Eco-Evolutionary Graph Theory: Regular Graphs can act as Amplifiers

The Moran model is celebrated for its analytical tractability, yet on network-structured populations it produces contradictory predictions dependent on a seemingly arbitrary choice of birth and death update rule, limiting its biological utility. Here we resolve this problem by decoupling birth and death processes and introducing vacant space. We show that this framework unifies existing models, finding that as the death rate tends to zero the ecological model converges to the death-Birth (dB) Moran process, while the Birth-death (Bd) fixation probability emerges as an upper bound in the limit of large fitness differentials. In this framework random regular and lattice graphs can increase the fixation probability of advantageous mutants and decrease the fixation probability of disadvantageous mutants. They are therefore amplifiers of selection, despite being neutral or suppressing in the Moran model, demonstrating how the introduction of vacant space alters evolutionary outcomes on population structures. This unifying approach is biologically motivated, with results varying continuously via scalar parameters rather than switching between discrete modelling choices. This enables its application in real-world scenarios and offers a better understanding of how population structures and connectivity promote or suppress evolution.