진화론과 수학 모델: 진화에 필요한 시간 계산하기

2010-2013년 즈음, “진화에 필요한 시간"에 관하여 지적설계론 진영과 생물학자들 사이에서 일련의 논쟁이 벌어진 적이 있었기에 여기 살짝 소개하고자 한다. (사실은 이미 다 반증된지 오래된 것이긴 하다.) 일단, 난 수학에 대한 지식은 거의 없으므로 논리와 근거, 그리고 결론 정도만 참고하였다.

(0) 지적설계론: "진화에는 선택해야 할 변이가 한 가지 늘어날 때마다 이를 위해 필요한 시간이 기하급수적으로 증가하기 때문에 지구의 나이라고 하는 45억년은 우연적 변이와 자연적 선택에 의한 진화를 일으키기에는 부족한 시간이다. (따라서 지금 수준의 진화가 가능하려면 외부의 '지적 설계자'의 개입이 필수적이다)"

"We Have No Excuse- A Scientific Case for Relating Life to Mind" (Part1) (Part2) by Robert Deyes

This article explains why Monod is wrong and the claim of chance fails. It fails because probability decreases exponentially at an accelerating rate as the complexity of a system increases only incrementally. Because of the phenomenal rate of reduction even billions and billions of years of time and opportunity are not adequate for chance to mimic the simplest functions of life.

To make matters worse, amino acids degrade very quickly. They are very unstable. So, while we are trying to get the first of 382 genes necessary for life, the environment is constantly switching off the machine. We don’t have billions of years. Maybe we have only an hour. We are like robbers in the bank caught by the police before we have time to run even a few of the trials necessary to get the vault open. The fact that renders the materialistic mechanism impotent is the exponential increase in the amount of probabilistic resources needed for the tasks chance claims to have performed. The exponential increase renders the resources available insufficient. Each additional step in the sequence exponentially increases the time needed to achieve any function, much less all of the function needed to comprise life.

The primary defect of the unobserved hypothesized process of biological evolution is the absurd implausibility of the claim that a random mechanism can produce the sophisticated array of functional systems needed to run life. The exponential increase in the time necessary for each new step needed to attain the required function is the killer. Like a house of cards, the assembly of machines themselves requires an orchestrated timing. One cannot start building a sand castle today and expect to finish the job a year later after natural selection has torn it down.

(1) 윌프 ＆ 이웬스: "진화에 필요한 시간 증가량은 변이마다 exponential 이 아니라 logarithmic 하게 필요하므로, 생명이 진화하기 위한 시간은 충분했다."

Wilf, H. S. ＆ Ewens, W. J. (2010). There's plenty of time for evolution. PNAS, 107: 22454-22456.

Objections to Darwinian evolution are often based on the time required to carry out the necessary mutations. Seemingly, exponential numbers of mutations are needed. We show that such estimates ignore the effects of natural selection, and that the numbers of necessary mutations are thereby reduced to about K log L, rather than KL, where L is the length of the genomic “word,” and K is the number of possible “letters” that can occupy any position in the word. The required theory makes contact with the theory of radix-exchange sorting in theoretical computer science, and the asymptotic analysis of certain sums that occur there.

(2) 유어트 ＆ 뎀스키 et. al.: "natural selection 으로는 적합한 mutation을 찾지 못하며, epistasis 등 다른 요소들을 제외하고 지나치게 단순화했기 때문에 진화에 시간이 충분했다는 것은 옳지 않은 주장이다"

Ewert, W., Dembski, W., Gauger, A., ＆ Marks II, R. (2012). Time and Information in Evolution. BIO-Complexity, 2012(0).

