How a mathematician (that's me) sees evolution

Continuing the discussion from Gil grabs some ammunition and shoots down Doug Axe's 2004 extrapolation by a factor of more than 10^44:

I first heard of evolution in high school, introduced as an interesting and controversial topic (actually in a religion class). It was interesting, and seemed to explain a lot of what we see. But I made no commitment to the idea at that time.

Perhaps 3 years later, as an undergraduate in a biology class (not my major), I learned more about evolution.

I tried some mathematical models – I guess that was simple minded population genetics. But I couldn’t see how it could work. So I remained non-committal.

The problem for me, as I saw it at that stage, was the natural selection seemed to be a kind of statistical convergence. And statistical convergence would be too slow and not sufficiently innovative to account for what we see. And I didn’t see how mutations could fill in the gap, short of an implausible sequence of mutations (giving “hopeful monsters”).

I guess that’s roughly the objection of the Wistar conference, the objection of Fred Hoyle and the objection of so many creationists.

But I didn’t stop there. A few years later – probably when I was in graduate school studying mathematics, I read Watson’s “The Double Helix”. That’s about the identification of DNA as the molecular basis for genetics.

There wasn’t anything directly in Watson’s book that convinced me. But the evidence from genetics and how well the evidence from genetics fitted the Linnaeus classification made a pretty convincing case in support of evolution. What remained was for me to work out how it was all possible, in the light of my earlier doubts.

It took me a while to solve that puzzle. And it mostly wasn’t an urgent issue. I had already been persuaded that the evolution picture was broadly correct, even if I did not know how to connect the dots.

I eventually did work through that puzzle, at least enough to satisfy me. So I’ll now give my current view of evolution, which is quite a bit different from how I had originally thought that it was supposed to work.

My current view of evolution

It is a population that evolves. And there is some genetic variation within that population.

The environment is forever changing. It might get hotter or wetter. A new predator shows up. A food staple disappears. Another potential food source shows up.

The population must attempt to adapt to the changing environment. It is adapt or die. In order to adapt, individual organisms change their behavior. Some are more successful than others. That’s where the existing variation comes in. That some are more successful than others is roughly what “natural selection” refers to. The variants that are more successful at adapting to the changed environment will do better. If there is not sufficient variation in the population, then there is a greater risk of extinction.

I see biological innovation as mostly a response to a dynamically changing environment. The already existing variation within the population is part of what make that possible. However, as the population changes to adapt to the changing environment, that will tend to reduce the amount of variation present in the population. The role of mutation is to replenish the reservoir of variation. And the recombination during meiosis helps spread this variation around.

If you think there needs to be purpose involved, then look to the apparently purposive response of organisms, as they modify their behavior in an attempt to adapt to the changing environment.


Hi Neil
Thanks for the op. How much of life’s diversity do think this population genetics model explains?

Are we allowed also to have complete knowledge of what every gene in the genome does (including their interactions) and how they interact with every environment, or do we just have to do it all with the equations of population genetics?

How about these 6 genes and the transition to human like sequences.

I still don’t know how “bits” are calculated, why the x axis should count as an ordered axis at all, such that one can determine a meaningful slope, and why increasing similarity to the human sequence should count as an information gain. Can you elucidate?


Bill won’t touch the fact his “sudden” big jumps of information actually took close to 100 million years.

Only in Nigel Tufnel mode…

The human like sequences did not transition from other modern species. A modern invertebrate is not an ancestor to the human lineage.


Probably all of it. But keep in mind that it depends on a dynamically changing environment. Evolution is one of the causes of change in the environment. But there are other causes of that. So maybe you want to include those as part of what explains diversity.

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Very nice.

So if a population is already optimized for a relatively static environment, there is little push to tilt towards away from the center of existing variation (say, size), and if other ecological niches are already filled by competitive species, there is limited pull. So then evolution would be more gradual. When the environment experiences change, as is guaranteed to eventually happen (climate or asteroids), compatibility is stressed and there is push to favor variation limits; and as new niches open up or are vacated (no dinos), there is pull. Thus, changing environment would push and pull for more vigorous evolution.

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How do you think the changing environment drives the origin of new biochemical features like we are seeing with transition between invertebrates and vertebrates?

It probably doesn’t. Those “new” features might not be new. They may have already been present at a low level within the variants in the population. They may have been added by earlier mutations.

What environmental change does, is make those feature more useful – even valuable. And, because of that, they proliferate within the changing population.


What “new biochemical features” are you thinking of?

What about them?

There’s an ancestral population with genes, mutations happen, they accumulate over many generations, today we see mutated versions of the ancestral genome that includes those genes in all the species that carry them.

What’s the problem again?

Your claim is the features are the result of earlier mutations and become active when the environment changes and they become useful?
Would you claim that wings with flight feathers arose from random mutation?

Firstly, I am not a biologist nor am I a natural historian. So I don’t pretend to know the detailed history here.

My view is already described above. Organisms – in this case precursors to birds – changed their behavior in order to deal with environment change. Presumably, as a result of a number of changes, we finished up with birds that could fly.

Yes, it is likely that mutations were involved in getting to that stage. But a mutation that suddenly allowed flight is unlikely. More likely is a series of other changes that eventually ended up with the ability to fly.


What is the mechanistic explanation for these changes?

There is more to the story, but sure. Why not?

The molecular evolution of feathers with direct evidence from fossils

You may recognize Mary H. Schweitzer’s name among the authors.

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You could not give a mechanistic account of driving to the supermarket. You could not give a mechanistic account of your own walking. Yet you demand a mechanistic account of the emergence of flight in birds?

You are playing a losers game.

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There is no irreducible complexity here. What is the mechanistic barrier?

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