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Organism-induced habitat restoration leads to bi-stability in metapopulations. (English) Zbl 1316.92076

Summary: Following R. Levins’ patch occupancy model [“Some demographic and genetic consequence of environmental heterogeneity for biological control”, Bull. Entomological Soc. Am. 15, No. 3, 237–240 (1969; doi:10.1093/besa/15.3.237)], we presented a differential-equation model, in which both the metapopulation dynamics and the dynamics of the fraction of suitable patches in the habitat are characterized. Habitat restoration induced by organism itself (internal restoration) and by other organisms or/and abiotic causes (external restoration) were incorporated in the model, together with habitat destruction. Stability analysis revealed the existence of alternative equilibriums (i.e., bi-stability) in the system. The internal restoration of habitat was identified as the trigger for the bi-stability, whereas the external restoration, in contrast, can eliminate the bi-stability from the system. The results, thus, emphasize the important role of the organism-environment feedback in biological conservation.

MSC:

92D25 Population dynamics (general)

References:

[1] Wilcove, D. S.; Rothstein, D.; Jason, D.; Phillips, A.; Losos, E., Quantifying threats to imperiled species in the United States, Bioscience, 48, 607-615 (1998)
[2] Hanski, I., Metapopulation Ecology (1999), Oxford University Press: Oxford University Press Oxford
[3] Levins, R., Some demographic and genetic consequence of environmental heterogeneity for biological control, Bull. Entomol. Soc. Am., 15, 237 (1969)
[4] Levins, R., Extinction, Lect. Notes Math., 2, 75 (1970) · Zbl 0241.92017
[5] Lande, R., Extinction thresholds in demographic models of territorial populations, Am. Nat., 130, 624 (1987)
[6] May, R. M., The role of ecological theory in planning reintroduction of endangered species, Symp. Zool. Soc. London, 62, 145 (1991)
[7] Nee, S.; May, R. M., Dynamics of metapopulations: habitat destruction and competitive coexistence, J. Ani. Ecol., 61, 37 (1992)
[8] Lawton, J. H.; Nee, S.; Letcher, A. J.; Harvey, P. H., Animal distributions: pattern and process, (Edwards, P. J.; May, R. M., Large-scale Ecology and Conservation Biology (1994), Blackwell Scientific Press: Blackwell Scientific Press Oxford), 41-58
[9] Nee, S., How populations persist, Nature, 367, 123 (1994)
[10] Jones, C. G.; Lawton, J. H.; Shachak, M., Organisms as ecosystem engineers, Oikos, 69, 373 (1994)
[11] Hastings, A.; Byers, J. E.; Crooks, J. A.; Cuddington, K.; Jones, C. G.; Lambrinos, J. G.; Talley, T. S.; Wilson, W. G., Ecosystem engineering in space and time, Ecol. Lett., 10, 153 (2007)
[12] Byers, J. E.; Cuddington, K.; Jones, C. G.; Talley, T. S.; Hastings, A.; Lambrinos, J. G.; Crooks, J. A.; Wilson, W., Using ecosystem engineers to restore ecological systems, Trends Ecol. Evol., 21, 9, 493 (2006)
[13] Mager, D. M.; Hui, C., A first record of biological soil crusts in the Cape Floristic Region, South African J. Sci., 108, 7/8, p. 4 (2012), Art. #1013
[14] Zarnetske, P. L.; Hacker, S. D.; Seabloom, E. W.; Ruggiero, P.; Killian, J. R.; Maddux, T. B.; Cox, D., Biophysical feedback mediates effects of invasive grasses on coastal dune shape, Ecology, 93, 6, 1439 (2012)
[15] Yue, D. X.; Hui, C.; Li, Z. Z., Niche construction for desert plants in individual and population scales: theoretical analysis and evidences from saksaul (Haloxylon ammodendron) forests, Israel J. Plant Sci., 52, 235 (2004)
[16] Hui, C.; Li, Z. Z.; Yue, D. X., Metapopulation dynamics and distribution, and environmental heterogeneity induced by niche construction, Ecol. Model., 177, 107 (2004)
[17] Hui, C.; Yue, D. X., Niche construction and polymorphism maintenance in metapopulation, Ecol. Res., 20, 115 (2005)
