[top] -- [home]
Much of the discussion below concerns Dr. Senapathy's probability computations for one gene mutating into another gene. A 10% change was used as a basis for change.
"Darwin felt that the individual variations in the population of an organism, and monstrous variations that occurred among them, provided the material basis for natural selection and adaptation, producing many different creatures from one original ancestor organism. His followers, until today, have essentially believed in this theory, but the theory is wrong, because of the following principles we derive in Chapter 3:
Evolutionists are bound to jump on me and show the production of one species of duck from another species of duck with a distinct variation in its color pattern or beak length, and say this proves Darwin was right. The distinction is that Darwin was only right in an extremely limited sense. It is important to understand that all the changes in an organism cannot take it beyond a certain level. There can be a large number or artificial breeds and natural varieties (which are now termed species) within the confines of each organism. This scenario is sufficient to mislead and confuse one into thinking that because individual variations and natural selection lead into new varieties (i.e., similar species, which is true), varieties lead to completely new organisms (which is absolutely false). A frog might evolve into a toad, but it can never evolve into a rabbit, or anything that is not distinctly frog-like. The supposed ladder of evolution, from worm to millipedes, from invertebrates to vertebrates such as fish, fish to amphibians, amphibians to reptiles, reptiles to birds, and reptiles to mammals is imaginary because new body parts can never be produced by any form of evolutionary change." (pages 100 - 102)
From Keith Robison: (reprise) Senapathy has committed his first error. He is claiming to be trying to prove that no genome can change by 10%, but he is basing the calculation on a particular 10% change. Using similar logic, I can prove that any bridge hand will never occur, or using a few assumptions of population genetics, that neither Senapathy nor I can possibly exist. The odds are just astronomical!
JM: But if you are going from a genome "A" to another genome "B" (given two such genomes of interest that are supposed to be connected by evolution and that their genes differ by 10%) then the differences are a particular 10%, so the math is appropriate in that case.
Keith: First, Senapathy doesn't restrict himself to this condition later in the book -- he uses it as a general proof later (and also in the post earlier in this thread) that NO genome can EVER change by 10%. Second, it is still an abuse of probabilities (see below)
And, of course, Senapathy has stacked the deck -- he is implicitly claiming that there is only a single set of changes which will distinguish two genes from each other functionally.
JM: There will be a single set of changes in the particular genome for going from "A" to "B". Given a set of changes, he computes the probability of THOSE particular changes occurring. I think that's fair. He need not compute the probability of ANY 10% change because any other 10% change would not result in the same organism "B".
Keith: But this is making the implicit assumption that there is only one
possible set of mutations to change A to B, and more importantly
it is assuming that there is only one possible B to change into.
For example, suppose I'm playing poker and I am originally dealt
As 5d 6h 7s 8c
but I end up showing
4s 5d 6h 7s 8c
what was my probability of converting my useless hand to a straight
by discarding the ace and drawing? It was not the probability
of drawing 8c, or even drawing any 8, but rather the probability
of drawing any 8 or any 3 -- there was more than one possible
straight I could draw.
In a similar way it is likely that there is more than one set of mutations which will convert the genome of species A into the genome of species B, and there are probably multiple possible species (C,D,E, etc) which A could mutate into.
Consider this: what is the probability that my parents gave birth to me? In the absence of recombination and mutation, each of my parents could have generated 2^23 possible gametes. The odds that I am the offspring of my parents is therefore 1/(2^46). By your argument, I therefore was not born of my parents.
I ask you this. Humans and chimps have extremely similar genomes, and I doubt even you would attempt to claim they sprung to life independently.
JM: According to Senapathy, they probably did. If there are unique genes in either genome, then he would say that they must have.
Keith: Yet chimps and humans show a number of key differences which must be genetic, and are quite extreme. For example, chimpanzee females develop a large swelling on their buttocks during reproductive heat. Where did those novel genes/pathways come from? Are you going to claim that is "normal" variation?
JM: The Senapathy test is: are there unique body parts or organs (and thus unique genes)? If so, they are independent organisms.
From Keith Robison: ...into a new gene, then the probability to achieve this is (1/300*)^100 or approximately 10^-350 [* -- the book has 1/3000 here, presumably a typo].
JM: I believe 1/3000 is correct. At that point he is talking about a gene of 1000 nucleotides.
Keith: I still suspect it's a typo -- n (the number of sites) goes in the exponent.
In the following,
m = frequency of mutations per nt per generation g = #generations n = # of nt changes being consideredSenapathy claims the calculation to be
(1) p(10% change) = ( [1/3]m )^nAssuming one generation per year, we can invert the probability to estimate the number of years required:
(2) years(10% change) = 1/( [1/3]m )^nBut the units of m are 1/generations:
(3) p(10% change) = ([1/3]m 1/generations)^nwhich means the units for (1) is generations^(-n)
and the units for (2) are years^n
To correct this, we should put g inside the parens
(4) p(10% change) = ( { [1/3]m 1/generations} {g generations} )^n
which can be simplified to
(5) p(10% change) = ( { [1/3]mg)^n
Which makes a certain amount of sense -- as the value of g approaches
the value of m, the probability should approach 1.I hope that's a clear... exposition of Senapathy's gross statistical bungling.
From Keith Robison: (reprise): "I still suspect it's a typo -- n (the number of sites) goes in the exponent."
It took some more mail with Jeff for me to finally see the light -- it's not a typo, but rather Senapathy's 3rd gross error in setting up the equation.
Senapathy claims that "if a gene is 1000 nucleotides long, and if it requires specific nucleotide changes at 100 positions (10% change) to change this gene into a new gene, then the probability to achieve this is (1/3000)^100..."
