The Probability of Evolution by Mutations

Dr. Zvi Shkedi

See also:
Evolution - Facts, Theories, and Fiction
Abiogenesis - Can Life Be Initiated Without a Creator?

All DNA is encoded with four nucleotide bases which serve as the gene-coding building blocks. The genetic codes of two closely related yet different species of mammals have an information contents difference of thousands of nucleotide base locations. A difference in less than 100 locations can produce different individuals within the same species or slight variations within a species; such a difference is not sufficient to produce a new species. The following analysis will demonstrate a probability calculation based on the information contents carried by 100 nucleotide base locations. There is nothing fundamental about the number 100. It is used only as a model for a lower limit. The difference between most closely-related species is much larger than 100 base locations, and, therefore, the actual probabilities are much lower than what the following analysis demonstrates.

Darwin and others have noted that there are no closely-spaced transitional creatures between species. There are many wishful speculations but no evidence for evolution of new species in small steps (as opposed to genetic enrichment within a species). Theoretically, there may be many viable mutations possible. But, in order to be a different species, in the absence of closely-spaced survivable transitional creatures, the irreducible minimum of information-contents difference must be greater than 100 nucleotide base locations. (This does not mean that there is only one survivable solution with a difference in 100 nucleotide locations. What it means is that the total number of possible random permutations divided by the number of survivable solutions has a lower limit equal to the information-contents equivalent of 100 nucleotide substitutions.) Therefore, the probability of randomly mutating one species to another, without external guidance, is less than one chance in 4^100 trials. 4^100 equals 10^60. Without external guidance, it will take more than a trillion trillions (10^24) of mammals, mutating and procreating ten thousand times per second for more than a trillion trillions of years, to randomly evolve one survivable creature of a new mammal species. In probability terms, it means that the probability of evolving one survivable creature of a new mammal species is less than 4^-100=10^-60.

Richard Dawkins disputed the validity of such calculations. He argued that evolution does not happen in large steps, but in many small steps. Let's explore this possibility. The smallest possible step in an evolutionary process is the survivable substitution of one nucleotide. If the irreducible minimum of a change from one species to another is the survivable substitution of 100 nucleotides, then, the change can be accomplished in 100 single-substitution steps. Such a process seems to be very intuitive and easy to follow, except for one complication - it requires an intelligent road guide. With the help of a road guide, each step has a probability of 1 to be correct. Obtaining 100 correct steps with the help of a road guide has a probability of 1^100=1. On the other hand, without a road guide, each step is random. Since we are calculating the lower limit of the irreducible minimum, each random step has a probability of 1 out of 4 choices to be correct. Natural selection, acting as a filter, will filter out the 3 wrong substitutions and keep (survive) the right one. The laws of probability dictate that if each step has a probability of 4^-1 to be correct (without assistance from a road guide), then, 100 consecutive steps have a probability of (4^-1)^100=4^-100=10^-60. We end up with the same result as shown before. (Every student who studied probability knows that, when tossing coins, the probability of getting all "heads" by throwing 100 coins at once or by throwing one coin 100 times without cheating, is exactly the same.)

As we can see, we have here a binary choice - the one-step-at-a-time change can occur either with a road guide or without a road guide. There is nothing in between. If a road-guide guides the process, it implies the presence of a Creator. If the road guide is built into the DNA code, being able to predict which future substitution will be the survivable one, it requires a prophetic designer to design the DNA with such prophetic capabilities. If the process occurs as a natural-selection filter without a road guide, it has a probability of 4^-100=10^-60 to be correct, which brings us back to the results of the original calculation.

This calculation does not prove the existence of a Creator. What this calculation does prove is that it would take many trillions of years to obtain the irreducible-minimum change without a Creator, regardless of whether the change occurs in one big step or in many small steps. Current estimates of millions or billions of years, which are based exclusively on geological considerations, do not allow sufficient time for such a random change to occur or to accumulate.

There are no organisms which can procreate ten thousand times per second. Planet earth never contained a trillion trillions of mammals. (The volume of planet earth is 10^21 cubic meters. 10^24 average mammals would occupy a volume greater than the entire volume of planet earth.) And, as far back as we can remember, the universe does not exist for a trillion trillions of years. Therefore, the hypothesis as if species can evolve into new species through the accumulation of random mutations, without external guidance, is nothing but a wishful speculation based on ignorance.

Pierre-Paul Grasse understood the consequences demonstrated by this calculation:
"The opportune appearance of mutations permitting animals and plants to meet their needs seems hard to believe. Yet the Darwinian theory is even more demanding: A single plant, a single animal would require thousands and thousands of lucky, appropriate events. Thus, miracles would become the rule; events with an infinitesimal probability could not fail to occur. ... There is no law against day dreaming, but science must not indulge in it."[1]
Based on his vast encyclopedic knowledge, Grasse summarized all the known measurable facts in this field:
"In spite of the intense pressure generated by artificial selection (eliminating any parent not answering the criteria of choice) over whole millennia, no new species are born... This is not a matter of opinion or subjective classification, but a measurable reality."[1]
With a probability of less than 10^-60, it is not a surprise that "no new species are born". This is the only measurable reality available in the field. All other arguments are nothing but opinions, wishful speculations, and subjective classifications designed to support the ideology.

