Multimode phenomenon in the population dynamics of animals with short live cycles

42 Fluctuation of animal populations continues to be one of the most interesting and mysterious ecological phenomena. A lot of evidence available to date sugg gests not only regular changes in population abunn dance, but also clear cycling of various dynamic modes in biological populations. The most striking and welllknown examples of changes in animal population dynamics are transitions between stable and cyclic phases in the lemming (Lemmus lemmus) populations all over southern Norr way [1] and in the reddgray vole (Clethrionomys rufocaa nus) populations in Finland [2]. The reverse situation can be also observed, when small fluctuations around the equilibrium state are replaced by either oscillatory or chaotic modes. For example, a trend of the snow goose population (Chen caerulescens) in the New York state (United States) to grow up monotonously for a long time has changed to irregular oscillations, probaa bly, because of exceeding the ecological capacity of the environment [3]. Another type of disturbed populaa tion dynamics is related to variation in the lengths of cycles. In particular, in Canada and the northern United States, there was a transition from twoo to threeeyear oscillations in the evening grosbeak (Coccoo thraustes vespertinus) population [4]. Note that similar phenomena were observed in the populations of lemm ming and some vole species, because the cycles with lengths of 2, 3, and 4 are characteristic of them [5, 6]. Moreover, there are situations when nonninteracting, practically identical populations of the same species display different dynamics. In particular, the laboraa tory experiments have demonstrated that, at the same initial population size and under similar conditions, two different antiiphased periodic modes may be observed in the flour beetle (Tribolium castaneum) populations [7]. Thus, there are situations when local populations have different (and sometimes radically different) modes of population dynamics at the same values of demographic parameters. This phenomenon of the dynamic mode dependence on initial conditions is referred to as multistability in the theory of dynamic systems [8]. Appearance of several different dynamic modes is possible when a system has several stable attractors, each serving as a stable point or being involved into a limiting set of attractors (e.g., an invariant curve). Hence, the term " multistability " is somewhat misleading in this context and, to our opinn ion, it is more convenient to use a new notion of " mull timode " to reflect the essence of the phenomenon occurring in real …