Again, ignoring his two other mistakes (incorrect statistical assumptions
and dropping the generations term now but reinserting it later in
the wrong place), he has succeeded in getting n (the number of sites
under study) in two places. If we reduce his equation to symbolics:
[(1/3)gene_size]^[gene_size/10]
A very impressive equation -- the probability of us observing a
single mutation amongst the collection of sites (the part of the equation
to the left of the exponential) goes DOWN as we consider more sites!
Of course, the size of the gene is irrelevant -- the only thing relevant is the number of sites we are interested in (which Senapathy has defined in terms of gene size) and the probability that a mutation at a site is one of interest (1/3). Of course, both of these numbers are derived from his unstated and incorrect assumptions. Senapathy's equation is also pretty impressive because it does not contain a term for the mutation rate -- he just casually compares the mutation rate to the output of his equation.
The embarrassing thing is that I missed this entirely when comparing my equation from scratch with his equation.
From Jeffrey Mattox:
Background:
This post concerns computations of the low probability of a gene undergoing a certain 10% change to become another gene. This concept is discussed early in Dr. Senapathy's book, Independent Birth of Organisms, and forms the basis for him saying it is unlikely for a gene to ever be changed into another gene. Keith Robison and others have objected to the mathematics and the method. If you are not interested in the details, just skip to the Conclusion where I'll tell you why none of this really matters anyway.
Old Business:
Keith asserts that Dr. Senapathy has made three mistakes. Keith's objections are:
Keith wrote:
m = frequency of mutations per nt per generation
Senapathy claims the calculation to be
p(10% change) = ( [1/3]m )^n
JM: I assume you meant: p = ( 1/[3m] )^nOn pages 36 and 37 of his book, Dr. Senapathy is not using "m" (mutation rate). He is only computing the probability of having a nucleotide change in a particular spot, independent of an external rate. Later on he incorporates the mutation rate. (I'll do it both ways below.)
Keith also wrote (Objection 1):
>... it is likely that there is more than one set of mutations which will convert the genome of species A into the genome of species B, and there are probably possible species (C, D, E, etc.) which A could mutate into.
JM: Yes, there are different sequences of mutations that will give the identical result ("B"). I will adjust for that, below. You argue that it is unfair to look for just one particular outcome, but it may also be unfair (in the other direction) to assume that a mere 10% change of any sort to any gene will produce a new organism. The objective is to use some numbers (rather than just words) to show that a certain change is so highly improbable that arguing about the conditions or degrees of fairness is futile.
Quoting Keith: Consider this: what is the probability that my parents gave birth to me? In the absence of recombination and mutation, each of my parents could have generated 2^23 possible gametes. The odds that I am the offspring of my parents is therefore 1/(2^46). By your argument, I therefore was not born of my parents.
JM: The probability of you or any particular individual being born is very low, that is true. But almost every possible combination of your parents' gametes would be viable (ignoring inherited diseases, etc.), and so some favorable result will probably occur. In the case of the genetic changes being considered here (the outcome of which is a supposedly a new organism), "success" is not so likely, so it is fair to put some restrictions on what outcomes are acceptable.
Keith also wrote (Objection 2):
>If a genome mutates at a rate of 10^-5 mutations per generation, then after how many generations would we expect every nucleotide to be hit by a mutation -- 10^5 generations!
JM: But that hardly gets you from genome "A" to genome "B." It is like taking a negative image of an entire picture rather than just inverting a small section in one corner. If every mutation and every intermediate was viable, then this would be a whole different world. We are not computing the likelihood of any change, just a supposedly viable one with a new gene. Although we are trying to mutate gene "A" all the other genes are mutating with the same probability.
Keith also wrote (Objection 3):
...he has succeeded in getting n (the number of sites under study) in two places. If we reduce his equation to symbolics:
[(1/3)gene_size]^[gene_size/10]
A very impressive equation -- the probability of us observing a single mutation amongst the collection of sites (the part of the equation to the left of the exponential) goes DOWN as we consider more sites!
JM: I assume you meant:
[1/(3*gene_size)]^[gene_size/10]But, that equation is correct. Dr. Senapathy is not computing the probability of a hit. Rather, given a hit, he is computing the probability of that hit occurring at a specified location. If you shoot into a forest until you hit a tree, the probability that you have hit a particular tree is inversely proportional to the number of trees in your field of view. At this point we are assuming that all shots are hits somewhere in the coding region of a particular gene. The probability of actually hitting the gene is applied later. (See details, below.)
Method 1 (Senapathy at page 36, Chapter 3):
I will run the numbers following the same sequence Dr. Senapathy does in his book. Later, I will repeat the math using the "Robison" method and show that the results are the same.
Definitions:
Outcome: mutating gene "A" a particular 10% to become gene "B"
"hit" means a mutation of one nt site in the coding region of "A"
L = length of gene "A" (not including any junk DNA), units "nt";
X = number of sites to be hit (10% of the gene), units "nt";
P = probability of a certain desired mutation of 10%, outcome "B"
Therefore:
X = L/10
probability of a hit at a particular location in the gene = 1/L
probability of a hit producing the correct AGCT = 1/3
probability of any hit being correct = 1/(3L)
a = probability of all X hits being correct = [1/(3L)]^X
(This ignores multiple hits at the same nt. If we did not
ignore this, it would increase the total hits required)
b = combinations of X hits that result in the same outcome = X!
P = b * a = X! * [1/(3L)]^X
Dr. Senapathy neglected the X factorial term. If that term is not
included, then P would be the probability that the X hits all happened in a
particular sequence. (This is the difference between using permutations
and combinations.)Now, with some numbers for a typical gene of length 1000 nt:
L = 1000 nt
X = L/10 = 100
P = 100! * [ 1/(3000)]^100
(now we'll lose the kids with their calculators)
log P = log 100! + [100 * log (1/3000)]
log P = 158 + [100 * (-3.48)] = -190
P = 10^-190
Dr. Senapathy computed 10^-350 because he left out the X factorial term.
