Probability and Evolution

[Asimov]

As a followup on my questions about mutations, I must now ask about Probability.

Probability is a tender subject with evolution, that much I'm aware of. Many Creationists tend to assume a number as to the probability that a mutation would occur.

Generally this probability is such a large number as to give others the impression that evolution is impossible short of a miracle.

However, and correct me if I'm wrong, one should not choose to ignore probability when forming scientific theories. If probability is ignored, then you run the risk of assuming when trying to "prove" said scientific theory.

In short, the greater the probility, the more rigorous the testing is needed to provide evidence that things happened the way the theory proposes.

Comments and constructive criticism are always welcome, these are just my thoughts concerning evolution. I am in no way trying to disprove evolution, I merely seek knowledge.

 

[JohnR7]

Probability is a tender subject with evolution,

Probability of what? You can have a probability of 00.0001 or you can have a proability of 99.999 & you would still be talking about evolution.
It all depends on what your talking about and how you define it.

 

[Arikay]

It does depend on what you are talking about.

The probability that a beneficial mutation has happened is 1 (as in 100% probability since it has been observed)
The probability that speciation can occur is 1.

Thus when someone comes along and says that probability says evolution is impossible, there must be an error in their math, since evolution has been observed.

Often probability calculations calculate how probable it would be for humans to evolve, of course its very small but thats because evolution wasn't aiming to get humans.
Its like the lottery. The probability that you will win the lottery is very small. The probability that someone somewhere will win the same lottery is much higher. Most probability arguments argue that since the chance of me winning the lottery is so small, the lottery obviously can't be won.

 

[Ryal Kane]

check out The Monty Hall Problem. It really messes with your head.

http://mathforum.org/dr.math/faq/faq.monty.hall.html

Ryal Kane

 

[Jet Black]

this sort of thing is what sex is for. you can have multiple trials on multiple different selection criteria, each of which may become embedded within the population and add together cumulatively to give the outcome. I really should try to work out how much sex increases the evolvability of a species.

 

[lucaspa]

As a followup on my questions about mutations, I must now ask about Probability.

Probability is a tender subject with evolution, that much I'm aware of. Many Creationists tend to assume a number as to the probability that a mutation would occur.

Probability is slippery. It depends on the input. All the creationist probability calculations I have seen (mostly on abiogenesis) are GIGO. Garbage in, garbage out.

Now, measurements of mutations show that the mutation rate is a little over 1 per genome. That means you have a mutation. So do I, and so does every one of the other 6 billion living humans.

Measurements also show that the harmful mutation rate is 2.6 per thousand mutations. Thus, the probability that a mutation is harmful -- will kill or impair the individual -- is 0.0026. Conversely, the probability that a mutation is either neutral or beneficial is .9974. Pretty good odds. Of course, neutral mutations can be beneficial if the environment changes.

However, and correct me if I'm wrong, one should not choose to ignore probability when forming scientific theories. If probability is ignored, then you run the risk of assuming when trying to "prove" said scientific theory.

Theories are determined correct or incorrect on data. Not probability.

What creationists overlook, however, is that natural selection is a method to decrease probability/improve the odds.

For instance, by random chance I have a probability of only 1 in 1024 of winning 10 straight coin tosses. But I guarantee you that I can find someone who can. Odds of 1. Virtual certainty. I use natural selection.

I start with 1024 people and pair them up. Then each pair tosses a coin. The 512 winners are selected to go to the next round. Again they are paired and do a coin toss; the 256 winners are selected to go to the next round. Repeat this 7 more times. Now you have 2 people who have won 9 coin tosses in a row. The winner of this round has won 10 coin tosses in a row. And it is a certainty that such a person will be found with this method. We have taken odds of 1 in 1024 and converted that into virtual certainty. Now, I don't know which individual will win the tosses, but it is certain that one of them will, given the algorithm of the competition. Evolution by natural selection is a competition algorithm, more complex but analogous to the single elimination tournament algorithm. And it cuts down odds.

I hope you are happy with the knowledge you've gotten here.

 

[billwald]

lucaspa is correct. probability only applies to future events. In discussing a historical event, one can possibly calculate the probability of that event happening a 2nd time. This has no effect on the original event.

