. Yet in practice the universal scaling law offers a general form of prediction in which one can calculate the frequency of occurrence of rarity phases of any given duration. Data on marine fish communities support the prediction of a − 3 2 power law underlying the dynamics of intermittently rare species. The scale-free dynamics reported here place intermittent rarity in the same class as the critical states of other nonlinear dynamical systems in the physical sciences. At a critical state, general laws govern the systems’ dynamics irrespective to the specific details of the interactions between constituents. Key phrases: Community persistence and mutual invasibility; Intermittent rarity resulting from interspecific competition; Intermittent rarity and weak invasibility; Intermittent rarity and chaos; Statistics of the dynamics of intermittently rare species; Power laws governing intermittent rarity; Universal scaling of rarity times; Examples of models showing intermittent rarity: the Gatto model, the Franke-Yakubu model and the Hochberg-Hawkins model.