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Chaos, noise, and extinction in models of population growth. (English) Zbl 0699.92020
Summary: A “hump-with-tail” map (i.e., with two extreme values) is derived to describe the growth of bobwhite quail populations. Although this map is shown to be capable of producing chaotic dynamics, analysis of field data suggests that the population is at a stable equilibrium. Thus the observed fluctuations in population density likely reflect random perturbations.
It is shown that populations governed by hump-with-tail maps are less prone to extinction in randomly fluctuating environments than hypothetical populations whose growth is governed by “one hump” maps, i.e., maps with a maximum as their only extremal value. Our observations emphasize the importance of considerations of noise in theoretical analysis of population growth and stability.

MSC:
92D25 Population dynamics (general)
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