Learning the Shape of Evolutionary Landscapes: Geometric Deep Learning Reveals Hidden Structure in Phenotype-to-Fitness Maps

Elucidating the complex relationships between genotypes, phenotypes, and fitness remains one of the fundamental challenges in evolutionary biology. Part of the difficulty arises from the enormous number of possible genotypes and the lack of understanding of the underlying phenotypic differences driving adaptation. Here, we present a computational method that takes advantage of modern high-throughput fitness measurements to learn a map from high-dimensional fitness profiles to a low-dimensional latent space in a geometry-informed manner. We demonstrate that our approach using a Riemannian Hamiltonian Variational Autoencoder (RHVAE) outperforms traditional linear dimensionality reduction techniques by capturing the nonlinear structure of the phenotype-fitness map. When applied to simulated adaptive dynamics, we show that the learned latent space retains information about the underlying adaptive phenotypic space and accurately reconstructs complex fitness landscapes. We then apply this method to a dataset of high-throughput fitness measurements of E. coli under different antibiotic pressures and demonstrate superior predictive power for out-of-sample data compared to linear approaches. Our work provides a data-driven implementation of Fishers geometric model of adaptation, transforming it from a theoretical framework into an empirically grounded approach for understanding evolutionary dynamics using modern deep learning methods.