Fisher information calculation in a complex ecological model: An optimal control-based approach

A new approach to the calculation of Fisher Information in a complex dynamic system is proposed in this work. The numerical strategy involves the successive solution of a series of optimal control problems to achieve the simultaneous estimation of the time cycle, as a fundamental parameter in the calculation of Fisher Information, and a set of Fisher Information average values, as well as the dynamic optimization of the system. A sequence of optimal control problems are solved first for estimating the time cycle, which is required to calculate the Fisher Information of the system. Then, the last optimization problem is solved to obtain not only the optimal profiles for the state and control variables, but also a set of time averaged Fisher Information values; such averaged values can be used to identify changes on the dynamic order of the system. Two illustrative examples are studied: a simple predator-prey Lotka-Volterra model is solved to explain the application of the numerical strategy for the estimation of the time cycle and time averaged Fisher Information values, and a proposed thirteen compartment socio-economic-ecological model, solved after the simple model to show the effectiveness of the approach to detect regime changes in a more complex system. The results of the simple model show a good approximation to the estimation of the time cycle after local minimum and maximum optimal points are obtained, since the system shows a regular cyclic behavior. For the larger model, the results confirm the effectiveness of the proposed optimal control based approach in more complex systems and the benefits of using Fisher Information average values to analyze the behavior of the system, while also identifying the policies that optimize the mass interactions among the compartments.