Another possible objection to the validity of this calculation is that evolution may have occurred one step at a time by preserving (surviving) each new successful substitution. Once the first successful substitution occurs, call it strain #1, it is preserved. The second substitution attempt will begin with strain #1. After a small number of random attempts, a second base location will be correctly substituted to form strain #2. Then, strain #3, #4, etc. At first sight it appears that the strains will quickly progress towards #100 which is the new species we think we are going to achieve.  Such a "quick" evolutionary process needs, however, to overcome two challenges:

a) It requires that each new strain be survivable. If such an evolutionary process, takes, say, one million years, then, on average, each new strain must survive for at least 10,000 years. We should see in nature, some evidence of a complete continuum of strains, what Darwin calls "transitional creatures", between the old species and the new species. Darwin admitted that such a continuum of transitional creatures was never observed. Up until today, such a continuum of transitional creatures was never observed. Lacking such a continuum of survivable strains, the "quick" evolutionary process cannot occur.

b) Once we get to strain #25, a new unexpected phenomenon will occur. The probability of correctly substituting a new base location will be equal to the probability of damaging a previously substituted location. The probability of correctly substituting each new base location is 1/4. Multiplying 1/4 by 75 available not-yet-substituted locations yields a "correct" substitution rate of 18.75 per unit of time. The probability of damaging each previously substituted location is 3/4. Multiplying 3/4 by 25 correctly-substituted locations yields a "damaging" substitution rate of 18.75 per unit of time. The "correct" substitution rate and the "damaging" substitution rate will reach an equilibrium. At this point, the random substitution process will fluctuate up and down around the 25% point. The probability of reverting back to the original species, traveling a distance of 25% of the road,  is much higher than the probability of reaching the new species, traveling a distance of 75% of the road. The new species will never be reached. (It is important to note that this 25% roadblock is independent of the number of base locations we are trying to substitute. An arbitrary number of 100 base locations was chosen as the lower limit for the model calculation. However, the 25% road block will occur regardless of the number of base locations in this calculation.) The process will keep fluctuating up and down around the 25% point. It will never reach its destination.

We can almost hear everyone screaming: "But, evolution does not have a destination!" True, evolution does not have a destination. This 25% point might as well be a de-facto end point. We will now have a species which varies randomly up and down around this 25% point. It may sometimes revert back to the beginning of the road, and, with an equal probability travel as far as 50% of the road. Fluctuating up and down an equilibrium point is exactly what the theory of evolution calls "variation within a species". No new species are born.

Pierre-Paul Grasse was familiar with all reported observations and experiments in this field. No one could have better summed up these observations and experiments:
"the mutations of bacteria and viruses are merely hereditary fluctuations around a median position; a swing to the right, a swing to the left, but no final evolutionary effect."[2]
The Lenski experiment[3] demonstrated that E. coli bacteria developed the ability to transport citrate across the cell wall under oxic conditions. This experiment subjected more than 10^11 cells per generation to extreme starvation conditions. 11 populations failed to develop this ability for 44,000 generations (per population), while one population developed it after 31,500 generations. That's a rate of one out of 515,000 generations. The authors acknowledge in their publication that "the mutation rate of the ancestral strain from Cit- to Cit+ is immeasurably low." In humans, 515,000 generations would take 10 million years. It would take that long in humans if the human population size was equal to the experiment population size. However, in the Lenski experiment the cell population size was 10^11 per generation, while in the early days the human population size was less than 10^7. Therefore, it would take humans a factor of 10,000 longer. It would take humans 100 billion years (10 million X 10,000), under extreme starvation conditions, just to evolve an equivalent improvement in the ability to absorb a more abundant food. At this rate, under natural conditions which are not that extreme, it would take many trillions of years to evolve more complex biological/ biochemical systems and a higher brain capacity.

Even the most "religious" evolutionists do not believe that humans evolved more than 2 million years ago. Evolution biologists never agreed with probability calculations showing that complex systems would take many trillions of years to evolve. With the Lenski experiment, evolution biologists have experimentally verified the correctness of these calculations. Yes, some evolutionary changes are fact, but, it would take many trillions of years to evolve a complex system or one animal from another.

If "evolution is fact", as evolutionists claim, then, geologists have a "trillions of years" problem to solve...


  1. Pierre-Paul Grasse, "Evolution of Living Organisms", 1977, p.103-104
  2. Pierre-Paul Grasse, "Evolution of Living Organisms", 1977, p.124-125
  3. Zachary D. Blount, Christina Z. Borland, and Richard E. Lenski, "Historical contingency and the evolution of a key innovation in an experimental population of Escherichia coli", PNAS June 10, 2008 Vol.105 No.23 p.7899–7906

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