Invasive species management in two-patch environments: Agricultural damage control in the raccoon (procyon lotor) problem, Hokkaido, Japan

We develop discrete-time models for analyzing the long run equilibrium outcomes on invasive species management in two-patch environments with migration. In particular, the focus is upon a situation where removal operations for invasive species are implemented only in one patch (controlled patch). The new features of the model are that (i) asymmetry in density dependent migration is considered, which may originate from impact of harvesting as well as heterogeneous habitat conditions, and (ii) the effect of density-dependent catchability is well-taken to account for the nature that required effort level to remove one individual may rise as the existing population decreases. The model is applied for agricultural damage control in the raccoon problem that has occurred in Hokkaido, Japan. Numerical illustration demonstrates that the long run equilibrium outcomes highly depend on the degree of asymmetry in migration as well as the sensitivity of catchability in response to a change in the population size of invasive species. Furthermore, we characterize the conditions under which the economically optimal effort levels are qualitatively affected by the above two factors and aiming at local extermination of invasive species in controlled patch is justified.catchability, meta-population, local extermination, removal effort, density dependent migration

Commuting difference operators arising from the elliptic C_2^{(1)}-face model

We study a pair of commuting difference operators arising from the elliptic C_2^{(1)}-face model. The operators, whose coefficients are expressed in terms of the Jacobi's elliptic theta function, act on the space of meromorphic functions on the weight space of the C_2 type simple Lie algebra. We show that the space of functions spanned by the level one characters of the affine Lie algebra sp(4,C) is invariant under the action of the difference operators.Comment: latex2e file, 19 pages, no figures; added reference