That would be OK if the actual "route" taken from "A" to "B" is important,
but that has not been stated as a condition -- that is, there is no reason
to test the intervening genome states for viability.We now have the probability ("P") of a gene being changed from "A" to "B" in a given number of hits ("X") on that gene. We use 1/P as a reasonable estimate of the likely number of "hits" needed to obtain that change, that is 10^190.
The next step is to compute how often the gene will be hit in a certain number of mutations of a genome. This is where the mutation rate and changes in the junk DNA factor into the result. Summarizing Dr. Senapathy at page 37:
m = mutation rate (range of 10^-9 to 10^-6 in animals,
per Futuyma, D. Evolutionary Biology), Senapathy is
generous and uses 10^-5 (changes per nt per generation)
S = genome size of 10^9 nt per genome (includes junk DNA)
c = number of nt changes per generation = S * m = 10,000
these will be spread randomly throughout the genome
N = genes in the genome = 10,000 (junk DNA is 90% of the genome)
H = changes ("hits") per gene per generation = c/N
Therefore:
H = c/N = 1 nt hit per gene per generation
1/P is the average number of hits needed to make the change
likely to have occurred in one gene
g = generations_required = #hits_required / hit_rate
years per generation = 1
Y = years for change = generations_required = (1/P) / H
Now, with the numbers:
P = 10^-190
Y = 1/(10^-190) / 1 = Years for gene "A" to become "B" = 10^190
Dr. Senapathy got the result 10^350 years, but it doesn't matter because
10^190 is still huge enough to preclude the change from ever being likely
to happen.
Method 2 (Robison):
Now, let's start over and approach this using the other method. The probability of hits on the genome being in the correct gene will be introduced while computing the probability of hitting a particular site in the gene. Also, we'll take into account the combinatorial issue in-line.
Definitions:
H = "hits" per gene = c/N = 1 nt per generation per gene
(thankfully, most of the work has been done above)
P(n) = probability of a hit on gene "A" being desirable (that
is, causing "A" to go to "B") on hit number "n" (0 to 99)
P(n) = [(number of still unhit sites)/L] * 1/3
Z = probability of a genome having gene "A" going to gene "B"
Z = product of 100 probabilities of hitting correct places
Z(n) = probability of any hit on genome being desirable
Z(n) = H * P(n) = P(n)
Z(0) = 100/(3000)
Z(1) = 99/3000
Z(n) = (100-n)/3000
The product of all Z(0-99) = Z
Z = Z(0) * Z(1) * .... * Z(99)
Z = n!/(3000^n)
Z = 100!/(3000^100)
log Z = log 100! - [100 * log 3000] = 158 - (100 * 3.48) = -190
Z = 10^-190
If you don't like the original idea of allowing gene "A" to change only
into a certain other gene "B," let's allow "A" to turn into any one of a
billion other genes (hmmm..... that would be "B" through "CFDGSXM").
[Objection 1] That Big-Zee would be the sum of a billion Little-Zees, or:
BigZee * 10^9 = 10^(-190 + 9) = 10^-181.That's not much better.
I'm only human -- a Senapathy independent organism, composed of a random assortment of genetic material, some pieces of which were copied from other genomes (thus accounting for my similarity to an ape) and some of which is unique (thus accounting for my ability to read and write), that just happens to be viable -- so I may have made a mistake in this report. If you have an alternative view, please present an equally detailed supporting set of explanations, equations, and numbers, and with as little emotion (but as much humor) as possible. In the end, all we really want to know in relation to this post is this: is it likely or not that macroevolution can occur by mutation?
In the grand scheme of things, this debate about whether or not genetic changes in a genome can bring about new organisms (that possess new body parts or genes) is not the central part of Dr. Senapathy's theory. He presents the arguments against macroevolution at the beginning of his book, but that debate has been raging for well over a century, and Dr. Senapathy does not need to keep it alive by himself. However, that material is there because it serves as a basis for later discussions about why his theory does not suffer from those same problems.
There are four parts to his book:
What has been overlooked is that Dr. Senapathy's theory complements Darwin's Origins by providing the many millions of initial organisms on which microevolution, Darwin's Special theory, operates. If Darwin had known more about DNA and genes in his time, it is possible he would have run the numbers himself, discovered that life may not have been so improbable after all, proposed a theory of independent births, and avoided the whole controversy over his General theory.
Thank you for your attention.
Jeffrey Mattox
From Wesley R. Elsberry: We know that tetraploidy (100% change) is sufficient, and we know that certain other less drastic changes to the genome can produce reproductive isolation and thus speciation. Now, whether a 10% change in some particular allele is sufficient to produce reproductive isolation might be problematic to determine. Whether that 10% change is necessary, which is what it seems that your argument is based upon, is a whole different kettle of fish.
Look, the issue isn't whether permutation or combination is used to analyze the change from clade A to clade B. The problem that Robison was trying to communicate is that a subpopulation of clade A is not constrained to only be modified to be the initial population of clade B. There exists a class of clades which would be functionally identical to B (have the same ecological niche sensu Hutchinson), each of which could be derived from clade A. Until you have a grasp of the size of the class of B-functional clades, your probability measures tell you nothing. And once you do come up with an estimate of the possible cardinality of the B-f class, I'll give you the next reason as to why you still haven't gotten the probability analysis locked up yet.
You haven't computed anything that says what outcomes are acceptable, because none of your probability analysis tackled the problem of what cardinality the B-f class has.
As I said before, once you do that, there remains more complexity in the analysis to be dealt with.
Another thing for you to consider: the same probability analysis that you give for a particular clade A -> clade B transition would apply to the clade A(t_0) -> clade A(t_n) transition. Senapathy probability apparently not only disproves 'common descent', but ordinary descent as well.
From Keith Robison (replying to Jeff Mattox): You missed what is essentially my 4th objection, and then fell prey to it -- that because the units of the calculation were not considered, the final answer is useless in the context it is being used in.
