Equilibrium Distributions of Populations of Biological Species on Networks of Social Sites.
Equilibrium Distributions of Populations of Biological Species on Networks of Social Sites.
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DOI：
10.1080/17513758.2018.1508762
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发表时间：
2019
影响因子：
2.8
通讯作者：
Wu Z
中科院分区：
文献类型：
--
作者：
Wang M;Zhou W;Wu Z
我们研究了生物种群如何分布在给定的社交网站网络上，以便他们通过连接的网站进行的社交联系可以最大化(或最小化)。这一问题在模拟群居(或独居)物种的行为方面有应用，如人类社会中社群的发展和独居动物在遥远栖息地的传播。我们证明了这个问题可以被描述为一个进化博弈，博弈的均衡状态对应于选择居住点的策略，每个策略都具有一定的概率，或者等价地对应于这些点上的人口分布。博弈具有对称的支付矩阵，因此可以通过相应的二次规划的解来分析：博弈的均衡策略是二次规划的KKT点，它可以是局部极大值、局部极小值或鞍点，但当且仅当它是严格的局部极大值时，它是进化稳定的。一般而言，为了最大限度地扩大社会联系，该物种倾向于在有密集连接的网络站点上传播，例如一个完整的子网络或换句话说，一个网络集团。我们证明了在均衡时，种群可能分布在网络集团上，也可能不分布在网络集团上，但平衡态的稳定性确实取决于所选子网络的结构。特别地，我们证明了群体在最大网络集团上的分布是进化稳定的，除非该集团“依附”到另一个相同或更大规模的集团，当群体能够切换或扩展到邻近集团以增加或至少保持其联系总数时。然而，非集团子网络上的人口分布在进化上总是不稳定的，或者充其量也就是弱进化稳定的，因为人口总是可以在不减少其联系总数的情况下离开当前的分布。我们的结论是，在最大网络集团上传播的策略不仅是均衡策略，而且在进化上比非集团子网络上的策略更稳定，从而从理论上重申了社会物种加入社会集团在社会网络中的进化优势。
We investigate the problem of how a population of biological species would distribute over a given network of social sites so that their social contacts through the connected sites can be maximized (or minimized). This problem has applications in modeling the behaviors of social (or solitary) species such as the development of social groups in human society and the spread of solitary animals in distant habitats. We show that this problem can be formulated as an evolutionary game, with the equilibrium state of the game corresponding to a strategy for choosing the residing sites, each with a certain probability, or equivalently, to a distribution of the population on these sites. The game has a symmetric payoff matrix, and can therefore be analyzed via the solution of a corresponding quadratic program: An equilibrium strategy of the game is a KKT point of the quadratic program, which may be a local maximizer, local minimizer, or saddle point, but it is evolutionarily stable if and only if it is a strict local maximizer. In general, with a goal to maximize the social contacts, the species tend to spread on network sites where there are dense connections such as a complete subnetwork or in other words, a network clique. We show that at equilibrium, the population may or may not distribute on a network clique, but the stability of the equilibrium state does depend on the structure of the selected subnetwork. In particular, we show that the distribution of the population on a maximal network clique is evolutionarily stable unless the clique is “attached” to another clique of the same or larger size, when the population may be able to switch or expand to the neighboring clique to increase or at least maintain its total amount of contacts. However, the distribution of the population on a non-clique subnetwork is always evolutionarily unstable or weakly evolutionarily stable at the very best, for the population can always move away from its current distribution without decreasing its total amount of contacts. We conclude that the strategies to spread on maximal network cliques are not only equilibrium strategies but also evolutionarily more stable than those on non-clique subnetworks, thus theoretically reaffirming the evolutionary advantages of joining social cliques in social networks for social species.
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DOI：
10.1136/bmj.a2338
发表时间：
2008-12-04
期刊：
BMJ (Clinical research ed.)
影响因子：
--
作者：
Fowler JH;Christakis NA
通讯作者：
Christakis NA
影响因子：
2.6
作者：
Huang, Yuanyuan;Hao, Yiping;Wu, Zhijun
通讯作者：
Wu, Zhijun
影响因子：
64.8
作者：
Ohtsuki, Hisashi;Hauert, Christoph;Nowak, Martin A.
通讯作者：
Nowak, Martin A.
影响因子：
16.6
作者：
Leventhal, Gabriel E.;Hill, Alison L.;Nowak, Martin A.;Bonhoeffer, Sebastian
通讯作者：
Bonhoeffer, Sebastian
影响因子：
10.2
作者：
Bomze, IM
通讯作者：
Bomze, IM