Haldane's Dilemma

Con says that “Haldane used the number 300 to account for rates that were realistic to him. Instead of using constants and solving for a variable, he used a variable to make another variable look reasonable. That is bad math.” Bad math? No, there's nothing wrong with Haldane's math. But perhaps he should have derived the number from first principles. Let's take the number 43 instead, which we know for a fact to represent rapid fixation as in the case of the Peppered Moth. So assuming that, on average, our ancestral population had a beneficial mutation reach fixation every 43 generations (instead of 300): 10,000,000 years / (20 years per generation * 43 generations) = ~11,000 Now all the traits that make us human, in contrast to our ape ancestor, must be accounted for by 11,000 base-pairs. This is not plausible: we differ from chimps by 35 million base-pairs, over 3,000x that number! And this is not even counting insertions or deletions. Haldane's Dilemma remains fatal for Evolution whether you plug in 300, or 43. Con says that “the mammal point is important in showing that human ancestors were able to sustain high reproductive rates as we are, of course mammals, but Haldane does not show this in his calculations.” This is incorrect. Mammals do not have a high reproductive rate; in fact, they have one of the lowest in the animal kingdom: i.e. Orangutans give birth to a single offspring every 6 years.(2) Con says that “I would like to remind PRO that the cost of substitution is "the substitution of one allele by another, if carried out by natural selection based on juvenile deaths." This is also incorrect. The cost of substitution is the reproductive rate required to make a hypothetical scenario plausible. If the cost cannot be payed, then the scenario is not plausible, and a practical person must conclude it didn't happen. It makes no sense for Con to claim the cost of substitution is “the substitution of one allele by another”. That's like saying the cost of substitution is a substitution, or the cost of a Honda Civic is a Honda Civic. Con says that “Obviously, with this low population, fixation would take a long time to occur. However, if the population was much higher, say, 95,000 (the current pop. of the western gorilla) fixation would happen really fast.” This makes no sense. Population size is almost irrelevant to the cost. How in the world is a larger population going to result in the faster fixation of a mutation in the entire population? Con has it backwards. Say I have 10 mice. 9 are black and 1 is pink. The pink phenotype can be fixated in the population by simply killing off the 9 black mice, leaving the 1 pink mouse. I'm not sure why Con thinks increasing the population size would make fixation happen faster. That means more individuals have to die for fixation to occur. You have to remember that increasing the population size increases the number of individuals that do not have the mutation to be substituted, and it's not as if increasing the number of non-mutated individuals makes the fixation of the mutation in the entire population occur any faster. Allow me to reiterate: the cost of substitution cannot be reduced by increasing the population size. Con says “[t]his is because as the population gets larger, more variations occur and recombination adds even more variation and causes fixation faster.” Yes, a larger population means more variations among the population, but not in an individual. Obviously, a population of 100 will receive mutations 100x faster than a population of 1. However, it's a non-sequitur to say that more variations among a population means that any single, particular variant will get fixated in the entire population faster. Con says “Haldane, and my opponent's calculations, only assume that one change is approaching fixation at a time. In other words, they assume that one gene change occurs, takes 300 years to successfully mix into the gene pool, and then another begins.” This is incorrect, and Haldane explicitly accounted for simultaneous substitutions in his calculations. I suggest Con read page 22 of Haldane's paper, where he says: “Can this slowness be avoided by selecting several genes at a time? I doubt it, for the following reason. Consider clonally reproducing bacteria, in which a number of disadvan- tageous genes are present, kept in being by mutation, each with frequencies of the order of 104. They become slightly advantageous through a change of environment or residual genotype. Among 1012 bacteria there might be one which possessed three such mutants. But since the cost of selection is proportional to the negative logarithm of the initial frequency the mean cost of selecting its descendants would be the same as that of selection for the three mutants in series[...]”(emphasis mine) Regardless, only one beneficial mutation can be fixated at a time, for interactions between concurrent mutations which are otherwise beneficial on their own, are antagonistic.(3) Con says, “I would like PRO to refer me to where Haldane accounts for sexual recombination, as I have read his article and cannot seem to find it.” Haldane does not explicitly say he accounts for sexual recombination. However, contrary to what Con claims, sexual recombination does not cause fixation to happen faster. It causes it to happen twice as slow, since a beneficial mutation only has a 50% chance of being passed on from one mother to the next generation as opposed to the case in asexual organisms, where it is almost certain to be passed on. It would be better for me to say that Haldane's math actually doesn't account for sexual recombination, since his math assumes that sexual recombination doesn't reduce the speed of fixation. But this helps my case, not Con's. Con says, “Genetic drift would increase the number of total mutations, no matter good or bad, so the net nucleotide difference would be higher. Let's say 1000 changes occurred due to drift (I am making this number up; it could be anything). This would automatically bring 1667 up to 2667.” Haldane's cost of substitution applies both to beneficial mutations, and neutral mutations which spontaneously accumulated in the population and later became beneficial due to environmental change. It's not reasonable to suggest neutral mutations would bring the 1667 number up any higher, since it's extraordinaryly unlikely for neutral mutations to get fixated in a population. And the 1667 number only applies to fixated mutations. Natural Selection cannot pressure a neutral mutation to get fixated, so Con is appealing to mathematically implausible absurdities to raise the 1667 number. Con's appealing to the chance of a particular, neutral mutations to spontaneously make its way into every single individual in a population, even while faced with factors that actively seek to prevent this from happening, like genetic drift. That's not reasonable. Con says, “Considering the average difference between humans is up to 30 million nucleotides (and this is just a count of single nucleotide polymorphisms), my point still stands.” This is irrelevant. All that matters is the fixated mutations in the human population, because that is what distinguishes us as humans from our supposed ape ancestors. (2) http://bioweb.uwlax.edu... (3) http://www.pnas.org...