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Assessing the fitness landscape revolution

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Abstract

According to Pigliucci and Kaplan, there is a revolution underway in how we understand fitness landscapes. Recent models suggest that a perennial problem in these landscapes—how to get from one peak across a fitness valley to another peak—is, in fact, non-existent. In this paper I assess the structure and the extent of Pigliucci and Kaplan’s proposed revolution and argue for two points. First, I provide an alternative interpretation of what underwrites this revolution, motivated by some recent work on model-based science. Second, I show that the implications of this revolution need to carefully assessed depending on question being asked, for peak-shifting is not central to all evolutionary questions that fitness landscapes have been used to explore.

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Notes

  1. Somewhat less common is to refer to fitness landscapes as things that exist “out there” in the world: “Many authors have assumed that the adaptive landscape is merely a metaphor ... These authors have ignored the possibility that the adaptive landscape—like mutation, drift, and inheritance—is an object for empirical study” (Arnold 2003, pp. 367–368).

  2. It is not clear how these metaphors might relate to any theory of literary metaphor, an area which itself has no univocal view on what metaphor is (Camp and Reimer 2006).

  3. In particular, I shall limit the informal description to topological configuration spaces—landscape structures whose neighbourhoods are defined by a set of independent dimensions (a euclidean vector space). This excludes pre-topological spaces, where neighbourhoods may be defined arbitrarily as a directed graph. Most (but not all) current landscape models in evolutionary biology are topological spaces (all of Gavrilets models, for example). For further details see (Stadler 2002; Stadler et al. 2002; Stadler and Stadler 2006).

  4. There is already an important difference between genotypic and phenotypic models in how change might occur in a particular dimension. Typically, any allele might change into any other allele, but changes along a phenotypic dimension are often themselves constrained in some way to small increments in (for example) size, shape, or angle.

  5. In general, fitness landscape models assume something like point mutations. This is, of course, a huge simplification. Some models do consider the affects of other types of mutation, such as unequal crossover (Shpak and Wagner 2000). The upshot is complicated, to say the least.

  6. Weisberg has pursued this idea, which Levins called robustness analysis (Levins 1966; Weisberg and Reisman 2008). However, it is not clear that what is going on here is exactly the same. Robustness analysis looks at how models with different idealizations produce the same results, with the intent of showing that the results are not simply artifacts of particular idealizations. In this case, however, one model provides reasons for believing the assumptions of another. This suggests that robustness is not the only relation of support that might obtain between multiple models.

  7. Pigliucci and Kaplan’ discussion may lead one to believe there is a single fitness landscape model that Gavrilets analyses (Pigliucci and Kaplan 2006, pp. 193–194). But they mention both a model from “percolation theory” and the “Bateson–Dobzhansky–Muller model”. These are distinct models.

  8. For example, many of Kauffman’s rugged landscapes have up to 24-dimensions (Kauffman 1993). Well beyond anything I can visualise!

  9. I take it that the assumption is that the fitness of neighbours is highly correlated depends on the phenotypes of neighbours being highly correlated.

  10. Speciation in Gavrilets’ sense of genetic divergence causing reproductive isolation (Gavrilets 2004, p. 9).

  11. See the “Generalized Russian Roulette Model” (Gavrilets 2004, p. 89).

  12. Niklas’ results suggest this is not an unreasonable assumption (Niklas 2004, p. 54).

  13. In a similar manner to how Gavrilets’ first established the holey properties of landscapes—what I have called the first step of his argument.

  14. Note that Gavrilets refers to the work on RNA landscapes in his book on speciation (and Pigliucci and Kaplan subsequently refer to it in their analysis of Gavrilets). Notably, it is used as additional justification for the presence of neutrality (step 1 of his argument, as I described it in “Speciation and fitness landscapes”). Despite their mention by Gavrilets and Pigliucci and Kaplan, however, these papers on RNA folding have little to do with speciation.

  15. There are some unresolved issues regarding the relationship between models and model descriptions here. Although the putative model system is RNA folding, the mathematical representations examined by Fontana already simplify what we know about actual RNA folding (For example, they ignore tertiary structure). So the is the model being used to understand evo-devo RNA folding, or a simplified model of RNA folding? I shall not attempt to address these issues here.

  16. Fontana points out that, strictly speaking, it is not the structure that is treated as the phenotype in this model, but the topology of pairings. This topology can be represented in various ways, one of which will show the shape of the folded RNA (Fontana 2002, Figure 1, p1165). For the discussion here, this distinction will not matter.

  17. RNA strands with the same secondary structure may not act the same, as they have different bases at different locations. So it is an assumption in these models is that the same secondary structure is sufficient to cause the same fitness.

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Calcott, B. Assessing the fitness landscape revolution. Biol Philos 23, 639–657 (2008). https://doi.org/10.1007/s10539-008-9127-9

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