When does periodic variation in resource growth allow robust coexistence of competing consumer species?

This article asks under what conditions and to what extent periodic variation in the growth rate of a single shared limiting resource facilitates the coexistence of two competing consumers that differ in having linear vs. nonlinear responses to that resource. The analysis explores the effects of four factors on the range of consumer characteristics that allow coexistence: (1) whether resource growth is biotic or abiotic; (2) the efficiency of the consumers in reducing the resource population; (3) the rapidity of the demographic response of the consumers to changes in resource density; and (4) the period and amplitude of the periodicity in resource growth. Coexistence of two competitors differing greatly in the linearity of their responses is most likely when (1) resource growth is biotic and (2) the consumers are relatively inefficient. The effects on coexistence of the third and fourth factors can be more complicated, particularly when the resource is biotic. However, in most cases coexistence occurs over a wider range of conditions when the linear consumer has a more rapid numerical response than the nonlinear consumer and when the period of environmental fluctuation is much longer than the minimum doubling time of the consumer populations. If the resource is biotic, consumer-resource cycles can be produced by the nonlinear consumer, and environmental cycles may either interfere with or reinforce these, contracting or expanding the conditions allowing coexistence. However, the interaction of endogenous cycles and periodic variation in resource growth generally has highly nonadditive effects on coexistence. These findings help explain why few previous experimental studies have demonstrated coexistence due to the relative nonlinearity of consumer responses.