Dynamics of taxonomic diversity

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Abstract
A general model of taxonomic diversity, incorporating diversity-dependent rates of origination and extinction, is constructed to examine the dynamic responses of diversity to perturbation. The model predicts that the trajectories of diversification increase and decrease are substantially different. The trajectories of diversity during disequilibrium conditions are displayed in phase diagrams to permit a simple graphical analysis of stability. A positive displacement of diversity from equilibrium results in a rapid decline in diversity and may involve an initial overshoot of the equilibrium condition. A negative displacement of equal magnitude results in a gradual increase in diversity. The model is expressed as a nonlinear difference equation to incorporate intrinsically a delay time due to the characteristic noninstantaneous response of origination and extinction. The model initially assumes a parabolic curve expressing total taxon origination rate as a function of diversity. A second model, constructed assuming a sigmoidal total taxon origination rate derived from considerations of allopatric speciation, enhances the asymmetry of the diversity response. The delayed recovery of the Triassic fauna is shown to be characteristic of return to equilibrium from an undersaturated condition, whereas the more rapid “catastrophic” decline in the Late Permian fauna is shown to be characteristic of return to equilibrium from the oversaturated condition. It is proposed, although not assumed, that perturbation may include a degree of selectivity related to the dispersal abilities of organisms, thereby enhancing the observed asymmetry.