Summations Only

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That's right. So then how does this change the mathematics

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Obviously if reality differs from the model, the model is wrong and must be changed. Whether you consider that a change in the mathematics or not is irrelevant.

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I've done the recombination calculation alone to study why recombination does not have a significant effect on the evolution of drug-resistant HIV.

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You aren't much of a mathematician if you think that examining one special case is enough to demonstrate a claim about the general case.

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The empirical evidence already is clear that rmns is not significantly altered by sexual reproduction. Combination herbicides are already known to impair the evolution of herbicide-resistant weeds. There are other examples as well.

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Again you insist on talking about a set of very similar special cases but claim to have a generally applicable model. You might wish to consider how it is that combination therapies work, yet multiply-resistant bacteria are such a problem. That might lead you to a useful insight in understanding why combination therapies work.

Let it be noted that I found the flaws in Kleinman's argument before he got around to properly presenting it (He still hasn't, but he has gone far enough to show that I was correct)

I have a question for you Kleinman. Since you militantly refuse to understand rmns how can you possibly know that a proper understanding would falsify evolution ?

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You don't think that the multiplication rule of probabilities is a roadblock?

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Quite obviously it is not. To anyone with a proper understanding of probability theory. I already explained why it is not.Do you concede that it is possible to generate sequences of arbitrarily small probability ? Or do you think that there is some limit that can't be passed ? Some minimum probability ?

Your problem is not understanding rmns in terms of drug resistance. Your problem is that you refuse to understand that drug resistance is a special case. And you will never understand rmns until you take off those blinkers and consider it in other contexts.

I would expect resistance to one drug to have a small benefit. The important thing is that the fitness remains noticably less than 1, even with resistance to one drug.

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Well if it isn't the multiplication rule of probabilities which has led to the success of combination therapy for the treatment of HIV, then what is it?

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Trying to change the subject is hardly a good argument. I have already explained the problem with your use of probability Message 95Now perhaps you could start by acknowledging that the multiplication rule for probabilities is in no way a roadblock to generating sequences of arbitrarily low probability. Do you even understand that much ?Edited by PaulK, : No reason given.

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How does evolution of drug resistance differ than evolution by rmns to any other kind of selection pressure?

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If you had been paying attention you would know. For drug resistance selection pressure comes in the form of an environmental factor which greatly reduces the fitness of all non-resistant members of the population.What happens in the case of soft selection where the fitness of the "original" strain remains high ? Where the only factor reducing it below 1 is competition with other members of the species who possess a recent mutation (or a mutation recently become advantageous due to environmental change)

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You can see this same thing with drug selection pressures

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That drug selection pressures have the same effect as drug selection pressures is hardly a great insight.

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You are describing the Lenski experiment which takes more than a thousand generations per beneficial mutation.

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I'm describing a general situation which is not expected to reduce the frequency of beneficial mutations. If you think it did in the Lenski experiments you need to show evidence and reasoning - to support both the claim of frequency, and that it is caused by soft selection.

Kleinman's argument is built on not understanding natural selection.It is based on a special case of natural selection, the evolution of drug resistance. In this case the selection is very strong, and it is hard selection. Moreover, since drugs directly attack the chemistry of the target organisms there is a very limited range of mutations - sometimes sets of mutations - that might defeat them.A proper understanding of natural selection would recognise that these features are relevant to the outcome and study how varying the strength of selection, the hardness of the selection and the possible counters to selective force affect the outcome.But that is not for Kleinman. He refuses to even consider it. And so he has failed to produce a general model of natural selection by not even trying.Equally he has failed to produce a probability argument by not trying. As I pointed out early on in the discussion it is not enough to show that a sequence of stochastic events is highly improbable. Such sequences tend to be improbable by their very nature. Kleinman needs more, yet we saw no sign of him making the effort. Indeed he seemed reluctant to even acknowledge the basic fact that highly improbable sequences can be easily generated.Now maybe Kleinman feels that we are all wrong and only the opinion of real experts matters. If so, I invite him to write up his argument as a general argument as evolution and to submit it to Science and Nature, and other top-tier journals dealing with evolutionary theory. I predict that he will not get far.