The Rate of Fitness-Valley Crossing in Sexual Populations - Biological adaptation dynamics

Sep 15, 2026

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Genetic interactions across multiple loci can create sign epistasis, where beneficial adaptation requires a combination of individually deleterious or neutral mutations, forcing populations to cross a fitness valley on a landscape. A theoretical framework analyzes the simplest two-locus fitness-valley model and determines how recombination reshapes crossing times over all key parameter regimes. Low recombination accelerates crossing relative to asexual evolution, whereas higher recombination retards it, yielding exponential growth of crossing time with population size when recombination is high and single mutants are strongly selected against. Optimal low recombination can reduce crossing times by orders of magnitude.

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Abstract

Sign epistasis and fitness valleys

Two-locus theoretical framework

Recombination effects across parameter regimes

Population-size scaling and selection against mutants

Implications for pathogens and vaccines

Copyright ! 2010 by the Genetics Society of America DOI: 10.1534/genetics.110.123240 The Rate of Fitness-Valley Crossing in Sexual Populations Daniel B. Weissman,*,1 Marcus W. Feldman† and Daniel S. Fisher‡ *Institute of Science and Technology Austria, A-3400 Klosterneuburg, Austria and †Department of Biology and ‡Department of Applied Physics, Stanford University, Stanford, California 94305 Manuscript received June 22, 2010 Accepted for publication September 27, 2010 ABSTRACT Biological traits result in part from interactions between different genetic loci. This can lead to sign epistasis, in which a beneﬁcial adaptation involves a combination of individually deleterious or neutral mutations; in this case, a population must cross a ‘‘ﬁtness valley’’ to adapt. Recombination can assist this process by combining mutations from different individuals or retard it by breaking up the adaptive combination. Here, we analyze the simplest ﬁtness valley, in which an adaptation requires one mutation at each of two loci to provide a ﬁtness beneﬁt. We present a theoretical analysis of the effect of recombination on the valley-crossing process across the full spectrum of possible parameter regimes. We ﬁnd that low recombination rates can speed up valley crossing relative to the asexual case, while higher recombination rates slow down valley crossing, with the transition between the two regimes occurring when therecombination rate between the loci is approximately equal to the selective advantage provided by the adaptation. In large populations, if the recombination rate is high and selection against single mutants is substantial, the time to cross the valley grows exponentially with population size, effectively meaning that the population cannot acquire the adaptation. Recombination at the optimal (low) rate can reduce the valleycrossing time by up to several orders of magnitude relative to that in an asexual population. MOST phenotypes depend on interactions between many different genes. For any given trait, there are likely to be many possible adaptations that involve combinations of mutations at different loci. Examples include signaling pathways that require coevolution of receptors and ligands (Goh et al. 2000), pathogens that may require several mutations to escape their hosts’immune response ortobecome resistant to drugs(Levinet al. 2000), and bacteria that require multiple mutations toevolvetheabilitytometabolizeanewnutrient(Blount et al. 2008) . While such complex adaptations may be acquired through successive individually beneﬁcial mutations (Bridgham et al. 2006), it is likely that some adaptations require a combination of mutations that are each individually neutral or deleterious in the absence of the other mutations. Using the ﬁtness landscape metaphor, populations must cross a‘‘ﬁtnessvalley’’to acquire such adaptations. Valley crossing provides a means for populations to escape local ‘‘ﬁtness peaks’’ or ‘‘plateaus’’where no single mutation isindividuallybeneﬁcial. Itmay also be a common mode of adaptation even when individuallybeneﬁcial mutations are available, especially in large populations (Weissman et al. 2009), as is typical of microbes or Drosophila. Understanding the dynamics of crossing ﬁtness valleys is particularly important for understanding pathogen 1 Corresponding author: Institute of Science and Technology Austria, Am Campus 1, A-3400 Klosterneuburg, [Austria. E-mail: dbw@ist.ac.at](Austria. E-mail: dbw@ist.ac.at) Genetics 186: 1389–1410 (December 2010) evolution. An adaptation that requires crossing a ﬁtness valley should generally be more difﬁcult for a population to acquire than an adaptation that can be reached by going straight ‘‘uphill.’’ For a method of combating a pathogen to be effective, it must be difﬁcult for the pathogen to adapt to it; this suggests that treatments should typically confront the pathogen with a ﬁtness valley. Similarly, for an attenuated strain of a virus

FAQs

What evolutionary process makes a fitness valley necessary for adaptation?

When beneficial adaptation depends on a specific combination of mutations at two loci, each mutation alone can be neutral or deleterious (sign epistasis). The population must therefore cross a fitness valley to reach the advantageous genotype combination.

How does recombination change the time required to cross a fitness valley?

Low recombination can speed valley crossing by assembling beneficial combinations from different individuals. Higher recombination often slows crossing by breaking apart those combinations.

When does valley crossing become effectively impossible for large populations?

In large populations, if recombination is high and selection against single mutants is substantial, the expected time to cross the valley increases exponentially with population size, effectively preventing acquisition of the adaptation.

Sep 15, 2026

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