Journal of Guangdong University of Technology ›› 2019, Vol. 36 ›› Issue (06): 38-44.doi: 10.12052/gdutxb.190068

• Comprehensive Studies • Previous Articles     Next Articles

A Spatio-temporal Dynamic Analysis of a Predation-competition System with Allee Effect

Liu Chen-lin, Zheng San-qiang, Han Xiao-zhuo   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2019-05-06 Online:2019-11-28 Published:2019-11-01

Abstract: The local population dynamics with Allee effect and its empirical research are one of the research hotspots in population ecology. Current studies show that the Allee effect caused by the low population density has complex impacts on the time dynamics and the spatial distribution of a single population or metapopulation. However, comprehensive understanding of how the Allee effect will affect the system dynamics in complex ecological relationships is not enough. An ecosystem containing predators with Allee effect and prey with competing relationship is established. And then, the effect of the Allee effect index and the population initial density on the population density and the spatial distribution of each species are analyzed by the ecosystem. The results show that the predators with Allee effect cause the system to produce damped oscillation, against the stability of predation-competition system; increasing the Allee effect threshold prompts the population density of predators to decrease, and the population density of preys to increase; the initial population size of predator has great impacts on the system, and if the initial value is large, the system finally reaches a stable state; however, if the initial value is small, the system is in chaos; the systems with Allee effect are more likely to generate an aggregated distribution pattern in space. These insights can provide necessary theoretical basis for species conservation.

Key words: Allee effects, predation-competition system, stability analysis, numerical simulation, spatial pattern

CLC Number: 

  • Q141
[1] ALLEE W C. Animal aggregations:a request for information[J]. The Condor, 1923, 25(4):129-131
[2] ETIENNE R S, HEMERIK L. The founder and Allee effects in the patch occupancy metapopulation model[M]//REYDON T A. C, HEMERIK L. Current themes in theoretical biology. New York:Springer, 2005:203-232.
[3] GREENE C M. Allee effects[J]. Encyclopedia of Ecology, 2008, 35(3):123-127
[4] LIU Z G, ZHAO X, ZHANG F P. Allee effects of local populations and the synchrony of metapopulation[J]. Acta Ecologica Sinica, 2012, 32(1):1-6
[5] GASCOIGNE J C, LIPCIUS R N. Allee effects driven by predation[J]. Journal of Applied Ecology, 2004, 41(5):801-810
[6] GASCOIGNE J, BEREC L, GREGORY S, et al. Dangerously few liaisons:a review of mate-finding Allee effects[J]. Population Ecology, 2009, 51(3):355-372
[7] AMARASEKARE P. Allee effects in metapopulation dynamics[J]. American Naturalist, 1998, 152(2):298-302
[8] WANG W X, ZHANG Y B, LIU C Z. Analysis of a discrete-time predator-prey system with Allee effect[J]. Ecological Complexity, 2011, 8(1):81-85
[9] HANSKI I. Uniting two general patterns in the distribution of species[J]. Science, 1997, 275(5298):397-400
[10] ZHOU S R, LIU Y F, WANG G. The stability of predator-prey systems subject to the Allee effects[J]. Theoretical Population Biology, 2005, 67(1):23-23
[11] MOROZOV A, ANDREW Y, PETROVSKII S, et al. Bifurcations and chaos in a predator-prey system with the Allee effect[J]. Proceedings Biological Sciences, 2004, 271(1546):1407-1414
[12] WANG G, LIANG X G, WANG F Z. The competitive dynamics of populations subject to an Allee effect[J]. Ecological Modelling, 1999, 124(2-3):183-192
[13] SINGH M K, BHADAURIA B S, SINGH B K. Bifurcation analysis of modified Leslie-Gower predator-prey model with double Allee effect[J]. Ain Shams Engineering Journal, 2016, 9(4):1263-1277
[14] BOUKAL D S, BEREC L. Single-species models of the Allee effect:extinction boundaries, sex ratios and mate encounters[J]. Journal of Theoretical Biology, 2002, 218(3):375-394
[15] 周淑荣, 王刚. 集合种群的似Allee效应[J]. 生物数学学报, 2002, 17(3):324-328 ZHOU S R, WANG G. Allee-like effects in metapopulation[J]. Journal of Biomathematics, 2002, 17(3):324-328
[16] 惠苍. 集合种群空间混沌的模拟研究以及Allee效应、拥挤效应与捕食效应对空间模式的影响[J]. 西北植物学报, 2004, 24(3):370-383 HUI C. Spatial chaos of metapopulation incurred by Allee effect, overcrowding effect and predation effect[J]. Acta Botanica Boreali-Occidentalia Sinica, 2004, 24(3):370-383
[17] KYLAFIS G, LOREAU M. Niche construction in the light of niche theory[J]. Ecology Letters, 2011, 14(2):82-90
[18] KANEKO K. Coupled map lattice[M]. Saarbrücken:Alphascript Publishing, 1991:237-247.
[19] 王志斌, 张旭峰. 均匀耦合映像格子中的时空周期图案[J]. 中北大学学报(自然科学版), 2000, 21(3):202-205 WANG Z B, ZHANG X F. Spatiotemporal periodic patterns in symmetrically coupled map lattices[J]. Journal of North University of China, 2000, 21(3):202-205
[20] BOCCARA N. Modeling complex systems[J]. Agricultural Economics, 2005, 58(2):65-66
[21] ZHANG F, LI Z Z, HUI C. Spatiotemporal dynamics and distribution patterns of cyclic competition in metapopulation[J]. Ecological Modelling, 2006, 193(3-4):721-735
[22] HUI C, LI Z. Distribution patterns of metapopulation determined by Allee effects[J]. Population Ecology, 2004, 46(1):55-63
[23] 王鑫厅, 王炜, 刘佳慧, 等. 植物种群空间分布格局测定的新方法:摄影定位法[J]. 植物生态学报, 2006, 30(4):571-575 WANG X T, WANG W, LIU J H, et al. A new method measuring plant population spatial patterns:photography orientation[J]. Chinese Journal of Plant Ecology, 2006, 30(4):571-575
[24] 莫昌健, 韩晓卓. 生态位构建作用对捕食-竞争系统的影响[J]. 生态科学, 2016, 35(5):73-81 MO C J, HAN X Z. The effects of niche construction on prey-competition system[J]. Ecological Science, 2016, 35(5):73-81
[25] 黄亚玲. Allee效应对具有生态位构建作用的捕食系统的影响[D]. 广州:广东工业大学, 2016.
[26] HUI C, LI Z. Dynamical complexity and metapopulation persistence[J]. Ecological Modelling, 2003, 164(2-3):201-209
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