Probabilistic thinking is pervasive in evolutionary theory. It’s not a bad thing, just something that needs to be acknowledged and appropriately handled.
Denial
Some go so far as to deny it, but in my experience these people are ideologues. These are critics of ID who complain about the lack of any numbers being attached to the probability arguments of ID proponents, and their denial is perhaps rooted in their fear of a tu quoque.
Where are their own probability calculations?
Incredulity
Another reason for their denial could be that they also love to accuse ID proponents of making arguments from incredulity, while being unwilling to face up to the fact that they are guilty of the same thing. Does evolutionary theory depend on arguments from incredulity? Almost certainly.
Take for example the idea that all extant life shares a common ancestor. It is based upon the idea that it is simply too implausible that life should arise more than once and yet share common features such as the genetic code.
We can be very sure there really is a single concestor of all surviving life forms on this planet. The evidence is that all that have ever been examined share (exactly in most cases, almost exactly in the rest) the same genetic code; and the genetic code is too detailed, in arbitrary aspects of its complexity, to have been invented twice.
Dawkins, Richard. The Ancestor’s Tale: A Pilgrimage to the Dawn of Evolution
An argument from incredulity.
Probabilities are Important
The importance of probablity in evolutionary thinking might best be seen in the following text:
If there are versions of the evolution theory that deny slow gradualism, and deny the central role of natural selection, they may be true in particular cases. But they cannot be the whole truth, for they deny the very heart of the evolution theory, which gives it the power to dissolve astronomical improbabilities and explain prodigies of apparent miracle.
Dawkins, Richard. The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe without Design
Independence of Events
While having said all this, I’d like to focus on the idea that evolutionary events are not independent and that this somehow rescues evolutionary theory from being guilty of appealing to vastly improbable outcomes, aka miracles.
Consider a toss of the dice in a game of craps. The odds of double six is 1/36. Sure, we can roll a single die twice, and the odds of a six on each roll is now only 1/6 vastly more likely to occur by chance (not really). 1/6 x 1/6 is still 1/36. The probabilities are multiplicative because the events are independent events. The fact that if you have two dice and you roll the first die until you get a six and then you keep that (by cumulative selection) and then roll the second die until you get the second six and now you have two sixes doesn’t change the probabilities one whit. Doesn’t that demonstrate that cumulative selection is helpless in reducing probabilities?
Well, you might say, you need to roll BOTH dice until only one of them shows a six and then keep that one and then roll the second die. But what in evolution is analogous to that?
Sure, if you roll two dice trying to roll a six you have a better chance of a six showing on one of the two dice than if you roll just one. It’s like rolling one die twice in an attempt to get a six rather than just once. Of course the probability of the second six would still be 1/6. But why aren’t justified in adding a third die after our first six is rolled so that once again we are trying to get a six from two dice and not just one? And doesn’t this again demonstrate that it is not cumulative selection at all that is responsible for the reduction in probability but rather the number of trials we allot each attempt to roll a six?
Closing
The fundamental question is why aren’t evolutionary events independent and thus multiplicative?
The secondary question is what is the true role of cumulative selection in reduction from the miraculous to the mere appearance of the miraculous?
I’m not a Dawkins fan, and I don’t agree with what is in those quotes. But then I can’t really be sure that Dawkins agrees with them either, because I have not checked the context in which those statements were made.
As for evolution and probability — the independence question isn’t really what you think it is. Probabilities can be very hard to estimate.
For example, you cannot simply try to calculate the probability of evolving an eye, because it was never a goal of evolution to evolve an eye. Roughly speaking, the goal is to improve the fitness of a population. And if it didn’t evolve an eye, maybe it would have evolved some other feature that was effective at improving fitness.
You cannot just look at the probability of a particular outcome. Instead you have to look at the probability of getting any of a large number of outcomes which could be effective at improving fitness.
I provided the books. What do you want, chapter and page? But why would that even matter, given your stance on truth?
What you should do, Neil, is create an OP setting out your theory regarding what is true and what is not true and why it matters. Surely you can grasp how others might think all your pronouncements are not to be taken as either true or false.
