## 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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## Quick introduction: Evolutionary game assay in Python

February 16, 2019 by Artem Kaznatcheev 4 Comments

It’s been a while since I’ve shared or discussed code on TheEGG. So to avoid always being too vague and theoretical, I want to use this post to explain how one would write some Python code to measure evolutionary games. This will be an annotated sketch of the game assay from our recent work on measuring evolutionary games in non-small cell lung cancer (Kaznatcheev et al., 2019).

The motivation for this post came about a month ago when Nathan Farrokhian was asking for some advice on how to repeat our game assay with a new experimental system. He has since done so (I think) by measuring the game between Gefitinib-sensitive and Gefitinib-resistant cell types. And I thought it would make a nice post in the quick introductions series.

Of course, the details of the system don’t matter. As long as you have an array of growth rates (call them yR and yG with corresponding errors yR_e and yG_e) and initial proportions of cell types (call them xR and xG) then you could repeat the assay. To see how to get to this array from more primitive measurements, see my old post on population dynamics from time-lapse microscopy. It also has Python code for your enjoyment.

In this post, I’ll go through the two final steps of the game assay. First, I’ll show how to fit and visualize fitness functions (Figure 3 in Kaznatcheev et al., 2019). Second, I’ll transform those fitness functions into game points and plot (Figure 4b in Kaznatcheev et al., 2019). I’ll save discussions of the non-linear game assay (see Appendix F in Kaznatcheev et al., 2019) for a future post.

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Filed under Commentary, Meta, Preliminary, Technical Tagged with empirical, mathematical oncology, operationalization, Python