Infectious Disease and Species Coexistence: A Model of Lotka-Volterra Form

Abstract

There is a growing body of evidence suggesting that infectious disease may influence the species composition of natural communities. We examine the effect of a shared infectious disease on species coexistence in a differential equation model that generalizes to two host species, a one-host one-disease model explored by Anderson and May (1979). In the Anderson-May model, the transmission rate is described by a "mass action" term; there is no acquired immunity; and the infectious disease is the only factor regulating population growth. These assumptions, which are generally more applicable to invertebrate than to vertebrate hosts, are carried over to our two-host model. We show that, just as in the familiar Lotka-Volterra model of direct competition, there are three possible outcomes to the interaction: (1) one host species may unilaterally exclude the other; (2) the two host species may coexist; or (3) either host may exclude the other, with the outcome depending on initial conditions. These outcomes are graphically expressed with isoclines similar to those generated by the Lotka-Volterra model, and the necessary and sufficient condition for species coexistence is given by an expression formally parallel to the coexistence criterion of the Lotka-Volterra model. The numbers of infected individuals sustained by a host species when alone and at equilibrium are shown to be comparable to carrying capacity in the Lotka-Volterra model. Similarly, we show that the ratio of between-species to within-species infection rates is analogous to the competition coefficient. The model identifies three ingredients that must be assessed to predict the consequences of shared infectious disease for species coexistence: the intrinsic capacity for increase of each host; the per capita birth, death, and recovery rates of infected individuals; and the pattern of within- and cross-species infections. The model also leads to two additional conclusions that appear to apply in a broader range of models. First, given certain assumptions, including the assumption that infectious disease is the only factor regulating population growth, at equilibrium the ratio of infected to uninfected individuals in any particular host species is independent of the presence or absence of alternative host species. Second, the basic model does not lead to stable coexistence for an infectious disease that is only transmitted between host species and not within host species (i.e., host-parasite systems involving alternate hosts, such as infectious diseases carried between definitive hosts by intermediate hosts). The paper concludes with some suggestions about how this model can be extended to a broader class of infectious disease systems.