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I was thinking about Stephen Jay Gould's view on evolution as pure "random walk" / Drunkard's Walk, increasing or decreasing complexity in basically random fashion, just limited by death if an organism becomes too simple and so increasing complexity without meaning that it somehow confers survival / fitness advantage.

Now, I've read elsewhere that at least some of the shark species (subspecies?) have existed in about unchanged forms for at least 100 million years (correct me if that's wrong) and alligators for 37 million years. 100M years or 37M years is pretty long even for evolution, so wouldn't it create pretty high chance that such long-running species would die out and/or evolve into species even more complex (per Gould's claim of complexity systematically increasing for purely random reasons)? Why would then what seems like about optimum fitness for particular environment persist so long?

Note: obviously I'm not a biologist or even student of biology, evolutionary biology is just my occasional interest. Apologies if I made basic mistakes in premises to this question.

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    $\begingroup$ You may be making a very common mistake in reasoning about probabilities. Yes, it is very unlikely that a particular species, picked at random, would persist largely unchanged for 37 million years, but at the same time it might be almost certain that some species would follow that course. The error is that you didn't pick a species at random, you picked it precisely because it showed that high degree of conservation. It's equivalent to accusing the winner of the lottery of cheating, because winning is so unlikely. Yet the lottery is designed so that somebody wins almost every time. $\endgroup$ Sep 3, 2019 at 17:43
  • $\begingroup$ You're also ignoring the optimization factor. Living in water puts some severe constraints on creatures, particularly on their shapes, due to hydrodynamics. Sharks in general have converged around a local optimum - and ichthyosaurs, dolphins, and tuna have converged around the same one. It takes a large evolutionary jump to get out of that optimum. And since what we see of fossils is mostly their shape, we don't see much change in general "sharkness". $\endgroup$
    – jamesqf
    Sep 4, 2019 at 3:31
  • $\begingroup$ @CharlesE.Grant Well... it's a different lottery winner almost every time, isn't it? Let's say we calculate the probability of alligators staying almost exactly the same over 37M years using binomial probability formula. $\endgroup$ Sep 5, 2019 at 10:59
  • $\begingroup$ @CharlesE.Grant: Calculation: p = 0.999999 (probability that gator species will stay the same over all generations), q is the usual complement, n = r = 37^6. Since n = r, Newton's binomial in the formula = 1, q^(n-r) = q^0 = 1 and so the whole formula boils down to p^r, presuming simplistically that 1 gator generation takes 1 year. Hence, the value is 0.999999^37000000. This probability is so low that my Gnome calculator doesn't even display the actual value, rounding it down to zero. $\endgroup$ Sep 5, 2019 at 11:00
  • $\begingroup$ @jamesqf: "You're also ignoring the optimization factor. Living in water puts some severe constraints on creatures, particularly on their shapes, due to hydrodynamics. Sharks in general have converged around a local optimum" - well... that's my point. Had constant selection pressure not kept shark's complexity pretty much the way it is, sharks would have evolved into something else, by Gould's argument evolution increasing complexity "mindlessly" via random walk, which is not happening. $\endgroup$ Sep 5, 2019 at 11:04

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Assuming there's an upper bound and a lower bound to complexity, e.g. it hopefully can't get simpler, physically, than an atom/quark and there are I'm sure, physical limitations to complexity (one is Galileo's square cube law). If evolution is truly random, we have a yin-yang effect. After evolution (whether complexification or simplification) hits the boundary walls, the random walk will reverse direction and move towards the other limit. However, in the simple simulations I've conducted, sometimes the random walk stays steady at max/min i.e. plateaus at the upper/lower bound, for some time, and then, "having nowhere else to go", proceeds in the opposite direction, towards the other limit.

In the diagram below of a 1D random walk, look at the region circled in purple. A tendency, albeit brief, to remain at minimum.

enter image description here

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