You post something and I shrug my shoulders. You don’t know what is true and what is false, and yet you think people should listen to you. Why?
Sure I can. It’s what Dawkins does. It’s a fundamental aspect of evolutionary theory.
I don’t have to do that. Evolutionists have to do that. It’s their theory. It’s their burden to show the probabilities involved. It’s their burden to show that the steps leading to some particular outcome are not independent. It’s their burden to show how their theory can be distinguished from the miraculous.
You forgot to include, “by accident.”
Because if the outcomes aren’t by accident, then the probability is surely different, right?
Whereas of course the theory of deliberate design has what to say?
I’m not clear on where your model addresses the issue of spread of a mutation (= the initial roll of 6) by a mechanism of population genetics between the rolls.
The probabilities to be determined in this simplistic but I* think useful idealization of evolution/population genetics are the probabilities of at least one roll of 6 twice in some member of the population, with the second role occuring after the mutation has spread by one of these mechanisms.
—————————–
*I am not a biologist!
BruceS,
So, one mutation, followed by 3 million years to fixate (a blink of an eye we are told) then a second, followed by another 3 million years, and so on…
How many mutations from a cow to a whale do you reckon? A blink of an eye, becomes a pretty long time. For that matter, how long to get an eye that blinks?
When you have billions of years…
How many do you reckon? After all, it’s you that is making the claim that no matter how many mutations required it’s not possible.
https://en.wikipedia.org/wiki/Evolution_of_the_eye
A couple of million years seems to be the answer.
Any other questions?
“The fact that if you have two dice and you roll the first die until you get a six and then you keep that (by cumulative selection) and then roll the second die until you get the second six and now you have two sixes doesn’t change the probabilities one whit.”
If I throw 2 dice simultaneously I need 36 throws for a double 6.
If I throw one dice I need six throws to get a 6.
If I throw a second dice I also need six throws to get a 6.
For the first double six I need 36 throws, for the second double six only 12 throws.
We have a theory that attempts to explain the origin of the eye.
You don’t. Yet instead of attempting to make what we do have better, you mock it and those that attempt to make it better.
I’m sure Jesus is proud.
OMagain,
Your responses seem to be written by a four year old, with dyslexia and a possible head injury. I am not saying you are like that (because that might be against Alan’s made up rules) I am saying your RESPONSES seem like that.
Just to make the obvious explicit: your points about the Dawkins quote you provide are criticisms of his popularization style.
ETA: And not of any specific science that might underlie that populatization.
I am not clear on how you captured the evolutionary accumulation of mutations.
That is, the second roll has to be of a die that got a six in a previous roll or of a copy of that die replacing one that did not. For simplicity, assume constant number of dice; copies then are spread by spreading of mutation (ie roll of six initially) replacing other dice that did not ) due to some evolutionary mechanism.
Sure. It can’t be that you can’t answer any of the questions that logically you’d have to know the answers to in order to make the claims you do. It can’t be that.
What is your explanation for the origin of the eye?
Probabilities and creationists, like oil and water
Why are you a theistic evolutionist then? Why not just be a straight up creationist?
I did not accuse you of taking it out of context. I merely expressed my own neutrality on judging Dawkins’ view.
You did not provide the books — you only provided the titles 🙂 And I don’t happen to have those books around.
I have a very restricted view of true/false. In my opinion, people are too quick to assert truth.
As I see it, scientific theories are neither true nor false. Yet they can be very important. We evaluate scientific theories on pragmatic grounds, rather than whether they are true or false.
That there was a single common ancestor turns out to be a very useful assumption on which to base our study of biology. Whether or not it was strictly true doesn’t actually matter. Based on your quotes, it matters to Dawkins. But it doesn’t matter to me. It’s pointless arguing whether it was strictly true, because we don’t have time machines to go back and verify. So I’ll stick with the pragmatics.
From the perspective of 2018 years ago (it’s Christmas, after all), the probability that a being would exist today with the exact same DNA sequence as Mung would be astronomically improbable. Yet he exists. This is the same flawed probability that the ID stable geniuses use to argue against evolution.
