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In the classical Lotka-Volterra population models, the interacting speciesaffect each other's growth rate. We propose an alternative model, in which thespecies affect each other through the limitation coefficients, rather thenthrough the growth rates. This appears to be more realistic: the presence offoxes is not likely to diminish the fertility of rabbits, but will contributeto limiting rabbit's population. Both the cases of predation and of competitionare considered, as well as competition in case of periodic coefficients. Ourmodel becomes linear when one switches to the reciprocals of the variables. Inanother direction we use a similar idea to derive a multiplicity result for aclass of periodic equations.

On the interaction of species capable of explosive growth