[The dynamics of Phanerozoic marine animal diversity agrees with the hyperbolic growth model].Zh Obshch Biol. 2007 Jan-Feb; 68(1):3-18.ZO
Generic diversity dynamics of the Phanerozoic marine animals is far better described by the hyperbolic model, widely used in demography and macrosociology, than by the exponential and logistic models from population dynamics traditionally employed for this purpose. Exponential and logistic models imply zero influence of interactions between taxa on the dynamics of diversity, with the exception of competing for unoccupied ecological space, whereas the hyperbolic model implies non-linear second-order positive feedback in the development of the biota. The hyperbolic human population growth is caused by positive feedback between population size and the rate of technological and cultural development (the more individuals, the more inventors, the more rapid progress, the more rapid growth of the Earth's bearing capacity; the smaller death-rate, the more accelerated growth-rate of the population). Probably there is also non-linear second-order positive feedback between diversity and community structure (the more genera, the higher alpha-diversity, which is defined as average number of genera per community, the more complicated and stable, "buffered" communities, the greater "taxonomic capacity of the environment" and average duration of the existence of genera; extinction rate dencreases, biodiversity growth-rate increases). The simplest mathematical model of biodiversity dynamics based on this assumption is confirmed by empirical data on alpha-diversity dynamics. Progressive complexification of marine communities during the Phanerozoic is also confirmed by the growing evennes of generic abundance distribution in paleocommunities.
