Cyclic population dynamics and random perturbations

Periodically oscillating populations have been c sistent interest in animal ecology since thei appearance in ecological literature (Elton 1924, Elton & Nicholson 1942). Several hypotheses been put forward (see, e.g. Ak9akaya 1992; Rc 1992) but no single process has arisen above oth universal means to cause and maintain cyclic dyn The hypotheses include, among others, evoking nal factors such as sunspot cycle (Elton 1924), cycle (Siivonen & Koskimies 1955), and weathei (Grange 1949). Along these lines, it has also suggested (Soper 1929; Bartlett 1957, 1960a,b; son et al. 1986; Townsend, Sutherland & Perrow Royama 1992) that continuously acting nonenvironmental disturbances may maintain popu cycles. The possible causes of periodic epidemic recently reviewed by Anderson & May (1991) lowing suit, we shall demonstrate that perturb of random strength affecting reproductive succ random intervals may very well sustain regular lations in otherwise stable populations. For the current purposes, consider a popu of animals obeying delayed density dependence denoting its size at time k

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