Research article Special Issues

Dynamics and spatio-temporal patterns in a prey–predator system with aposematic prey

  • Received: 20 February 2019 Accepted: 26 April 2019 Published: 01 May 2019
  • We analyze the impact of aposematic time and searching efficiency of prey on the temporal and spatio-temporal dynamics of a diffusive prey-predator system. Here, our assumption is that the prey population primarily invests its total time in two activities——(ⅰ) defense against predation and (ⅱ) searching for food, followed by growth-induced reproduction, whereas, predators do not involve in self-defense. Moreover, we consider that the reproduction rate of prey and the rate of predation have a negative linear correlation with the amount of time invested for aposematism. Based on the presumptions, we find that unlike searching efficiency of prey, the aposematic time can diminish the proportion in which prey and predator coexist when it crosses a certain threshold, and at the extreme aposematism, the entire population drives into the extinction. The proposed dynamics undergoes Hopf-bifurcation with respect to the searching efficiency of prey. We examine the individual effect of aposematic time and searching efficiency on the formation of regular Turing patterns——the low to medium to high values of defense-time and food searching efficiency generate 'spots' to 'stripes' to 'holes' pattern, respectively; however, the combined impact of both presents only non-Turing 'spot' pattern with the 'predominance of predators, ' which happens through the Turing-Hopf bifurcation.

    Citation: Sourav Kumar Sasmal, Jeet Banerjee, Yasuhiro Takeuchi. Dynamics and spatio-temporal patterns in a prey–predator system with aposematic prey[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3864-3884. doi: 10.3934/mbe.2019191

    Related Papers:

  • We analyze the impact of aposematic time and searching efficiency of prey on the temporal and spatio-temporal dynamics of a diffusive prey-predator system. Here, our assumption is that the prey population primarily invests its total time in two activities——(ⅰ) defense against predation and (ⅱ) searching for food, followed by growth-induced reproduction, whereas, predators do not involve in self-defense. Moreover, we consider that the reproduction rate of prey and the rate of predation have a negative linear correlation with the amount of time invested for aposematism. Based on the presumptions, we find that unlike searching efficiency of prey, the aposematic time can diminish the proportion in which prey and predator coexist when it crosses a certain threshold, and at the extreme aposematism, the entire population drives into the extinction. The proposed dynamics undergoes Hopf-bifurcation with respect to the searching efficiency of prey. We examine the individual effect of aposematic time and searching efficiency on the formation of regular Turing patterns——the low to medium to high values of defense-time and food searching efficiency generate 'spots' to 'stripes' to 'holes' pattern, respectively; however, the combined impact of both presents only non-Turing 'spot' pattern with the 'predominance of predators, ' which happens through the Turing-Hopf bifurcation.


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    [1] R. M. May, Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos, Science, 186 (1974), 645–647.
    [2] J. Banerjee, S. K. Sasmal and R. K. Layek, Supercritical and subcritical Hopf-bifurcations in a two-delayed prey–predator system with density-dependent mortality of predator and strong Allee effect in prey, BioSystems, 180 (2019), 19–37.
    [3] S. K. Sasmal, Population dynamics with multiple Allee effects induced by fear factors–A mathe-matical study on prey–predator interactions, Appl. Math. Model., 64 (2018), 1–14.
    [4] J. Banerjee, T. Ranjan and R. K. Layek, Dynamics of cancer progression and suppression: A novel evolutionary game theory based approach, 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), (2015), 5367–5371.
    [5] J. Banerjee, T. Ranjan and R. K. Layek, Stability Analysis of Population Dynamics Model in
    [6] Microbial Biofilms with Non-participating Strains, 7th ACM International Conference on Bioin-formatics, Computational Biology, and Health Informatics, (201, 220–230.
    [7] 6. M. Wang, A. L. Schaefer, A. A. Dandekar, et al., Quorum sensing and policing of Pseudomonas aeruginosa social cheaters, Proceed. Nat. Aca. Sci., 112 (2015), 2182191.
    [8] 7. J. Banerjee, R. K. Layek, S. K. Sasmal, et al., Delayed evolutionary model for public goods competition with policing in phenotypically-variant bacterial biofilms, Europhys. Let., (2019) (in press).
    [9] 8. M. Stevens and G. D. Ruxton, Linking the evolution and form of warning coloration in nature, Proceed. Royal Soc. B Biol. Sci., 27(2011), 417–426.
    [10] 9. J. Skelhorn, C. G. Halpin and C. Rowe, Learning about aposematic prey, Behav. Ecol., 27 (2016), 955–964.
    [11] 10. J. Skelhorn and C. Rowe, Predators' toxin burdens influence their strategic decisions to eat toxic prey, Curr. Biol., 17 (2007), 1479–1483.
    [12] 11. C. G. Halpin, J. Skelhorn and C. Rowe, Predators' decisions to eat defended prey depend on the size of undefended prey, Animal Behav., 85 (2013), 1315–1321.
    [13] 12. K. E. Smith, C. G. Halpin and C. Rowe, Body size matters for aposematic prey during predator aversion learning, Behav. Process., 109 (2014), 173–179.
    [14] 13. J. E. Huheey, Mathematical models of mimicry, Am. Nat., 131 (1988), S22–S41.
    [15] 14. J. C. Santos, L. A. Coloma and D. C. Cannatella, Multiple, recurring origins of aposematism and diet specialization in poison frogs, Proceed. Nat. Aca. Sci., 100 (2003), 12792–12797.
    [16] 15. R. A. Saporito, R. Zuercher, M. Roberts, et al., Experimental evidence for aposematism in the dendrobatid poison frog Oophaga pumilio, Copeia, 2007 (2007), 1006–1011.
    [17] 16. J. C. Santos and D. C. Cannatella, Phenotypic integration emerges from aposematism and scale in poison frogs, Proceed. Nat. Aca. Sci., 108 (2011), 6-6180.
    [18] 17. E. D. Brodie III, Differential avoidance of coral snake banded patterns by free-ranging avian predators in Costa Rica, Evolution, 47 (1993), 227–235.
    [19] 18. Y. Takeuchi, W. Wang, S. Nakaoka, et al., Dynamical adaptation of parental care, Bull. Math. Biol., 71 (2009), 931–951.
    [20] 19. S. Chakraborty, P. K. Tiwari, S. K. Sasmal, et al., Interactive effects of prey refuge and additional food for predator in a diffusive predator-prey system, Appl. Math. Model., 47 (7), 128–140.
    [21] 20. D. Alonso, F. Bartumeus and J. Catalan, Mutual interference between predators can give rise to Turing spatial patterns, Ecology, 83 (2002), 28–34.
    [22] 21. J. R. Meyer, S. P. Ellner, N. G. Hairston, et al., Prey evolution on the time scale of predator–prey dynamics revealed by allele-specific quantitative PCR, Proceed. Nat. Aca. Sci., 103 (2006), 10690–10695.
    [23] 22. L. Lindström, R. V. Alatalo, J. Mappes, et al., Can aposematic signals evolve by gradual change?, Nature, 397 (1999), 249–251.
    [24] 23. J. Gohli and G. Högstedt, Explaining the evolution of warning coloration: Secreted secondary defence chemicals may facilitate the evolution of visual aposematic signals, PLoS One, 4 (2009), e5779.
    [25] 24. J. B. Barnett, C. Michalis, N. E. Scott-Samuel, et al., Distance-dependent defensive coloration in the poison frog Dendrobates tinctorius, Dendrobatidae, Proceed. Nat. Aca. Sci., 115 (2018), 6416–6421.
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