Evolution as an algorithm (Part One)

Evolution as an algorithm

While Monod characterised evolution in terms of its most basic features, Daniel Dennett has championed a conception of evolution at the next higher level of abstraction. He proposes that Darwin’s theory of natural selectionshould be thought of as an algorithm.

Some features of the world can be satisfactorily described in terms of laws and equations. Newton’s inverse-square law of gravitation is a perfect example. Others require statistical descriptions. But a faithful abstraction of natural selection needs to capture its cumulative and temporal character. Algorithms do this in ways that differential equations cannot.

Unlike typical discoveries in the sciences, an algorithm once uncovered, is no longer up for debate. The closest analogue is with mathematical theorems. Once Pythagoras had developed his theorem relating the lengths of the sides of right triangles, it could not be undeveloped. There is much to be gained from thinking of natural selection in algorithmic terms, and it is as unlikely to be refuted as Pythagoras’ theorem. This is one more reason why Dennett refers to natural selection as ‘Darwin’s Dangerous Idea.’

It is once we start thinking of life in algorithmic terms, that the power of Darwin’s theory becomes shockingly clear. It is a matter of common experience that offspring inherit traits from their parents, and that no two descendants are completely alike. Darwin recognised that whichever offspring had been born with variations that were somehow more profitable than its peers - however slight these variations may be - they would pass on these advantageous traits to more offspring than their less advantaged contemporaries. The advantageous traits would then spread and become commonplace within the population. This kind of system lends itself to algorithmic modelling. Imagine two variables representing the fitness of ‘normal’ members of a species (variable a), and a mutant, b. The mutation is very minor, perhaps corresponding to a slight strengthening of teeth, giving b a 1% fitness advantage in cases where that strength is helpful. We are in the abstract world of mathematics and algorithms, so if b > a on average it is inevitable that b will continue to increase and the number of b organisms will come to significantly outnumber the a organisms. The only question is how many generation it will take. The new fitness value for the overall population will have become normalized at 101% compared to where we started. The stage is now set for the eventual emergence of another beneficial mutation that will see the whole species renormalized to a still higher value of fitness. Of course, neutral mutations and deleterious mutations will occur as well, but at the simplistic level of description provided here, these have essentially no net effect because beneficial mutations are inherited more often - by definition, and therefore inevitably overwhelm the non-beneficial mutations.

Importantly, at this level of description there is no difference between so-called ‘micro’ and ‘macro evolution.’ While common sense allows that descendents with stronger teeth may come to outnumber those with weak teeth (micro-evolution), when viewed in abstract algorithmic terms, the same mechanism accounts for any adaptation whatsoever, including macro-evolutionary changes. Darwin was quite correct to observe “I can see no limit to this power” and conclude that it could serve to drive the origin of species.

However loudly Darwin’s critics protest, this level of explanation of adaptation is powerful and irrefutable. Dennett is correct to claim natural selection is about as likely to be refuted as is a return to a pre-Copernican geocentric view of the cosmos. Once understood, the idea is so obvious as to be self-evident.

Unfortunately, its immense explanatory power and irrefutable nature is also its Achilles’ heel. Expressed in the abstract terms laid out so far it can explain any and every adaptation; we have not specified the interval between generations, so by default the value of b reaches infinity almost immediately, as does the population of b organisms. In order to serve as an explanation for adaptations in terrestrial biology, the algorithm of natural selection needs to be properly ‘parameterised.’ The same holds true for Newton’s ‘f = ma.’ This formula tells us nothing useful about an actual event in the world until parameters of force, mass or acceleration are known.

In evolution, specifying parameters is no easy task. Real-world populations compete for multiple resources, and lives are lived out in specific but changing environments. One of the key parameters is the net effect of natural selection. Since it is not the only force acting on populations, depending on the parameters that are plugged into the algorithm, it is possible that other factors could overwhelm it temporarily, or even in the long run. However, if on average, it has the slightest net effect, natural selection will serve as a possible explanation for any adaptation (in fact, every adaptation) that is logically possible in any given environment.

The present situation is one where the mechanism and theoretical power of natural selection is not in doubt, but its place within an account of the actual terrestrial biological history is dependent upon it being correctly parameterised and placed within a larger model of the 3.8 billion year history of life on Earth.