Nobody is talking about a single sequence here. That is a straw man and you know it.
You might be misinterpreting where Taq agreed with you that "the longer a sequence is the less probable any single sequence is." This is all part of the sharpshooter analogy. To briefly explain it again, the new nucleotide sequence resulting from a beneficial mutation is highly unlikely, but it is no more unlikely than the original sequence.
The sharpshooter analogy comes into play when someone claims that only a specific beneficial mutation, i.e., a specific sequence in a specific gene, is necessary for improved adaptation in the existing environment, but that's not true. There are thousands of genes and hundreds or thousands or millions or billions or trillions of reproductive events every day, depending upon the reproductive rate of the organism in question. Almost every reproductive event includes random mutations, and some tiny percentage of them will produce improved adaptation.
But a tiny, tiny percentage of a huge, huge number is still a healthy number. For example, about 400,000 human babies are born every day, and on average each has about 50 mutations, mostly SNP's. That's a total of 2 million random human mutations every day. What percentage of all possible mutations would produce improved adaptation? I don't know, but let's say that a beneficial mutation has only a 1 in a billion chance, or 1 in 10-9
. This means that the likelihood of a beneficial mutation in a human baby on any given day is 1 - (1-10-9
)(2 × 106)
= .2%. There are 365 days in a year, so the probability of a beneficial mutation in any given year is 1 - (1-.002)365
= .52. So there's a 52% probability of a beneficial mutation somewhere in the human population every year.
And that's using a probability of 1 in a billion for a beneficial mutation. According to Population Genetics Made Simple
the probability is much higher than that.
Funny how you always work towards nested hierarchy. Biased much?
A nested hierarchy is what is observed in nature. Accepting observations of the real world isn't bias.