[18] Han, X. Z.; Li, Z. Z.; Hui, C.; Zhang, F., Polymorphism maintenance in a spatially structured population: a two-locus genetic model of niche construction, Ecol. Model., 192, 160 (2006)
[19] Han, X. Z.; Hui, C.; Zhang, Y. Y., Effects of time-lagged niche construction on metapopulation dynamics and environmental heterogeneity, Appl. Math. Comput., 215, 449 (2009) · Zbl 1171.92038
[20] Hanski, I.; Moilanen, A.; Gyllenberg, M., Minimum viable metapopulation size, Am. Nat., 147, 527 (1996)
[21] Carr, J., Applications of Center Manifold Theory (1981), Springer: Springer New York · Zbl 0464.58001
[22] Casagrandi, R.; Gatto, M., A persistence criterion for metapopulations, Theor. Popul. Biol., 61, 115 (2002) · Zbl 1040.92043
[23] Gyllenberg, M.; Hanski, I., Habitat deterioration, habitat destruction, and metapopulation persistence in a heterogenous landscape, Theor. Popul. Biol., 52, 198 (1997) · Zbl 0890.92022
[24] Petchey, O. L.; Gonzalez, A.; Wilson, H. B., Effects on population persistence: the interaction between environmental noise colour, intraspecific competition and space, Proc. Biol. Sci., 264, 1841 (1997)
[25] Chesson, P. L., Persistence of a Markovian population in a patchy environment, Z. Wahrscheinlichkeitstheor., 66, 97 (1984) · Zbl 0522.92018
[26] Hui, C.; Li, Z. Z., Dynamical complexity and metapopulation persistence, Ecol. Model., 164, 201 (2003)
[27] Zhang, F.; Hui, C.; Han, X. Z.; Li, Z. Z., Evolution of cooperation in patchy habitat under patch decay and isolation, Ecol. Res., 20, 461 (2005)
[28] Hui, C.; Zhang, F.; Han, X. Z.; Li, Z. Z., Cooperation evolution and self-regulation dynamics in metapopulation: stage-equilibrium hypothesis, Ecol. Model., 184, 397 (2005)
[29] Patten, M. A.; Wolfe, D. H.; Shochat, E.; Sherrod, S. K., Habitat fragmentation, rapid evolution and population persistence, Evol. Ecol. Res., 7, 235 (2005)
[30] Allee, W. C., The Social Life of Animals (1938), Heinemann: Heinemann London
[31] Taylor, C. M.; Hastings, A., Allee effects in biological invasions, Ecol. Lett., 8, 895 (2005)
[32] Wright, J. P.; Jones, C. G., The concept of organisms as ecosystem engineers ten years on: progress, limitations, and challenges, Bioscience, 56, 203 (2006)
[33] Chapin, F. S.; Walker, B. H.; Hobbs, R. J.; Hooper, D. U.; Lawton, J. H.; Sala, O. E.; Tilman, D., Biotic control over the functioning of ecosystems, Science, 277, 500 (1997)
[34] Badano, E. I.; Cavieres, L. A., Impacts of ecosystem engineers on community attributes: effects of cushion plants at different elevations of the Chilean Andes, Diversity Distrib., 12, 388 (2006)
[35] Badano, E. I.; Jones, C. G.; Cavieres, L. A.; Wright, J. P., Assessing impacts of ecosystem engineers on community organization: a general approach illustrated by effects of a high-Andean cushion plant, Oikos, 115, 365 (2006)
[36] Laland, K. N.; Odling-Smee, F. J.; Feldman, M. W., Evolutionary consequences of niche construction and their implications for ecology, Proc. Nat. Acad. Sci. USA, 96, 10242 (1999)
[37] Gurney, W. S.C.; Lawton, J. H., The population dynamics of ecosystem engineers, Oikos, 76, 273 (1996)
[38] Cuddington, K.; Wilson, W. G.; Hastings, A., Ecosystem engineers: feedback and population dynamics, Am. Nat., 173, 488 (2009)
[39] Wright, J. P.; Gurney, W. S.C.; Jones, C. G., Patch dynamics in a landscape modified by ecosystem engineers, Oikos, 105, 336 (2004)
[40] Kurtz, T., Solution of ordinary differential equations as limits of pure jump Markov process, J. Appl. Probab., 7, 49 (1970) · Zbl 0191.47301
[41] Hanski, I., Metapopulation dynamics, Nature, 396, 41 (1998)
[42] Zhang, F.; Li, Z. Z.; Hui, C., Spatiotemporal dynamics and distribution patterns of cyclic competition in metapopulation, Ecol. Model., 193, 721 (2006)
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