Harvesting, census timing and "hidden" hydra effects

Ecological Complexity

Volumn 14, Issue , 2013, Pages 95-107

  Hilker, Frank M ^a   Liz, Eduardo ^b  

^a University of Bath   (United Kingdom)

^b UNIVERSITY OF VIGO   (Spain)

Author keywords

Constant feedback control; Hydra effect; Limiter control; Periodic difference equation; Population management

Indexed keywords

HYDRA;

EID: 84877110792     PISSN: 1476945X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ecocom.2013.02.002     Document Type: Article

References (64)

1. Abrams P.A. When does greater mortality increase population size? The long history and diverse mechanisms underlying the hydra effect. Ecology Letters 2009, 12:462-474.
2. Alligood K.T., Sauer T.D., Yorke J.A. Chaos. An Introduction to Dynamical Systems 1997, Springer, New York.
3. Åström M., Lundberg P., Lundberg S. Population dynamics with sequential density-dependencies. Oikos 1996, 75:174-181.
4. Bartmann R.M., White G.C., Carpenter L.H. Compensatory mortality in a Colorado mule deer population. Wildlife Monographs 1992, 121:1-39.
5. Beverton R.J.H., Holt S.J. On the Dynamics of Exploited Fish Populations. Vol. II of Fishery Investigations 1957, Ministry of Agriculture, Fisheries and Food.
6. Boyce M.S., Sinclair A.R.E., White G.C. Seasonal compensation of predation and harvesting. Oikos 1999, 87:419-426.
7. Braverman E., Liz E. Global stabilization of periodic orbits using a proportional feedback control with pulses. Nonlinear Dynamics 2012, 67:2467-2475.
8. Bunn D.W. Applied Decision Analysis 1984, McGraw-Hill, New York.
9. Cánovas J.S., Linero A., Peralta-Salas D. Dynamic Parrondo's paradox. Physica D 2006, 218:177-184.
10. Matrix Population Models. Construction, Analysis, and Interpretation 2001, Sinauer Associates, Sunderland, MA. H. Caswell (Ed.).
11. Clark C.W. Mathematical Bioeconomics. The Optimal Management of Renewable Resources 1990, John Wiley, New York.
12. Costa M.I., Faria L.D. Induced oscillations generated by protective threshold policies in the management of exploited populations. Natural Resource Modeling 2011, 24:183-206.
13. Costantino R.F., Cushing J.M., Dennis B., Desharnais R.A., Henson S.M. Resonant population cycles in temporally fluctuating habitats. Bulletin of Mathematical Biology 1998, 60:247-273.
14. Natural Enemies: The Population Biology of Predators, Parasites and Diseases 1992, Wiley-Blackwell, Oxford. M.J. Crawley (Ed.).
15. Cushing J.M., Henson S.M. Global dynamics of some periodically forced, monotone difference equations. Journal of Difference Equations and Applications 2001, 7:859-872.
16. Dattani J., Blake J.C.H., Hilker F.M. Target-oriented chaos control. Physics Letters A 2011, 375:3986-3992.
17. Doubleday W.G. Harvesting in matrix population models. Biometrics 1975, 31:189-200.
18. Elaydi S., Sacker R.J. Periodic difference equations, population biology and the Cushing-Henson conjectures. Mathematical Biosciences 2006, 201:195-207.
19. Elaydi S.N., Luís R., Oliveira H. Towards a theory of periodic difference equations and its application to population dynamics. Dynamics, Games and Science I 2011, 287-321. Springer, Berlin. A.A.P. Mauricio Matos Peixoto, D.A. Rand (Eds.).
20. Errington P.L. Vulnerability of Bob-White populations to predation. Ecology 1934, 15:110-127.
21. Errington P.L. Of Predation and Life 1971, Iowa State University Press, Ames, IA.
22. Eskola H.T.M., Geritz S.A.H. On the mechanistic derivation of various discrete-time population models. Bulletin of Mathematical Biology 2007, 69:329-346.
23. Franco, D., Liz, E., 2013. A two-parameter method for chaos control and targeting in one-dimensional maps. International Journal of Bifurcation and Chaos 23, 1350003.
24. Franco D., Perán J. Stabilization of population dynamics via threshold harvesting strategies. Ecological Complexity 2013, 14:85-94.
25. Freckleton R.P., Silva Matos D.M., Bovi M.L.A., Watkinson A.R. Predicting the impacts of harvesting using structured population models: the importance of density-dependence and timing of harvest for a tropical palm tree. Journal of Applied Ecology 2003, 40:846-858.
26. Henson S.M., Cushing J.M. The effect of periodic habitat fluctuations on a nonlinear insect population model. Journal of Mathematical Biology 1997, 36:201-226.
27. Hilborn R., Walters C.J., Ludwig D. Sustainable exploitation of renewable resources. Annual Review of Ecology and Systematics 1995, 26:45-67.
28. Hilker F.M., Westerhoff F.H. Paradox of simple limiter control. Physical Review E 2006, 73:052901.
29. Hilker F.M., Westerhoff F.H. Preventing extinction and outbreaks in chaotic populations. American Naturalist 2007, 170:232-241.
30. Hone J. Analysis of Vertebrate Pest Control 2007, Cambridge University Press, Cambridge.
31. Jonzén N., Lundberg P. Temporally structured density dependence and population management. Annales Zoologici Fennici 1999, 36:39-44.
32. Kokko H. Optimal and suboptimal use of compensatory responses to harvesting: timing of hunting as an example. Wildlife Biology 2001, 7:141-150.
