Adaptation of species as response to climate change: Predator-prey mathematical model
Most of the species currently threatened with extinction seem to be under the pressure of unsuitable environmental conditions; e.g., climate change, scarce food resource, habitat fragmentation. One should expect species to have forms of resilience against such extinction. The point here is to examin...
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| Published in | AIMS mathematics Vol. 5; no. 4; pp. 3875 - 3898 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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AIMS Press
01.01.2020
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| Online Access | Get full text |
| ISSN | 2473-6988 2473-6988 |
| DOI | 10.3934/math.2020251 |
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| Abstract | Most of the species currently threatened with extinction seem to be under the pressure of unsuitable environmental conditions; e.g., climate change, scarce food resource, habitat fragmentation. One should expect species to have forms of resilience against such extinction. The point here is to examine the effect of spatial gradients on species survival against increasing temperature arising from climate change. Therefore, we start with the question of whether, when faced with extinction stemming from climate change, a spatial gradient and a beachhead have the power to prevent extinction. This problem is addressed theoretically using a coupled reaction diffusion equation for a predator-prey system in which the prey experiences an Allee effect. It is demonstrated that there exists a relationship between the slope of the gradient and the beachhead at which the predator-prey system can stably survive. The tendency of the system can be defined by a function where the system includes the threshold point for extinction, that separates the areas of extinction and survival. The findings reveal that spatial gradient can be used as a precaution, when the species faces to extinction, for species to create new habitat and sustain its persistence. Therefore, in this paper, it is shown that, in theory, the recovery of species from unsuitable environmental conditions can be achieved. This can be possible by taking into account the spatial gradient to slow down the forthcoming ecological extinction, and thus extend the system a while as an adaptation mechanism. |
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| AbstractList | Most of the species currently threatened with extinction seem to be under the pressure of unsuitable environmental conditions; e.g., climate change, scarce food resource, habitat fragmentation. One should expect species to have forms of resilience against such extinction. The point here is to examine the effect of spatial gradients on species survival against increasing temperature arising from climate change. Therefore, we start with the question of whether, when faced with extinction stemming from climate change, a spatial gradient and a beachhead have the power to prevent extinction. This problem is addressed theoretically using a coupled reaction diffusion equation for a predator-prey system in which the prey experiences an Allee effect. It is demonstrated that there exists a relationship between the slope of the gradient and the beachhead at which the predator-prey system can stably survive. The tendency of the system can be defined by a function where the system includes the threshold point for extinction, that separates the areas of extinction and survival. The findings reveal that spatial gradient can be used as a precaution, when the species faces to extinction, for species to create new habitat and sustain its persistence. Therefore, in this paper, it is shown that, in theory, the recovery of species from unsuitable environmental conditions can be achieved. This can be possible by taking into account the spatial gradient to slow down the forthcoming ecological extinction, and thus extend the system a while as an adaptation mechanism. |
| Author | Sekerci, Yadigar |
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| CitedBy_id | crossref_primary_10_1140_epjp_s13360_020_00800_2 crossref_primary_10_1140_epjp_s13360_024_05880_y crossref_primary_10_1016_j_ecolmodel_2020_109244 |
| Cites_doi | 10.1098/rspa.2004.1404 10.1016/j.tpb.2006.12.006 10.1016/j.ecocom.2018.10.004 10.1038/s41586-019-1230-3 10.1007/s00285-010-0332-1 10.1038/nature06111 10.1126/science.1101867 10.1046/j.1461-0248.2001.00193.x 10.1016/j.jtbi.2005.05.021 10.1890/04-0823 10.1006/bulm.2001.0239 10.1111/j.1365-2656.2012.02038.x 10.1098/rspb.1993.0001 10.1016/j.nonrwa.2018.05.018 10.1006/tpbi.1993.1007 10.2307/2479933 10.1016/S0025-5564(01)00048-7 10.1006/tpbi.2000.1509 10.1016/j.tree.2004.11.012 10.1016/j.ecocom.2014.05.003 10.1038/nature01274 10.1086/303320 10.2307/2420377 10.2307/1943577 10.1016/j.mbs.2007.02.006 10.1007/s12080-009-0060-6 10.1016/j.jtbi.2017.04.018 10.1007/s40745-016-0096-6 10.1046/j.1461-0248.2002.00324.x 10.1186/1687-1847-2013-1 10.1016/j.ecocom.2014.10.006 10.1007/s11538-015-0126-0 10.1016/j.ecocom.2014.05.001 10.2307/2479596 10.1016/j.bulm.2004.09.003 10.1016/j.ecocom.2014.05.007 10.1007/s11538-015-0108-2 |
