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Patterns of Dynamical Behaviour in Single-Species Populations

M. P. Hassell, J. H. Lawton and R. M. May
Journal of Animal Ecology
Vol. 45, No. 2 (Jun., 1976), pp. 471-486
DOI: 10.2307/3886
Stable URL: http://www.jstor.org/stable/3886
Page Count: 16
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Patterns of Dynamical Behaviour in Single-Species Populations
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Abstract

(1) A variety of data on field and laboratory populations is reviewed in which there is little or no overlap between generations. These data are then fitted to a simple, non-linear, density dependent population model. (2) A rich spectrum of dynamical behaviour is possible in such a non-linear model (ranging from a stable equilibrium point, through stable cycles, to apparently chaotic population fluctuations). In the particular model discussed, these stability properties hinge upon two parameters. These have been estimated for a variety of insect populations enabling us to compare the dynamical behaviour of real populations with that which is theoretically possible. (3) We find the majority of populations show a monotonic return to a stable equilibrium point following a disturbance, with relatively few examples of oscillatory damping or low-order limit cycles. (4) Examples of stable cyclic behaviour, or of chaotic fluctuations, are mostly found in laboratory populations. In such cases, the absence of many natural mortality factors, or of dispersal, may tend to exaggerate non-linear aspects of the dynamics. (5) The observed range of fluctuations in various populations is tabulated. These are discussed in relation to the predicted ranges of fluctuation where limit cycles or chaos occur. The conclusion supports that of (3) above; namely that most natural populations will tend to return to a stable equilibrium point following a disturbance.

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