So we went from 10^8 (random use of 200x), to 10^7 (human generation time) to 10^6 (mouse generation time). Then knock off another 100 because it’s the smaller number that matters (for reasons we haven’t gotten to yet). So… 10^4 give or take.
Now the challenge: What was the time since the most recent common ancestor between mouse and human, and what happens when you divide that time by the number above?
There is no point here IMO as the time to generate a new gene based on Lynch’s estimates will exceed available evolutionary time and will also exceed Behe’s estimate due to:
-The number of changes (Lynch 2 max Behe 6 max) in mammal gene families changes can exceed several hundred. (issue for both Behe and Lynch models)
-changes to mammal genes are often deleterious where Lynch assumes neutral (Issue for Lynch model)
-generations of mammals are much longer then bacteria (Issue for both Behe and Lynch model).
-bacterial populations can get much larger then mammal populations (issue for both Behe and Lynch)
Gene duplication and subsequent variation is not a viable evolutionary mechanism in mammals and other vertebrates. It also has not been experimentally demonstrated in bacteria.
Again there is no point. The models show that the waiting time is excessive depending on generation times, gene duplication times, number of changes to find a functional adaption, and the amount of deleterious mutations.
We all know these conditions are substantially less favorable in bacteria then in mammals and vertebrates.
Why don’t we talk about mechanisms that may not have this type of challenge?
We are comparing 2 similar population genetic models with different working assumptions. This discussion is not about the math it is about the assumptions plugged into the mathematical models.
My point is very simple. When these models are applied to vertebrates (and associated generation times, gene duplication times, deleterious mutations, and sequence divergence between observed genes in the same family) it is clearly evident that what we observe in genetic variation between different mammals and vertebrates cannot be caused by gene duplication and associated variation.
You have put yourself in the situation of making a claim which you are incapable of verifying. I have no doubt that you believe you are correct, but the reason for that belief doesn’t seem to have anything to do with math. If it did, then you should be able to express those reasons clearly - and mathematically.
It’s a little bit unfair to put you on the spot and demand you produce supporting math. At the same time it is unfair to everyone else that you keep making this singular claim, over and over again, and expect people to accept it on your say-so. (Seriously, you must have brought this up in dozens of threads.)
I would be satisfied if you could make some effort to understand why this particular mathematical claim is flawed. No one can force this - you have to do the work yourself to really understand it. A little time spent with paper and pencil can do wonders for understanding.
The question is what assumptions are accurate given the make up of mammals, vertebrates and the magnitude of changes observed. This one is not hard if you are willing foo face reality and look at the models, the available empirical data and the assumptions objectively.
If you want to use the models to show how a vertebrate gene once copied can find new function through hundreds of random changes and fix in a population I would be interested but this looks like a waste of time at this point.
The comparative models above are for 2 changes.They are essentially informative toy models.
Behe and Lynch already created a mathematical model. I am not interested in reinventing the wheel, a wheel that will simply tell us that gene duplication and random change are not a viable explanatory mechanism for the observed diversity of genes in mammals given the results of the bacterial toy models.
Part of the job is to make estimates and judge if there is reason to do the work. I have not seen any viable mammal models that shows how gene duplication and random change can consistently generate genes in new populations. There seems to be good reason that no one is taking this on.