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Intraguild predation with evolutionary dispersal in a spatially heterogeneous environment

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Abstract

In many cases, the motility of species in a certain region can depend on the conditions of the local habitat, such as the availability of food and other resources for survival. For example, if resources are insufficient, the motility rate of a species is high, as they move in search of food. In this paper, we present intraguild predation (IGP) models with a nonuniform random dispersal, called starvation-driven diffusion, which is affected by the local conditions of habitats in heterogeneous environments. We consider a Lotka–Volterra-type model incorporating such dispersals, to understand how a nonuniform random dispersal affects the fitness of each species in a heterogeneous region. Our conclusion is that a nonuniform dispersal increases the fitness of species in a spatially heterogeneous environment. The results are obtained through an eigenvalue analysis of the semi-trivial steady state solutions for the linearized operator derived from the model with nonuniform random diffusion on IGPrey and IGPredator, respectively. Finally, a simulation and its biological interpretations are presented based on our results.

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References

  • Amarasekare P (2000) Coexistence of competing parasitoids on a patchily distributed host: local vs. spatial mechanisms. Ecology 81:1286–1296

    Article  Google Scholar 

  • Amarasekare P (2003) Diversity–stability relationships in multi-trophic systems: an empirical exploration. J Anim Ecol 72:713–724

    Article  Google Scholar 

  • Amarasekare P (2006) Productivity, dispersal and the coexistence of intraguild predators and prey. J Theor Biol 243:121–133

    Article  MathSciNet  Google Scholar 

  • Amarasekare P (2007) Spatial dynamics of communities with intraguild predation: the role of dispersal strategies. Am Nat 170:819–831

    Article  Google Scholar 

  • Ambrose W (1984) Role of predatory infauna in structuring marine soft-bottom communities. Mar Ecol Prog Ser 17:109–115

    Article  Google Scholar 

  • Arim M, Marquet P (2004) Intraguild predation: a widespread interaction related to species biology. Ecol Lett 7:557–564

    Article  Google Scholar 

  • Bampfylde CJ, Lewis MA (2007) Biological control through intraguild predation: case studies in pest control, invasive species and range expansion. Bull Math Biol 69:1031–1066

    Article  MathSciNet  MATH  Google Scholar 

  • Cantrell RS, Cosner C (2003) Wiley series in mathematical and computational biology. Spatial ecology via reaction–diffusion equations. Wiley, Chichester

    MATH  Google Scholar 

  • Cho E, Kim Y-J (2013) Starvation driven diffusion as a survival strategy of biological organisms. Bull Math Biol 76(5):845–870

    Article  MathSciNet  MATH  Google Scholar 

  • Choi W, Ahn I (2018) Evolutionary dispersal in a predator-prey interaction system with spatially heterogeneous environment (preprint)

  • Choi W, Ahn I (2019) Strong competition model with non-uniform dispersal in a heterogeneous environment. Appl Math Lett 88:96–102

    Article  MathSciNet  MATH  Google Scholar 

  • Cohen D, Levin SA (1991) Dispersal in patchy environments: the effects of temporal and spatial structure. Theor Popul Biol 39(1):63–99

    Article  MathSciNet  MATH  Google Scholar 

  • Dieckman U, OHara B, Weisser W (1999) The evolutionary ecology of dispersal. Trends Ecol Evol 14(3):88–90

    Article  Google Scholar 

  • Diehl S, Feissel M (2000) Effects of enrichment on three-level food chains with omnivory. Am Nat 155:200–218

    Google Scholar 

  • Dockery J, Hutson V, Mischaikow K, Pernarowski M (1998) The evolution of slow dispersal rates: a reaction diffusion model. J Math Biol 37(1):61–83

    Article  MathSciNet  MATH  Google Scholar 

  • Doncaster CP (1992) Testing the role of intraguild predation in regulating hedgehog populations. Proc R Soc Lond B 249:113–117

    Article  Google Scholar 

  • Holt R, McPeek M (1996) Chaotic population dynamics favors the evolution of dispersal. Am Nat 148:709–718

    Article  Google Scholar 

  • Holt R, Polis G (1997) A theoretical framework for intraguild predation. Am Nat 149:745–764

    Article  Google Scholar 

  • Hutson V, Mischaikow K, Polcik P (2001) The evolution of dispersal rates in a heterogeneous time-periodic environment. J Math Biol 43(6):501–533

    Article  MathSciNet  MATH  Google Scholar 

  • Johansson F (1993) Intraguild predation and cannibalism in odonate larvae: effects of foraging behaviour and zooplankton availability. Oikos 66:80–87

    Article  Google Scholar 

  • Johnson M, Gaines M (1990) Evolution of dispersal: theoretical models and empirical tests using birds and mammels. Annu Rev Ecol Syst 21:449–480

    Article  Google Scholar 

  • Keeling M (1999) Spatial models of interacting populations. In: McGlade J (ed) Advanced ecological theory: principles and applications. Blackwell Science, Oxford

    Google Scholar 

  • Kim Y-J, Kwon O (2016) Evolution of dispersal with starvation measure and coexistence. Bull Math Biol 78:254279

    Article  MathSciNet  MATH  Google Scholar 

  • Kim Y-J, Kwon O, Li F (2013) Evolution of dispersal toward fitness. Bull Math Biol 75:2472–2498

