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Abstract:

Ruggedness—the prevalence of fitness peaks—and navigability—the existence of fitness-increasing paths to a target—are key factors affecting evolution on fitness landscapes. Here, we analyze these properties in landscapes that inherit biophysically grounded genotype–phenotype (GP) maps. By assuming a random phenotype-fitness assignment as a baseline, the structure of the GP maps is included without imposing further fitness correlations. We show analytically that the expected ruggedness can be predicted from two quantities: the sizes of neutral components (NCs)—mutationally connected genotype sets with the same phenotype—and their evolvabilities, defined as the number of distinct phenotypes among the NC’s mutational neighbors. Other features—such as robustness—influence ruggedness only indirectly via correlations with evolvability. Numerical results across diverse GP maps confirm that NC size and evolvability alone suffice to predict both the mean prevalence and heights of peaks. These calculations also provide new insights: Under random phenotype-fitness assignment, peaks arising from high-evolvability NCs have higher expected fitness than those from low-evolvability NCs. Thus, when evolvability correlates positively with NC size, the formation of large low-fitness peaks is impeded. We further derive an approximate scaling law for the minimal average evolvability required for navigability. Our framework applies broadly across GP maps, providing general insight into when and why fitness landscapes are expected to be rugged or navigable.

Abstract:

We establish twisted SnSe 2 as a tunable platform for simulating dimension-dependent correlated physics, distinct from conventional K-valley moiré systems. By constructing interacting Wannier models, we show that the stacking configuration dictates the effective lattice geometry. In AA-stacked bilayers, a momentumspace nonsymmorphic symmetry constrains the single-particle hopping within each valley to be effectively one-dimensional while still allowing fully two-dimensional interactions, thereby giving rise to an effective quasi-one-dimensional system. This dimensional reduction stabilizes exotic phases including dimerized states with finite residual entropy, valence bond solids, and quantum paramagnetism. Conversely, AB stacking maps to a frustrated Kagome lattice; here, strong interactions drive the emergence of a classical spin liquid. The high tunability of this moiré system, which allows control over both the filling and interaction strength (via twist angle), renders twisted SnSe 2 a versatile platform for realizing a wide range of exotic correlated quantum phases.