Parameter Identification in Ecological Systems via Discontinuous and Singular Control Regimes

Policy decisions regarding commercial harvesting of aquatic species by (typically governmental) regulatory agencies are often based in part upon field data, simulation results, and mathematical models. Regulatory agencies may limit or expand seasons, determine total harvest allowed, increase or decrease licensure fees, and raise or lower taxation rates in response to the state of the ecological system. Ultimately, the regulatory agency uses such measures to ensure viable populations in an attempt to balance ecosystem health and benefits for society. Such decisions impact commercial fishing ventures affecting the nature of harvesting efforts and their intensity. Conclusions drawn from mathematical models of ecological systems, and derived simulation results which affect this reality are highly dependent upon the validity of information available. Knowledge or estimates of critical parameters such as intrinsic growth rate, carrying capacity, etc. and dynamic variables such as biomass levels dictate the usefulness of analytical and numerical analyses. The purpose of this treatment is to illustrate that control laws applied to mathematical models of species dynamics may be used to discern estimates of parameters that inherently exist in such models in an effort to provide more valuable information upon which to base policy decisions. Dynamic models of both single-species evolution and predator-prey interactions are examined.