 

[Aeschylus]

lucaspa is correct. probability only applies to future events. In discussing a historical event, one can possibly calculate the probability of that event happening a 2nd time. This has no effect on the original event.

That's true to a certain extent, you cannot rightly use the proabilty argument to say something didn't happen. For example if I win the UK lottery which has a probabilty of 14 million to 1, when someone comes to my house to present an oversized cheque my next door neighbour cannot say "You haven't won the lottery as that's highly improbable!" as I clearly I have won the lottery! What is observed can only lead to one conclusion - that I have won the lottery, so such arguments from probailty fail.

Lets say we have two hypothesises that both perfectly explain all observations, we then work put that in the beginning the chances that the route that one hypothesis puts forward was more likely, we migh conclude that that hypothesis is more likely to be correct. Howvere this relies on sevreal things: the hypothesises producing the same predictions for all observations so far, we used exactlythe same method to work out the probailty of the two happening, etc.

I hope I have explained why a probailty argument can never falisify evolution, but the point is moot, as despite the ramblings of scientifically and mathematically illiterate creationists we simply do not have enough knowledge to assign a probailty to evolution, infact we do not even have enough knoweldge to even sya whether it was unlikely or likely!

 

[Jet Black]

I think that the only important area in this is the probaility of the formation of the first replicator, since given an imperfect replicator, and given limited resources, and assuming that no total extinction occurs between the formation of the replicator and the moment under analysis, there will be an evolutionarily based outcome, since given these things, there really is no way to stop evolution.

 

[Asimov]

I think that the only important area in this is the probaility of the formation of the first replicator, since given an imperfect replicator, and given limited resources, and assuming that no total extinction occurs between the formation of the replicator and the moment under analysis, there will be an evolutionarily based outcome, since given these things, there really is no way to stop evolution.

Then, how would one calculate the probability, or improbability of such an action occuring?

Evolution doesn't deal with how organisms began (abiogenesis), does it deal with how a certain organ, or part of an organism began? If so, how can we make a compelling argument that isn't based on assumptions if we are to teach others that even if something is unlikely, we have data to support (for example) that an eye evolved this way, without them laughing at us incredulously.

 

[the_gloaming]

Now, measurements of mutations show that the mutation rate is a little over 1 per genome. That means you have a mutation. So do I, and so does every one of the other 6 billion living humans.

Measurements also show that the harmful mutation rate is 2.6 per thousand mutations. Thus, the probability that a mutation is harmful -- will kill or impair the individual -- is 0.0026. Conversely, the probability that a mutation is either neutral or beneficial is .9974. Pretty good odds. Of course, neutral mutations can be beneficial if the environment changes.

I'm just wondering where you got this data for mutation rates, and the calculations involved. You must be talking about the mutation rate for the whole genome, i.e including introns and repetitive DNA, rather than just the coding part of the genome where a mutation would be much more likely to be harmful than 0.0026.

Presuming you are talking about the whole genome, then how is it possible for a neutral mutation in a non coding part of the genome (i.e where most of the mutations will occur) to become beneficial due to an environmental change ?

 

[lucaspa]

I'm just wondering where you got this data for mutation rates, and the calculations involved. You must be talking about the mutation rate for the whole genome, i.e including introns and repetitive DNA, rather than just the coding part of the genome where a mutation would be much more likely to be harmful than 0.0026.

The study is going to, perforce, be looking at the coding parts to detect harmful mutations. However, that is compared to the mutation rate for the entire genome.

PD Keightley and A Caballero, Genomic mutation rates for lifetime reproductive output and lifespan in Caenorhabditis elegans. Proc. Natl. Acad. Sci. USA 94: 3823-3827, 1997

Presuming you are talking about the whole genome, then how is it possible for a neutral mutation in a non coding part of the genome (i.e where most of the mutations will occur) to become beneficial due to an environmental change ?

Many neutral mutations change one hydrophobic amino acid -- leucine, say -- to another -- say isoleucine -- which does not change the protein configuration much. BUT, that configuration may confer greater activity in a different temperature or pH range, so when the environment changes, those individuals with that allele have a protein that functions well in that new environment.

