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Biologists study these population structures to understand how genes flow. The problem was that biologists had only loose ideas about how specific population structures might affect natural selection. To find more generalizable strategies, Nowak turned to graph theory. Mathematical graphs are structures that represent the dynamic relations among sets of items: Individual items sit at the vertices of the structure; the lines, or edges, between every pair of items describe their connection.
In evolutionary graph theory, individual organisms occupy every vertex. Over time, an individual has some probability of spawning an identical offspring, which can replace an individual on a neighboring vertex, but it also faces its own risks of being replaced by some individual from the next generation.
The right patterns of weighted connections can stand in for behaviors in living populations: For example, connections that make it more likely that lineages will become isolated from the rest of a population can represent migrations. With graphs, Nowak could depict diverse population structures as mathematical abstractions. He could then rigorously explore how mutants with extra fitness would fare in each scenario. Those efforts led to a Nature paper in which Nowak and two colleagues showed how strongly certain population structures can suppress or enhance the effects of natural selection.
Those structures stymie evolution by denying advantageous mutations any chance to take over a population. The opposite is true, however, for a structure dubbed the Star, in which fitter mutations spread more effectively. Because the Star magnifies the effects of natural selection, the scientists labeled it an amplifier. Even better is the Superstar, which they called a strong amplifier because it ensures that mutants who are even slightly more fit will eventually replace all other individuals.
Yet that certainty came with a catch. He and his group had already spent years developing an understanding of similar problems involving graph theory and probabilities, and they thought the intuitions and insights they had developed might prove useful on this evolution problem. They realized that all potential strong amplifiers would have certain features in common, such as hubs and self-loops. Therefore, the successful production of a component functioning organism requires, at least , successive, successful such "mutations," each of which is highly unlikely.
Even evolutionists recognize that true mutations are very rare, and beneficial mutations are extremely rare—not more than one out of a thousand mutations are beneficial, at the very most.
But let us give the evolutionist the benefit of every consideration. Assume that, at each mutational step, there is equally as much chance for it to be good as bad.
Thus, the probability for the success of each mutation is assumed to be one out of two, or one-half. The number 10 60 , if written out, would be "one" followed by sixty "zeros.
Lest anyone think that a part system is unreasonably complex, it should be noted that even a one-celled plant or animal may have millions of molecular "parts. The evolutionist might react by saying that even though any one such mutating organism might not be successful, surely some around the world would be, especially in the 10 billion years or 10 18 seconds of assumed earth history.
Therefore, let us imagine that every one of the earth's 10 14 square feet of surface harbors a billion i. Each system can thus go through its mutations in seconds and then, if it is unsuccessful, start over for a new try. Multiplying all these numbers together, there would be a total possible number of attempts to develop a component system equal to 10 14 10 9 10 16 , or 10 39 attempts. All this means that the chance that any kind of a component integrated functioning organism could be developed by mutation and natural selection just once, anywhere in the world, in all the assumed expanse of geologic time, is less than one chance out of a billion trillion.
What possible conclusion, therefore, can we derive from such considerations as this except that evolution by mutation and natural selection is mathematically and logically indefensible! There have been many other ways in which creationist writers have used probability arguments to refute evolutionism, especially the idea of random changes preserved, if beneficial, by natural selection.
James Coppedge devoted almost an entire book, Evolution: Possible or Impossible Zondervan, , pp. I have also used other probability-type arguments to the same end see, e. The first such book, so far as I know, to use mathematics and probability in refuting evolution was written by a pastor, W.
Williams, way back in Entitled, Evolution Disproved , it made a great impression on me when I first read it about , at a time when I myself was still struggling with evolution. In fact, evolutionists themselves have attacked traditional Darwinism on the same basis see the Wistar Institute Symposium, Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution, , pp. While these scientists did not reject evolution itself, they did insist that the Darwinian randomness postulate would never work.
Furthermore, since the law of increasing entropy, or the second law of thermodynamics, is essentially a statement of probabilities, many writers have also used that law itself to show that evolution on any significant scale is essentially impossible. Evolutionists have usually ignored the arguments or else used vacuous arguments against them "Anything can happen given enough time"; "The earth is an open system, so the second law doesn't apply"; "Order can arise out of chaos through dissipative structures"; etc.
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