Theoretical Ecology

, Volume 9, Issue 4, pp 487–499 | Cite as

The effects of predation on seasonally migrating populations

ORIGINAL PAPER

Abstract

Interspecific interactions may occur for just a brief period each year before the populations involved become spatially separated. For instance, the range of a migrating population may overlap with that of a population of predators for a single season. In this work, we outline a framework for examining how this kind of ‘transient’ predation influences the dynamics of the prey population. A time-dependent switching system is used to partition the annual cycle into distinct segments. We then consider the effect of a single predatory interaction during a particular season, with the associated predators characterised as either generalists or specialists. We show that generalist predation potentially can allow multiple stable limit cycles to exist. Predation by specialists may cause prey abundance to oscillate over long time periods. This is shown to be a consequence of over-exploitation of newborn prey individuals. The habitat-based formulation extends naturally to the study of interannual variation in environmental conditions. We illustrate how such changes may cause migrant populations to undergo sudden changes in numbers that are not readily reversible.

Keywords

Seasonality Predation Migration Population dynamics Multi-stability 

References

  1. Adolfsson J, Dankowicz H, Nordmark A (2001) 3d passive walkers: finding periodic gaits in the presence of discontinuities. Nonlinear Dyn. 24:205–229CrossRefGoogle Scholar
  2. Andersen R, Karlsen I, Austmo LB, Odden J, Linnell J, Gaillard JM (2007) Selectivity of eurasian lynx Lynx lynx and recreational hunters for age, sex and body condition in roe deer Capreolus capreolus. Wildl Biol 13:467–474CrossRefGoogle Scholar
  3. Beddington JR (1975) Mutual interference between parasites or predators and its effect on searching efficiency. J Anim Ecol 44(1):331–340CrossRefGoogle Scholar
  4. Brunton DH (1986) Fatal antipredator behavior of a killdeer. Wilson Bull 98:605–607Google Scholar
  5. Charnov EL (1976) Optimal foraging: attack strategy of a mantid. Am Nat 110(971):141–151CrossRefGoogle Scholar
  6. Cox GW, Ricklefs RE (1977) Species diversity and ecological release in caribbean land bird faunas. Oikos 28:113–122CrossRefGoogle Scholar
  7. Dankowicz H, Piiroinen PT (2002) Exploiting discontinuities for stabilization of recurrent motions. Dyn Syst 17:317–342CrossRefGoogle Scholar
  8. Donohue JG, Piiroinen PT (2015) Mathematical modelling of seasonal migration with applications to climate change. Ecol Model 299:79–94CrossRefGoogle Scholar
  9. Dragesund O, Hamre J, Ulltang O (1980) Biology and population dynamics of the norwegian spring-spawning herring. Rapp PV Reun Cons Int Explor Mer 177:43–71Google Scholar
  10. Erbach A, Lutscher F, Seo G (2013) Bistability and limit cycles in generalist predator-prey dynamics. Ecol Complex 14:48–55CrossRefGoogle Scholar
  11. Fryxell JM, Sinclair ARE, Greever J (1988) Why are migratory ungulates so abundant? Am Nat 131 (6):781–798CrossRefGoogle Scholar
  12. Hastings A (1983) Age-dependent predation is not a simple process. i. continuous time models. Theor Popul Biol 23:347–362CrossRefGoogle Scholar
  13. Hastings A (2013) Multiple stable states and regime shifts in ecological systems. Mathematics Today February 2013:37–39Google Scholar
  14. Hilderbrand GV, Schwartz CC, Robins CT, Jacoby ME, Hanley TA, Arthur SM, Servheen C (1999) The importance of meat, particularly salmon, to body size, population productivity, and conservation of north american brown bears. Can J Zool 77:132–138CrossRefGoogle Scholar
  15. Holdo RM, Holt RD, Sinclair AR, Godley BJ, Thirgood S (2011) Migration impacts on communities and ecosystems: empirical evidence and theoretical insights. In: Milner-gulland EJ, Fryxell JM, Sinclair ARE (eds) Animal migration: a synthesis. Oxford University Press, pp 131–143Google Scholar