    MathSciNet  MATH  Google Scholar 

  • Kim Y-J, Kwon O, Li F (2014) Global asymptotic stability and the ideal free distribution in a starvation driven diffusion. J Math Biol 68:1341–1370

    Article  MathSciNet  MATH  Google Scholar 

  • Ko W, Ryu K (2009) Coexistence states of a nonlinear Lotka–Volterra type predator–prey model with cross-diffusion. Nonlinear Anal 71(12):1109–1115

    Article  MathSciNet  MATH  Google Scholar 

  • Kwon D, Kim Y (2015) The effect of starvation driven diffusion in a prey–predator model [Video file]. https://www.youtube.com/watch?v=-YdHlPvQuEc. Accessed 20 Oct 2017

  • Lam KY, Lou Y (2014) Evolutionary stable and convergent stable strategies in reaction–diffusion models for conditional dispersal. Bull Math Biol 76:261–291

    Article  MathSciNet  MATH  Google Scholar 

  • Lam KY, Ni WM (2010) Limiting profiles of semilinear elliptic equations with large advection in population dynamics. Discrete Contin Dyn Syst 28:1051–1067

    Article  MathSciNet  MATH  Google Scholar 

  • Leibold MA, Holyoak M, Mouquet N, Amarasekare P, Chase JM, Hoopes MF, Hold RD et al (2004) The metacommunity concept: a framework for multi-scale community ecology. Ecol Lett 7:601–613

    Article  Google Scholar 

  • MacNeil C, Prenter J, Briffa M, Fielding NJ, Dick JTA, Riddell G (2004) The replacement of a native freshwater amphipod by an invader: roles for differential environmental degradation and intraguild predation. Can J Fish Aquat Sci 61:1627–1635

    Article  Google Scholar 

  • McPeek M, Holt R (1992) The evolution of dispersal in spatially and temporally varying environments. Am Nat 140:1010–1027

    Article  Google Scholar 

  • Nagylaki T (1992) Biomathematics: introduction to theoretical population genetics, vol 21. Springer, Berlin

    Book  MATH  Google Scholar 

  • Ni W-M (2011) CBMS-NSF regional conference series in applied mathematics: the mathematics of diffusion, vol 82. SIAM, Philadelphia

    Google Scholar 

  • Noonburg E, Abrams PA (2005) Transient dynamics and prey species coexistence with shared resources and predator. Am Nat 165:322–335

    Article  Google Scholar 

  • Okubo A, Levin SA (2001) Interdisciplinary applied mathematics. Diffusion and ecological problems: modern perspectives, vol 14, 2nd edn. Springer, New York

    Book  Google Scholar 

  • Polis GA, Holt RD (1992) Intraguild predation: the dynamics of complex trophic interactions. Trends Ecol Evol 7:151–154

    Article  Google Scholar 

  • Polis GA, McCormick SJ (1987) Intraguild predation and competition among desert scorpions. Ecology 68(2):332–343

    Article  Google Scholar 

  • Polis GA, Myers CA, Holt RD (1989) The ecology and evolution of intraguild predation Potential competitors that eat each other. Annu Rev Ecol Syst 20:297–330

    Article  Google Scholar 

  • Ryan D, Cantrell RS (2015) Avoidance behavior in intraguild predation communities: a cross-diffusion model. DCDS 35:1641–1663

    Article  MathSciNet  MATH  Google Scholar 

  • Sieber M, Hilker F (2011) Prey, predators, parasites: Intraguild predation or simpler community modules in disguise? J Anim Ecol 80:414–421

    Article  Google Scholar 

  • Skellam JG (1972) The formulation and interpretation of mathematical models of diffusionary processes in population biology, the mathematical theory of the dynamics of biological population. Academic Press, New York

    Google Scholar 

  • Travis JMJ, Dytham C (1999) Habitat persistence, habitat availability and the evolution of dispersal. Proc R Soc Lond B 266:723–728

    Article  Google Scholar 

  • Wissinger SA, Sparks GB, Rouse GL, Brown WS, Steltzer H (1996) Intraguild predation and cannibalism among larvae of detritivorous caddisflies in subalpine wetlands. Ecology 77:2421–2430

    Article  Google Scholar 

  • Zwolfer H (1971) The structure and effect of parasite complexes attacking phytophagous host insects. In: den Boer PJ, Gradwell GR (eds) Dynamics of populations. PUDOC, Wageningen, pp 405–418

    Google Scholar 

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Acknowledgements

The authors thank the referee for careful reading and valuable comments which have helped to improve the presentation of this paper. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT & Future Planning (No. NRF-2015R1A2A2A01007013) and partially by NRF Grant (No. 2017R1E1A1A03070652) funded by the Korea Government (MSIT).

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  1. Department of Mathematics, Korea University, 145, Anam-ro, Seoul, 02841, Korea

    Wonhyung Choi

  2. Department of Mathematics, Korea University, 2511, Sejong-ro, Sejong, 30019, Korea

    Seunghyeon Baek & Inkyung Ahn

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  1. Wonhyung Choi
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  2. Seunghyeon Baek
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  3. Inkyung Ahn
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Correspondence to Inkyung Ahn.

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Choi, W., Baek, S. & Ahn, I. Intraguild predation with evolutionary dispersal in a spatially heterogeneous environment. J. Math. Biol. 78, 2141–2169 (2019). https://doi.org/10.1007/s00285-019-01336-5

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