Some of the non-coding parts of the genome are used to bind transcription factors -- the proteins that tell a gene to be expressed. Thus, they act as part of the control of gene expression even tho they do not code for proteins themselves. So, changing the binding constant for a transcription factor such that it will bind still bind at higher temperature, say, will protect the organism if the temperature of the environment changes -- genes will still be expressed as normal.

Heat shock protein 90 (HSP90) acts exactly this way -- binding to DNA to preserve configuration (suppress overexpresssion) during heat stress on the organism.

 

[lucaspa]

Then, how would one calculate the probability, or improbability of such an action occuring?

Evolution doesn't deal with how organisms began (abiogenesis), does it deal with how a certain organ, or part of an organism began? If so, how can we make a compelling argument that isn't based on assumptions if we are to teach others that even if something is unlikely, we have data to support (for example) that an eye evolved this way, without them laughing at us incredulously.

You blew right by my post showing how cumulative selection lowers odds, didn't you?

Your post goes to GIGO when it talks about the probability of an action occurring. You are talking about the probability of a particular action. But the particular action isn't necessary. Instead we are talking about the probability of a class.

Let my try to illustrate with 2 examples.

1. Four friends sit down for a night of playing bridge. They play 10 hands. Now, if you calculate the probability of each of them getting the hands they were dealt in the sequence they were dealt, you end up with a very, very small probability. It would look "impossible". How then, does anyone play bridge? The answer, of course, is that the probability of getting a hand with which you can play bridge is 1. Absolutely certain. No bridge session has to be that particular bridge session.

2. If I dry heat a mixture of amino acids, the probability of getting a 50 amino acid protein with a specific amino acid sequence is very very small. Nearly impossible. However, the probability of getting a protein with some type of biological activity is 1. Absolutely certain. If I have a mole of amino acids -- 6.022 x 10^23 molecules of amino acids (about 100 grams), I will get about 1 x 10^22 proteins. If the average cell needs 10 million proteins, I will have enough protein molecules for 10^15 cells. Now, among those 10^15 cells, what are the odds that one of them will have a mixture of proteins such that it will be alive? Absolute certainty.

The same thing applies to organs. The odds that the particular human eye would evolve might be large, but the odds that some type of eye will evolve is absolutely certain. There are too many molecules that react to light and too many configurations of cells to focus light that natural selection can't find one of them. After all, look at all the variations of the vertebrate eye (of which the human eye is only one). There are over 20,000 species of vertebrates, and they all differ in some minor respect from each other.

Now, we are getting a handle on how some specific organ systems have evolved. The genes are being unraveled. Examples include the eye. Here is some reading for you to do on particular organ systems if you are interested:

http://www.gwu.edu/~darwin/BiSc151/NoCoelom/Precoelom.html
David N. Reznick, Mariana Mateos, and Mark S. Springer Independent Origins and Rapid Evolution of the Placenta in the Fish Genus Poeciliopsis Science 298: 1018-1020, Nov. 1, 2002. Intermediate steps in same genus. http://www.u.arizona.edu/~mmateos/reznicketal.pdf News article at: http://www.sciencemag.org/cgi/content/full/298/5595/945a
2. RO Prum and AH Brush, Which came first, the feather or the bird? Scientific American, 84-93, March 2003.
5. http://abcnews.go.com/sections/science/DailyNews/octopus990310.html Turning octopus suckers into light bulbs
6. http://ajp.amjpathol.org/cgi/content/abstract/164/3/1099?ct change in BMP gives many phenotypic changes in organs. Modifies several organs at once

Int J Dev Biol 1997 Dec;41(6):835-42 Pax-6, eyes absent, and Prox 1 in eye development.

Tomarev SI
Laboratory of Molecular and Developmental Biology, National Eye Institute, NIH, Bethesda, MD 20892-2730, USA. tomarev@fcrfv1.ncifcrf.gov

"Eyes in different systematic groups including arthropods, molluscs and vertebrates probably have a common evolutionary origin. As a consequence of this, related genes are used for regulation of the early steps of eye development in different organisms. In this review, I briefly summarize data on three gene families which might be essential for eye development across species: Pax-6/eyeless, Eya/eyes absent and Prox/prospero with emphasis on our contribution here. Mechanisms of eye formation and the generation of different types of eyes in the course of evolution are discussed."

 

[Asimov]

You blew right by my post showing how cumulative selection lowers odds, didn't you?