Quoting JM: On pages 36 and 37 of his book, Dr. Senapathy is not using 3m2 (mutation rate). He is only computing the probability of having a nucleotide change in a particular spot, independent of an external rate. Later on he incorporates the mutation rate. (I'll do it both ways below.)
Keith: And that is where he bungles, because his comparison is between values with vastly different units!! What you and Senapathy are attempting to calculate is the probability that particular genome A will change to particular genome B in 1 generation. Since nobody is claiming this, it is a straw man.
Again, in your equations you attempt to calculate a probability and then at the end compare it to the mutation rate. This approach does not work! The probability of any mutation occurring is dependent on the mutation rate, which carries units of generations^-1. Your tiny values for the probability for N sites changing contains a term of generations^N which you have ignored! Why don't you rework your equations with the mutation rate built into them and units carried through? If I am wrong, it will be irrelevant.
Look at it another way -- if we make the simplifying assumption that the genome receives a constant number of mutations a year, and that number is 1/10000 nt, where did all those other mutations end up? Is Newt Gingrich aware of the gaping mutation deficit???
Quoting JM: In the grand scheme of things, this debate about whether or not genetic changes in a genome can bring about new organisms (that possess new body parts or genes) is not the central part of Dr. Senapathy's theory.
Keith: Actually, it is critical on several counts
From Jeffrey Mattox (replying to Keith Robison)
I spent all of three days preparing that long post of mine and working through the equations, complete with units and numbers. I checked all the units, and carried them through, just as you have suggested. Then, I stepped up to the s.b.e. blackboard, and I put up the math and the numbers for you to see. So, now it's your turn. You rework the equations and show me how it ought to be.
Please do what I did: define the variables, then show the equations, the units, and the numbers. And, just so we can compare apples and oranges, please assume the same starting point at least for one example (L=1000, 10% change, S=10^9, N=10^4, etc.) and show where Dr. Senapathy and I have gone wrong. I don't mean to sound "dense," but all you have done so far, Keith, is complain about the equations and logic, but you have not shown any details, and the few times you've come close to the details you did things like misplace parenthesis and I wasn't certain of what you really meant. I honestly want to see your logic and results, so I can lay them right down beside mine (and hence Dr. S's.).
Keith: (reprise): Look at it another way -- if we make the simplifying assumption that the genome receives a constant number of mutations a year, and that number is 1/10000 nt, where did all those other mutations end up?
JM: Most of the point mutations would hit in the non-coding regions. Those that hit important stuff would (1) lead to normal variants of the same genes (e.g., due to degeneracy of codons, normal variant proteins, etc.), (2) lead to defective genes, or (3) turn genes "off" that were "on" (or vice versa). (Reference: Dr. S. "IBO" pages 151-165.)
From Keith Robison: Ignoring for the moment the wrong choice of model, suppose we look at a collection of N sites in a known genome, and for each one decide a mutation. I.e., at each site X, it will go to Y (X->Y).
The probability that at one site we will observe nucleotide X mutating to not X (!X) after 1 generation is the mutation rate, m.
(1) P(X->!X) = mSince only a change to Y is of interest, and only 1/3 of mutations of X are X->Y
(2) P(X->Y) = m(1/3)The probability that all that all N have undergone X->Y is the product of the individual probabilities; since these are all equal, we can just raise to the power N
(3) P(allX->allY) = [m(1/3)]^NBut again, the important term m is in units of reciprocal generations, and is inside the exponentiation. By failing to carry the units through, we have lost something. So we try again, adding the g (generations) term
(2a) P(X->Y) = m(1/3)gNow the units of P(X-Y) aren't reciprocal generations anymore, and so when we take the power we don't get odd units
(3a) P(allX->allY) = [m(1/3)g]^NDoes this make intuitive sense? Well, let's rearrange (2a)
(2) P(X->Y) = mg(1/3)If we make multiple trials for an event with a known probability, then the probability of that event ever occurring is approximately the product of the probability and the number of trials (mg).
Quoting JM: Most of the point mutations would hit in the non-coding regions. Those that hit important stuff would (1) lead to normal variants of the same genes (e.g., due to degeneracy of codons, normal variant proteins, etc.), (2) lead to defective genes, or (3) turn genes "off" that were "on" (or vice versa). (Reference: Dr. S. "IBO" pages 151-165.)
Keith: You've missed my point -- perhaps due to the way I worded it. You've "proven" that two extant genomes of 10% difference cannot possibly be evolutionarily related. Your proof has nothing to do with biological function -- you have attempted to demonstrate that the raw possibility does not exist.
But we know that the genome is experiencing change at a known flux in the range of 10^-5 - 10^9 per generation (10^-5 is what Senapathy uses). How do you reconcile these two facts? At 10^-5, a 10% change would accumulate every 10^4 generations (ignoring back-mutation). In other words, in the absence of selection the genome MUST be changing, but your proof attempts to show that it CANNOT be changing.
Something you might try with your equations -- what level of genomic change will it allow in one year's time? If the answer isn't the mutation rate (or the rate of acceptable mutations (1/3)m ) then there is obvious problem with the equations, which could be in their assumptions, derivation, or the context in which the final value is being used*.
* -- I could not have passed many a math course without applying checks on myself such as these.
From Dave Oldridge (quoting JM): But if you are going from a genome "A" to another genome "B" (given two such genomes of interest that are supposed to be connected by evolution and that their genes differ by 10%) then the differences are a particular 10%, so the math is appropriate in that case.
Dave: You are not "going from genome "A" to genome "B", though. Senapathy is starting with Genome B and trying to "prove" that it didn't originate in genome "A" which is an entirely different matter in which the improbability of any of the putative "steps" in the process plays no serious part. Consider, for example, the improbability of each of the "steps" that create a Senapathy or an Oldridge or a Mattox from human ancestors 8000 years ago. The odds against these PARTICULAR results are enormous, yet, by Senapathy's argument, this proves that none of us could really be descended from our ancestors of 8000 years ago.
