Convergence Proves Evolution is Impossible

It has been recently documented that multiple genes identified in echolocating bats and dolphins exhibit striking similarities in nucleotide sequences (molecular convergence).^1,7

The existence of identical complex genetic code sequences in two unrelated species can easily disprove evolution through the application of statistical probability mathematics. In this brief analysis, the following assumptions are made:

The genome size of a bottlenose dolphin is 2,298,460,478 nucleotide base pairs^2. This number will be assumed to be the genome size for the proposed ancestor of toothed whales.

Toothed whales are believed to have evolved echolocation over a period of about six million years.

Molecular analysis of bats, dolphins and at least five other mammals revealed that 200 genes had independently changed to result in very similar genetic sequences.^4

Throwing all of the variables on the side of evolution, the following assumptions are made:

It will be assumed that echolocation evolved from a population of 600,000 dolphin ancestors (the current world population of bottlenose dolphins). This is to allow for the maximum number of mutations over the evolutionary history of echolocation. In reality, the modern evolution synthesis proposes much smaller populations for evolution to be possible.

Echolocation in marine mammals is believed to have evolved in 6 million years. To give evolution every benefit of the doubt, my calculation will be based on 12 million years of evolution.

The fact that most mutations are recessive will be ignored.

All mutations will be presumed to be point mutations… the most favorable type of mutation for probability challenges.

It will be assumed that natural selection can select one nucleotide at a time. [this is obviously a huge concession to evolution, given the fact that DNA is a complex code with overlapping messages, intricate algorithms and data compression. It is also known that natural selection cannot select one nucleotide at a time.^8]

I am ignoring that the linear sequence of nucleotides is only one aspect of the complexity of DNA. It is a multi-dimensional code, which further adds to the improbability to its creation through mutations.

I am ignoring that the genes considered constitute only a part of the genes that enable echolocation. The necessary co-evolution of complex behavior changes, which would have required tens of thousands of specific nucleotide substitutions, are not considered.   Three genes—Cdh23, Pcdh15, and Otof—involved in different steps in the auditory aspect of the echolocation system have been identified. The total number of base pairs for these three genes is between 20,855 – 21,137.^3

I am assuming a lowest possible nucleotide substitution (a codon of three nucleotides) for each of the 200 convergent genes. I am ignoring the improbability of these 200 convergent genes having appeared in five other mammal lineages.

I am only considering the possibility of evolution of identical genes twice in nature. Actually, this system supposedly evolved in three independent lineages. I am also ignoring the improbability of this same process having occurred multiple times in multiple other unrelated lineages.

The probability of a mutation becoming fixed in the population is 1 in 500^5. To give evolution an advantage, I will assume that twice the number of mutations (1 in 250) will become fixed in the population.

With all of the above concessions, mathematical testing is undertaken. I will begin with a population of dolphins totaling 600,000. The average mutation rate in mammals is 2.2 x 10^-9 per base pair per year.^6 This adds up to a total of 5.06 mutations per year per individual. 5.06 x 600,000 x 12,000,000 years = 36,432,000,000,000 total mutations over the evolutionary history of echolocation in toothed whales. Assume that only one codon (unit of three nucleotides) is all that is required to create a convergent gene… this would be at least 600 nucleotides.

The probability of the evolution of the first step of the proposed evolution of 200 convergent genes in bats and dolphins is calculated using the following three variables:

The success probability is calculated as an inverse of the genome size (2.298 billion nucleotides) divided by 3 [there are three possible nucleotide replacements (ATCG) for each point mutation. This is divided by 250 (twice the probability of a mutation becoming fixed in the population. ^5]

The probability of random occurrences of the minimum number of changes (3 nucleotides to make one codon) for each convergent gene is calculated using the binomial distribution formula:

P (success probability of each trial) = 0.0000000000058

N (number of trials) = 36,432000000000

X (number of successes) = 600

Cumulative probability is 4.82 x 10^-623.

It is possible for two people to each roll five dice and, by luck, achieve the same results.

It is impossible for two people to each roll one thousand dice and achieve the same results.

In a similar manner, it is mathematically impossible for random events (mutations) to create nearly identical genes twice.

In this analysis, I have given evolution every conceivable advantage, including the unrealistic belief that natural selection can seize every favorable mutation and eliminate all unfavorable mutations. I have only calculated a tiny element of what would be required to create the complex genetic code for echolocation (600 nucleotides). In reality, at least many tens of thousands of specific nucleotide substitutions would have been required. I have not calculated the even more fantastic improbability of this having occurred three times in three separate lineages (twice in bats and once in dolphins).

Even with these liberal concessions, the probability the very first step of 200 similar genes evolving twice through mutations is still utterly impossible. For those unfamiliar with exponential mathematics, a probability of 10^-80 is equivalent to the likelihood of correctly selecting a particular atom in the visible universe. With this in mind, a probability of

4.82 x 10^-623 is far beyond the reach of possibility.

  1. Parker, Joe, et al: “Genome-wide signatures of convergent evolution in echolocating mammals”, Nature (502), pg. 228-231, 10 Oct. 2013
  2. Human Genome Sequencing Center
  4. Pennisi, Elizabeth: “Bats and Dolphins Evolved Echolocation in the Same Way”,

Science Sept. 4, 2013.

5. Lee Spetner, PhD, Not by Chance! Shattering the Modern Theory of Evolution, Brooklyn, NY, The Judaica Press, 1997

6. Kumar and Subramanian: “Mutation rates in mammalian genomes”, PNAS, Jan 22, 2002, 99(2) 803-808

7. Cell Press. "In bats and whales, convergence in echolocation ability runs deep." ScienceDaily. ScienceDaily, 27 January 2010.

 8. Sanford, John C.: Genetic Entropy & the Mystery of the Genome, Third Edition, 2008, FMS Publications, pg. 61