Phase- and density-dependent population dynamics in Norwegian lemmings: interaction between deterministic and stochastic processes

Abstract

We analysed two 26–year long (1970 to 1995) time–series on annual population growth rates of Norwegian lemmings (Lemmus lemmus) from Finse, south Norway, using a threshold autoregressive (TAR) approach. We demonstrate that the population dynamics is both phase– and density–dependent. The phase–dependence accounts for the observed nonlinearity. We used the deduced stochastic model structure as a basis for evaluating the dynamic properties of this system. The dynamics is characterized either by limit cycles or chaos (the latter with a strong semi–periodic component). Stochasticity is seen to play an important role in the determination of the periodicity. The ecological implications of these statistical and mathematical results are discussed.