JM: Keith also brought up that objection. Dr. Senapathy was showing that the time required for a particular 10% change to a gene made through random point mutations would be prohibitive. Even if you allow billions of "OK" outcomes to billions of genes, the time needed is huge.
Your human comparison is not the same thing. We are not organisms produced through random changes due to point mutations. We are the products of biological processes that, more often than not, produce viable results. On the other hand, mutations produce defective genes and non-viable results more often than not, or they produce normal variants of the same gene. Our relationships to our ancestors follow a non-random path. The selection of traits might be random, but the outcome is known -- humans with the same genes and body parts.
From Paul S Winalski: It seems to me this is at the crux of the argument over Dr. Senapathy's theory: can point mutations result in the large-scale morphological differences that distinguish the major taxa? Dr. Senapathy and his supporters say no. Supporters of traditional models of evolutionary speciation say yes. I don't think we can settle the question until we know a lot more about the biochemistry of cell, tissue, and organ differentiation during embryonic development than we know now.
From Dave Oldridge: Far from being appropriate, the math is being egregiously abused.
JM: The Senapathy test is: are there unique body parts or organs (and thus unique genes)? If so, they are independent organisms.
Dave: Senapathy's also pretty much ignores the data in the fossil record.
JM: The fossil record supports his theory 100%. We don't even have to discuss whether or not the fossil record supports Darwin's macroevolution. The gaps in the record, the sudden appearances of organisms, the uniqueness of the Burgess Shale creatures, the lack of transitional forms, etc., etc., etc., and even the commonalities between organisms, are all predicted, bulls-eye-style, by Senapathy's theory.
Dave: If his interpretation of it is to be taken at face value, then new species ought to be crawling out of ponds everywhere, all the time...
JM: No, certainly not now. The productivity of the primordial pond ceased long ago because of changing conditions (e.g., the environment, lack of enough DNA material). Senapathy makes this very clear in his book, although he does not attach a date to the demise of the pond.
Keith: ...Furthermore, if Senapathy's theory has any merit, it ought to be easy for him to demonstrate it in the lab by actually producing new species from an artificial "soup."
JM: He does not claim to know the proper conditions, but no doubt we will be able to do this some day. It did happen at least once, so there can be no doubt that it is possible. Along that same line, if it happened once, why not twice -- or a few billion times?
From Keith Robison: Revisiting yet again whether statistics proves that evolution can never occur. Given:
P probability of gene A changing to gene B by a specified 10% change
L length of a typical gene
X number of changes required for 10% change = L/10
Senapathy's claim was:
P = [1/(3*L)]^X
which Mattox amended to:
P = X! * [1/(3*L)]^X
Which both yield very big numbers. Compare these to the number of
mutations raining down on a gene over any realistic period, and
its clear there is a serious shortage of needed mutations to drive
evolutionary change.
I spent the weekend thinking this over and going through the calculations, and there is nothing mathematically wrong with Mattox's equations.
But, a statistical equation is only as valid as the context to which it is replied. Underlying every statistical equation is a model, and the equation is a quantitative assertion of that model. IF the model is not relevant, than neither is the equation.
Well, as has been discussed here, Senapathy silently makes the assumption that there is only 1 particular 10% change which could distinguish A from B. Not only does he fail to state the assumption, but he ignores it later on and uses his equation as a proof that NO gene can EVER change by 10%. But more importantly, the model underlying both Senapathy's and Mattox's equation is a straw man, and not important.
Let's start by constructing some models of how evolution might work. We'll keep the extra assumption that a particular 10% change is required, and that no other 10% change will do.
Suppose the change from A to B requires X mutations, and these must accumulate in a particular order. But, under any real model of evolution selection exists, so once we have seen the next mutation in the series it is preserved by selection.
To see any particular sites, it will take 1/m (m=mutation rate, >>1 ) generations to observe a mutation at that site, and 1/3 of the mutations are to a "wrong" nucleotide. Therefore, after 3*1/m generations (on average) the target mutation should occur and be fixed by selection. Now we can start waiting for the 2nd mutation in series. Therefore, under this model the number of generations required (g).
g = X*3*1/mAnother possible model is to remove the restriction that the mutations must occur in a set order. Under this model, if ANY of the target mutations occur they are fixed by selection. Running the model backwards, the last (Xth) on will still require 3*1/m generations to occur, but the (X-1)th will require 3*1/m*1/2 generations, the (X-2)th 3*1/m*1/3 generations, and the 1st will require 3*1/m*1/X generations. I.e.
k=X
g = 3*1/m * sigma(1/k)
k=1
Alas, that last term is called the harmonic series, and it does not
converge and so we cannot just convert it to a nice round limit.
But it does go up pretty slowly. Perhaps someone more mathematically
astute can provide the formula, but here are some samples from a
program which calculated them
k=1..X
X sum(1/k)
1 1.00
10 2.93
100 5.19
1000 7.49
10000 9.79
100000 12.09
1000000 14.39
So, for the case of 100 mutations, this model reduces the time
>from 100 * 3*1/m to 5.2 * 3*1/m. Not bad. Realistically,
evolution is likely to sometimes follow the one model and
sometimes the other, and changing conditions probably shift
the set of "target" mutations (i.e. A->B first involving a tack
towards B', but B' is never reached).If these models produce results, even under the unsupported assumption of only a single target B, compatible with evolution, then what model underlies Senapathy's and Mattox's equations?
