How a mathematician (that's me) sees evolution

I am asking if you have one. If you don’t that is fine.

Start with 110 new keratin proteins or the organization of at least 60000 nucleotides to build them.

Neil is not claiming a mechanism in his proposal so I agree there is not problem with irreducibly complexity as it is targeted at the Darwinian mechanisms RMNS.

ROFL!

Yes. You need a few more squares. One that says “Can you model it?”, “Ubiquitin/Actin/Wnt signaling pathway”, “Ewert’s dependency graph”, “Apoptosis in embryo development”, “the spliceosome”, and “Sal’s flower”.

“New” sounds pretty serious. Obviously they cannot be so new as to not be classified as keratin. How new is each keratin protein?

Really, I am trying to imagine what this looks like in your world. Are you saying, every time there is a variation of a protein called for, some agent for design comes around to wrench on the DNA, and this has gone on for the history of life on earth?

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What would you accept as a mechanistic explanation?

In my world you need to organize at least 60000 nucleotides to build a flight feather. This is just the beginning of the origin of flight. How this came into existence is a significant challenge. This is just an example of a complex adaption with multiple moving parts to implement.

Again Neil is not promoting a mechanism so this is not an issue in this discussion.

In our world you need to organize at least 60000 nucleotides to build an extant flight feather. But nobody except clueless ID-Creationists think extant feathers were identical to the first simple proto-feathers.

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But you appear to understand the principles better than many biologists do.

Exactly.

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Why did you pose this question, Joe?

My answer would be that equations in population genetics are mathematical models of biological reality. The models abstract and idealize reality but still capture enough of that reality to be empirically verifiable and so help us explain and predict changes in the statistical distribution of genomes of individuals in a population.

Is that what you had in mind?

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Surely the claim that the jump is remarkable is a claim about different rates of change? Therefore the X axis should be an axis of absolute time.

But it isn’t, is it? It’s an arbitrary axis representing a sort of scala naturae.

BruceS, to actually model in realistic detail the genotypic and phenotypic changes that led, say, to the development of feathers in dinosaurs, we would need to have a comprehensive understanding of what all genes in the dinosaur did, what mutations could occur in them, and we’d have to know a lot about the dinosaur’s environment. Not only don’t we have that level of understanding of any species, there are many species whose present or past existence we are still unaware of. It is a similar situation in geology: if someone asks whether the laws of physics can account for a particular mountain range, yes, in principle, they can. But they don’t let us model it in detail unless we know an awful lot more about the local geology than we are likely to actually know.

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@Joe_Felsenstein I totally agree.

But isn’t it a shame that Joe and other biologists have to make that point repeatedly?

In my dream world, Joe would instead spend that time creating an online course from his population genetics or phylogenetics books.

Of course, he would need some undergrad flunkies to do the grunt work for that, so that’s also an issue too, I suppose, now that Joe is Emeritus.

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@Joe_Felsenstein did make his book on population genetics available online for free, right?

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Yes, I have it, but an online course to supplement it would be useful, at least for lazy people like me.

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Developing an online course is a huge amount of work. But you can go to the course website (for the last time I gave it, in 2017) which you will find here. There you will find (on a linked page) audio recordings of my lectures (all but one of them), and slides for some lectures. The lectures were mostly chalk-talk format with equations written on the whiteboard. References in my talks to page numbers in the online text will be slightly wrong, as they refer to the 2015 version of the text. Web pages for earlier years of the course can be found by changing the year in the link to earlier odd-numbered years.
This was a course on the theory of population genetics. For a more balanced, more accessible – and not free – coverage of both theory and observational/experimental data, there is Rasmus Nielsen and Monty Slatkin’s book. There is also a very good freely readable and downloadable set of notes for a graduate-level course at University of California, Davis by Graham Coop which will be found here.

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Bruce quoting Joe Felsenstein:

The equations of population genetics are fairly decoupled from the relation of the organism to it’s environment. As Lewontin says:

The problem is that it is not entirely clear what fitness is. Darwin took the metaphorical sense of fitness literally. The natural properties of different types resulted in their differential “fit” into the environment in which they lived. The better the fit to the environment the more likely they were to survive and the greater their rate of reproduction. This differential rate of reproduction would then result in a change of abundance of the different types.

In modern evolutionary theory, however, “fitness” is no longer a characterization of the relation of the organism to the environment that leads to reproductive consequences, but is meant to be a quantitative expression of the differential reproductive schedules themselves. Darwin’s sense of fit has been completely bypassed.

For example, we know a shark isn’t “fit” to live in a desert environment. That’s obvious from the physical systems it has! The aspects of the shark that don’t make it adapted to the desert aren’t really captured by pop gen math except to say:

\LARGE W_{Shark In Desert} = 0

where W_{SharkInDesert} is the number of offspring a shark in the dessert will have that go on to reproduce, which is ZERO.

But this sort of just says the obvious, but not really the reasons why the shark can’t live in the desert in terms of what biological equipment it lacks to live in the desert!

I believe this is actually known to happen in Iceland.

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So the Icelanders can jump it?