Competition for Resources Among Consumers
Part of the Springer Advanced Texts in Life Sciences book series (SATLIFE)
In the previous chapter we examined growth of populations whose reproductive rate was constant. In nature, the rate of population growth very often varies. If r varies randomly, a population may become extinct or, alternatively, suffer enormous increases in abundance, since the reproductive potential of any species is capable of producing very large numbers of new individuals. Since few environments are overwhelmed by living organisms, there must be mechanisms that inhibit increase in abundance as density increases. This, in brief, is the theory behind the logistic equation,* first suggested by P. F. Verhulst in 1838 and later derived independently by R. Pearl and L. J. Reed in 1920 (Hutchinson, 1978). The logistic equation is
which is the exponential growth equation modified by a factor (K - N)/K that reduces dN/dt as the number of individuals (N) increases and approaches the carrying capacity of the particular environment (K). This results in a sigmoid pattern of population growth, in which N has a smooth, decelerating approach to K.
$$dN/dt = rn(K - N)/K,$$
KeywordsBiomass Fishing Defend Detritus
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- *.The logistic is just one form of sigmoid growth. There are many other ways to describe such growth, including applications of Michaelis—Menten curves (Slater, 1979), Gompertz curves (dN/dt = rN log (K/N)) (Margalef, 1974) or exponential curves (Gallopin, 1971). Further alternative expressions are discussed by Hutchinson (1978).Google Scholar
- *.Such a life cycle where fish return to freshwater to breed is referred to as anadromous. Fishes such as eels that live mainly in freshwater and return to the ocean to breed are referred to as catadromous. In the case of eels, breeding takes place in deep waters of the Sargasso Sea.Google Scholar
- *.For demographic purposes recruitment refers to the maturing of individuals into the adult age classes. In fishery publications, recruitment is defined as the appearance of a cohort into the catch due to their having grown large enough to be caught given the mesh size of the fishing gear.Google Scholar
© Springer Science+Business Media New York 1984