I'll confess I'm not certain. But, a very similar equation results from the following problem:
Suppose you have 5 6-sided dice, each a different color (Red, Blue, Green, Yellow, Purple). The probability of rolling them and coming up
R-1 B-2 G-3 Y-4 P-5is (1/6)^5. The probability of just getting any combination of 1,2,3,4,5 is
(1/6)^5 * 5!Based on this, I would conclude that both are concerned with the probability that in a sample of X mutations you will see the X mutations you are interested in. Senapathy's equation demands that you see the X mutations in a particular order, whereas Mattox's allows you to see the mutations in any order within your sample of size X. Since neither is what is claimed under Darwinism, they are both irrelevant.
From: pitt@sci.wfeb.edu: It seems to me that the problem is not 'A to B' but 'A to X'. It is true that if you demand that an unlikely event occur twice you will not get good odds, but natural selection does not demand and instant replay.
The odds that Senapathy gives are like those for one person playing a lottery twice (with odds of 1/1,000,000) and winning twice.
(1/(1,000,000)) X (1/(1,000,000)) = 1/1,000,000,000,000If you ask what are the odds of anybody playing twice and winning twice, and everyone in the world play then:
1st play 5,000,000,000(people) X (1/(1,000,000)) = 5,000(winners)
2nd play 5,000(winner) X (1/(1,000,000)) = 1/200
Quite a different result.
From Jeffrey Mattox: In a previous post, I supplied a detailed example of the math behind Dr. Senapathy's assertion that point mutations won't get you a new gene for a new organism (gene "A" going to "B"). I challenged Keith to show how my math was incorrect and to provide an alternative set of equations and/or numbers.
Keith replied: I spent the weekend thinking this over and going through the calculations, and there is nothing mathematically wrong with Mattox's equations. ....what model underlies Senapathy's and Mattox's equations? I'll confess I'm not certain.
JM: Then Keith constructs two models that he feels more accurately describe macroevolution. He kindly uses the same assumptions (a particular 10% change is required, and that no other 10% change will do).
Keith continues: ...under any real model of evolution, selection exists, so once we have seen the next mutation in the series it is preserved by selection. After 3*1/m generations (on average) the target mutation should occur and be fixed by selection. Now we can start waiting for the 2nd mutation in series. Therefore, under this model the number of generations required (g).
g = X * 3*1/m
JM: Whoa! There are three major problems with this "sticky ratchet" method:
Re: #2: That's part of the model -- that selection is preventing any movement backwards of the ratchet.
Re: #3: Again, an explicit part of the model. Selection is completely forcing the remaining positions to stay constant.
JM: How can you even justify this flexibility mathematically? In effect, you are ADDING the probabilities rather than taking their PRODUCT. When you play Scrabble, the letters in your hand and those already played on the board won't change, but in our real life game, any of them may get hit by a mutation and ruin your plans.
Keith: Yes! Because the question isn't whether we will ever see all the mutations in a cluster, but rather whether over an extended period we can accumulate those X mutations. This is the heart of the problem with Dr. S's calculations and your modification of them -- they calculate the probability of A spontaneously changing by 10% to B, not whether mutation+selection could evolve A into B. Unfortunately, they are claimed to apply to the latter case.
JM: I find this thread very interesting -- that is, what is the correct model, assuming there is a way to model this given the conditions (size, 10%, etc.)? Keith says Senapathy's model is not what is claimed under Darwinism, and perhaps he is correct, but these new suggestions are no improvement.
Keith: Yes, I have posited a rather strong form of the argument -- that selection is 100% at the "untargeted" positions and that selection prevents the ratchet from slipping backwards. And under this model, evolution is plenty possible, even with the restrictive assumption that there was only 1 possible B distinct from A.
And, as has been pointed out here before, that assumption is a whopper and simply an assertion. In particular, many of the observed changes between gene A and gene B are probably neutral (we know this based on looking a populations and species which Senapathy would claim do have a common origin). So while we may observe a 10% difference, there may (for the sake of the models presented above) really be only a 1% difference which is absolutely required. Just making this change shifts the Mattox equation P value from 10^-190 to ~10^-29. Available data would also suggest that there are frequently multiple changes which can generate similar functional differences (the most obvious being that in many cases there are 2 possible nucleotide substitutions which can cause the same amino acid substitution).
So a realistic model of evolution would modify both the "extreme selection" assumption I explicitly made, and the "only 1 possible B" assumption which Senapathy implicitly made for the derivations (and then completely ignores when applying his result). I think you'll find the latter will more than balance the former.
From Dave Oldridge: The fundamental issue with Senapathy's math is that he assumes that what DID happen could not have happened simply because it is highly improbable. That whole line of reasoning is fallacious. Highly improbable things DO happen. Indeed, they are happening all around us every day.
And in all this discussion of gene A turning into gene B, it seems to be forgotten that nobody has shown that gene A must needs turn into gene B at all. It could just as easily turn into gene C or gene Q or some other variant without that doing any real damage to Darwinian evolution.
And Keith is correct. In fact, Senapathy's model PRECLUDES Darwinian evolution as a premise (see above).
From Jeffrey Mattox: Keith Robison has moved the discussion on whether or not Dr. Senapathy's numbers are correct (after concluding they are based on the equations) to a discussion of whether or not Senapathy's macroevolution model is correct (and Keith concludes it is not but for reasons uncertain).
Keith wrote: ...the model underlying both Senapathy's and Mattox's equation is a straw man, and not important. ...what model underlies Senapathy's and Mattox's equations? I'll confess I'm not certain.
JM: Dr. Senapathy and I assumed a certain 10% change in one gene would convert gene "A" into gene "B," and we computed the probability of that through multiplication, resulting in a number so small (10^-190) as to make the event impossible. Keith used a different model (I call it the "sticky ratchet" method), ended up adding the probabilities, and came up with a much different number.
Keith: I made more assumptions in order to produce an alternative model, and as a path to identifying the model underlying Dr. S's equations. And under this model, evolution is plenty possible, ....
