There have been numerous mathematical challenges to the theory of evolution by natural selection. All of them can be safely assumed to be valid.
Sir Ronald Fisher, a world expert on the mathematics of evolution, has shown that the odds of the survival of a single mutation with a survival benefit of 0.1% greater than the rest of the population is 500 to 1 against – because the majority of mutants are eradicated by random effects. In other words, only 1 in 500 mutants with a positive benefit of 0.1% will end up taking over the entire population.
The chance that a specific change to a specific nucleotide will occur during a step is thus 1/600, and the odds that it will also take over the population is 1/500. The total odds are thus 1/600 * 1/500 or 1/300,000. This needs to happen 500 times in a row (the number of steps required to arrive at a new species). We thus need to multiply 1/300,000 by itself 500 times. The odds against this happening are approximately 3.6 x 102738 to 1, or viewed the other way round, the chance of this happening is 2.7 x 10-2739.
Of course, one cannot simply assume that only one mutation is available at every step. How many positive mutations are available? Nobody knows the answer to this. So Spetner turns the question around: for evolution to have a reasonable chance of working, how many positive mutations must be available at each step for the model to deliver a new species?
What constitutes a “reasonable chance”? A chance of one in a thousand could reflect the observation that for every species alive today approximately 1,000 have gone extinct. However, as some species go for a very long time without changing – the well recorded phenomenon of stasis – Spetner chooses a chance of 1 in 1,000,000.
The chance of a single step succeeding must be large – because we need to multiply it by itself 500 times (for the 500 steps) so that it comes out as close to 1/1,000,000 as possible (i.e. the chance of 1 in a million). The smallest number that will do this is 0.9727 as
1 – (1 – 1/300,000 ) 1,080,000 = 0.9727
So if the odds that a specific nucleotide will mutate and take over a population are to be 0.9727 for each step, there must be 1,080,000 potential positive adaptive copying errors for each of the 500 steps to arrive at a 1 in a 1,000,000 chance for the development of a new species.
The thing to keep in mind is that all of them are correct. Literally all of them, because there are a plethora of ways to prove that a thing that cannot be is not possible. The only problem with most of these mathematical arguments is that they are probability-based, which means that all the Darwinian true faithful hear when these vast improbabilities are presented to them is “so, you’re saying there is a chance.”
The advantage of my Impossibility of Mutational Fixation argument is that it a) is easy to understand and mathematically confirm and b) leaves no room whatsoever for epicycles, extensions, and other excuses to avoid abandoning what is observably a conclusively falsified hypothesis. But this takes absolutely nothing away from all the other evolutionary skeptics who have provided correct disproofs of the Neo-Darwinian synthesis both before and since genetic science provided us with the ability to state, with scientific, mathematic, and philosophic certainty, that evolution by natural selection not only never happened, but was never even possible.