Saturday, 7 June 2014

Attractor? You keep using that word...

I've criticized the (bad) Claidiere/Sperber 2014 paper here recently - in my article titled: Is cultural evolution different because it is constructive?

This post goes after the paper's basic terminology. The paper defines the term 'attractor' to mean:

We can then characterize an attractor as any type whose relative frequency tends to increase over time.

This is a terribly broad definition of 'attractor' - and it is nothing like what the term is usually used to mean in complex systems theory. This is what the term "attractor" usually means:

In dynamical systems, an attractor is a set of physical properties toward which a system tends to evolve, regardless of the starting conditions of the system. Property values that get close enough to the attractor values remain close even if slightly disturbed.

I do not see the rationale for redefining 'attractor' to mean: anything that is subject to a relative increase in frequency. 'Attractor' is an ordinary English word - as well as an existing technical term. No matter how you cut it, it just doesn't mean anything like what Claidiere/Sperber say it means.

There's a long tradition of people using the term 'attractor' in its standard sense from complex systems theory in biology while talking about adaptive peaks on fitness landscapes. For example, look at the work on N/K fitness landscapes. I see no reason whatsoever to mess up this situation - by redefining a standard term to mean something counter-intuitive and confusing.

The Claidiere/Sperber definition of attractor is not just non-standard - it seems to be of no practical use. Defining an attractor as: "any type whose relative frequency tends to increase over time" makes anything decreasing in frequency slower than the fastest-decreasing type into an 'attractor' (relative to that most rapidly-decreasing type). What's the point of that? It seems practically useless as a classification scheme. Almost every type becomes an 'attractor'. The standard definition of 'attractor' doesn't suffer from this property - where practically everything is an 'attractor'.

Lastly, I am generally opposed to characterizing biological systems as subject to attraction - without making any mention of repulsion. Attraction-only dynamical systems are well known – e.g. gravitation. However, there are also dynamical systems with attraction and repulsion – e.g. electromagnetism. Repulsive selective forces are well known in biology – e.g. “divergent selection”. So: evolution is more like an electromagnetic system than a gravitational one in this respect. We probably don't want 'attraction-only' treatments of evolution becoming common - people will just get confused by them.

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