On the methods for determining density-dependence by means of regression.

The determination of density-dependence of a mortality process is attempted by taking the linear regression of the logarithm of population density (or k defined by Varley and Gradwell, 1960) against the logarithm of previous density, based on the assumption that the slope, b, of the line is smaller than unity for log density-log density relationship or larger than zero for k-log density relationship. It was concluded, however, that the following three factors violate the basic assumption, providing no density-dependence. 1. In a Morris plot based on serial data, the value of b tends to be near the value of r. Thus, when the relationship is strongly affected by chance factors, giving remarkably scattered points on graph, the value of b tends to be always lower than unity. 2. When the independent variables (log previous density) are subject to sampling error, the value of b tends to be smaller than unity for density-density relations or larger than zero for k-density relations. 3. In Morris plot, where log densities are used twice as an independent and a dependent variables excepting the first and the last generation, the effect of timelag strongly reduces the value of b when the number of generations is not large.