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Individuals of different types, may it be genetic, cultural, or else, withdifferent levels of fitness often compete for reproduction and survival. Afitter type generally has higher chances of disseminating their copies to otherindividuals. The fixation probability of a single mutant type introduced in apopulation of wild-type individuals quantifies how likely the mutant typespreads. How much the excess fitness of the mutant type increases its fixationprobability, namely, the selection pressure, is important in assessing theimpact of the introduced mutant. Previous studies mostly based on undirectedand unweighted contact networks of individuals showed that the selectionpressure depends on the structure of networks and the rule of reproduction.Real networks underlying ecological and social interactions are usuallydirected or weighted. Here we examine how the selection pressure is modulatedby directionality of interactions under several update rules. Our conclusionsare twofold. First, directionality discounts the selection pressure fordifferent networks and update rules. Second, given a network, the update rulesin which death events precede reproduction events significantly decrease theselection pressure than the other rules.

Directionality of contact networks suppresses selection pressure in evolutionary dynamics