The Intrinsic Rate of Increase and the Overlap of Successive Generations in a Population of Guillemots (Uria aalge Pont.)

Abstract

Starting at some origin of time with a "zero" generation of juveniles and adults, and assuming that some given rates of fertility and mortality remained constant, the generation-distributions of a breeding population of the common guillemot at time t have been built up over a period of 20 years. Because, potentially, the adult guillemot is a relatively long-lived bird, the overlap of the successive generations gradually becomes quite marked, and it was estimated that after 20 years there would be 7 generations represented in the breeding population, including some survivors of the original "zero" generation from which the rest were descended. These generation-distributions of the breeding population at time t were found to possess 2 interesting properties: provided that fertility remained constant, then the proportion of individuals falling into the n = 0, 1, 2 ... generation classes at time t, remained the same if the original life-table was changed by an additional force of mortality which was independent of age; and that after about 5 years the means of these distributions ([image]t) increased linearly with, regard to time, the rate of increase per unit of time being related to the "mean length of a generation" defined, in the perfectly general case, by [image] in which lx is the usual life-table''function and mx the maternal frequency function at age x, and r the intrinsic rate of increase of the population. This period of T is the same when r [not equal] 0 as the "mean length of a generation" given by the other mathematical definitions which have been made in the past; and it is suggested mat this definition is the most meaningful from the biological point of view. Given these calculated generation-distributions of the breeding population at time t, it was possible to make a rough estimate of the changes which might be expected in the average percentage of "bridled" birds over a period of 20 years, assuming this genotype to be a single factor recessive or dominant. For values of the selection coefficient s ^r 0.5, it was evident that the rate of change was very slow, due to the overlap of successive generations. These findings have some relevance to the surveys which have been made over 20 years of the percentages of bridled guillemots at various breeding colonies since, in making such counts, the individuals belonging to the different generations cannot be distinguished from each other.