Predicting Irregularities in Population Cycles

Oscillating population data often exhibit cycle irregularities such as episodes of damped oscillation and abrupt changes of cycle phase. The prediction of such irregularities is of interest in applications ranging from food production to wildlife management. We use concepts from dynamical systems theory to present a model-based method for quantifying the risk of impending cycle irregularity.

[1]  Cheryl J. Briggs,et al.  What causes generation cycles in populations of stored-product moths? , 2000 .

[2]  W. Ricker.  Stock and Recruitment , 1954 .

[3]  Jim M Cushing,et al.  Basins of attraction: population dynamics with two stable 4‐cycles , 2002 .

[4]  A. Nicholson,et al.  The Self-Adjustment of Populations to Change , 1957 .

[5]  W M Schaffer,et al.  Transient periodicity and episodic predictability in biological dynamics. , 1993, IMA journal of mathematics applied in medicine and biology.

[6]  R. Costantino,et al.  Experimentally induced transitions in the dynamic behaviour of insect populations , 1995, Nature.

[7]  R F Costantino,et al.  Genetic analysis of a population of Tribolium II. Metabolic pattern of corn oil sensitive anomaly3 , 1968, Heredity.

[8]  Ian P. Woiwod,et al.  Estimating Chaos in an Insect Population , 1997 .

[9]  P. J. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[10]  R F Costantino,et al.  Lattice Effects Observed in Chaotic Dynamics of Experimental Populations , 2001, Science.

[11]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[12]  Michael A. McCarthy,et al.  Stochastic population models for wildlife management , 1995 .

[13]  B T Grenfell,et al.  Noisy Clockwork: Time Series Analysis of Population Fluctuations in Animals , 2001, Science.

[14]  Robert A. Desharnais,et al.  Population Dynamics and the Tribolium Model: Genetics and Demography , 1991, Monographs on Theoretical and Applied Genetics.

[15]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[16]  Jim M Cushing,et al.  Chaos and population control of insect outbreaks , 2001 .

[17]  Brian Dennis,et al.  Multiple attractors, saddles, and population dynamics in periodic habitats , 1999, Bulletin of mathematical biology.

[18]  S. Ellner,et al.  Crossing the hopf bifurcation in a live predator-prey system. , 2000, Science.

[19]  J. L. Hayward,et al.  PREDICTING DYNAMICS OF AGGREGATE LOAFING BEHAVIOR IN GLAUCOUS-WINGED GULLS (LARUS GLAUCESCENS) AT A WASHINGTON COLONY , 2004 .

[20]  Jim M Cushing,et al.  Transitions in population dynamics: Equilibria to periodic cycles to aperiodic cycles , 1997 .

[21]  Brian Dennis,et al.  Chaotic Dynamics in an Insect Population , 1997, Science.

[22]  G. F. Gause.  The struggle for existence , 1971 .

[23]  R. Costantino,et al.  NONLINEAR DEMOGRAPHIC DYNAMICS: MATHEMATICAL MODELS, STATISTICAL METHODS, AND BIOLOGICAL EXPERIMENTS' , 1995 .

[24]  James H. Matis,et al.  Stochastic Population Models , 2000 .

[25]  Jim M Cushing,et al.  The effect of periodic habitat fluctuations on a nonlinear insect population model , 1997 .

[26]  S. Utida,et al.  Population Fluctuation, an Experimental and Theoretical Approach , 1957 .

[27]  Jim M Cushing,et al.  Chaos in Ecology: Experimental Nonlinear Dynamics , 2002 .

[28]  Leah Edelstein-Keshet,et al.  Mathematical models in biology , 2005, Classics in applied mathematics.

[29]  Gábor Domokos,et al.  Random perturbations and lattice effects in chaotic population dynamics. , 2002, Science.

[30]  Robert A. Desharnais,et al.  Stable demographic limit cycles in laboratory populations of Tribolium castaneum , 1987 .

[31]  Jim M Cushing,et al.  A chaotic attractor in ecology: theory and experimental data , 2001 .

[32]  Jim M Cushing,et al.  Phase switching in population cycles , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[33]  P. Moran,et al.  Some remarks on animal population dynamics. , 1950, Biometrics.

[34]  R. F. Costantino,et al.  GENETIC ANALYSIS OF A POPULATION OF TRIBOLIUM: VII. STABILITY: RESPONSE TO GENETIC AND DEMOGRAPHIC PERTURBATIONS , 1980 .

[35]  Jim M Cushing,et al.  ESTIMATING CHAOS AND COMPLEX DYNAMICS IN AN INSECT POPULATION , 2001 .

[36]  R F Costantino,et al.  Nonlinear population dynamics: models, experiments and data. , 1998, Journal of theoretical biology.

[37]  R F Costantino,et al.  Resonant population cycles in temporally fluctuating habitats , 1998, Bulletin of mathematical biology.

[38]  Jim M Cushing,et al.  An interdisciplinary approach to understanding nonlinear ecological dynamics , 1996 .

[39]  Costantino,et al.  Moving toward an unstable equilibrium: saddle nodes in population systems , 1998 .

[40]  R M May,et al.  Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos , 1974, Science.