On the theory of some stochastic compartmental systems in ecological work

Vita.The first and second order cumulants of some multi-compartment stochastic models important to ecological problems are derived. The models investigated are the n-compartment irreversible, catenary model and the n-compartment general irreversible model with birth, death and immigration in each compartment for both linear donor controlled and linear recipient controlled transfers between compartments. The cumulants of the combined donor and recipient controlled, general irreversible model is also derived. Simulated data of a two-compartment system for both linear donor controlled and linear recipient controlled transfer rates are used to demonstrate the feasibility of obtaining estimates of the parameters through use of the modified Gauss-Newton estimation procedure. By simultaneously fitting the first and second cumulants of the donor controlled model to the means and variances of each compartment, it is shown that separate estimates of the birth and death rate can be obtained which is not possible when fitting the first cumulants to the data