I'm sorry if it seems that way, I'm trying to digest a lot of stuff you guys are saying, I read everyones posts, and yours was particularly helpful, I guess I didn't understand all of it.

1. Four friends sit down for a night of playing bridge. They play 10 hands. Now, if you calculate the probability of each of them getting the hands they were dealt in the sequence they were dealt, you end up with a very, very small probability. It would look "impossible". How then, does anyone play bridge? The answer, of course, is that the probability of getting a hand with which you can play bridge is 1. Absolutely certain. No bridge session has to be that particular bridge session.

Now I understand! Thank you very much lucaspa!
When I have time, I will read over those links you've posted.

 

[the_gloaming]

PD Keightley and A Caballero, Genomic mutation rates for lifetime reproductive output and lifespan in Caenorhabditis elegans. Proc. Natl. Acad. Sci. USA 94: 3823-3827, 1997

First of all, thanks for the explanation of neutral mutations. It was at that point, much to my embarrassment, that I realised I'd made the mistake of confusing neutral mutations and synonymous mutations. So, oops.

Secondly, I noticed your source was on C. elegans rather than humans which is probably why your figures don't match what I'd been reading. In the textbook I've been reading (Human Molecular Genetics 3, Strachan/Read, 2004) they suggest the total number of mutations occurring in the human genome has been calculated at 175 per generation (Nachman/Crowell, 2000). Now, I'm not sure if they've missed out a decimal point between the 1 and the 7, but if not then that's a lot higher than the C. elegans study of 1 per genome which of course means a much greater potential rate of evolution. Am I missing something ?

The actual paragraph from the book is :

"Eyre-Walker and Keightley (1999) estimated a deleterious rate of 1.6 mutations per person per generation on the assumption of 60 000 human genes. Recalculating on the basis of the more recent estimate of 30 000 genes with an average coding sequence of 1.6kb gives a deleterious rate of about 0.84 out 2.2 coding DNA mutations per person per generation. Coding DNA accounts for less than 1.5% of the human genome and on the basis of an estimated average mutation rate of about 2.5 x 10^-8 mutations per nucleotide site, the total number of mutations occurring in our diploid genome has been calculated to be about 175 per generation (Nachman and Crowell, 2000)."

So basically:

a) approx 175 total genome mutations per generation
b) out of these, only approx 2.2 mutations occur in coding DNA (the rest in non-coding)
c) out of the approx 2.2 mutations which occur in coding DNA, approximately 0.84 are deleterious.

lucaspa, does that seem an accurate understanding of the paragraph ? Thanks!

 

[billwald]

ASIMOV

This is why probability only applies to future events.

 

[lucaspa]

So basically:

a) approx 175 total genome mutations per generation
b) out of these, only approx 2.2 mutations occur in coding DNA (the rest in non-coding)
c) out of the approx 2.2 mutations which occur in coding DNA, approximately 0.84 are deleterious.

lucaspa, does that seem an accurate understanding of the paragraph ?

That does seem to be what they are saying. Based on the reverse calculations of the 1999 paper. Now, I have the PDF file of that paper. The C.elegans paper was done by direct observation of generations as they happened. The human paper is an estimate based on some assumptions on human evolution:

"Under conservative assumptions, we estimate that an average of 4.2 amino-acid-altering mutations per diploid per generation have occurred in the human lineage since humans separated from chimpanzees. Of these mutations, we estimate that at least 38% have been eliminated by natural selection, indicating that there have been more than 1.6 new deleterious mutations per diploid genome per generation."

Also, the humans were under natural selection while the C. elegans weren't and that C. elegans are hermaphroditic. This allows a more precise determination with the C. elegans. Less variability.

More from the human paper:
"We estimated rates of synonymous substitution per nucleotide, and rates of substitution that result in changes in amino acids per codon, along the human lineage after the human±chimpanzee split for 46 protein-coding sequences from humans and chimpanzees,using another primate species as an outgroup (Table 1)." So it's a sample of only 46 sequences.

So, we have different methods giving different results. That's what you were missing from the textbook. The different methods.

 

[the_gloaming]

Thanks lucaspa. I attempted to add to your reputation (not that you need any more :-D) but I need to spread it around more first apparently.