Does evolution have a chance?

[Micaiah]

Ebia, think of it this way. I roll a six sided dice twenty times and come up with a sequence of numbers from each roll. What it the probability of repeating this with the same numbers being rolled in the same sequence.

Your method please - then I will explain again how this relates to convergence.

 

[ebia]

It's rather hard to calculate the odds of bats and dolphins both evolving echolocation independently because we don't know what the odds of either group doing so were.

Given that both inherited from their more basal common ancestor the ability to vocalise, and stereophonic hearing apparatus, it may not be that unlikely at all. Even humans have a very basic echolocational ability, not that it's good enough for us to use for anything.

What I don't get is why he doesn't his probability even more unlikely by throwing in the chance of koalas, lions and hedgehogs all coincidentally NOT evolving echo location.

 

[Jet Black]

then I will explain again how this relates to convergence.

I have to say I am looking forward to this.

 

[ebia]

Ebia, think of it this way. I roll a six sided dice twenty times and come up with a sequence of numbers from each roll. What it the probability of repeating this with the same numbers being rolled in the same sequence.

Let me clarify - you make one set of 20 rolls to produce an ordered set of 20 numbers.

You now ask what for the probability of repeating that exact same ordered sequence with a single try that you have not yet made.


The probability is (1/6)^20

Your method please.

Hopefully self-evident, since this is a much simpler case than previously discussed.

 

[Jet Black]

What I don't get is why he doesn't his probability even more unlikely by throwing in the chance of koalas, lions and hedgehogs all coincidentally NOT evolving echo location.

add to that, what we have in both cases is organisms are put into an environment which repeatedly preferentially selects for individuals that have a certain ability. In the case of dolphins and bats, that ability is the fine tuning of their hearing and auditory analysis systems. Fine they have both reached the same result in that they echolocate, but in each case, did they take the one unique path to that eventual ability, or are there billions of possible phenotypical solutions to that ability and hence countless trillions of possible genetic solutions?

 

[ebia]

I have to say I am looking forward to this.

Me too. Almost worth staying up late for.

 

[Karl - Liberal Backslider]

I think the thing that's being missed here is the non-random element of natural selection, which does push evolution along particular pathways - putting the eyes at the front of an organism so that it can see where it's going, for example.

So whilst rolling the same sequence twice is unlikely, rolling a Yahtzee twice in succession is far less unlikely if I'm allowed to select the sixes and have three rolls of remaining non-six dice, than if I'm just expected to get two Yahtzees out of six random rolls of five dice - i.e. if I'm allowed to select particular randomly generated outcomes. If I select for Yahtzees in this manner, I get far more Yahtzees than I do any other set of five numbers. I can't be arsed to do the maths, but it's quite common to get two in a single game, which consists of, IIRC, only twelve turns of three selective throws. Of course, sometimes you get none, so lets say you get a Yahtzee once in 50 sets of three throws. Without selection, you can only get one in (6 ^ 5) - which is 1 in 7776. Of course, with three throws, that's 1 in 2592 sets of three throws. Rather different, isn't it?

If you're not familiar with Yahtzee, it's a bit like poker dice, but with ordinary dice and a nice box from MB Games. A Yahtzee is five sixes on five dice. But I digress.

What is fascinating here is that when convergence occurs the resemblence is superficial. Dorsal fins on whales and fish. Wings on bats and pterodactyls. The genetic bases of these are different, which is what would be expected from evolutionary theory. Micaiah raises an apparent exception - this gene present in independent sighted organisms. But the point here is that their common ancestor had the gene, even though it hadn't evolved eyes based on it at that point. Similarly, bats' and dolphins' common ancestor had a voice and two ears, even though it hadn't evolved echolocation from that basis yet.

Give me two sixes already, and I can get a Yahtzee pretty often with three throws still to go

 

[Micaiah]

Thank you. And that is the basis for the calculation on convergence.

Step 1. - Spetner estimated that at each step of the development of a certain trait, there were a million possible sites at which a base pair substitution could be made that would meet the requirements of the NDT. (Please don't ask me to repeat those requirements - again).

Step 2. - Estimate the total number of steps required for the development of a new species.

Step 3. - Determine the probability of this same path being taken twice, which models convergence in two animals.

The calculation is really quite straight forward. (If it wasn't, I probably wouldn't follow the argument.)

P(Step 1.) = 1/1,000,000
P(Step 2.) = (1/1,000,000)^2
P(Step 3.) = (1/1,000,000)^3
.
.
.
P(Step n.) = (1/1,000,000)^n

You can do the calculations to model what happens in the genome, or in the physical characteristics of the animal. Spetner notes that there would be fewer steps with the latter approach, but even if you reduced the number of steps by a third, you would still get extremely low probabilities.

You may claim that there is more than one order for the supposed evolution of the trait, and while that may be the case, Spetner states it does not substantially reduce the probabilities.

 

[Micaiah]

Okay, I've responded to your questions, please respond to the following:

I am searching for clear examples of convergence. Ideally what I'm looking for are two traits in an animal that are the same and where that can be shown genetically. For example two animals with identical genes that cannot be explained in terms of the evolutionists basal genes. I'm not saying the other examples don't demonstrate the improbabaility of convergence, just that an example such as that would be more clear cut.

