A CONSIDERATION ON THE THEORY OF ENVIRONMENTAL DENSITY

Abstract

A mathematical model is presented to explain the spatial distribution of animal populations which is principally controlled by the environmental conditions. A dynamical equation for the spatial movement of animals in such systems is formulated on an assumption that their movement is under influence of the following fundamental forces : 1) the dispersive force which is associated with random movement of animals in the space ; 2)the attractive force which induces directed movements of animals toward favorable environments;3) population pressure due to interferences between individual animals. By applying this analysis to the population system with discrete spatial changes of the environmental conditions, a distribution function is derived and it is shown that the result becomes equivalent to the Morisita's equation formulated in his theory of "enviornmental density". The analysis is further extended to the population system with continuously changing environmental condition and the stationary density distribution is analytically obtained. By taking advantage of some specific features of the equation, an experimental procedure to estimate the kinetic parameters associated with the postulated fundamental forces is discussed.