Scaling behavior of fixation paths in Moran processes on complex graphs

The trajectory to fixation in an evolutionary process is strongly influenced by the structure of the population on which it unfolds. In this work, we employ a regression-based approach to predict the fixation path in a range of complex graphs. In our framework, the fixation path itself is not used as the target variable in the learning procedure. Instead, we aim to estimate the probability of moving forward in the process (denoted by λ in the literature) using a regression model. Once λ is obtained, previously established results for the Moran process allow us to readily reconstruct the fixation path. As graph size grows, the fixation path exhibits a characteristic scaling behavior. This observation motivates our use of regression techniques to infer the fixation path in complex graphs. Since simulating evolutionary dynamics on large populations is both time-consuming and computationally expensive, leveraging machine learning methods enables us to conserve these critical resources.