Much to Mung’s disappointment, he was never the goal; he is the result of generations of random meetings, random couplings, meiotic events and ancestors with sufficient fitness to reproduce. Who would have predicted, or wanted, that? 😉
If god exists, miracles are dime a dozen, so not really improbable events at all.
dazz,
Are you saying that if God exists the resurrection of Jesus was a chip shot
🙂
I’m saying that the probability of miracles is determined by the frequency at which they happen, just like everything else. Going by google, there were 10 other resurrections other than Jesus according to the bible, so yeah, if that shit was true, resurrections were not too improbable at all at the time
ETA: I guess that’s exclusively a frequentist view and a bayesian would disagree
Sorry, but your example is beyond wrong.
The number of throws required to get a six in either case are the numbers required **on average** (that is, averaged over a large number of samples). It should be obvious that I might throw a double six **on my very first throw** (does that support a prior probability of such an outcome being 1.0?).
In any case, the probabilities of achieving a double six are identical in both scenarios (1 in 36). Throwing the dice in parallel or in sequence doesn’t change the combined probabilities of getting two sixes, or the rules for calculating them. Since the throws are independent events, you multiply the odds in both cases.
I would not describe Seqenenre as “beyond wrong”, rather I would use the term “poorly expressed”.
The expected number of rolls to get a six is six.
This is true for the red die and for the blue die.
If you roll both dice together, then the expected number of (double) rolls to get double six is 36.
HOWEVER, if you stop rolling a die when it lands showing six, then the expected number of rolls for each die is six.
This is true whether you do one die first, then the other, or if you start with both at once. Just remember to count double rolls as two in this latter case…
When talking about probabilities it is important to be very explicit about the processes that one is describing. The OP avoids doing this, presumably for comedic effect.
Under a modified version of that protocal, the expected number of rolls would be even smaller – in fact, only 9.
1. Take two dice and roll them together
2. The expected number of double rolls before you get a six on either die is 3
3. As soon as either die shows a six, put that die aside
4. Continue to roll the second die until it shows a six
5. The expected number of further rolls before six shows up on the second die is 6
6. Ergo the expected total number of rolls (double or single) required to achieve a double six is 9
7. This is a bit misleading since the expected total number of rolls of any die in the protocol is still 12
Yes, that is what I meant by “Just remember to count double rolls as two in this latter case”.
I only mentioned it, as it speaks to the whole “You need 100 changes for this transition, and if each of them takes 1,000 generations to fix, then you need 100,000 generations for this transition…” fallacy.
There’s no reason to introduce that model of rolling dice as analogous to evolution. Mung is without excuse after being involved in a number of discussions about the weasel algorithm and other similar topics.
Been busy. Just dipping in for a moment. I see Mung has claimed:
What utter nonsense.
We observe that the genetic code is almost universal across all extant organisms. The parsimonious explanation is relatedness.
Mung seems to have entered into a very confused position. Apparently he thinks cumulative selection is some sort of myth that is not capable of bringing about complex adaptations, because the individual steps in the process are independent events, and so he can multiply up the probability of each step and arrive at an insanely low number for the final adaptation (however many iterations later he chooses to draw the line).
And this, it appears he thinks, shows that selection does not alter the probabilities of establishing a complex adaptation.
This can be debunked with a simple simulation. In fact the BoxCar2D simulation disproves the claim.
Imagine having to wait for a high-performance (score >800 on “The Hills” terrain) car in the BoxCar2D simulation to be created in one go by random assembly but without selection? That would be incredibly unlikely to happen. I’ve never seen it just so happen to create a score >800 car right on the first go (or in the first generation, even with a hundred members), yet it will consistently and reliably produce such cars when the selection process is allowed to run.
Why is that the case, if the compound probability of each “increment” in the evolution of the high performance car, is supposed to factor up into a probabilistic miracle?
Somehow Mung’s argument fails to actually account for the fact that selection has that capacity to preserve things that work well over things that work less well. That is why you get will-functioning complex adaptations down the line, even though the compound probability of each iteration leads to a vanishingly unlikely result. Selection really is what does that, and we can see it happen with out own eyes.
