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A population’s spatial structure affects the rate of genetic change and the outcome of natural selection. These effects can be modeled mathematically using the Birth-death process on graphs. Individuals occupy the vertices of a weighted graph, and reproduce into neighboring vertices based on fitness. A key quantity is the probability that a mutant type will sweep to fixation, as a function of the mutant’s fitness. Graphs that increase the fixation probability of beneficial mutations, and decrease that of deleterious mutations, are said to amplify selection. However, fixation probabilities are difficult to compute for an arbitrary graph. Here we derive an expression for the fixation probability, of a weakly-selected mutation, in terms of the time for two lineages to coalesce. This expression enables weak-selection fixation probabilities to be computed, for an arbitrary weighted graph, in polynomial time. Applying this method, we explore the range of possible effects of graph structure on natural selection, genetic drift, and the balance between the two. Using exhaustive analysis of small graphs and a genetic search algorithm, we identify families of graphs with striking effects on fixation probability, and we analyze these families mathematically. Our work reveals the nuanced effects of graph structure on natural selection and neutral drift. In particular, we show how these notions depend critically on the process by which mutations arise.

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608 Background: The role of CN for mRCC treated with ICI is not well defined. Our aim was to evaluate the role of CN for mRCC treated by ICI or TT using a propensity score-based analysis. Methods: We retrospectively assessed patients who were diagnosed with de novo mRCC and who had started first line systemic therapy (ICI or TT) between 2009 and 2019 using the International Metastatic RCC Database Consortium (IMDC). Overall Survival (OS) was compared between patients receiving CN and those treated by systemic therapies alone, using the Kaplan-Meier method and Cox regressions, in the TT and ICI arms separately. In order to account for treatment selection bias, inverse probability of treatment weighting (IPTW) of propensity scores, based on 14 confounding variables, was used and variables were considered balanced if standardized mean difference (SMD) < 0.1. For variables with SMD≥0.1, residual confounding was adjusted for using multivariable models. Results: 3856 patients had been treated by TT (2470 CN+ & 1386 CN-) and 198 by ICI (143 CN+ & 55 CN-). Median follow-up was 38.5 months. After IPTW, baseline characteristics were largely balanced between the CN+ and CN- arms, in the TT and ICI groups (14/14 and 12/14 with SMD < 0.1, respectively). CN was associated with significantly improved OS in both the ICI (Hazard Ratio [HR] = 0.39 [0.19-0.83]) and TT (HR = 0.56 [0.51-0.62]) groups. The interaction term between CN and therapy type (ICI vs TT) was not statistically significant (p = 0.43). The point estimates of the HRs were consistent in sensitivity analyses using multivariable models. Conclusions: In a propensity score-based analysis, CN was found to be associated with a significant OS benefit in patients treated by either ICI or TT. While this study is not a substitute for randomized controlled trials (e.g. CARMENA), the results suggest that CN may still play a role in selected patients in the ICI era.[Table: see text]

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