33. Kokko H., Lindström J. Seasonal density dependence, timing of mortality, and sustainable harvesting. Ecological Modelling 1998, 110:293-304.
34. Kon R. Attenuant cycles of population models with periodic carrying capacity. Journal of Difference Equations and Applications 2005, 11:423-430.
35. Kot M., Schaffer W.M. The effects of seasonality on discrete models of population growth. Theoretical Population Biology 1984, 26:340-360.
36. Liz E. Complex dynamics of survival and extinction in simple population models with harvesting. Theoretical Ecology 2010, 3:209-221.
37. Liz E. How to control chaotic behaviour and population size with proportional feedback. Physics Letters A 2010, 374:725-728.
38. Liz E., Pilarczyk P. Global dynamics in a stage-structured discrete-time population model with harvesting. Journal of Theoretical Biology 2012, 297:148-165.
39. Liz E., Ruiz-Herrera A. The hydra effect, bubbles, and chaos in a simple discrete population model with constant effort harvesting. Journal of Mathematical Biology 2012, 65:997-1016.
40. Lutscher F., Petrovskii S.V. The importance of census times in discrete-time growth-dispersal models. Journal of Biological Dynamics 2008, 2:55-63.
41. Mertens S.K., Yearsley J.M., van den Bosch F., Gilligan C.A. Transient population dynamics in periodic matrix models: methodology and effects of cyclic permutations. Ecology 2006, 87:2338-2348.
42. Milner J.M., Bonenfant C., Mysterud A. Hunting Bambi-evaluating the basis for selective harvesting of juveniles. European Journal of Wildlife Research 2011, 57:565-574.
43. Milner-Gulland E.J., Mace R. Conservation of Biological Resources 1998, Wiley-Blackwell, Malden.
44. Nicholson J.D. Responses of North American duck populations to exploitation. Bird Population Studies: Relevance to Conservation and Management 1991, 498-525. Oxford University Press, Oxford. C.M. Perrins, J.-D. Lebreton, G.J.M. Hirons (Eds.).
45. Peacock-López E. Seasonality as a Parrondian game. Physics Letters A 2011, 375:3124-3129.
46. Pötzsche C. Bifurcations in a periodic discrete-time environment. Nonlinear Analysis: Real World Applications 2013, 14:53-82.
47. Pöysä H., Elmberg J., Gunnarsson G., Nummi P., Sjöberg G.G., Sjöberg K. Ecological basis of sustainable harvesting: is the prevailing paradigm of compensatory mortality still valid?. Oikos 2004, 104:612-615.
48. Putman R.J., Moore N.P. Impact of deer in lowland Britain on agriculture, forestry and conservation habitats. Mammal Review 1998, 28:141-164.
49. Ratikainen I.I., Gill J.A., Gunnarsson T.G., Sutherland W.J., Kokko H. When density dependence is not instantaneous: theoretical developments and management implications. Ecology Letters 2008, 11:184-198.
50. Reis M.S., Fantini A.C., Nodari R.O., Reis A., Guerra M.P., Mantovani A. Management and conservation of natural populations in Atlantic rain forest: the case study of palm heart (Euterpe eduli Martius). Biotropica 2000, 32:894-902.
51. Ricker W.E. Stock and recruitment. Journal of Fisheries Research Board of Canada 1954, 11:559-623.
52. Robinette W.L., Hancock N.V., Jones D.A. The Oak Creek mule deer herd in Utah 1977, Utah State Division of Wildlife Resources, Salt Lake City.
53. Sandercock B.K., Nilsen E.B., Brøseth H., Pedersen H.C. Is hunting mortality additive or compensatory to natural mortality? Effects of experimental harvest on the survival and cause-specific mortality of willow ptarmigan. Journal of Animal Ecology 2011, 80:244-258.
54. Schreiber S.J. Chaos and population disappearances in simple ecological models. Journal of Mathematical Biology 2001, 42:239-260.
55. Seno H. A paradox in discrete single species population dynamics with harvesting/thinning. Mathematical Biosciences 2008, 214:63-69.
56. Sieber M., Hilker F.M. The hydra effect in predator-prey models. Journal of Mathematical Biology 2012, 64:341-360.
57. Simberloff D. How much information on population biology is needed to manage introduced species?. Conservation Biology 2003, 17:83-92.
58. Sinha S. Unidirectional adaptive dynamics. Physical Review E 1994, 49:4832-4842.
59. Sinha S., Parthasarathy S. Unusual dynamics of extinction in a simple ecological model. Proceedings of the National Academy of Sciences of the United States of America 1996, 93:1504-1508.
60. Stoop R., Wagner C. Scaling properties of simple limiter control. Physical Review Letters 2003, 90:154101.
61. Struhsaker T.T. A biologists perspective on the role of sustainable harvest in conservation. Conservation Biology 1998, 12:930-932.
62. Vandermeer J., Yodzis P. Basin boundary collision as a model of discontinuous change in ecosystems. Ecology 1999, 80:1817-1827.
63. Yakubu A.-A., Li N., Conrad J.M., Zeeman M.-L. Constant proportion harvest policies: dynamic implications in the Pacific halibut and Atlantic cod fisheries. Mathematical Biosciences 2011, 232:66-77.
64. Zipkin E.F., Kraft C.E., Cooch E.G., Sullivan P.J. When can efforts to control nuisance and invasive species backfire?. Ecological Applications 2009, 19:1585-1595.