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Evolutionary dynamics on sequential temporal networks

Fig 2

Fixation probabilities of sequential temporal networks and static networks.

We present three examples for illustrating the analytical result in Eq (6). The number of nodes in the first and second snapshots is denoted as m₁ and m₂, and the increment of nodes (edges) in the second and third snapshots is denoted as Δm₁ (ΔK₁) and Δm₂ (ΔK₂). a, The number of nodes grows exponentially, fulfilling Eq (6a) (i.e. Δm₁ = 3 > m₁ = 2 and Δm₂ = 6 > m₂ = 5). Then the fixation probability of sequential temporal network, , is greater than that of its static counterpart, . b, The increase in the number of nodes and edges fulfills Eq (6b) (i.e. Δm₁ = 1 < m₁ = 6, ΔK₁ = 2 < 2.4 and Δm₂ = 2 < m₂ = 7, ΔK₂ = 6 < 6.4). As a result, the fixation probability is still higher in the sequential temporal network (). c, When each pair of adjacent snapshots does not satisfy Eqs (6a) and (6b) (i.e. Δm₁ = 1 < m₁ = 6, ΔK₁ = 3 > 2.4 and Δm₂ = 2 < m₂ = 7, ΔK₂ = 8 > 7.2), the fixation probability becomes greater in the static network ().

doi: https://doi.org/10.1371/journal.pcbi.1011333.g002