Counting generations of M&Ms

Allan Miller’s post Randomness and evolution deals with neutral drift in the Moran model applied to a bag of M&Ms. Much of the discussion has focused on the question of counting generations in a situation where they overlap. I think it’s a good idea to divert that part of the discussion into its own thread.

Here are the rules. Start with a population of N M&Ms. A randomly chosen M&M dies. Another randomly chosen M&M gives birth to a child M&M. Repeat.

Because the focus of this thread is generation count and not fixation, we will pay no attention to the colors of M&Ms.

How do we count generations of M&Ms?

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Randomness and evolution – An Interactive toy

Lizzie Allan Miller said:

Here’s a simple experiment one can actually try. Take a bag of M&M’s, and without peeking reach in and grab one. Eat it. Then grab another and return it to the bag with another one, from a separate bag, of the same colour. Give it a shake. I guarantee (and if you tell me how big your bag is I’ll have a bet on how long it’ll take) that your bag will end up containing only one colour. Every time. I can’t tell you which colour it will be, but fixation will happen.

I’ve written an interactive browser based version you can explore this idea with.

http://mandmcounter.appspot.com/emeniem.html

color

 

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Darwin backwards?

What is it with ID proponents and gambling?  Or rather, what is it that makes people who play p0ker and roulette think that that gives them a relevant background for statistical hypothesis testing and an understanding of stochastic processes such as evolution?  Today, “niwrad”, has a post at UD, with one of the most extraordinary garblings of evolutionary theory I think I have yet seen.  He has decided that p0ker is an appropriate model this time (makes a change from coin tossing, I guess).

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Randomness and evolution

Here’s a simple experiment one can actually try. Take a bag of M&M’s, and without peeking reach in and grab one. Eat it. Then grab another and return it to the bag with another one, from a separate bag, of the same colour. Give it a shake. I guarantee (and if you tell me how big your bag is I’ll have a bet on how long it’ll take) that your bag will end up containing only one colour. Every time. I can’t tell you which colour it will be, but fixation will happen.
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Random Mutations: vjtorley

vjtorley, at UD, writes a post entitled It’s time for scientists to come clean with the public about evolution and the origin of life that includes this:

Edward Frenkel, a professor of mathematics at the University of California, Berkeley, recently reviewed a book titled, Probably Approximately Correct: Nature’s Algorithms for Learning and Prospering in a Complex World (Basic Books, 2013) by computer scientist Leslie Valiant, in a report for the New York Times (Evolution, Speeded by Computation, September 30, 2013). The following excerpt conveys the gist of Dr. Valiant’s conclusions:

The evolution of species, as Darwin taught us, relies on natural selection. But Dr. Valiant argues that if all the mutations that drive evolution were simply random and equally distributed, it would proceed at an impossibly slow and inefficient pace.

Darwin’s theory “has the gaping gap that it can make no quantitative predictions as far as the number of generations needed for the evolution of a behavior of a certain complexity,” he writes. “We need to explain how evolution is possible at all, how we got from no life, or from very simple life, to life as complex as we find it on earth today. This is the BIG question.”

Dr. Valiant proposes that natural selection is supplemented by ecorithms, which enable organisms to learn and adapt more efficiently. Not all mutations are realized with equal probability; those that are more beneficial are more likely to occur. In other words, evolution is accelerated by computation.

The criticisms being made here of the Darwinian theory of evolution are pretty devastating: not only is it far too slow to generate life in all its diversity, but it’s also utterly incapable of making quantitative predictions about the time required for a structure of known complexity to evolve, by natural selection. And there’s no reason to believe that the “nearly neutral theory of evolution” espoused by biologists such as Professor Larry Moran would fare any better, in this regard.

 

Dr Torley is a scholar and a gentleman and someone for whom I have a great deal of personal respect. In fact I owe him more than one debt of personal kindness.  But that does not mean that I think his ideas are correct, and I submit he is profoundly wrong here in an extremely useful way.  Unusually, the passage he cites is very specific about the kind of randomness that cannot be the kind of randomness that would produce Darwinian evolution: equally distributed.

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A Statistics Question for Barry Arrington

Re your post here:

  • If you came across a table on which was set 500 coins (no tossing involved) and all 500 coins displayed the “heads” side of the coin, how on earth would you test “chance” as a hypothesis to explain this particular configuration of coins on a table?

Even if the observer was not party to the information that there was “no tossing  involved”?

The reason I ask, is that you seem to have revealed an conceptual error that IMO bedevils much discussion about evolution as an explanation for the complexity of life.

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