The probability of improvement in Fisher's geometric model: A probabilistic approach

- We use a probabilistic approach to derive the probability of improvement in Fisher's geometric model of adaptation.
- Our approach provides an alternative interpretation of the main result of the model in terms of the model's parameters.
- This probabilistic approach can be used to solve additional problems in Fisher's geometric model.

Fisher developed his geometric model to support the micro-mutationalism hypothesis which claims that small mutations are more likely to be beneficial and therefore to contribute to evolution and adaptation. While others have provided a general solution to the model using geometric approaches, we derive an equivalent general solution using a probabilistic approach. Our approach to Fisher's geometric model provides alternative intuition and interpretation of the solution in terms of the model's parameters: for mutation to improve a phenotype, its relative beneficial effect must be larger than the ratio of its total effect and twice the difference between the current phenotype and the optimal one. Our approach provides new insight into this classical model of adaptive evolution.