Calculating the chances of the evolution of a T4 bacteriophage virus.
"We can even handicap ourselves with a rate of additive mutation of once per 200 quadrillion reproductions. Even then we will still see one such mutation per two million generations, for a rate of one relevant mutation every 548 years. Of these, as we have already noted, bad mutations will vanish with no effect, but useful ones will persist, and will rapidly acquire the same population statistics. Indeed, a single T4 mutant, with the given estimates, will reach the trillion population mark in less than two days -- this is perhaps why evolution sometimes appears punctuated, for it can take centuries or even millennia for an advantage to be gained through new mutations, but once gained it can be exploited even to the point of total dominance in a matter of days or years in single-celled populations, a mere instant of geological time.
At any rate, given the above guesses, what are the odds of the T4 genome arising through natural selection within one billion years?
n = 1,824,818 (number of mutant proto-T4's)
p = .05 (the chance of a beneficial proto-T4 mutation)
q = 1 - p = .95
m = n*p = 91,241
s = (n*p*q)^0.5 = 294.4
Now, if x = 61,538 (the total number of correct mutations needed), then z = (x-m)/s = -100.9. In other words, the evolution of the T4 bacteriophage is essentially guaranteed to occur in less than a billion years, provided all the conditions are right, and the rates of reproduction and mutation are as estimated above. However, if the math is done, and our estimations are correct, it can be shown that the evolution of an organism like the T4 must take more than 500 million years, since the odds within that period of time are close enough to zero for the event to be regarded as virtually impossible. In fact, the odds start to drop below 50% when the time falls under 675 million years. Of course, all of that changes if we become more realistic, and credit the T4 ancestors with populations in the thousands of trillions, generations by the hour or even the minute, and relevant mutations at a rate of one every several trillions of replications."
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