title: How Good Are Statistical Models at Approximating Complex Fitness Landscapes?
abstract: Fitness landscapes determine the course of adaptation by constraining and shaping evolutionary trajectories. Knowledge of the structure of a fitness landscape can thus predict evolutionary outcomes. Empirical fitness landscapes, however, have so far only offered limited insight into real-world questions, as the high dimensionality of sequence spaces makes it impossible to exhaustively measure the fitness of all variants of biologically meaningful sequences. We must therefore revert to statistical descriptions of fitness landscapes that are based on a sparse sample of fitness measurements. It remains unclear, however, how much data are required for such statistical descriptions to be useful. Here, we assess the ability of regression models accounting for single and pairwise mutations to correctly approximate a complex quasi-empirical fitness landscape. We compare approximations based on various sampling regimes of an RNA landscape and find that the sampling regime strongly influences the quality of the regression. On the one hand it is generally impossible to generate sufficient samples to achieve a good approximation of the complete fitness landscape, and on the other hand systematic sampling schemes can only provide a good description of the immediate neighborhood of a sequence of interest. Nevertheless, we obtain a remarkably good and unbiased fit to the local landscape when using sequences from a population that has evolved under strong selection. Thus, current statistical methods can provide a good approximation to the landscape of naturally evolving populations.
authors.affiliation: Department of Biosystems Science and Engineering, ETH Zürich, Basel, Switzerland Insitute for Integrative Biology, ETH Zürich, Zürich, Switzerland Swiss Institute of Bioinformatics, Switzerland louis.duplessis@env.ethz.ch.
authors.forename: Louis
authors.initials: L
authors.lastname: du Plessis
authors.affiliation: Insitute for Integrative Biology, ETH Zürich, Zürich, Switzerland Department of Civil and Environmental Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA.
authors.forename: Gabriel E
authors.initials: GE
authors.lastname: Leventhal
authors.affiliation: Insitute for Integrative Biology, ETH Zürich, Zürich, Switzerland.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Bonhoeffer
mesh_terms: D000222:Adaptation, Physiological; D005075:Biological Evolution; D001699:Biometry / Q000379:methods; D004843:Epistasis, Genetic; D019143:Evolution, Molecular; D056084:Genetic Fitness; D006801:Humans; D008957:Models, Genetic; D015233:Models, Statistical; D009154:Mutation; D012313:RNA / Q000235:genetics; D012641:Selection, Genetic / Q000235:genetics; D017423:Sequence Analysis, RNA / Q000379:methods
chemical_list: D012313:RNA
keywords: RNA secondary structure; epistasis; fitness landscapes; penalized regression.