Musings of the ASA Director Emeritus
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This blog compiles the occasional musings of Randy Isaac who was ASA Executive Director from 2005 to 2016 and is now ASA Director Emeritus.

 

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Probabilities and Feedback

Posted By Randall D. Isaac, Sunday, May 27, 2018

One of the most common arguments used against evolution is that of probabilities. Someone will calculate the probability of a protein or a collection of biomolecules and show that the probability that it was formed by chance is 1 in a number so large that it takes an impressive number of digits just to write it down. The conclusion offered is that the probability is so low that anyone who believes in evolution must be ignorant and so biased toward evolution that they cannot think straight. Many people like to quote Herbert Yockey’s article “A calculation of the probability of spontaneous biogenesis by information theory”, in Journal of Theoretical Biology, 67:377–398, 1977.  He shows how many different combinations of amino acids are possible and he concludes that abiogenesis is impossible since the probability is on the order of 1 in 1065 that even a simple protein could form at random. Therefore evolution cannot even get started. Another favorite approach is to quote Fred Hoyle who, in a sidebar called “Hoyle on Evolution” in Nature, Vol 294, page 105, Nov. 12, 1981, cites the number 1 in 1040,000 as the odds of abiogenesis. Furthermore, Hoyle reportedly said the odds were comparable with the chance that “a tornado sweeping through a junk-yard might assemble a Boeing 747 from the materials therein”.

Much has been written to show the fallacies of this line of argument. The point I wish to emphasize in this post is the importance of feedback in thinking about probabilities. I have previously pointed out in a post on January 7, 2018 and in a letter to the editor in March 2012, the error in using combinations to derive probabilities. Evolution is a gradual process of change involving a high degree of parallelism and many steps, as I have shown in my review of the book Introduction to Evolutionary Informatics. Perhaps the most important element is that of feedback. It is not just the existence of many steps in evolution, but the role of feedback at each step. Survival to procreate is the crucial feedback factor that distinguishes any population of organisms or molecules. That is a feedback mechanism that provides active real-time information about the direction for evolution.

The importance of feedback has been shown mathematically by Herbert S. Wilf and Warren J. Ewens in their article “There’s plenty of time for evolution” in PNAS, December 28, 2010, vol. 107, no. 52, pp 22454–22456. They conclude that while combination-based probabilities scale exponentially, if there is any feedback those probabilities scale logarithmically. That is, for N elements, each selected from x possible values, the number of combinations scales as 1 in xN. However, with feedback at each step, the probability of success scales proportionally to 1 in x log(N). That is a very large difference. But their math isn’t easy to follow. A good way to illustrate the importance of feedback is to consider a familiar game.

The game of Mastermind, or any of the many variations of it, demonstrates the tremendous impact of feedback. In the game, two players each secretly select a short sequence of elements such as colors, numbers, letters, or words. Then the other player is challenged to guess that selection. For instance, one player may select the number 53882. The other player has a 1 in 100,000 chance of guessing it at random. This is equivalent to the scenarios that Yockey, Hoyle, and others would calculate. If this were the approach used in the game, both players would tire and starve long before the game was over. However, the game becomes interesting when some feedback is introduced. At each guess, the first player responds with some elementary feedback about the guess. Depending on the specific rules being used, it may be how many digits are correct, whether they are in the right position, or even which ones are correct, etc. With this feedback, the second player can usually guess the answer in about ten or fewer guesses. This makes the game challenging and interesting and possible. The probability drops from 1 in 100,000 to nearly 1 that the answer will be obtained.

In evolution, the feedback in each generation is the determination of which subset of the population will be the source of procreation for the subsequent generation. Unlike Mastermind, no intelligent being is required to make this determination. It includes all the individuals of that species that survive in the current environment and are able to reproduce. On average, this will tend to include a disproportionate number of those most likely to survive in a slowly changing environment. With a large amount of parallelism and continual feedback, the probability of attaining the combination of molecules necessary for life is very high.

Tags:  evolution  Evolutionary Creation  Probabilities 

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Theistic Evolution: Creative Power

Posted By Randall D. Isaac, Sunday, January 7, 2018

One of the major scientific critiques of theistic evolution offered by the authors is that the theory of evolution does not include mechanisms with adequate creative power to explain the complex and diverse biosphere. Therefore, they say, theistic evolutionists inappropriately attempt to reconcile Christianity with an inadequate scientific theory.

To assess the creative power of evolution, the authors ask, in effect, “What is the probability that random mutations, as proposed by the theory of evolution, could account for the existence of all the biomolecules, such as proteins, that are necessary for life?” In chapter 3, Matti Leisola writes: “Twenty amino acids are the building blocks of the proteins present in all living organisms, from bacteria to humans. The average protein is about 300 amino acids in length, more precisely, 267 for bacterial and 361 for eukaryotic proteins. These 300 amino acids can be ordered in 20300 (10390) different ways.” (p. 150-151) Using a multitude of detailed examples, the various authors calculate the enormous number of combinations of amino acids that are possible. They show that the fraction of those combinations that are functional is a vanishingly small number. To illustrate the argument, they offer examples such as bike locks, Shakespeare, and language. Hence, the probability that random mutations, even those starting from a known functioning biomolecule, could result in a complete set of the necessary biomolecules is effectively zero.

This argument is repeated in many different ways but the underlying principle is always the same. A probability of life based on the number of possible combinations of the building blocks of life is zero. Therefore, the theory of evolution has inadequate creative power to explain life.

I would suggest that the authors are considering the wrong question. It is well known that a posteriori probabilities are notoriously tricky. In evolution, we only know the a posteriori result and any probability must be treated with care. Dealing with this issue involves teleology which will be discussed in future posts.

The most important reason why this is the wrong question is that valid probabilities cannot be calculated, particularly using combinations, if the possible combinations aren’t all equally probable, or nearly so. In dealing a deck of cards, this is accomplished with a reshuffle before dealing each hand. In evolution, there is no reshuffle. Instead, there is active feedback at every generation that influences which combinations will continue to be pursued. With this feedback, probabilities can only be assessed if all known feedback processes can be identified and evaluated in detail. This cannot be done for evolution. The mutation processes we observe in nature are not just simple nucleotide or amino acid changes but large-scale changes such as chromosomal crossover in gamete formation, horizontal gene transfer, transposons, retroviruses, and many more, and most likely some we have yet to identify. Survival provides feedback at each generation about which combination will be sustained. As a result, probabilities are very weak arguments for or against the theory of evolution. 

Combination approaches to probability are known to scale exponentially with the number of components. This means, as in the quote above, that even average sized proteins involve an extremely large number of possible combinations. It can be shown mathematically that when feedback exists, probabilities scale much more slowly, perhaps as a power law or even logarithmically, depending on the type of feedback. This changes the outlook from impossible to the realm of possibility. This is the case for evolution. When the feedback from natural selection at each generation is taken into account, the probabilities no longer scale exponentially. The claim that evolution does not have the requisite creative power is not compelling.l.

It is nevertheless a mind-boggling claim to think that today’s diversity of life could ever have come from a simple population of primitive life. The right question to ask is not about the probabilities of evolution but to ask about evidence of what actually did happen. This is the topic of other claims in the book that we will discuss in future posts.

Tags:  Probabilities  theistic evolution 

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