g-rh@cca.CCA.COM (Richard Harter) (04/04/88)
In article <369@nancy.UUCP> straney@msudoc.UUCP (Ronald W. DeBry) writes: }This isn't a summary, but a note about some recent mathematical work that }I've been meaning to bring up. Unfortunately, I've been too busy/lazy }to look up the references. I'm talking about two papers that were }published about a year - year and a half ago. One was by Russ Lande, I }can't remeber the author(s) of the other one. At least one was in }Nature (I think both were), and one had the title "Neo-darwinism }predicts punctuated equilibrium". } They started by assuming the standard Sewall Wright "adaptave }surface", which has one dimension for each gene. Gene combinations that }are good (have a high fitness) are represented as "adaptive peaks". }Under Wright's shifting balance model, the exact location of the peaks }changes with time, since the fitness of any particular combination of }alleles is a complex result of interactions between: 1) the environment }and each allele at each gene; and 2) each allele with all the other }alleles. Since both the environment and the genetic makeup of the }population are constantly changing, the peaks keep moving, and the }population keeps climbing a hill that is always moving out from under }it, so to speak. The classic problem, of course, isn't how you climb }the hill - the population's average fitness will increase each }generation by selection; it's how you move from one peak to a totally }different peak. } No point in going through the math (especially since I can't right }now), but an analogy makes the result fairly clear. Turn the adaptive }landscape upsidedown, and make the population's composite genotype a }marble. It's very much like the game where you roll the marble around a }flat surface from one hole to another, except that the some of the holes }are quite deep. Gravity is what drives the population towards the holes, }instead of selection. Shaking the table represents the combined effects }of the shifting environment and random changes in gene frequencies }caused by sampling error (drift). If the ball is in a particularly deep }hole, then only rarely wil it pop out due to the shaking, but when it }does, it will probably not fall back into the same hole, and will only }spend a very short time moving randomly across the flat table top before }it falls into another hole. } That simple sounding analogy actually fits the authors' simulation }studies remarkably well. I am cross-posting the above to sci.bio on the grounds that it of interest beyond the talk.origins group. Here are some general comments: The entire Sewall Wright approach is essentially a linear systems approach -- the effect of genetic variation and of environmental change on fitness is treated as though small changes in the parameters (genetic content and environment) have small changes in the fitness. Linear adaptive systems can track change very well as long as the response time of the system is quicker than the rate of change. A well known feature of linear systems is that the amount of change required in the control function depends on the direction of change in the error function. To put it in biological terms a small change in degree of fitness may require a small change in adaptation or a large one, depending on the kind of change in environment. One would expect, then, two different kinds of effects -- one is the bouncing marble effect alluded to above, where the population jumps from one niche to another. The other is extinction, when the environment alters in a way that the population cannot respond to. A second comment has to do with the heighth (or depth) and narrowness of niches. In a prolific environment there are both narrow niches and broad niches. Occupants of the broad niches cannot move into the narrow niches because they are already filled. In the table analogy above, we might say there are many marbles and that the holes appear in broad valleys. Some marbles fill the holes -- other occupy the broad valleys and cannot move into the holes because they are already filled. In the event of depopulation due to drastic environmental change the narrow niches go first -- they are most subject to extinction. They are then recreated and filled by the occupants of the broad valleys. Another issue which is not dealt with in the above model is positive feedback between populations. In a prolific environment niches tend to narrow, deepen, and increase in number. This is not a fault in the model, which is dealing with a single population. However the biosphere is a family of populations; one would expect that there are effects associated with being a member of family that are exhibited when one considers the individual in isolation. -- In the fields of Hell where the grass grows high Are the graves of dreams allowed to die. Richard Harter, SMDS Inc.