The point is that the probability of independent events are multiplied, whether in dice or in evolution. It’s not an analogy, it’s an example.
If you don’t think that’s the case in evolution why not?
Cumulative selection doesn’t invalidate the independence of the events and so it doesn’t solve the improbability problem. The probability of the events are still multiplied because they are independent. If not why not.
Yes it does. At each generation the dice are loaded by selection. Advantageous traits are more likely to proliferate.
They are Mung, but particular independent events are much more likely to be retained, leading incrementally to establishment of that vastly improbable outcome many iterations down the line.
Calculating how unlikely the eventual outcome is becomes meaningless when such unlikely outcomes invariably result from the process.
Of what use is it to do the calculation, and come up with an extremely small probability, when we can see such unlikely outcomes evolve incrementally over and over again?
It’s not like the number we can calculate somehow makes it so the process we see in the BoxCar2D simulation didn’t actually take place. Score >800 cars consistently evolve, yet are very unlikely to just be produced in one fell swoop in the first generation. So what is the calculation supposed to tell us? That selection is a miracle worker? It doesn’t look miraculous to me, whatever that is even supposed to mean. I can sit here and see every generation play out before my eyes, with random physical changes to the cars subjected to their effect on the performance of the car.
Yes, it is the fact that some of the events are kept for the next generation. Each event, each mutation is independent, but some of them are kept and passed on in favor over others. This is what allows a well performing complex adaptation to gradually evolve, it is paid for in the deaths of lots of individuals who were peeled off along the way.
The events are NOT independent, in the mathematical sense of the word.
I’ll do it with dice:
Here’s the protocol:
I roll a red die, until it comes up heads.
Then I roll a blue die, until it comes up heads.
Then I roll a green die, until it comes up heads.
Every single time I roll a die, the probability I roll a six = 1/6. This never changes. The probability that any particular roll produces a six is independent of the other rolls.
However, the fact that I am rolling a green die is NOT INDEPENDENT of the rolls of the red die. And therefore, the probability that my fifth overall roll is a green six depends on what happened with the red and blue dice.
The probability that I get a green six on my tenth roll, given that I am rolling a green die is still 1/6. That “given” phrase matters.
I’ll do it with cards:
If I draw a card at random from a conventional deck, the probability that it is a spade is 1/4.
The probability that I draw to fill my flush is 9/47, not 1/4.
I may have mentioned this before…
Thus, although which particular mutations occur today is not affected by which mutations occurred previously given that we have a living organism and even intelligent people often refer to mutations as “independent”, it remains the case that, speaking from the strictly mathematical “can I multiply these numbers?” perspective, the mutations are NOT independent.
IDists need to be able to calculate the conditional probabilities if they want to multiply numbers together (or add bits, heh).
Given their demonstrated inability to comprehend the problem, I doubt they will ever manage that.
:p
Also Mung, you don’t seem to understand what an argument from personal incredulity is. Alan already addressed you on that, what Dawkins is doing there is applying the principle of parsimony, he’s not simply saying “I can’t believe the genetic code emerged twice”. A single event explains why the code is common to all life forms. Two or more independent origins of the same code would require another explanation. How is that not obvious?
Now compare that with “this or that is so complex that NS+RV couldn’t have possibly done it”. There is NOTHING there except for mere assertion.
You’re the only one trying to play tu-quoque here, and your failing to show that evolution is just as bad reasoning as ID, and you’re also tacitly admitting all the charges on IDism as being incredibly poor reasoning.
I’ve always thought the creationist understanding is that legs are not functional until they are long enough to reach the ground.
Yes this makes sense to me, but I don’t understand what you go on to say here:
It is not obvious to me why you can’t multiply them as if they are independent events. Can you elaborate?
Oh, by the way. If the same code happened to emerge twice, we would have two independent trees of life, unless one of the trees went extinct, that is. Or would it also be an argument from incredulity to affirm that it would be very hard to believe that two separate origins of life forms with the same genetic code, would just happen to share sequence similarity in a way that it now looks like a single origin? Of course not. To reconcile the idea of two separate origins with the data requires outlandish assumptions like those
The probability of fixation is just another probability that has to be calculated and included in the overall scenario. If it’s an independent event it has to be multiplied.
