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

The three surveys of the distribution of the bridled form of the common guillemot (Uria aalge Pont.), made in 1938-39, 1948-50 and 1959-60 (Southern 1962), raise a problem which is of some interest in population mathematics. The common guillemot starts breeding at the age of 3 years, approximately, and the probability of an adult bird surviving over a year was estimated by Southern, Carrick & Potter (1965) at a colony at Whinnyfold, Aberdeenshire, to be around P = 0-85-0-88 over 3 years of observation of colour-ringed birds. Assuming this annual survival rate to remain constant, this would mean that an adult alive aged 3 years might, on the average, have a further expectancy of life of around 7-8 years. Suppose that a breeding population was first visited in 1938 and a count was made of the number of bridled birds among the total breeding adults, which will be termed the 'zero' generation of adults. Then it is evident that any subsequent recounts in later years would be made on a population of adults composed of a gradually increasing number of overlapping generations. Since in doing the actual counts, birds belonging to the individual generations cannot be distinguished from each other, the percentage of bridled birds estimated in this way must necessarily be an average figure taken over all existing generations descended from the original 'zero' generation. It is therefore of some interest to consider the form of these 'generation-distributions' and the way they build up as time goes on. Given these distributions, it is then possible to see what changes might be expected in this 'average' proportion of bridled birds, assuming this genotype is a single factor recessive or dominant (no further details are known of the genetic control), and that the mating within the individual generations is at random, for each Southern (1951) gives some evidence. But, in the first place, it is necessary to consider the possible intrinsic rate of increase of a guillemot population.