Control of structured populations by harvest

It has long been recognized that demographic structure within a population can significantly affect the likely outcomes of harvest. Many studies have focussed on equilibrium dynamics and maximization of the value of the harvest taken. However, in some cases the management objective is to maintain the population at a abundance that is significantly below the carrying capacity. Achieving such an objective by harvest can be complicated by the presence of significant structure (age or stage) in the target population. In such cases, optimal harvest strategies must account for differences among age- or stage-classes of individuals in their relative contribution to the demography of the population. In addition, structured populations are also characterized by transient non-linear dynamics following perturbation, such that even under an equilibrium harvest, the population may exhibit significant momentum, increasing or decreasing before cessation of growth. Using simple linear time-invariant models, we show that if harvest levels are set dynamically (e.g., annually) then transient effects can be as or more important than equilibrium outcomes. We show that appropriate harvest rates can be complicated by uncertainty about the demographic structure of the population, or limited control over the structure of the harvest taken.

[1]  Alvin L. Jensen,et al.  Density-dependent matrix yield equation for optimal harvest of age-structured wildlife populations , 1996 .

[2]  J. Grand,et al.  Population Momentum: Implications for Wildlife Management , 2006 .

[3]  Cindy E. Hauser,et al.  Optimal control of Atlantic population Canada geese , 2005 .

[4]  J. Grand,et al.  Population momentum across vertebrate life histories , 2006 .

[5]  E. Milner‐Gulland A population model for the management of the saiga antelope , 1994 .

[6]  J. Gurevitch,et al.  Population Numbers Count: Tools for Near‐Term Demographic Analysis , 2000, The American Naturalist.

[7]  H. Campa,et al.  White-tailed deer management options model (DeerMOM): design, quantification, and application , 1999 .

[8]  Wayne M. Getz,et al.  Population harvesting: demographic models of fish, forest, and animal resources. , 1990 .

[9]  W. G. Doubleday HARVESTING IN MATRIX POPULATION MODELS , 1975 .

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

[11]  ON THE RELATION BETWEEN REPRODUCTIVE VALUE AND OPTIMAL PREDATION. , 1960, Proceedings of the National Academy of Sciences of the United States of America.

[12]  W. Getz The Ultimate-Sustainable-Yield Problem in Nonlinear Age-Structured Populations* , 1980 .

[13]  J. Lebreton,et al.  Optimizing removals to control a metapopulation: application to the yellow legged herring gull (Larus cachinnans) , 2001 .

[14]  B K Williams,et al.  Adaptive optimization and the harvest of biological populations. , 1996, Mathematical biosciences.

[15]  G. Manson,et al.  HARVESTING STRATEGIES FOR AGE-STABLE POPULATIONS , 1981 .

[16]  William J. Reed,et al.  Optimum Age-Specific Harvesting in a Nonlinear Population Model , 1980 .

[17]  Chris Rorres,et al.  Optimal harvesting policy for an age-specific population , 1975 .

[18]  J. Grand,et al.  Transient population dynamics:relations to life history and initial population state , 2005 .

[19]  Bernt-Erik Sæther,et al.  Optimal harvest of age-structured populations of moose Alces alces in a fluctuating environment , 2001, Wildlife Biology.

[20]  Ray Hilborn,et al.  The Influence of Model Structure on Conclusions about the Viability and Harvesting of Serengeti Wildebeest , 1997 .

[21]  Alvin L. Jensen,et al.  Sex and age structured matrix model applied to harvesting a white tailed deer population , 2000 .

[22]  Carl J. Walters,et al.  Adaptive Management of Renewable Resources , 1986 .

[23]  E. Seneta Non-negative Matrices and Markov Chains , 2008 .

[24]  R. M. Arthur ON THE RELATION BETWEEN REPRODUCTIVE VALUE AND OPTIMAL PREDATION. , 1960 .

[25]  J. Beddington,et al.  356 NOTE: Optimum Age Specific Harvesting of a Population , 1973 .

[26]  F. Johnson,et al.  MANAGING NORTH AMERICAN WATERFOWL IN THE FACE OF UNCERTAINTY , 1995 .

[27]  C. Hunter,et al.  THE IMPORTANCE OF ENVIRONMENTAL VARIABILITY AND MANAGEMENT CONTROL ERROR TO OPTIMAL HARVEST POLICIES , 2004 .

[28]  E. Milner‐Gulland,et al.  Sex‐Biased Harvesting and Population Dynamics in Ungulates: Implications for Conservation and Sustainable Use , 1994 .

[29]  R. A. Fisher,et al.  The Genetical Theory of Natural Selection , 1931 .

[30]  A Population Dynamics Model for the Management of Buffon's kob (Kobus kob kob) in the Bénoué National Park Complex, Cameroon , 2004 .

[31]  E. J. Milner-Gulland,et al.  A STOCHASTIC DYNAMIC PROGRAMMING MODEL FOR THE MANAGEMENT OF THE SAIGA ANTELOPE , 1997 .

[32]  Max Stocker,et al.  Ungulate population dynamics and optimization models , 1983 .