Empirical fitness landscapes and the predictability of evolution

Journal name:
Nature Reviews Genetics
Volume:
15,
Pages:
480–490
Year published:
DOI:
doi:10.1038/nrg3744
Published online

Abstract

The genotype–fitness map (that is, the fitness landscape) is a key determinant of evolution, yet it has mostly been used as a superficial metaphor because we know little about its structure. This is now changing, as real fitness landscapes are being analysed by constructing genotypes with all possible combinations of small sets of mutations observed in phylogenies or in evolution experiments. In turn, these first glimpses of empirical fitness landscapes inspire theoretical analyses of the predictability of evolution. Here, we review these recent empirical and theoretical developments, identify methodological issues and organizing principles, and discuss possibilities to develop more realistic fitness landscape models.

At a glance

Figures

  1. Development of the fitness landscape concept.
    Figure 1: Development of the fitness landscape concept.

    A fitness landscape can be visualized as a 'mountainous' landscape in three dimensions with genotypes arranged in the x–y plane and fitness on the z axis (part a). The landscape shown is rugged with three fitness peaks separated by fitness 'valleys', and two imaginary evolutionary trajectories are shown by white dots and arrows. Wright's two-dimensional “field of gene combinations” (Ref. 8) is shown (part b). Fitness maximum and minimum are represented as “+” and “−”, respectively; dotted lines are contours of equal fitness. A recent example of an empirical fitness landscape involves four mutations in the antibiotic resistance enzyme β-lactamase TEM1, which cause increased resistance to cefotaxime44 (part c). Nodes represent the 24 (that is, 16) genotypes; 0 and 1 indicate wild-type and mutant amino acids, respectively. Arrows connect genotypes that differ by a single mutation and point towards genotypes with higher resistance. Bold black arrows indicate the 'greedy' walk (which substitutes the existing genotype with the largest-benefit mutation among the mutations available at each step) from wild-type (0000) to the global maximum (1010).

  2. Approaches for the empirical study of fitness landscapes.
    Figure 2: Approaches for the empirical study of fitness landscapes.

    Experimental approaches for studying small-scale fitness landscapes share three essential components: a set of mutations of interest is identified (part A); mutants are constructed to carry all 2L possible combinations of the L selected mutations (in this case, L = 3, and 0 and 1 indicate the absence and presence of the mutation, respectively) (part B); and the fitness or a fitness proxy (for example, antibiotic resistance) is measured for all genotypes. Mutations of interest can come from three different sources: from phylogenetic analyses that infer the ancestor of extant genotypes (part Aa); from microbial evolution experiments in which mutations co-occur in an evolving lineage (part Ab); or from sets of mutants that each carry a single mutation (part Ac), such as alternative mutations that cause antibiotic resistance. The a posteriori approaches (parts Aa, Ab) are less likely to find much sign epistasis because these mutations have collectively 'survived' the selective pressure, whereas the a priori approach (part Ac) does not suffer from this bias.

  3. Trends in the ruggedness of empirical fitness landscapes.
    Figure 3: Trends in the ruggedness of empirical fitness landscapes.

    Three measures that quantify the ruggedness are shown for a subset of eight available fitness landscapes: the number of fitness maxima (Nmax), the fraction of mutation pairs with sign epistasis or reciprocal sign epistasis (fepi) and the roughness/slope ratio (r/s) (Box 1). For landscapes of different sizes to be comparable, all measures were calculated for subgraphs of size four10. Each plot compares two ruggedness measures for the eight landscapes, which belong to one of three classes with respect to the type of mutations involved: collectively beneficial mutations, individually beneficial mutations or individually deleterious mutations. Currently, no landscapes exist for collectively deleterious mutations. The 4–8 mutations of each landscape affect either a single gene or multiple genes in a range of microbial species, and fitness (F), growth rate (GR) or resistance (R) is measured. For comparison, expected values for a fully additive landscape (green) and a maximally rugged landscape (red; which is represented by the house-of-cards (HoC) model) are shown. Although the three measures capture different types of epistasis, they correlate reasonably well. The available empirical fitness landscapes show considerable ruggedness, especially if the combined fitness effect of mutations is unknown.

  4. Evolutionary predictability is affected by population size.
    Figure 4: Evolutionary predictability is affected by population size.

    Mutational trajectories are shown for populations of small, intermediate and large sizes on a rugged three-locus fitness landscape with global maximum 111 and local maximum 100. Nodes represent genotypes (in which 0 and 1 indicate the absence and presence of each of three mutations, respectively), and edges connect genotypes that differ in a single mutation. Arrows show mutational trajectories, which start from the wild type (000) and are realized in a limited time period that is sufficient for the fixation of a single mutation in populations of small or intermediate sizes. The width of the arrows indicates the repeatability of trajectories, which is a measure of evolutionary predictability. The small population is in the strong-selection–weak-mutation (SSWM) regime, in which different trajectories are realized owing to the chance occurrence and subsequent fixation of mutations, and predictability is therefore low. At intermediate population size, clonal interference causes the preferential fixation of the mutation with the largest benefit among the three available mutations, thereby maximizing predictability. In even larger populations, multiple mutations may sometimes fix simultaneously, which allows 'valley crossing' and decreases predictability.

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Affiliations

  1. Laboratory of Genetics, Wageningen University, Droevendaalsesteeg 1, 6708PB Wageningen, The Netherlands.

    • J. Arjan G.M. de Visser
  2. Institute for Theoretical Physics, University of Cologne, Zülpicher Str. 77, 50937 Köln, Germany.

    • Joachim Krug

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  • J. Arjan G.M. de Visser

    J. Arjan G. M. de Visser is an evolutionary geneticist who uses experiments with microorganisms to address the causes and constraints of evolution. He graduated in 1996 from Wageningen University, the Netherlands, where he carried out research on experimental tests of epistasis among deleterious mutations. During postdoctoral work at Michigan State University, East Lansing, USA, he studied evolutionary consequences of high mutation rates. Since 2001, he is on the faculty at Wageningen University, where he studies, among others, the evolutionary causes and consequences of empirical fitness landscapes. Arjan G. M. de Visser's homepage.

  • Joachim Krug

    Joachim Krug is a theoretical physicist with a background in statistical physics. After graduating from Ludwig Maximilians Universität in Munich, Germany, in 1989, he held appointments at the International Business Machines (IBM) T. J. Watson Research Center, New York, USA; Forschungszentrum Jülich, Germany; and the University of Duisburg-Essen, Germany. He entered the field of evolutionary biology when he moved to the University of Cologne, Germany, in 2004, and is primarily interested in developing models of adaptation in the context of microbial evolution. Joachim Krug's homepage.

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