JM: Keith's new assumptions about macroevolution are:
Keith, I will let you look for a better model, and I will be happy to discuss any ideas. You are right, it does not matter, because all models are straw men. There is no correct model because macroevolution by point mutations does not occur. You can look all you want, and I assert that you will not be able to accurately model macroevolution nor provide any evidence that your model or assumptions are correct -- for the same reason that I could not prove the earth is flat or that the sun revolves around the earth.
From Dave Oldridge: (reprise) Consider, for example, the improbability of each of the "steps" that create a Senapathy or an Oldridge or a Mattox from human ancestors 8000 years ago. The odds against these PARTICULAR results are enormous, yet, by Senapathy's argument, this proves that none of us could really be descended from our ancestors of 8000 years ago.
JM: (reprise) Keith also brought up that objection. Dr. Senapathy was showing that the time required for a particular 10% change to a gene made through random point mutations would be prohibitive. Even if you allow billions of "OK" outcomes to billions of genes, the time needed is huge.
Dave: And there you spell it right out. A PARTICULAR 10% change is meaningless, since evolution has never been hypothesized to be particular about the changes it produces. The particularity is an artificial factor and totally irrelevant to the issue.
JM: Your human comparison is not the same thing. We are not organisms produced through random changes due to point mutations. We are the products of biological processes that, more often than not, produce viable results.
Dave: So is everything that EVER evolved. You are missing the point -- or simply don't care to see it. You CANNOT take last night's poker hands in the exact order that they occurred and use the (vast) improbability of that set of events as "evidence" for the impossibility of poker games.
Well, you can actually, but please don't expect anyone with any knowledge of probability theory to agree with you.
JM: On the other hand, mutations produce defective genes and non-viable results more often than not, or they produce normal variants of the same gene. Our relationships to our ancestors follow a non-random path. The selection of traits might be random, but the outcome is known -- humans with the same genes and body parts.
Dave: And so does the natural selection of all organisms follow a non-random path. That was precisely what set Darwin off in the direction he went. He observed that far more organisms were produced than ever survived. Now in humans, the bulk of that selection happens to spermatozoa, but the effect is still the same.
JM: We are just bouncing this word argument back and forth, so I will work on a better reply based on probability theory. I will even look for a consultant on this who lives and dies by math alone....
Dave: You'll probably have to explain the problem very clearly to him. Few mathematicians have much of an idea about what goes on in biological reproduction systems. However, you should note that probability theory is not very much help here. However improbable a particular outcome is, it remains the particular outcome. If the system permits 10^300 possible outcomes, all of equal probability, one of those will still occur. It is an abuse of probability theory to argue that, since it was highly improbable then it probably did not occur. The minute it HAS occurred, it's probability changes to precisely 1.
JM: OK, but show me how a point mutation could lead to a new body part without selection all along the path to the new set of genes (and we're no longer talking a single 10% change here!). I hear your (and Keith's) objection to the "particular 10% change" being a backdoor approach (that is, it's unfair to specify the outcome in advance), but that is no less of a problem than you assuming all point mutations to any beneficial new gene is going to be selected (or at least leaving the creature viable) at each step along the way.
From Keith Robison: (quoting JM) On the other hand, mutations produce defective genes and non-viable results more often than not, or they produce normal variants of the same gene.
Keith: Exactly -- and the various statistical arguments from you and Senapathy fail to take this into account. If we view two genes which differ at X positions, it is quite difficult to determine which (if any) of those X differences have a functional significance. We know by looking at existing data that many changes are neutral (the most obvious example being 3rd position changes in codons).
Put another way, we know of genes with apparently interchangeable function which differ by >10%, and we know of genes with recognizably distinct function which differ by less than 10%. The assumptions of Senapathy's statistical model are bogus.
The kicker is that the Senapathy/Mattox "disproofs" also clobber portions of Senapathy's theory. Conservation of gene order (synteny) has been observed between taxa which Senapathy claims are independent lines (such as rodents and humans or mammals and birds). Since the odds against the same gene order appearing randomly are immense, Senapathy claims that this is evidence for DNA from existing organisms being recycled back into his primordial pond. Ignoring for the moment the shear (sic :-) difficulties of chromosome-sized DNAs getting recycled, there is another problem -- many genes showing synteny differ by >10% !!
The underlying assumptions of the "disproof" are simply incompatible with the available data, and hence the whole calculation is bogus.
From Keith Robison: (quoting JM) There is no correct model because macroevolution by point mutations does not occur. You can look all you want, and I assert that you will not be able to accurately model macroevolution nor provide any evidence that your model or assumptions are correct -- for the same reason that I could not prove the earth is flat or that the sun revolves around the earth.
Keith: This is a rather bold assertion -- any support for it?
We can establish the following:
Point #2 is quite inconsistent with Senapathy's theory, but is consistent
with descent-and-modification (Darwin). Because there is so much
evidence pointing this way, we must infer that macroevolution has
taken place. Simply because we are potentially ignorant of its
exact processes doesn't mean the phenomenon doesn't exist.
Also, various potential components of macroevolution have been observed -- new genes appearing, reprogramming of expression patterns, etc.
So we have both strong reason to believe macroevolution must take place, and plausible components for it to take place. We also know that quite substantial differences can arise in a species over relatively short times -- i.e. your distinction between macro- and micro- evolution is tenuous. In dogs, we can see that domestication has resulted in a startling variety of distinct forms, as well as genetically-programmed behaviors. If we did not know that all dogs are indeed one species, I am sure Senapathy would point to them as an impossibility for evolution to produce, since there are so many "novelties" apparently present in them.
Most of all, Darwinism is a productive theory which can guide biological experimentation (see the most recent Nature for a nice example of such in regards to vertebrate limb development). Aside from some amazingly inaccurate retrodictions, Senapathy's larger theory (many independent origins) is useless. I have yet to see a testable prediction of Senapathy's theory which falls in his favor -- which is no surprise, since many of the suppositions in support of the theory are either wrong or overstated (e.g. the "negative-exponential distribution" of exon sizes -- the distribution looks far more like the truncated exponential distribution mentioned by Stoltzfus et al). Other parts of his theory (particularly the "seed cells") are so implausible that one wonders if they are to be read as parody.
