A focus on long-run sustainability of a harvested prey predator system in the presence of alternative prey.

Within the framework of a general equilibrium model we study the long-run dynamics of a prey-predator model in the presence of an alternative prey. Our results show that sustainability, i.e. a positive value of the population in the long run, essentially depends on individual harvesting efforts and digesting factors relative to alternative prey. A detailed bifurcation analysis evidences the richness of possible long-run dynamics. Our model clearly shows that the role of an alternative prey must be taken into consideration when studying prey-predator dynamics.

[1]  Gian Italo Bischi,et al.  The Role of Competition, Expectations and Harvesting Costs in Commercial Fishing , 2002 .

[2]  J. Hale,et al.  Ordinary Differential Equations , 2019, Fundamentals of Numerical Mathematics for Physicists and Engineers.

[3]  Peeyush Chandra,et al.  A model for fishery resource with reserve area , 2003 .

[4]  P. Spencer,et al.  A simple predator–prey model of exploited marine fish populations incorporating alternative prey , 1996 .

[5]  K. S. Chaudhuri,et al.  On non-selective harvesting of a multispecies fishery , 2002 .

[6]  Vito Fragnelli,et al.  Game practice and the environment , 2004 .

[7]  R. Vance,et al.  Predation and Resource Partitioning in One Predator -- Two Prey Model Communities , 1978, The American Naturalist.

[8]  Tönu Puu,et al.  Oligopoly Dynamics : Models and Tools , 2002 .

[9]  Leonard J. Mirman,et al.  Externalities, Market Power, and Resource Extraction , 1999 .

[10]  Sze-Bi Hsu,et al.  Some results on global stability of a predator-prey system , 1982 .

[11]  Colin W. Clark,et al.  Mathematical Bioeconomics: The Optimal Management of Renewable Resources. , 1993 .

[12]  P. Abrams,et al.  Positive Indirect Effects Between Prey Species that Share Predators , 1996 .

[13]  Mike Mesterton-Gibbons,et al.  GAME‐THEORETIC RESOURCE MODELING , 1993 .

[14]  C. S. Holling,et al.  The functional response of predators to prey density and its role in mimicry and population regulation. , 1965 .

[15]  C Feliziani,et al.  The tragedy of commons , 2011 .

[16]  H. Gordon,et al.  The economic theory of a common-property resource: The fishery , 1954, Journal of Political Economy.

[17]  J. M. Nelsen,et al.  Clinical and psychological effects of marihuana in man. , 1968, Science.