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| References | 44 M. R. Owen, M. A. Lewis (48) M. Siccha, M. Kucera (23) B. Chakraborty, N. Bairagi (53) H. A. Gleason (18) J. Z. Farkas, A. Y. Morozov, E. G. Arashkevich (21) M. A. Lewis, P. Kareiva (45) C. Cosner (9) Y. Sekerci, S. Petrovskii (33) P. Kyriazopoulos, J. Nathan, E. Meron (12) 51 M. Doebeli, U. Dieckmann (15) 10 V. Dakos, E. H. van Nes, R. Donangelo (54) M. Pascual, F. Guichard (57) 55 13 H. A. Gleason (17) L. Jonkers, H. Hillebrand, M. Kucera (22) 1 4 6 S. Petrovskii, A. Morozov, E. Venturino (3) S. V. Petrovskii, H. Malchow (46) S. Petrovskii, H. Malchow, B. L. Li (49) 24 25 27 28 O. Bonnefon, J. Coville, J. Garnier (11) J. Wang, J. Shi, J. Wei (37) S. Petrovskii, Y. Sekerci, E. Venturino (31) M. H. Wang, M. Kot (42) H. A. Gleason (16) W. F. Fagan, J. G. Bishop (47) M. Pascual (19) J. Wang, J. Shi, J. Wei (36) H. Berestycki, L. Desvillettes, O. Diekmann (8) 30 32 J. A. Sherratt (41) 35 E. Post (20) M. Rietkerk, S. C. Dekker, P. C. de Ruiter (58) J. Martin, B. van Moorter, E. Revilla (52) S. Petrovskii, A. Morozov, B. L. Li (7) A. S. Ackleh, L. J. Allen, J. Carter (34) A. Morozov, S. Petrovskii, B. L. Li (2) R. Han, B. Dai (5) R. H. Whittaker (14) G. A. Van Voorn, L. Hemerik, M. P. Boer (38) 43 S. Kéfi, M. Rietkerk, C. L. Alados (56) |
| References_xml | – ident: 49 article-title: i>An exact solution of a diffusive predator-prey system</i publication-title: Proc. R. Soc. A. doi: 10.1098/rspa.2004.1404 – ident: 34 article-title: i>Establishing a beachhead: a stochastic population model with an Allee effect applied to species invasion</i publication-title: Theor. Popul. Biol. doi: 10.1016/j.tpb.2006.12.006 – ident: 53 article-title: i>Complexity in a prey-predator model with prey refuge and diffusion</i publication-title: Ecol. Complex. doi: 10.1016/j.ecocom.2018.10.004 – ident: 22 article-title: i>Global change drives modern plankton communities away from the pre-industrial state</i publication-title: Nature doi: 10.1038/s41586-019-1230-3 – ident: 25 article-title: i>Hypothesis for origin of planktonic patchiness</i – ident: 27 article-title: i>Spatial dynamics of predator-prey system with hunting cooperation in predators and type I functional response</i – ident: 36 article-title: i>Predator-prey system with strong Allee effect in prey</i publication-title: J. Math. Biol. doi: 10.1007/s00285-010-0332-1 – ident: 56 article-title: t al. Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems</i publication-title: Nature doi: 10.1038/nature06111 – ident: 58 article-title: t al. Self-organized patchiness and catastrophic shifts in ecosystems</i publication-title: Science doi: 10.1126/science.1101867 – ident: 6 article-title: t al. Pattern dynamics in a diffusive predator-prey model with hunting cooperations</i – ident: 41 article-title: i>Periodic travelling waves in cyclic predator-prey systems</i publication-title: Ecol. Lett. doi: 10.1046/j.1461-0248.2001.00193.x – ident: 13 article-title: J. T. Curtis, The Vegetation of – ident: 2 article-title: i>Spatiotemporal complexity of patchy invasion in a predatorprey system with the Allee effect</i publication-title: J. Theor. Biol. doi: 10.1016/j.jtbi.2005.05.021 – ident: 20 article-title: i>Large-scale spatial gradients in herbivore population dynamics</i publication-title: Ecology doi: 10.1890/04-0823 – ident: 48 article-title: i>How predation can slow, stop or reverse a prey invasion</i publication-title: B. Math. Biol. doi: 10.1006/bulm.2001.0239 – ident: 52 article-title: t al. Reciprocal modulation of internal and external factors determines individual movements</i publication-title: J. Anim. Ecol. doi: 10.1111/j.1365-2656.2012.02038.x – ident: 19 article-title: i>Diffusion-induced chaos in a spatial predator-prey system</i publication-title: Proc. R. Soc. Lond. B. doi: 10.1098/rspb.1993.0001 – ident: 5 article-title: i>Spatiotemporal pattern formation and selection induced by nonlinear crossdiffusion in a toxic-phytoplankton-zooplankton model with Allee effect</i publication-title: Nonlinear Anal.: Real World Appl. doi: 10.1016/j.nonrwa.2018.05.018 – ident: 55 article-title: t al. Transient phenomena in ecology</i – ident: 51 article-title: i>Critical domain problem for the reaction-telegraph equation model of population dynamics</i – ident: 45 article-title: i>Allee dynamics and the spread of invading organisms</i publication-title: Theor. Popul. Biol. doi: 10.1006/tpbi.1993.1007 – ident: 4 article-title: i>Pattern formation