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

We analysed two 26-year long (1970-1995) 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

Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs

Theme 4 - Simulation et optimisation de systemes complexes - Projet MathfiSIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.1999 n.3749 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Limit cycles in Norwegian lemmings: tensions between phase-dependence and density-dependence

Ever since Elton, the 3–5 year density cycles in lemmings (and other microtines) in Fennoscandia have troubled scientists. Explanations have involved intrinsic regulation and trophic interactions. We have analysed yearly changes in fall abundances for lemmings over 25 years from two local mountain sites in South Norway. These time series appear to have an underlying nonlinear structure of order two. Fitting a piece-wise linear threshold model of maximum order two, the most parsimonious model was, however, of first order for both series. The resulting dynamics from this model is a limit cycle. Reformulating the model in terms of abundances yields a model which combines (delayed) density-dependent effects and the influence of the cyclic phase. The delayed density-dependence of one part of the model is consistent with an effect of specialist predators during the peak and crash phases of the cycle, although other trophic interactions cannot be excluded

Density dependence in wood mouse

We analysed the effects of Quercus crispula acorn abundance on the density dependence of the large Japanese wood mouse Apodemus speciosus using time series data (1992-2007). The data were obtained in a forest in northern Hokkaido, Japan, by live-trapping rodents and directly counting acorns on the ground. Acorn abundance in one year clearly influenced the abundance of wood mice in the following year in all models examined based on the Gompertz and Ricker model; in addition, the abundance of wood mice had effects on the population. Acorn abundance influenced the strength of density dependence (intraspecific competition) of the wood mouse population. When the abundance of acorns was high, density dependence was relaxed, and as a result the equilibrium density at which the population growth rate decreased to zero became higher. Those effects of acorn abundance were regarded as a nonlinear perturbation effect (sensu Royama 1992). The nonlinearity of density dependence was also detected; higher densities had stronger effects on population growth rates