Regulation by the absolute number in the population

John Davison ¹

¹ From the Department of Zoology, University of Vermont, Burlington, Vermont 05401

Planaria reproduce by transverse fission. Isolated worms increase in number exponentially, while social animals at the same density are inhibited in terms of numerical increase, but over a 25 day period undergo a larger increase in mass. Isolated posterior fission products reproduce faster than isolated anterior fission products. Regulation of population growth is independent of density over a 16-fold range and regulatory factors cannot be demonstrated in the medium. Regulation of population growth depends on direct contact between animals. Fission period varies from individual to individual and from period to period for a given individual. Doubling time is related to the absolute number of individuals comprising the population as follows:

P_N = (P_M · N)/(K + N),

where P_N is the doubling period of a population of N individuals, P_M is the doubling time of an infinitely large population, N is the number of individuals in the population, and K is the number of individuals in a population the period of which is one-half P_M. At 22°–24°C P_M is estimated to be 43.3 days and K is 1.87 individuals. A model system assumes that inhibitor flows through the population from animal to animal from the slowest to the fastest animal in the population thus acting to synchronize population increase as well as to determine the rate of population growth. A possible source of the inhibitor is discussed.

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