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Keywords:
phase shift; coral bleaching; harvesting; Hopf bifurcation
phase shift; coral bleaching; harvesting; Hopf bifurcation
Summary:
Coral reefs can undergo relatively rapid changes in the dominant biota, a phenomenon referred to as phase shift. Degradation of coral reefs is often associated with changes in community structure towards a macroalgae-dominated reef ecosystem due to the reduction in herbivory caused by overfishing. We investigate the coral-macroalgal phase shift due to the effects of harvesting of herbivorous reef fish by means of a continuous time model in the food chain. Conditions for local asymptotic stability of steady states are derived. We have shown that under certain conditions the system is uniformly persistent in presence of all the organisms. Moreover, it is shown that the system undergoes a Hopf bifurcation when the carrying capacity of macroalgae crosses certain critical value. Computer simulations have been carried out to illustrate different analytical results.
References:
[1] Bender, D., Diaz-Pulido, G., Dove, S.: Effects of macroalgae on corals recovering from disturbance. J. Exp. Mar. Biol. Ecol. 429 (2012), 15-19. DOI 10.1016/j.jembe.2012.06.014
[2] Bhattacharyya, J., Pal, S.: Coexistence of competing predators in a coral reef ecosystem. Nonlinear Anal., Real World Appl. 12 (2011), 965-978. DOI 10.1016/j.nonrwa.2010.08.020 | MR 2736185 | Zbl 1203.92059
[3] Box, S. J., Mumby, P. J.: Effect of macroalgal competition on growth and survival of juvenile Caribbean corals. Mar. Ecol. Prog. Ser. 342 (2007), 139-149. DOI 10.3354/meps342139
[4] Bruno, J. F., Precht, W. F., Vroom, P. S., Aronson, R. B.: Coral reef baselines: How much macroalgae is natural?. Marine Pollution Bull. 80 (2014), 24-29. DOI 10.1016/j.marpolbul.2014.01.010
[5] Bruno, J. F., Sweatman, H., Precht, W. F., Selig, E. R., Schutte, V. G. W.: Assessing evidence of phase shifts from coral to macroalgal dominance on coral reefs. Ecology 90 (2009), 1478-1484. DOI 10.1890/08-1781.1
[6] Cantrell, R. S., Cosner, C.: On the dynamics of predator-prey models with the Beddington-DeAngelis functional response. J. Math. Anal. Appl. 257 (2001), 206-222. DOI 10.1006/jmaa.2000.7343 | MR 1824675 | Zbl 0991.34046
[7] Cheal, A. J., MacNeil, M. A., Cripps, E., Emslie, M. J., Jonker, M., Schaffelke, B., Sweatman, H.: Coral-macroalgal phase shifts or reef resilience: Links with diversity and functional roles of herbivorous fishes on the Great Barrier Reef. Coral Reefs 29 (2010), 1005-1015. DOI 10.1007/s00338-010-0661-y
[8] Cui, J., Takeuchi, Y.: Permanence, extinction and periodic solution of predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 317 (2006), 464-474. DOI 10.1016/j.jmaa.2005.10.011 | MR 2209573 | Zbl 1102.34033
[9] Evans, R. D., Wilson, S. K., Field, S. N., Moore, J. A. Y.: Importance of macroalgal fields as coral reef fish nursery habitat in north-west Australia. Mar. Biol. 161 (2014), 599-607. DOI 10.1007/s00227-013-2362-x
[10] Feng, J., Wang, H., Huang, D., Li, S.: Alternative attractors in marine ecosystems: A comparative analysis of fishing effects. Ecological Modelling 195 (2006), 377-384. DOI 10.1016/j.ecolmodel.2005.11.033
[11] Gupta, R. P., Chandra, P.: Bifurcation analysis of modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting. J. Math. Anal. Appl. 398 (2013), 278-295. DOI 10.1016/j.jmaa.2012.08.057 | MR 2984333 | Zbl 1259.34035
[12] Harriott, V. J., Banks, S. A.: Latitudinal variation in coral communities in eastern Australia: A qualitative biophysical model of factors regulating coral reefs. Coral Reefs 21 (2002), 83-94. DOI 10.1007/s00338-001-0201-x