Wilf and Ewens argue in a recent paper that there is plenty of time for evolution to occur. They base this claim on a mathematical model in which beneficial mutations accumulate simultaneously and independently, thus allowing changes that require a large number of mutations to evolve over comparatively short time periods. Because changes evolve independently and in parallel rather than sequentially, their model scales logarithmically rather than exponentially. This approach does not accurately reflect biological evolution, however, for two main reasons. First, within their model are implicit information sources, including the equivalent of a highly informed oracle that prophesies when a mutation is “correct,” thus accelerating the search by the evolutionary process. Natural selection, in contrast, does not have access to information about future benefits of a particular mutation, or where in the global fitness landscape a particular mutation is relative to a particular target. It can only assess mutations based on their current effect on fitness in the local fitness landscape. Thus the presence of this oracle makes their model radically different from a real biological search through fitness space. Wilf and Ewens also make unrealistic biological assumptions that, in effect, simplify the search. They assume no epistasis between beneficial mutations, no linkage between loci, and an unrealistic population size and base mutation rate, thus increasing the pool of beneficial mutations to be searched. They neglect the effects of genetic drift on the probability of fixation and the negative effects of simultaneously accumulating deleterious mutations. Finally, in their model they represent each genetic locus as a single letter. By doing so, they ignore the enormous sequence complexity of actual genetic loci (typically hundreds or thousands of nucleotides long), and vastly oversimplify the search for functional variants. In similar fashion, they assume that each evolutionary “advance” requires a change to just one locus, despite the clear evidence that most biological functions are the product of multiple gene products working together. Ignoring these biological realities infuses considerable active information into their model and eases the model’s evolutionary process.

(3) 코버트 ＆ 렌스키 et. al.: "오히려 deleterious 한 mutation 이 있어야 natural selection에 의한 적응적 진화에 유리하며, 특정 epistatis 의 경우 진화가 오히려 빨라질 수도 있음"

Arthur W. Covert III, Richard E. Lenski, Claus O. Wilke, and Charles Ofria (2013). Experiments on the role of deleterious mutations as stepping stones in adaptive evolution. PNAS 110 (34), E3171-E3178.

"Many evolutionary studies assume that deleterious mutations necessarily impede adaptive evolution. However, a later mutation that is conditionally beneficial may interact with a deleterious predecessor before it is eliminated, thereby providing access to adaptations that might otherwise be inaccessible. It is unknown whether such sign-epistatic recoveries are inconsequential events or an important factor in evolution, owing to the difficulty of monitoring the effects and fates of all mutations during experiments with biological organisms. Here, we used digital organisms to compare the extent of adaptive evolution in populations when deleterious mutations were disallowed with control populations in which such mutations were allowed. Significantly higher fitness levels were achieved over the long term in the control populations because some of the deleterious mutations served as stepping stones across otherwise impassable fitness valleys. As a consequence, initially deleterious mutations facilitated the evolution of complex, beneficial functions. We also examined the effects of disallowing neutral mutations, of varying the mutation rate, and of sexual recombination. Populations evolving without neutral mutations were able to leverage deleterious and compensatory mutation pairs to overcome, at least partially, the absence of neutral mutations. Substantially raising or lowering the mutation rate reduced or eliminated the long-term benefit of deleterious mutations, but introducing recombination did not. Our work demonstrates that deleterious mutations can play an important role in adaptive evolution under at least some conditions."

참고:

"Covert et al. (2013) showed in simulations that certain types of epistasis can actually speed up evolution. (Disclaimer: I’m an author on the Covert paper.)" by Claus Wilke

(4) 뎀스키: FAIL

〉Dembski == Dumbski
TRUE

참고:

1. "How Mathematics Can Prove Evolution" by David Orenstein
2. "Science and Pseudoscience" by Jason Rosenhouse
3. Rosenhouse, J. (2001). "How anti-evolutionists abuse mathematics" The Mathematical Intelligencer, Vol. 23, No. 4, Fall 2001, pp. 3-8.
   
   

원글:

https://byuldbyul.blogspot.com/2015/12/blog-post_29.html
https://brunch.co.kr/@byuldbyul/4