A Population Genetics for Small Evolution

A Population Genetics for Small Evolution

David A. Plaisted


The standard model of population genetics on which the theory of evolution is based makes some unrealistic assumptions. In its place, I would like to propose a model for estimating the rate at which evolution can occur, and for limiting the amount of evolution that is possible. A consequence of this model is that all life could not have originated from a common ancestor. Of course, all models are abstractions, as is standard population genetics, and so the conclusions reached are not necessarily binding on reality. For example, some organisms can change their rates of mutation, and many other complexities could be mentioned. But this model helps us to see what the constraints on evolution are. And I think that I now understand some of the basic principles of population genetics after discussions on talk.origins. The model I am presenting is based on simple axiomatic properties of mutations, and attempts to avoid the criticism directed at my scenario of a fish evolving to an amphibian. This was criticized because it assumes a direction to evolution. This new model does not assume any predetermined direction to evolution.

My purpose is not to refute evolution or prove creation. I don't think that either is possible, but prefer to reason based on the weight of evidence, which I believe is in favor of creation..

The simple (standard?) population genetics model in which beneficial mutations are not too rare and, when combined, are still beneficial, does not correspond to reality in all cases, as a number of considerations can show. And of course, this is undoubtedly no surprise to population geneticists. In fact, if beneficial mutations are not too rare and can always combine and remain beneficial, then under certain reasonable assumptions, one can show that a random genome would be better adapted than an existing organism.

A more realistic model is that beneficial mutations can cause other, previously beneficial mutations to become harmful. Thus the benefits to be obtained by independent mutations are correlated in some way, positively or negatively. Suppose that 1/20 of non-neutral mutations are beneficial. (Actually, 1/1000 is a better figure, and even this is probably too high.) Suppose that if mutations A and B are beneficial, then after A occurs, the chance that B will still be beneficial is 1/20. (This is an extreme case, for the sake of argument.) The justification for this is that if all parts of the organism are closely interrelated, then a change to anything will affect all other parts of the organism in an unpredictable, nearly random, way. This means that the chance that an arbitrary mutation B will be beneficial after A is 1/20, regardless of whether B was beneficial before A or not. The effect of this is to make it difficult for mutations to arise independently. It essentially forces them to combine sequentially, so that each beneficial mutation has to arise in an individual having the preceding beneficial mutations. This constrains the rate at which mutations can accumulate.

So we can say that a portion of the genome is tightly correlated (highly constrained) if separate mutations A and B in this portion combine as mentioned above. In such a tightly correlated region, mutations must accumulate sequentially. However, there may be more than one such region, and these regions may be independent of one another. Thus, the two regions could evolve independently, increasing the possible rate of evolution. There may also be loosely correlated (loosely constrained) regions of the genome. In the loosely correlated regions, beneficial mutations may be more numerous.

Also, I imagine that in a tightly correlated region of the genome, the probability of a beneficial mutation is more like 1/1000 or one in a million, since each change is affecting so many other parts of the organism. This would probably lead to a rate of one beneficial mutation in about 10 or 20 generations, and probably many more generations would be required. If there were a number of tightly correlated regions, largely independent of each other, the rate of evolution could be greater. For example, lungs and legs could evolve in parallel. It is also possible that a tightly correlated region of the organism cannot evolve significantly at all. In a loosely constrained region of the genome, beneficial mutations may be much more common, and evolution could occur much faster.

By a detailed study, one could possibly discover what the correlations between various mutations are, and gain a better view of what the possible rates of evolution would be. One can see this approach as formalizing Behe's "irreducible systems," but not so as to prevent evolution, just making it more difficult. And this has the advantage of being quantititive and testable experimentally. Furthermore, by counting numbers of generations and sizes of genomes, one can estimate whether evolution could have occurred in various past time periods, such as during the Cambrian explosion when many organisms seem significantly to have changed. During this time, a significant portion of the genome must have been changed (unless all of these organisms had precursors which did not leave fossils). Of course, copyings can change much of the genome at once, but these should leave their traces in the genome for us to observe. And whether most of the change to the genome has occurred in the pre-Cambrian era or later, one can still estimate the possibility of evolution having occurred. This would also require estimating how many parts of the organism could evolve independently in parallel, but since an organism is so highly interconnected, one would not expect this to be very many. Even legs and lungs are closely correlated with each other.

Now, one can make the model more extreme. One can say that a beneficial mutation can cause some previous mutations that were beneficial to become harmful. Suppose that a new beneficial mutation causes about 1/100 of previous beneficial mutations to become harmful. Then when there are about 100 mutations altogether, the net effect of a new "beneficial" mutation is neutra (or even harmful), so it becomes harder and harder to find beneficial mutations. This puts a limit on the amount of evolution that can occur. This is a way of formalizing the idea that evolution can occur only within certain limits, and argues against a common origin for all of life. If the 1/100 is replaced by 1/1000, then the amount of evolution possible would be larger. The fact that harmful mutations tend to die out would increase the amount of evolution possible, but only by a small constant factor, I think, since the harmful mutations would continually be produced.

The concept of beneficial and harmful mutations is to some extent dependent on the environment. However, most harmful mutations are always harmful. Even if we say that a mutation is beneficial if it is beneficial in any plausible environment, this argument still works, since only a small number of mutations are beneficial in any plausible environment.

The above concepts give us tools with which to study the possibility that the evolution of all life from a common ancestor could have occurred. I believe that a careful consideration would argue against the possibility of evolution having occurred in the time assumed to have been available for it. Also, the complexity of life leads me to believe that the limited evolution scenario is likely. These statistical considerations help to formalize the intuition that evolution is difficult, unlikely, or amazing, however one prefers to view it. These help to formalize the intuitive idea that life is highly organized, and difficult to explain by chance constructions. Again, all of these arguments may be well known to population geneticists, but they may provide some food for thought for readers of this page and stimulate some discussion.

By the way, there is a reference in Behe's book to a book entitled "Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution" (Wistar Institute Press, Philadelphia, 1967) which readers may want to consult. I haven't read it myself.

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