A couple of questions to evolutionists:

1. Do you know of any cases where this has occured?

2. How do evolutionists explain this?

 

[Micaiah]

This was a summary repeat of the calulations given in 104 to 119.

By the way Ebia, can you tell me again how to do the birthday problem. I did know it once and now it has me rattled.

 

[ebia]

Thank you. And that is the basis for the calculation on convergence.

Except for virtually every word I bolded (deliberately) in my previous post. Which I bolded because they are vitally important to the answer.

 

[Micaiah]

I think the thing that's being missed here is the non-random element of natural selection, which does push evolution along particular pathways - putting the eyes at the front of an organism so that it can see where it's going, for example.

That is hidden in the number 1,000,000. Youa are looking through a keyhole.

So whilst rolling the same sequence twice is unlikely, rolling a Yahtzee twice in succession is far less unlikely if I'm allowed to select the sixes and have three rolls of remaining non-six dice, than if I'm just expected to get two Yahtzees out of six random rolls of five dice - i.e. if I'm allowed to select particular randomly generated outcomes. If I select for Yahtzees in this manner, I get far more Yahtzees than I do any other set of five numbers. I can't be arsed to do the maths, but it's quite common to get two in a single game, which consists of, IIRC, only twelve turns of three selective throws. Of course, sometimes you get none, so lets say you get a Yahtzee once in 50 sets of three throws. Without selection, you can only get one in (6 ^ 5) - which is 1 in 7776. Of course, with three throws, that's 1 in 2592 sets of three throws. Rather different, isn't it?

If you're not familiar with Yahtzee, it's a bit like poker dice, but with ordinary dice and a nice box from MB Games. A Yahtzee is five sixes on five dice. But I digress.

Played it often and tried to determine a good strategy based on probabilities. See comments above.

What is fascinating here is that when convergence occurs the resemblence is superficial. Dorsal fins on whales and fish. Wings on bats and pterodactyls. The genetic bases of these are different, which is what would be expected from evolutionary theory. Micaiah raises an apparent exception - this gene present in independent sighted organisms. But the point here is that their common ancestor had the gene, even though it hadn't evolved eyes based on it at that point. Similarly, bats' and dolphins' common ancestor had a voice and two ears, even though it hadn't evolved echolocation from that basis yet.

See comments above.

 

[Karl - Liberal Backslider]

Okay, I've responded to your questions, please respond to the following:

Jet responded to that earlier. There are no such cases. Where a genetic basis is shared, the gene is always present in the basal population.

 

[Karl - Liberal Backslider]

Thank you. And that is the basis for the calculation on convergence.

Step 1. - Spetner estimated that at each step of the development of a certain trait, there were a million possible sites at which a base pair substitution could be made that would meet the requirements of the NDT. (Please don't ask me to repeat those requirements - again).

Step 2. - Estimate the total number of steps required for the development of a new species.

Step 3. - Determine the probability of this same path being taken twice, which models convergence in two animals.

The calculation is really quite straight forward. (If it wasn't, I probably wouldn't follow the argument.)

P(Step 1.) = 1/1,000,000
P(Step 2.) = (1/1,000,000)^2
P(Step 3.) = (1/1,000,000)^3
.
.
.
P(Step n.) = (1/1,000,000)^n

You can do the calculations to model what happens in the genome, or in the physical characteristics of the animal. Spetner notes that there would be fewer steps with the latter approach, but even if you reduced the number of steps by a third, you would still get extremely low probabilities.

You may claim that there is more than one order for the supposed evolution of the trait, and while that may be the case, Spetner states it does not substantially reduce the probabilities.

But you're calculating the probability of exactly the same mutation happening in the same gene. No-one is proposing that that occurs. Convergence involves similar structures occuring through different genetic pathways.

 

[Micaiah]

Jet responded to that earlier. There are no such cases. Where a genetic basis is shared, the gene is always present in the basal population.

Any references confirming this is the case or was this something received by divine inspiration.

 

[Micaiah]

But you're calculating the probability of exactly the same mutation happening in the same gene. No-one is proposing that that occurs. Convergence involves similar structures occuring through different genetic pathways.

You may have a point. I noted above the comment by Spetner that though there may be several slightly different paths to convergence, it doesn't alter the calculation significantly. If you think that is the case, perhaps you could demonstrate mathematically how this is the case.

 

[Karl - Liberal Backslider]

Any references confirming this is the case or was this something received by divine inspiration.

You are asking me to prove a negative?

More to the point, do you have evidence of a case where an identical gene has apparently evolved seperately in different lineages? Since Spetner's whole argument is that this is a problem for evolution if it occurs, the burden is rather on him (or you) to find such an example. We've demonstrated that this eye gene is not such a one. Do you have any other candidates?

 

[Micaiah]

Okay, so we agree that no one has checked out all genes of all animals exhibiting convergence and demonstrated that all are accounted for by basal genes.

Are you and Jet Black saying that of all studies conducted to date, none have been found to exhibit this, or are you saying that you are not aware of any?

 

[Jet Black]

Okay, I've responded to your questions, please respond to the following:

I responded to that already.

 

[Jet Black]

Are you and Jet Black saying that of all studies conducted to date, none have been found to exhibit this, or are you saying that you are not aware of any?

how can I answer the first one unless I am totally sure that I have read every line of every research paper on the topic?

I am certainly not aware of any cases of what you are asking for.