of a diffusive predator-prey model with strong Allee effect and nonconstant death rate</i – ident: 35 article-title: i>Pattern formation in a model oxygen-plankton system</i – ident: 17 article-title: i>The individualist concept of the plant association</i publication-title: Bull. Torrey Bot. Club doi: 10.2307/2479933 – ident: 42 article-title: i>Speeds of invasion in a model with strong or weak Allee effects</i publication-title: Math. Biosci. doi: 10.1016/S0025-5564(01)00048-7 – ident: 46 article-title: i>Wave of chaos: New mechanism of pattern formation in spatiotemporal population dynamics</i publication-title: Theor. Popul. Biol. doi: 10.1006/tpbi.2000.1509 – ident: 43 article-title: i>Global dynamics of two phytoplankton-zooplankton models with toxic substances effect</i – ident: 57 article-title: i>Critically and disturbance in spatial ecological system</i publication-title: Trends Ecol. Evol. doi: 10.1016/j.tree.2004.11.012 – ident: 11 article-title: t al. The spatio-temporal dynamics of neutral genetic diversity</i publication-title: Ecol. Complex. doi: 10.1016/j.ecocom.2014.05.003 – ident: 15 article-title: i>Speciation along environmental gradients</i publication-title: Nature doi: 10.1038/nature01274 – ident: 10 article-title: i>Climate change effects on fractional order prey-predator model</i – ident: 47 article-title: i>Trophic interactions during primary succession: Herbivores slow a plant reinvasion at Mount St. Helens</i publication-title: Am. Nat. doi: 10.1086/303320 – ident: 18 article-title: i>The individualistic concept of the plant association</i publication-title: Am. Midl. Nat. doi: 10.2307/2420377 – ident: 14 article-title: i>Vegetation of the great smoky mountains</i publication-title: Ecol. Monogr. doi: 10.2307/1943577 – ident: 38 article-title: t al., Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect</i publication-title: Math. Biosci. doi: 10.1016/j.mbs.2007.02.006 – ident: 54 article-title: t al. Spatial correlation as leading indicator of catastrophic shifts</i publication-title: Theor. Ecol. doi: 10.1007/s12080-009-0060-6 – ident: 31 article-title: i>Regime shifts and ecological catastrophes in a model of plankton-oxygen dynamics under the climate change</i publication-title: J. Theor. Biol. doi: 10.1016/j.jtbi.2017.04.018 – ident: 28 article-title: i>The chemical basis of morphogenesis</i – ident: 30 article-title: A. Morozov, K. Abbott, K. Cuddington, et al. Long transients in – ident: 23 article-title: i>ForCenS, a curated database of planktonic foraminifera census counts in marine surface sediment samples</i publication-title: Sci. Data doi: 10.1007/s40745-016-0096-6 – ident: 1 article-title: W. C. Allee, Animal – ident: 44 article-title: i>A prey-predator model with Holling II functional response and the carrying capacity of predator depending on its prey</i – ident: 3 article-title: i>Allee effect makes possible patchy invasion in a predatorprey system</i publication-title: Ecol. Lett. doi: 10.1046/j.1461-0248.2002.00324.x – ident: 37 article-title: i>Nonexistence of periodic orbits for predator-prey system with strong Allee effect in prey populations</i publication-title: Electron. J. Differ. Eq. doi: 10.1186/1687-1847-2013-1 – ident: 8 article-title: i>Can climate change lead to gap formation?</i publication-title: Ecol. Complex. doi: 10.1016/j.ecocom.2014.10.006 – ident: 33 article-title: i>Mathematical modelling of plankton-oxygen dynamics under the climate change</i publication-title: B. Math. Biol. doi: 10.1007/s11538-015-0126-0 – ident: 12 article-title: i>Species coexistence by front pinning</i publication-title: Ecol. Complex. doi: 10.1016/j.ecocom.2014.05.001 – ident: 24 article-title: t al. Biodiversity redistribution under climate change: Impacts on ecosystems and human well-being</i – ident: 16 article-title: i>The structure and development of the plant association</i publication-title: Bull. Torrey Bot. Club doi: 10.2307/2479596 – ident: 7 article-title: i>Regimes of biological invasion in a predator-prey system with the Allee effect</i publication-title: B. Math. Biol. doi: 10.1016/j.bulm.2004.09.003 – ident: 32 article-title: i>Global warming can lead to depletion of oxygen by disrupting phytoplankton photosynthesis: a mathematical modelling approach</i – ident: 9 article-title: i>Challenges in modelling biological invasions and population distributions in a changing climate</i publication-title: Ecol. Complex. doi: 10.1016/j.ecocom.2014.05.007 – ident: 21 article-title: t al. Revisiting the stability of spatially heterogeneous predator-prey systems under eutrophication</i publication-title: B. Math. Biol. doi: 10.1007/s11538-015-0108-2 |
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| Title | Adaptation of species as response to climate change: Predator-prey mathematical model |
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