The fitting of the logistic equation to the rate of increase of population density

Conclusion and Summary Though there are many problems on the usefulness of the logistic curve, it may be necessary to examine before discussing these problems whether or not the actual data fit to the theoretical values. It has been clarified in this paper that the relation between the population density and its rate of increase per individual described by the differential equation (1) is represented by a straight line on a finite difference diagram on which N i+1 −N i / N i values are plotted against N i+1 . Utilizing this linear relation we may examine the fittness of the logistic curve to the actual data and when it is fitted we may estimate the parameters of the logistic equation by (5) and (6). The result of the application of this method to the experimental populations of azuki bean weevil indicates that the relation between parent and progeny densities fits well to the logistic type as has been proved by Fujita and Utida (1953) who utilized the linear reltion between 1/ R +2σ and parent density where R is the apparent rate of reproduction and σ is a constant dependent primarily upon the length of adult life (0≦σ≦1).