"Submodular fitness landscapes"Krug, JoachimSubmodularity is a property of set functions that is formally equivalent to the condition of universal negative epistasis of genotypic fitness landscapes defined on a binary sequence space [1]. Universal epistasis holds if all epistastic interactions, when oriented along a common direction in sequence space, are of a definite sign [1,2]. Submodular fitness landscapes are highly accessible, in the sense that the size of the basin of attraction of a fitness peak is bounded below by a number that grows exponentially with the sequence length L. In a typical submodular landscape, the number of peaks also grows exponentially in L. Submodularity therefore provides a promising conceptual framework for understanding the structure of large-scape empirical fitness landscapes that combine high ruggedness with high accessibility [3]. In this talk, I will explain the connection between submodularity, universal negative epistasis, and accessibility, and describe how submodularity arises generically from combining linear genotype-phenotype maps with concave phenotype-fitness functions. I will argue that the class of submodular fitness landscapes is remarkably broad, including representatives such as Fisher's geometric model [4] and tradeoff-induced fitness landscapes [5]. References: [1] J. Krug, D. Oros. Evolutionary accessibility of random and structured fitness landscapes. arXiv:2311.17432 [2] K. Crona, J. Krug, M. Srivastava. Geometry of fitness landscapes: peaks, shapes and universal positive epistasis. J. Math. Biol. 86:62 (2023) [3] A. Papkou, L. Garcia-Pastor, J.A. Escudero, A. Wagner. A rugged yet easily navigable fitness landscape. Science 382:eadh3860 (2023) [4] S. Hwang, S.-C. Park, J. Krug. Genotypic Complexity of Fisher’s Geometric Model. Genetics 206:1049–1079 (2017) [5] S.G. Das, S.O.L. Direito, B. Waclaw, R.J. Allen, J. Krug. Predictable properties of fitness landscapes induced by adaptational tradeoffs. eLife 9:e55155 (2020) |
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