Exploring the rift between update rules in evolutionary graph theory: The natural death rates can drive suppression of natural selection in structured populations

Evolutionary graph theory (EGT) is the study of evolutionary dynamics in structured populations. A well-known result in evolutionary graph theory is that the spread of mutation (measured by fixation probability) is impacted by the graph type chosen and the update rule. For example, the star graph is an amplifier of natural selection under the Birth-death (Bd) update rule but a suppressor of natural selection under the death-Birth (dB) update rule. Although typically studied in discrete-time, a continuous-time EGT model has been found to recover Bd and dB results as special cases. Using this model, we show that changing the natural (intrinsic) death rate can cause a shift from Bd to dB dynamics. Assuming the mutant is advantageous, we show that if the natural death rate is asymptotically greater than 1/sqrt(N) the star graph is a suppressor, where N is the number of nodes. As N goes to infinity, the natural death rate required to drive the star to a suppressor therefore tends towards zero, so as the size of the graph increases, the star graph is likely to be suppressing for any non-zero natural death rate. We then extend the analysis to more complex graphs through numerical simulation, and summarise how the behaviour of graphs change as a function of the natural death rate, finding most graphs switch from amplifier to suppressor. The magnitude of the death rate required to drive a graph to suppress selection varies non-monotonically with the birth rate advantage of mutants.