An interdisciplinary approach to understanding nonlinear ecological dynamics

Abstract We describe a research program which covers a spectrum of activities essential to testing nonlinear population theory: from the translation of the biology into the formal language of mathematics, to the analysis of mathematical models, to the development and application of statistical techniques for the analysis of data, to the design and implementation of biological experiments. The statistical analyses, mathematics, and biology are thoroughly integrated. We review several aspects of our current research effort that demonstrate this integration.

[1]  P. Holgate,et al.  Matrix Population Models. , 1990 .

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

[3]  D. B. Mertz,et al.  Cannibalism of Pupae by Mixed-Species Populations of Adult Tribolium , 1970, Physiological Zoology.

[4]  Ganapati P. Patil,et al.  The gamma distribution and weighted multimodal gamma distributions as models of population abundance , 1984 .

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

[6]  Brian Dennis,et al.  Analysis of Steady‐State Populations With the Gamma Abundance Model: Application to Tribolium , 1988 .

[7]  Ramón Margalef.  Perspectives in Ecological Theory , 1968 .

[8]  J. Neyman,et al.  Struggle for Existence. The Tribolium Model: Biological and Statistical Aspects , 1956 .

[9]  J. C. Allen,et al.  Nonlinear Dynamics and Chaos in Insect Populations , 1992 .

[10]  Jesse A. Logan,et al.  Chaos and insect ecology , 1990 .

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

[12]  Peter Kareiva,et al.  5. Renewing the Dialogue between Theory and Experiments in Population Ecology , 1989 .

[13]  Brian Dennis,et al.  Estimation of Growth and Extinction Parameters for Endangered Species , 1991 .

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

[15]  C. E. King,et al.  Population Biology and the Tribolium Model , 1972 .

[16]  R. Costantino,et al.  GAMMA DISTRIBUTIONS OF ADULT NUMBERS FOR TRIBOLIUM POPULATIONS IN THE REGION OF THEIR STEADY STATES , 1981 .

[17]  R. May,et al.  Bifurcations and Dynamic Complexity in Simple Ecological Models , 1976, The American Naturalist.

[18]  R. Costantino,et al.  Genetic analysis of a population of Tribolium. IX: Maximization of population size and the concept of a stochastic equilibrium , 1990 .

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

[20]  Royal N. Champman.  The Quantitative Analysis of Environmental Factors , 1928 .

[21]  David B. Mertz,et al.  THE TRIBOLIUM MODEL AND THE MATHEMATICS 4036 OF POPULATION GROWTH , 1972 .

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

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

[24]  Jim M Cushing,et al.  NONLINEAR MATRIX MODELS AND POPULATION DYNAMICS , 1988 .

[25]  S. Ellner,et al.  Chaos in Ecology: Is Mother Nature a Strange Attractor?* , 1993 .

[26]  D. B. Mertz,et al.  The Cannibalism of Pupae by Adult Flour Beetles , 1968, Physiological Zoology.

[27]  Brian Dennis,et al.  ALLEE EFFECTS: POPULATION GROWTH, CRITICAL DENSITY, AND THE CHANCE OF EXTINCTION , 1989 .

[28]  M. Bartlett.  Chance or Chaos , 1990 .

[29]  Nelson G. Hairston,et al.  Ecological Experiments: Purpose, Design and Execution , 1989 .

[30]  H. I. Freedman.  Deterministic mathematical models in population ecology , 1982 .