## Quick introduction: Generalizing the NK-model of fitness landscapes

February 23, 2019 5 Comments

As regular readers of TheEGG know, I’ve been interested in fitness landscapes for many years. At their most basic, a fitness landscape is an almost unworkably vague idea: it is just a mapping from some description of organisms (usually a string corresponding to a genotype or phenotype) to fitness, alongside some notion of locality — i.e. some descriptions being closer to each other than to some other descriptions. Usually, fitness landscapes are studied over combinatorially large genotypic spaces on many loci, with locality coming form something like point mutations at each locus. These spaces are exponentially large in the number of loci. As such, no matter how rapidly next-generation sequencing and fitness assays expand, we will not be able to treat a fitness landscape as simply an array of numbers and measure each fitness. At least for any moderate or larger number of genes.

The space is just too big.

As such, we can’t consider an arbitrary mapping from genotypes to fitness. Instead, we need to consider compact representations.

Ever since Julian Z. Xue first introduced me to it, my favorite compact representation has probably been the NK-model of fitness landscapes. In this post, I will rehearse the definition of what I’d call the *classic* NK-model. But I’ll then consider how the model would have been defined if it was originally proposed by a mathematician or computer scientists. I’ll call this the *generalized* NK-model and argue that it isn’t only mathematically more natural but also biologically more sensible.

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