ABSTRACT
Introducing the effect of extinction into the so-called replicator equations (mathematically equivalent to the Lotka-Volterra equations) of population dynamics, we construct a general mathematical model of ecosystems. In the model, the diversity of species, i.e. the dimension of the equation, is a time-dependent variable. By the explicit introduction of the effect of extinction, the system shows very different behavior from the original replicator equation and leads to mass extinction when the system initially has high diversity. The present theory can serve as a mathematical foundation for the paleontologic theory for mass extinction.
