基于复杂网络理论构建包含等级生长单位的互花米草克隆植株多重关系网络,分析该网络结构,获取了互花米草的生长特征及其株丛间彼此回避竞争的生态学策略。将囚徒困境演化博弈模型引入互花米草克隆植株多重关系网络,通过对网络上演化博弈现象的刻画,展现了按照不同的规则选取网络中的合作节点时网络的特征:随机均匀选取初始合作节点时,合作频率随着背叛诱惑值的增加逐渐下降;选择不同类型的生物体单位为初始合作节点,选取株丛间根状茎间隔点,演化博弈到达稳态时,合作者的比例随着背叛诱惑值的增加而逐渐减小,这意味着根状茎节点为互花米草生长的关键节点。
This paper constructs the empirical network of the clonal plant multiple relation treelike networks based on the spatial configuration of Spartina alterniflora to explore the evolutionary game characteristics. First, we study the structure properties of Spartina alterniflora, which reflect the ecological strategy that avoiding competition between each other. Second, the model of the evolutionary Prisoner’s Dilemma game is introduced into the Spartina alterniflora treelike network. Initially, the distribution of strategies among the nodes in the network obeys two different rules: distributed randomly, with fc decreasing with the increasing of b, in accordance with different types of Spartina alterniflora biological units, the rhizome nodes between the neighboring bunches play an important role.
[1] Nowak M A, May R. Evolutionary games and spatial chaos[J].Nature, 1992, 359(6398): 826-829.
[2] Szabó G, Fath G. Evolutionary games on graphs[J].Phys Reports, 2007,446(4/5/6): 97-216.
[3] Szabó G, Toke C. Evolutionary prisioner’s dilemma game on a square lattice[J].Phys Rev E, 1998,58(1): 69-73.
[4] Vukov J, Szabó G, Szolnoki A. Cooperation in the noisy case: prisioner’s dilemma game on two types of regular random graphs[J].Phys Rev E, 2006, 73(6): 067103.
[5] Watts D J, Strogatz S H. Collective dynamics of 'small-world' networks.[J].Nature, 1998, 393(6684): 440-442.
[6] Newman M E J, Watts D J. Renormalization group analysis of the small-world network model[J].Physics Letter A, 1999, 263(4): 341-346.
[7] Wu Z X, Xu X J, Huang Z G, et al. Evolutionary prisoner’s dilemma game with dynamic preferential selection[J].Physical Review E, 2006, 74(2): 021107.
[8] Santos F C, Rodrigues J F, Pacheco J M. Epidemic spreading and cooperation dynamics on homogeneous small-world networks[J].Physical Review E, 2005, 72(5): 056128.
[9] Kim B J, Trusina A, Holme P, et al. Dynamic instabilities induced by asymmetric influence: prisoners’ dilemma game in small-world networks[J].Physical Review E, 2002, 66(2): 021907.
[10] Barabási A L, Albert R. Emergence of scaling in random networks[J].Science, 1999, 286(5439): 509-512.
[11] Santos F C, Pacheco J M. Scale-free networks provide a unifying framework for the emergence of cooperation[J].Physical Review Letters, 2005, 95(9): 098104.
[12] Wu Z X, Xu X J, Huang Z G, et al. Evolutionary prisoner’s dilemma game with dynamic preferential selection[J].Physical Review E, 2006, 74(2): 021107.
[13] Santos F C, Pacheco J M, Lenaerts T. Evolutionary dynamics of social dilemmas in structured heterogeneous populations[J].Proceedings of the National Academy of Sciences of the United States of America, 2006, 103(9): 3490-3494.
[14] Rong Z, Li X, Wang X F. Roles of mixing patterns in cooperation on a scale-free networked games[J].Physical Review E, 2007, 76(2): 027101.
[15] Rong Z, Yang H X, Wang W X. Feedback reciprocity mechanism promotes the cooperation of highly clustered scale-free networks[J].Physical Review E, 2010, 82(4): 047101.
[16] Grace J B. The adaptive significance of clonal reproduction in angiosperms: an aquatic perspective[J].Aquatic Botany, 1993, 44(2): 159-180.
[17] Ellstrand N C, Roose M L. Patterns of genotypic diversity in clonal plant species[J].American Journal of Botany, 1987, 74(1): 123-131.
[18] 王卿. 互花米草在上海崇明东滩的入侵历史、分布现状和扩张趋势的预测[J].长江流域资源与环境, 2011, 20(6): 690-696.
Wang Qing. Spartaina alterniflora invasion in chongming dongtan, Shanghai: history, status and prediction[J].Resources and Environment in the Yangtze Basin, 2011, 20(6): 690-696.
[19] 陈希, 钱江海, 韩定定. L空间和P空间模型下的树状结构网络[J].计算机应用研究, 2015, (1):45-47.
Chen Xi, Qian Jianghai, Han Dingding. Tree network under space L and space P model[J].Application Research of Computers, 2015, (1):45-47.
[20] Wilkinson G S. Reciprocal food sharing in the vampire bat[J].Nature, 1984, 308(5955): 181.