[13] Hughes, T. P., Graham, N. A. J., Jackson, J. B. C., Mumby, P. J., Steneck, R. S.: Rising to the challenge of sustaining coral reef resilience. Trends Ecol. Evol. 25 (2010), 633-642. DOI 10.1016/j.tree.2010.07.011
[14] Jessen, C., Roder, C., Lizcano, J. F. V., Voolstra, C. R., Wild, C.: In-situ effects of simulated overfishing and eutrophication on benthic coral reef algae growth, succession, and composition in the Central Red Sea. Plos One 8 (2013), Article ID e66992, 13 pages. DOI 10.1371/journal.pone.0066992
[15] Kramer, D. B.: Adaptive harvesting in a multiple-species coral-reef food web. Ecol. Soc. 13 (2007), Article ID 17, 25 pages. DOI 10.5751/ES-02314-130117
[16] Lenzini, P., Rebaza, J.: Nonconstant predator harvesting on ratio-dependent predator-prey models. Appl. Math. Sci., Ruse 4 (2010), 791-803. MR 2595517 | Zbl 1189.37098
[17] Lirman, D.: Competition between macroalgae and corals: Effects of herbivore exclusion and increased algal biomass on coral survivorship and growth. Coral Reefs 19 (2001), 392-399. DOI 10.1007/s003380000125
[18] Littler, M. M., Littler, D. S., Brooks, B. L.: Harmful algae on tropical coral reefs: Bottom-up eutrophication and top-down herbivory. Harmful Algae 5 (2006), 565-585. DOI 10.1016/j.hal.2005.11.003
[19] McCook, L. J., Jompa, J., Diaz-Pulido, G.: Competition between corals and algae on coral reefs: A review of evidence and mechanisms. Coral Reefs 19 (2001), 400-417. DOI 10.1007/s003380000129
[20] McManus, J. W., Polsenberg, J. F.: Coral-algal phase shifts on coral reefs: Ecological and environmental aspects. Progress in Oceanography 60 (2004), 263-279. DOI 10.1016/j.pocean.2004.02.014
[21] Mumby, P. J.: Phase shifts and the stability of macroalgal communities on Caribbean coral reefs. Coral Reefs 28 (2009), 761-773. DOI 10.1007/s00338-009-0506-8
[22] Mumby, P. J., Foster, N. L., Fahy, E. A. G.: Patch dynamics of coral reef macroalgae under chronic and acute disturbance. Coral Reefs 24 (2005), 681-692. DOI 10.1007/s00338-005-0058-5
[23] Mumby, P. J., Steneck, R. S.: Coral reef management and conservation in light of rapidly evolving ecological paradigms. Trends Ecol. Evol. 23 (2008), 555-563. DOI 10.1016/j.tree.2008.06.011
[24] Murray, G. P. D., Stillman, R. A., Gozlan, R. E., Britton, J. R.: Experimental predictions of the functional response of a freshwater fish. Ethology 119 (2013), 751-761. DOI 10.1111/eth.12117
[25] Poore, A. B.: On the theory and application of Hopf-Friedrichs bifurcation theory. Arch. Ration. Mech. Anal. 60 (1976), 371-393. DOI 10.1007/BF00248886 | MR 0404766 | Zbl 0358.34005
[26] Ruan, S.: Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling. J. Math. Biol. 31 (1993), 633-654. DOI 10.1007/BF00161202 | MR 1237092 | Zbl 0779.92021
[27] Siekmann, I., Malchow, H., Venturino, E.: An extension of the Beretta-Kuang model of viral diseases. Math. Biosci. Eng. 5 (2008), 549-565. DOI 10.3934/mbe.2008.5.549 | MR 2492346 | Zbl 1158.92320
[28] Smith, J. E., Hunter, C. L., Smith, C. M.: The effects of top-down versus bottom-up control on benthic coral reef community structure. Oecologia 163 (2010), 497-507. DOI 10.1007/s00442-009-1546-z
[29] J. E. Smith, M. Shaw, R. A. Edwards, D. Obura, O. Pantos, E. Sala, S. A. Sandin, S. Smriga, M. Hatay, F. L. Rohwer: Indirect effects of algae on coral: Algae-mediated, microbe-induced coral mortality. Ecol. Lett. 9 (2006), 835-845. DOI 10.1111/j.1461-0248.2006.00937.x
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