Senapathy's theory is, overall, a complete loss. It simply isn't compatible with an awful lot of data.
From Dave Oldridge: (quoting JM) OK, but show me how a point mutation could lead to a new body part without selection all along the path to the new set of genes (and we're no longer talking a single 10% change here!).
Dave: I don't see it as a real problem. First of all, new body parts are quite rare in the fossil record. What we see a lot of is modified body parts. Lobe-fin fins become limbs. Forelimbs become wings or flippers and so on. In some cases it's clear that even partial developments along these lines will confer a selective advantage. In other cases, we must look for a somewhat different pathways. For example, feathers confer heat-retention, and advantage in cold weather.
Wing-like forelimbs can also function as insect nets. At some point, one function leads to the beginnings of selective advantage for some totally new, emergent function. And we also have to consider the very large effects produced by small changes in those particular genes that control development.
And environmental selection isn't the only game in town. I'll grant you that genetic drift probably plays a significant part as well as sexual selection.
From Chris Colby: Mutation is the ultimate source of new genetic variation. Without it, evolution would grind to a halt. However, the other mechanisms also come into play, changing the frequency of new variants in a gene pool. There's more to evolution than mutation.
Natural selection "sifts" through the genetic variation supplied by mutation to bring about adaptive change.
New features are the result of mutation. If they are favorable, natural selection will cause these features to increase in frequency in a population. (It's actually a little more complicated than this, drift causes most new beneficial mutations to be lost, but the same mutant can pop up repeatedly and eventually get "caught" by natural selection.)
Biologists used to think that the probability of a mutation arising was independent of any potential fitness benefit. In short, a "good" mutation wasn't any more likely to occur simply because it was good. Recently, this idea has been challenged by a number of workers. Initially, two lines of evidence were put forth -- deviations from the Luria-Delbruck distribution and the appearance of late-arising mutants on bacterial plates.
If mutations arise at random with respect to fitness, the number of mutants found in a series of parallel cultures founded from a single clone should fit a certain distribution (called the Luria- Delbruck). If mutations were induced by a potential fitness benefit (i.e. if bacteria could "choose" the correct mutation), the number of mutants should fit a Poisson distribution. Cairns found that Lac+ mutants in an experiment where Lac+ mutants would be favored fit a hybrid of these two distributions and concluded that some mutations were induced by selection.
It was later shown (by Steward, et. al.) that there are many factors that can cause deviations from Luria-Delruck. So, this line of experimentation was abandoned.
The other line of evidence dealt with late-arising mutants on petri dishes. In these experiments, cells were plated on petri dishes. These cells could not survive on the medium provided (for example Lac- cells, unable to utilize the sugar lactose, were plated on a medium where lactose was the only carbon source). But, a single mutation could correct this defect (i.e. make them Lac+). Initially, a few Lac+ colonies were seen. These were the results of random, spontaneous mutations in the culture before plating. But, from day four on, new mutants began appearing. In many of these experiments, around 200 new Lac+ colonies appear by 2 weeks. Then, they quit appearing. When mutations at other loci are screened for, they are not found. (Also, Foster has shown the mutational spectrum of late mutants is narrower than early mutants.) This was interpreted as evidence that bacteria could choose, or selectively retain, mutations that were beneficial.
This caused a lot of controversy. There are two classes of explanation for this hypothesis:
If the mechanism is found to be truly-directed, this is a major new plank in the evolutionary platform. If artifactual, it is much less exciting. I think the latter will be the case.
It is somewhat disturbing that this hypothesis has been around since 1988 and the controversy has not been resolved. If truly-directed, the adaptive mutagenesis hypothesis would force some changes in evolutionary theory. (Even if not, it's still interesting, IMHO. See my paper in the July 1995 Genetics for details.) The proponents of adaptive mutagenesis have done experiments in a variety of different organisms and at different loci. Supporters of adaptive mutagenesis see this as an attempt to determine the generality of the effect. Skeptics interpret this as dodging criticisms. It would be nice if the proponents would pick their best case, and do all they can to test the model. Since they are the ones making the extraordinary claim, the burden of proof is on them. On the other hand, I don't think the harshest critics of adaptive mutagenesis have come up with a good accounting of where all the late-arising mutations are coming from.
Having important questions remain unanswered for long periods of time is the hallmark of crappy, pseudo-scientific fields (like ecology, psycho- logy or sociology). If a question is well formulated, an answer should be quickly found. I had dinner with one biologist at the evolution meetings who compared adaptive mutagenesis to cold fusion -- the difference was the skeptics of cold fusion were quickly able to crush the competing hypothesis. The answer to this question can be obtained cheaply; all we need are petri dishes and a few sequencing rigs; it isn't as if we need to build a super-collider to get an answer. Why can't we, as biologists, get this over with?
From Richard A. Boyd: I have to agree ... that ALL evolution relies on mutation. Natural selection and genetic drift both need a gene pool from which to select from (or drift within). The breadth of the gene pool was created by mutations within the population. BTW there was (is?) a politician in Tacoma named Gene Pool running for state rep a few years ago -my students gave me one of his campaign signs, which I cherish.
On a larger scale, all speciation is based upon mutation (and subsequent selection) so that transfer of genes into a population from another population (same or different species, genera, or taxa at any level) is possible because those external genes originated by mutation (i.e. the different taxon from which the outside genes are derived was itself produced by mutation somewhere along the line).
Bottom line ... without mutation, there would only be one very primitive life form and each individual would be identical, save environmental/developmental variations. Of course multiple origins would probably lead to multiple forms, but only a few, and all very primitive solutions to life on earth. Mutation must underlie all variation, and therefore all selection, drift, or gene introduction.