THE AGE STRUCTURE OF POPULATION-DEPENDENT GENERAL BRANCHING PROCESSES IN ENVIRONMENTS WITH A HIGH CARRYING CAPACITY

Abstract. The age structure of populations supercritical below and subcritical above a car-rying capacity is investigated, the result being a law of large numbers, as the capacity increases and time passes, provided the starting population is not little. 1. Preliminaries and Assumptions General branching processes describe populations where individuals live, reproduce, and die clonally and independently according to any fixed pattern allowing random variation between individuals, [8]. They can be rendered even more general by allowing life-spans and reproduction to be influenced by population size, through population and age dependent hazard and birth rates. (Not to complicate matters, we assume continuous life-spans and reproductions. The time discrete case is parallell.) In [13] the size of such populations was studied, the parameter K referring to a threshhold or carrying capacity, above which the population is too large to sustain itself: if it is larger than K, reproduction turns subcritical. Thus, consider a hazard rate hKz (u) of a u-aged individual in a population of size z. At death the individual might split into a random number of offspring, again depending upon both population size and mother’s age then. Write mKz (u) and