具有列维飞行与布朗运动特征的循环竞争博弈及物种稳定共存条件

王栋; 唐长庆; 田宝国; 曲亮生; 张金春; 狄增如

doi:10.7498/aps.63.168701

摘要

循环竞争博弈常被用来研究物种多样性. 以前有关循环竞争博弈的研究工作所考虑的相互作用距离模式包括最近邻、取固定距离或一定距离以内的随机值，这与实际情况不相符. 考虑到实际生物系统中物种个体做列维飞行与布朗运动的情况广泛存在，综合考虑了最近邻相互作用模式和列维飞行（布朗运动）长程相互作用模式，对循环竞争博弈及保持物种多样性的条件进行了研究. 得到了最大飞行距离与选择概率的临界关系（包括Logistic式和指数式关系），进一步得到了幂指数与选择概率的临界关系，以及保持物种共存的条件.

关键词:

Abstract

Cyclical game is often used to study the biodiversity in ecosystem. However, the interaction distance mode considered in previous studies of cyclical game is only the interaction between nearest neighbors, a fixed distance, or a random value of fixed distance among the individuals of species. This is not consistent with the actual situation. In this paper, considering the fact that Levy flight and Brownian motion widespreadly exist in ecosystem, and comprehensively considering the nearest-neighbor-interaction and long-range-interaction given by Levy flight and Brownian motion, the cyclical game and conditions of maintaining biodiversity are investigated. The critical relation of maximal step length of flight versus choosing probability is presented, including Logistic and exponent relations. Further the critical relation between power-law exponent and choosing probability is found. The condition of maintaining species coexistence is also found.

Keywords:

作者及机构信息

1.
海军航空工程学院基础部, 烟台 264001;

2.
北京师范大学系统科学学院, 北京 100875;

3.
海军航空工程学院研究生管理大队, 烟台 264001

基金项目: 国家自然科学基金（批准号：61174150，60974084）和教育部新世纪优秀人才支持计划（批准号：NCET-09-0228）资助的课题.

Authors and contacts

1.
Department of Basic Science, Naval Aeronautical and Astronautical University, Yantai 264001, China;

2.
School of Systems Science, Beijing Normal University, Beijing 100875, China;

3.
Administrant Brigade of Postgraduate, Naval Aeronautical and Astronautical University, Yantai 264001, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61174150, 60974084) and the Program for the New Century Excellent Talents in University of Ministry of Education, China (Grant No. NCET-09-0228).

参考文献

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[38]	Metzler R, Klafter J 2000 Phys. Rep. 339 1

施引文献

[1]	Sinervo B, Lively C M 1996 Nature 380 240
[2]	Kerr B, Riley M A, Feldman M W, Bohannan B J M 2002 Nature 418 171
[3]	Kirkup B C, Riley M A 2004 Nature 428 412
[4]	Jackson J B C, Buss L 1975 Proc. Natl. Acad. Sci. USA 72 5160
[5]	Paquin C E, Adams J 1983 Nature 306 368
[6]	Gilg O, Hanski I, Sittler B 2003 Science 302 866
[7]	Reichenbach T, Mobilia M, Frey E 2007 Nature 448 1046
[8]	Reichenbach T, Mobilia M, Frey E 2007 Phys. Rev. Lett. 99 238105
[9]	Reichenbach T, Mobilia M, Frey E 2008 J. Theor. Biol. 254 368
[10]	Reichenbach T, Frey E 2008 Phys. Rev. Lett. 101 058102
[11]	Wang W M, Wang W J, Lin Y Z, Tan Y J 2011 Chin. Phys. B 20 034702
[12]	Quan J, Wang X J 2011 Chin. Phys. B 20 030203
[13]	Ying C Y, Hua D Y, Wang L Y 2007 J. Phys. A: Math. Theor. 40 4477
[14]	Sun R S, Hua D Y 2009 Chin. Phys. Lett. 26 086403
[15]	Hua D Y, Dai L C, Lin C 2013 Europhys. Lett. 101 38004
[16]	Zhang G Y, Chen Y, Qi W K, Qing S M 2009 Phys. Rev. E 79 062901
[17]	Szabo G, Fath G 2007 Phys. Rep. 446 97
[18]	Shi H J, Wang W X, Yang R, Lai Y C 2010 Phys. Rev. E 81 030901R
[19]	Ni X, Wang W X, Lai Y C, Grebogi C 2010 Phys. Rev. E 82 066211
[20]	Wang W X, Ni X, Lai Y C, Grebogi C 2011 Phys. Rev. E 83 11917
[21]	Nossal R 1983 J. Stat. Phys. 30 391
[22]	Viswanathan G M, Afanasyev V, Buldyrev S V, Murphy E J, Prince P A, Stanley H E 1996 Nature 381 413
[23]	Levandowsky M, White B S, Schuster F L 1997 Acta Protozool. 36 237
[24]	Ramos F G, Mateos J L, Miramontes O, Cocho G, Larralde H, Ayala O B 2004 Behav. Ecol. Sociobiol. 55 223
[25]	Dieterich P, Klages R, Preuss R, Schwab A 2008 Proc. Natl. Acad. Sci. USA 105 459
[26]	Humphries N E, Queiroz N, Dyer J R M, Pade N G, Musyl M K, Schaefer K M, Fuller D W, Brunnschweiler J M, Doyle T K, Houghton J D R, Hays G C, Jones C S, Noble L R, Wearmouth V J, Southall E J, Sims D W 2010 Nature 465 1066
[27]	Viswanathan G M, Raposo E P, da Luz M G E 2008 Phys. Life Rev. 5 133
[28]	Bartumeus F, Peters F, Pueyo S, Marrase C, Catalan J 2003 Proc. Natl. Acad. Sci. USA 100 12771
[29]	Bartumeus F 2007 Fractals 15 151
[30]	Sims D W, Southall E J, Humphries N E, Hays G C, Bradshaw C J A, Pitchford J W, James A, Ahmed M Z, Brierley A S, Hindell M A, Morritt D, Musyl M K, Righton D, Shepard E L C, Wearmouth V J, Wilson R P, Witt M J, Metcalfe J D 2008 Nature 451 1098
[31]	Sims D W, Righton D, Pitchford J W 2007 J. Anim. Ecol. 76 222
[32]	Travis J 2007 Science 318 742
[33]	Buchanan M 2008 Nature 453 714
[34]	Wang D, Zhuang Q, Fan Y, Di Z R 2013 Chin. Phys. B 22 128702
[35]	Gillespie D T 1976 J. Comput. Phys. 22 403
[36]	Gillespie D T 1977 J. Phys. Chem. 81 2340
[37]	Hastings A, Petrovskii S, Morozov A 2011 Biol. Lett. 7 163
[38]	Metzler R, Klafter J 2000 Phys. Rep. 339 1

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