Characterizing the effect of population heterogeneity on evolutionary dynamics on complex networks

Abstract

Recently, the impact of network structure on evolutionary dynamics has been at the center of attention when studying the evolutionary process of structured populations. This paper aims at finding out the key structural feature of network to capture its impact on evolutionary dynamics. To this end, a novel concept called heat heterogeneity is introduced to characterize the structural heterogeneity of network, and the correlation between heat heterogeneity of structure and outcome of evolutionary dynamics is further investigated on various networks. It is found that the heat heterogeneity mainly determines the impact of network structure on evolutionary dynamics on complex networks. In detail, the heat heterogeneity readjusts the selection effect on evolutionary dynamics. Networks with high heat heterogeneity amplify the selection effect on the birth-death process and suppress the selection effect on the death-birth process. Based on the above results, an effective algorithm is proposed to generate selection adjusters with desired size and average degree.

Fast and asymptotic computation of the fixation probability for Moran processes on graphs

“…For complete bipartite graphs, after erasing all non-trivial loops, partial symmetries arise asymptotically in the Moran process and reduce the Moran process to the particular case of a star graph. This is an important step since it shed some new light on the asymptotic behaviour of the fixation on bipartite graphs, which has recently been dealt with from other points of view in [9] and [21].…”

“…In particular, a star graph is a bipartite graph K m,1 . The fixation probability for these graphs has been also studied in [9] and [21].…”

“…We call loop-erasing the loop suppression in this graph S, avoiding to remain in the same state in two consecutive steps and providing the Embedded Markov chain (EMC) associated to the process. This technique is used here to compute asymptotically the average fixation probability for complete bipartite graphs, generalising the Star Theorem of [11], see also [1], [9] and [21]. Expected time to absorption (fixation or extinction) of this EMC has been studied for circular, complete and star graphs in [7].…”

Evolution of cooperation in Axelrod tournament using cellular automata

“…First fitness function is the ''random'', that is, when an individual dies, the new individual will choose any of the strategies among its neighbors. If we consider the after death characteristic of such approach, it may be partially interpreted either as a voter model [30] or a death-birth process [31].…”

Moments Inequalities for NBRUrp Distributions with Hypotheses Testing Applications

“…It is easily seen that = ( = | > ), that is, the probability that the component with lifetime causes the system failure given that the system has survived up to time (cf. Zardasht and Asadi [27] for several reliability properties, Tan and Lü [26] for some biological background, and Lü and Chen [20] , Chen et al [9] and Zhou et al [28] for some real world applications). Formally, in view of the function, the lifetime random variable is said to be smaller than in the order (denoted by ≤ ) if and only if ≤ 0.5, ∀ > 0.…”