Shades of Galton….


In his fourth-floor lab at Harvard University, Michael Desai has created hundreds of identical worlds in order to watch evolution at work. Each of his meticulously controlled environments is home to a separate strain of baker's yeast. Every 12 hours, Desai's robot assistants pluck out the fastest-growing yeast in each world, selecting the fittest to live on, and discard the rest. Desai then monitors the strains as they evolve over the course of 500 generations. His experiment, which other scientists say is unprecedented in scale, seeks to gain insight into a question that has long bedeviled biologists: If we could start the world over again, would life evolve the same way?

Stefan Jovanovich writes: 

The absence of time's arrow is fascinating. The "fittest" compete in a world where the rules are constant and invariable - "meticulously controlled" - while everything we know says that the rules are always changing in ways that even we brilliant humans fail to predict. Still worse for the purposes of experiment, the rules sometimes instantly and violently, even as they obey all of our entirely predictable laws of physics.

Ralph Vince comments: 

This has nothing to do with "fitness," and everything to do with randomness.

Take X scenarios. At each discrete point in time, they branch into one of these X scenarios, such that after Q discrete periods, you have X^Q branches.

Your "expectation," (not in the classic sense) is the sorted median outcome (whereas the classic sense expectation is the probability weighted mean outcome, and I contend that in the limit, i.e. as Q->infinity, they converge *).

About this sorted mean outcome (at QP0, in the paper this thread pertains to) there is a vast region of similar-outcome branches. It sounds to me as though this experiment has lass to do with evolutionary "fitness" and more to do with artifacts of expectation in finite time.

I am working on a proof of *, but working on it with respect to continuously-distributed outcomes (as opposed to discrete "scenarios") as well as continuous(though fininte) time, rather an discrete increments of time to Q.

It is a struggle.

Mr. Isomorphisms adds: 

This may not be what you're looking for in proving *. But the other day I worked out that you can exploit the "soft max" identity (seen in tropical geometry and elsewhere) to get analytic formulae for the median, third-from-top, etc. (only with log base âˆΕΎ) which might get you where you need to go.

max = log_t ( t^a + t^b + t^c ), t going to infinity

min = log_t 1/( t^-a + t^-b + t^-c ), t going to infinity

second_max = max( {a,b,c} - max({a,b,c}) )

With recursion you can get all the way to the middle. (Now since we've turned the median into a continuous function we can take derivatives, which I haven't simplified or played around with since I realized one can do this. But I don't think that relates to your * — just hoping the method would.)

Steve Ellison comments: 

Regarding Shane's original question, yes, there is a phenomenon known as evolutionary convergence. Isolated areas with similar conditions often have similar life forms that developed independently. For example, cacti originated in the Western Hemisphere, but there are plants that originated in Eastern Hemisphere deserts that also store water and have spiky exteriors.

Gary Rogan writes: 

Clearly there are niches in the environment, just like there are in the economy, the market, the arts, sports, etc. It seems self-evident that a species that thrives on a Pacific island is likely to be different from a species being able to survive in the Arctic or at the bottom of the ocean. Not having "a single, cannibalizing species inhabiting the planet" only speaks to the niches in the environment not some complicated problem with evolution.

Ralph Vince adds: 

Perhaps we DO, in effect, have one, cannibalizing species, depending on how broad the field of view of our lens of examination.. How many animal life forms on the planet have but one eye? "Evolution" having eliminated that not-so-robust construction in all earthly environments. Is our notion of "species," which we believe to exhibit a vast array of life forms, only show us carbon-bases life forms with, at most, five senses. In that sense, is a penguin so much different from a scorpion from a human being? The notion itself of "food chain," with such biochemically similar life forms, is, in effect, an exercise in cannibalism. 

Gary Rogan writes: 

Since the evidence points to life arising or being successfully introduced to Earth just once, it's not surprising that we only have carbon-based life forms. And just because a scorpion shares a lot of genes and proteins with penguins doesn't mean they are of the same species, simply based on the definition of the word: to be so classified they'd have to be able to interbreed. I'm now no longer sure what the point is, but hopefully "descent with modifications" is not in question.

Ralph Vince clarifies: 

My point simply put, is that I don't find "evolution," or "Survival of the Fittest," an adequate model, i.e. a panacea for how life arose and differentiated (to the restricted sense that it has) on earth. I find it too simplistic of a solution, believe there are likely many other explanations (all of which are, in a limited sense, true, similar to the wave/particle properties of light) and am interested in any other explanations (there is not a debate here, aside from one which I don't believe you ascribe to of "Fitness" being an explanation for all life on earth).

For example, (to the best of my knowledge) every living thing seems to fit somewhere into the food chain. Perhaps there is an overriding-yet-undiscovered mechanism requiring this as a license for life on earth? (And if not, why not? A stupid question, unanswered, is still an unanswered question. I believe evolution seems to explain so much that we use it to explain where a different mechanism may be the driving one, yet, occluded by the seemingly-obvious-to-us explanation of "fitness"). Evolution is a powerful explanation, but it does not explain everything.Not that I have a problem with "fitness" as a driver here — clearly it is, so I am not at odds with you there (though I am not so sure life was introduced on earth only once, again, viral and fungal life is a difficult leap from living cells). So I simply wonder of what other driving mechanisms are at work here that we are unaware of.

Gary Rogan writes: 

Ralph, as it's generally hard to prove a negative, especially in open-ended complicated situation, I can't argue that there are other forces at work. As for fitting somewhere on the food chain, all carbon-based life forms eventually get weak and if not eaten at that point die. Weak or dead concentrated proteins and other valuable chemicals present too rich and too easy a food source not to be consumed by something, so this particular point doesn't instill a sense of wonder in me, but perhaps there is more to it than meets my eye.

We should keep in mind that on the average over any appreciable number of generations every existing species or otherwise categorized collection of biological creatures has almost exactly one descendent per individual, otherwise within a short span of time the group's mass would exceed that of the planet or conversely disappear. Therefore available resources present arguably the highest hurdle on the success of species, but as Hamlet said, "There are more things in heaven and earth, Horatio, than are dreamt of in you philosophy."

Ed Stewart writes: 

Speaking of the food chain, I think the concept of the tropic level has some serious application to the markets, as I the chair documented in his first book. Might be particularly good model to analyze the impact of various stimulus measures - what level the stimulus directly stimulates, then who feeds on that level directly and indirectly for investments opportunity.

anonymous writes: 

There are no marsupials above the Wallace Line above Australia. Below there are the myriad odd and strange life forms in Australia. It was a function of geology creating distinct eco zones and separate paths of development of life forms.


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