Rumraket,
Why? Ancestry.
Imagine an organism that cannot die and grows by cell division, irrespective of genotype.
Mutation A arises once, when there are 1,000 in the pop’n.
Mutation B arises once, when there are 1,000,000 in the pop’n.
Today, there are 1,000,000,000 in pop’n.
The probability that a randomly selected individual has
Mutation A: 1 in 1,000
Mutation B: 1 in 1,000,000
Mutation A AND mutation B:
Oh-err, that’s more complicated: It’s probably 0 (if B arose in an unmutated individual, then P(A|B) = 0)
But it might be 1 in 1,000,000, if B occurred in an individual that had A [P(A|B) = 1]. Saying “our best estimate is 1 in 1,000,000,000” is not terribly informative…
If you introduce differential reproduction or sex, then you *definitely* cannot multiply the probabilities.
Suppose that we are in a population with only one copy of a particular gene, so that it is a haploid population of size
. Suppose that there are 4 states of that sire, A, C, G, and T. Each has a fitness, so we have 
, 
, 
, and 
, let’s say 0.5, 0.7, 0.9, and 1.0. If we are currently in state A, there is some probability, say 
, that the state changes. Let’s have mutation be symmetrical (what is known as the Jukes-Cantor model). The adult individual of genotype A gives rise to lots of offspring, a fraction 
of them being C, 
of them being G, and 
of them being T. All the rest, 
of them, are the original genotype, A.
Each has a fitness, and we weight each by it. So the proportions in the very large number of newborns are proportional to
, 
, 
, and 
. There is only one surviving adult after density-dependent population size limitation acts. It will be selected from those proportions with probabilities equal to them, each divided by their sum.
That is what a standard population-genetic Wright-Fisher model will do. From this, I leave it to you all as an exercise to show that the probabilities of successive changes are not independent. They do form a Markov Process, but not a series of independent draws of A, C, G, and T from some distribution.
If I’m not mistaken, the case ultimately settles into an equilibrium distribution, in that the probability that it is state A in the long run is
, in state C the probability is 
, in state G 
, and in state T 
. It bounces around among these states, more infrequently the smaller is 
, but with these frequencies in the long run.
The nonindepence is shown by the fact that if you start in state T, the chance that you will change to state A in one generation is smaller than if you instead start in state C.
DNA_Jock,
This is also the problem with the ‘hypermutation’ scenarios required or invented to get modern diversity patterns off of the Ark. You can’t get there without generating the tree structure – ie, you’d need to telescope generations, and not merely to go forth and multiply …
(ETA: I see oher posters have made the same point to you as I do in following but in different ways. So I’ll bow out now to avoid further repetition in your thread.)
Joe explains this if you want to dive into the math of Markov processes. The key is that current state matters, so you cannot use a model which ignores it.
And in useful models of evolution, current state includes not just whether a single mutation occurred in 1/N individuals, but also how many individuals it spread to in subsequent generations.
A model which ignores this fact is the dice roll model that treats each die independently and says the next generation for the dice rolls is just the outcome of the previous roll, nothing more.
If that is not the model that concerns you, please let me know the model of independence you are using and how it applies to evolution.
If you are just saying that if two events are independent, then you multiply the probabilities, they of course you are trivially correct. But what does that have to do with evolution?
BruceS,
What does assigning a fitness before reproduction have to do with evolution? All measures of fitness are retroactive.
That which reproduced was the fit one. We know because we defined it as such.
Not sure what that has to do with my post or the OP.
In any event, don’t confuse how we can measure something with what something is.
https://plato.stanford.edu/entries/fitness/
This is what it has to do with your post.
And this.
Wow, that is quite a source you reference. For those who don’t believe in the concept of fitness that is.
Its a list of all the reasons why fitness can’t be adequately defined.
Thanks for that.
Its essentially a repeat of every criticism of fitness that I have made here.
BruceS,
I hope Allan and Jock..and Joe, don’t read your link. You are going to give them ulcers.
Like you read it. You stopped right after the introduction, didn’t you?