Epistasis and empirical fitness landscapes

Biologists tend to focus on nuances — to the point that Rutherford considered the field as stamp-collecting — and very local properties of systems, leading at times to rather reductionist views. These approaches are useful for connecting to experiment, but can be shown to underspecify conceptual models that need a more holistic approach. In the case of fitness landscapes, the metric that biologists study is epistasis — the amount of between locus interactions — and is usually considered for the interaction of just two loci at a time; although Beerenwinkel et al. (2007a,b) have recently introduced a geometric theory of gene interaction for considering epistasis across any number of loci. In contrast, more holistic measures can be as simple as the number of peaks in the landscape, or the computational or as complicated as the global combinatorial features of interest to theoretical computer scientists. In this post I discuss connections between the two and provide a brief overview of the empirical work on fitness landscapes.

Epistasis in fitness graphs of two loci. Arrows point from lower fitness to higher fitness, and AB always has higher fitness than ab. From left to right no epistasis, sign epistasis, reverse sign epistasis.

Epistasis in fitness graphs of two loci. Arrows point from lower fitness to higher fitness, and AB always has higher fitness than ab. From left to right no epistasis, sign epistasis, reverse sign epistasis.


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Fitness landscapes as mental and mathematical models of evolution

A figure from Wright's 1932 paper introducing fitness landscapes. I am surprised at how modern it looks.

A figure from Wright’s 1932 paper introducing fitness landscapes. I am surprised at how modern it looks.

As Jacob Scott pointed out, everybody — theorist or experimentalist — “has a logical construct (a model) in his or her head” when studying anything. This model might be mathematically explicit or implicit in the mind, but it is there and if the world is mechanistic (or if we only want to consider mechanistic theories of the world) then so is the model. One of the goals of philosophy (as well as theoretical parts of science) is to study these implicit (or explicit) models and understand if they have any fundamental limitations or introduce biases that might be independent of the empirical world that we hope they represent. Since theoretical computer science is a natural extension of the analytic approach to philosophy, and since it is perfectly adapted for studying abstract mechanistic models, it is my hope to use computer science to enlighten our understanding of our mental models. In the case of evolution, the prevalent mental (and later mathematical) model that I want to study was introduced in 1932 by Sewall Wright — the fitness landscape.
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Micro-vs-macro evolution is a purely methodological distinction

Evolution of CreationismOn the internet, the terms macroevolution and microevolution (especially together) are usually used primarily in creationist rhetoric. As such, it is usually best to avoid them, especially when talking to non-scientists. The main mistake creationist perpetuate when thinking about micro-vs-macro evolution, is that the two are somehow different and distinct physical processes. This is simply not the case, they are both just evolution. The scientific distinction between the terms, comes not from the physical world around us, but from how we choose to talk about it. When a biologist says “microevolution” or “macroevolution” they are actually signaling what kind of questions they are interested in asking, or what sort of tools they plan on using.
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