Using a coupled integral projection model to investigate interspecific competition during an invasion: An application to silver carp (Hypophthalmichthys molitrix) and gizzard shad (Dorosoma cepedianum)
As a generalization of stage-based matrix models, integral projection models (IPMs) have been used to describe the size-based dynamics of wildlife and fisheries populations. Although some matrix models have explicitly included species interactions, few IPMs have expanded beyond single species, which limits their ability to describe the competitive dynamics of co-occuring taxa. We present a coupled system of IPMs where intra- and inter-specific competition may reciprocally affect the life-histories of two species. We investigated the potential role that competition has on two overlapping fish species in the upper Mississippi River system: the native gizzard shad ( Dorosoma cepedianum ) and the invasive silver carp ( Hypophthalmichthys molitrix ). Numerical simulations of this system indicated that the coupled IPMs could exhibit asymptotic behaviors similar to traditional, non-linear competition models. Specifically, by altering the competition coefficients, we demonstrate this model's ability to detect competitive exclusion, species coexistence, and dual extinction outcomes.