Posted by Matt Young on February 21, 2007 01:30 PM
Last week I went to a colloquium given by Douglas Robertson of the University of Colorado. Professor Robertson began with two observations:
Changes in fitness functions can cause changes in the distributions of phenotypes.
Changes in the distribution of phenotypes can cause changes in fitness functions.
Biologists, according to Professor Robertson, agree with the statements but yawn. Electrical engineers, by contrast, immediately recognize the possibility for positive feedback and announce, “That population is toast.” I am not an electrical engineer, but I am a fellow traveler, and Professor Robertson’s work, um, resonated with me.
For the uninitiated, positive feedback is what you get when the lecturer wanders too close to the loudspeaker, and the microphone picks up sounds from the loudspeaker. As the sounds are amplified and repeatedly fed back into the loudspeaker, you hear a loud shriek. Even in a quiet room, if the gain of the amplifier is high enough, a very small fluctuation in the amplifier voltage can set a positive-feedback loop into action. The electrical engineers are suggesting that something similar may happen to a species, and runaway amplification of one or more features of the phenotype will lead the species to decreased fitness and extinction.
With his colleague, Michael Grant, Professor Robertson has developed a simple mathematical model, which you can see animated here, http://cires.colorado.edu/~doug/extinct/ . The model includes a fitness function (a graph of fitness as a function of some feature such as size) and certain assumptions about the population. One of the more interesting simulations concerns a broad fitness function with a secondary spike on the high side of the peak.
To explain the secondary spike, Professor Robertson notes that the optimum height of a giraffe in isolation might be, say, 4 m. But in the presence of other giraffes, maybe there is an advantage to being 4.5 m tall, so you can get at leaves that other giraffes cannot. If that advantage is enough, then it can overcome the fact the 4.5-m giraffe has otherwise lower fitness than the rest of the herd. The simulation shows that the average height of the giraffes increases monotonically, even as average fitness decreases, and the population heads for extinction.
Another simulation uses a fitness function that consists of two peaks separated by a short distance. The population begins on the shorter peak, stays there for many generations, then comparatively swiftly makes a transition to the second, taller peak: punctuated equilibrium. Such stasis followed by a sudden shift would presumably be hard to account for with a linear model, but it is a natural consequence of the feedback model.
Though it is only one-dimensional and very preliminary, the model seems to account for Cope’s law (the observation that with time most species increase in size), punctuated equilibrium, periodic extinctions, and outlandish sexually selected adaptations like the peacock’s tail and the elk’s antlers. I am mildly surprised that biologists have shown little interest in the model since it was developed in the mid-90’s. I found the simulations intriguing and would be curious to hear informed opinions from others.