  16. Holling CS (1959a) The components of predation as revealed by a study of small-mammal predation of the european pine sawfly. Can Entomol 91(5):293–320Google Scholar
  17. Holling CS (1959b) Some characteristics of simple types of predation and parasitism. Can Entomol 91 (7):385–398Google Scholar
  18. Knopff KH, Knopff AA, Kortello A, Boyce MS (2010) Cougar kill rate and prey composition in a multiprey system. J Wildl Manag 74:1435–1447CrossRefGoogle Scholar
  19. Knudsen E, Lindén A, et al. (2011) Challenging claims in the study of migratory birds and climate change. Biol Rev 86:928–946CrossRefPubMedGoogle Scholar
  20. Kuznetsov YA (2004) Elements of applied bifurcation theory. Springer, New YorkCrossRefGoogle Scholar
  21. Lillegård M, Engen S, Sther BE, Toresen R (2005) Harvesting strategies for norwegian spring-spawning herring. Oikos 110:567– 577CrossRefGoogle Scholar
  22. Linnell JD, Aanes R, Andersen R (1995) Who killed bambi? The role of predation in the neonatal mortality of temperate ungulates. Wildl Biol 1(4):209–223Google Scholar
  23. O’Donoghue M, Boutin S, Krebs CJ, Zuleta G, Murray DL, Hofer EJ (1998) Functional responses of coyotes and lynx to the snowshoe hare cycle. Ecol 79(4):1193–1208CrossRefGoogle Scholar
  24. Panzacchi M, Linnell JDC, Odden J, Odden M, Andersen R (2008) When a generalist becomes a specialist: patterns of red fox predation on roe deer fawns under contrasting conditions. Can J Zool 86:116–126CrossRefGoogle Scholar
  25. Pavlová V, Berec L (2011) Impacts of predation on dynamics of age-structured prey: Allee effects and multi-stability. Theoretical Ecology 5:533–544CrossRefGoogle Scholar
  26. Rinaldi S, Muratori S, Kuznetsov Y (1993) Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities. Bull Math Biol 55:15–35CrossRefGoogle Scholar
  27. Ruelle D, Takens F (1971) On the nature of turbulence. Commun Math Phys 20:167–192CrossRefGoogle Scholar
  28. Samelius G, Alisauskas R T, Larivière S (2011) Seasonal pulses of migratory prey and annual variation in small mammal abundance affect abundance and reproduction by arctic foxes. Polar Biol 34:1475–1484CrossRefGoogle Scholar
  29. Sand H, Wabakken P, Zimmermann B, Johansson O, Pedersen HC, Liberg O (2008) Summer kill rates and predation pattern in a wolf-moose system: can we rely on winter estimates? Oecologia 156:53–64CrossRefPubMedGoogle Scholar
  30. Scheffer M, Rinaldi S, Kuznetsov YA, van Nes EH (1997) Seasonal dynamics of daphnia and algae explained as a periodically forced predator-prey system. Oikos 80:519–532CrossRefGoogle Scholar
  31. Seip DR (1992) Factors limiting woodland caribou populations and their interrelationships with wolves and moose in southeastern british columbia. Can J Zool 70(8):1494–1503CrossRefGoogle Scholar
  32. Smith WP (1987) Maternal defence in columbian white tailed deer: when is it worth it? Am Nat 130:310–316CrossRefGoogle Scholar
  33. Smout S, Asseburg C, Matthiopoulos J, Fernández C, Redpath S, Thirgood S, Harwood J (2010) The functional response of a generalist predator. PLoS ONE 5(5)Google Scholar
  34. Turchin P (2003) Complex population dynamics: a Theoretical/Empirical synthesis. Princeton University Press, PrincetonGoogle Scholar
  35. Van Leeuwen E, Brännström Å, Jansen VAA, Dieckmann U, Rossberg AG (2013) A generalized functional response for predators that switch between multiple prey species. J Theor Biol 328:89–98CrossRefPubMedGoogle Scholar
  36. Willson MF, Womble JN (2006) Vertebrate exploitation of pulsed marine prey: a review and the example of spawning herring. Rev Fish Biol Fish 16:183–200CrossRefGoogle Scholar
  37. Willson MF, Gende SM, Marston BH (1998) Fishes and the forest. Bioscience 48:455–462CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.MACSI, Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland
  2. 2.School of Mathematics, Statistics and Applied MathematicsNational University of Ireland, GalwayGalwayIreland

Personalised recommendations