Determination of critical variables in a microbial predator–prey system by catastrophe theory

Abstract

THE differential or difference equations that are used customarily to describe predator–prey interactions can give many insights into the behaviour of simple ecosystems, but only rarely can they be used to predict the population densities of real organisms with any accuracy. Thus even given long-term observations of population densities it is often difficult to deduce very much about the behaviour of the organisms. We present here an analysis in which we use population measurements to determine the variables that govern the response of an amoebal predator to its prey. Our results support the suggestion of Curds and Cock-burn¹ that it is the prey–predator ratio rather than the prey density to which the amoebae are sensitive. We have arrived at our conclusions by applying catastrophe theory² in a way that we believe will be useful in many other contexts.