I don't know why we're talking about this. I don't know why I'm addressing this claim directly.
Wogoga:
Your claim is so obviously and trivially false I'd much rather take my time making ad hominems, but this has gone on too far.
First, you assume that there is only one way for a phenotype to be encoded by a genotype. This is not the case. Just as there are a huge number of different ways to write a computer program to perform a single task, there are tons of different genetic codes that can perform a given task. For example, I had a friend in college that did genetic engineering in plants. The way they did this was using a special bacteria that would basically just insert copies of a gene coding a protein whereever. Basically is was a gene shotgun. Nonetheless, this technique was effective.
Two, I'm not going to address your argument from complexity until you make it clear and coherent. Moreover, your example using the brain has been addressed by the others in this thread. It is false as well as inconsequential.
Now lets look at the numbers you provided initially...
Originally Posted by
wogoga
Take the case of humans after their separation from chimps some million years ago. An upper limit to the number of individuals having been born since then is 10^16 (i.e. 10^9 newborns per year for 10^7 years).
Originally Posted by
wogoga
Let us assume that three factors must be affected for an increase in fitness to emerge. So even if the probability of a beneficial mutation in a newborn were as high as 10^-5 for each factor, the probability that beneficial mutations occur for all three factors is 10^-15, i.e. extremely improbable.
So neo-Darwinism requires essentially this hypothesis:
Every evolutionary innovation can produced by a sequence of single-step mutations, each of which alone responsible for a relevant increase in fitness.
So just to summarize.
10^9 newborns per year(I'll actually assume this is the individuals in a generation so your argument makes sense)
10^7 years
10^-5 probability for each relevant factor
3 factors.
For example, you cite, 10^-15 as the probability all 3 factors would occur in any single individual simultaneously. This is true.
But evolution doesn't work this way. As you say, "each of which alone (is) responsible for a relevant increase in fitness".
10^9*10^-5=10^4 We can expect one beneficial mutation to occur in as many as 10000 individuals per generation.
So after the first year of our thought experiment we have:
10000 individuals with mutation A
10000 individuals with mutation B
10000 individuals with mutation C
The probability that any one of these individuals has any two mutations is unlikely and the probability that any one individual has all three is infinitesimally small at this point. But, since each of these mutations increases fitness independently, we can assume that these individuals will do better than the others. Increasing their numbers in the next generation. So lets say the number of individuals inheriting each one of the 3 mutations doubles each generation.
Then in generation 2 we have 20000 individuals with A by inheritance, 10000 with A by mutation. The same for the others leading to 10000+20000= 30000 each of A,B,C in generation 2.
So at this point we can write the recurrence relation describing this growth:
P(t) = 2*P(t-1)-1(ignoring the factor of 10000)
The first few numbers are 1,3,7,15,31,63
Its easy to fit an analytic function to this sequence: P(t)=2^t-1
So P(17) *10000= 2^17-1*10000=131071*10^4 =~ 1.31*10^9 individuals with each mutation. Since the number of individuals with each mutation is greater than the number of individuals in any generation, we can infer all individuals will have all 3 mutations. (This might be thought of as an application of the pigeonhole principle.)
Two things are clear from the recurrence relation:
1. Wogoga's numbers are wildly generous
2. Because the recurrence relation is exponential even far more conservative numbers will not yield a significantly different result.
Obviously this is a simplified model, but this is the simplified correct analysis that grows out of Wogoga's initial suppositions. Other complexities won't change the fundamental fact that this demonstrates. Once an individual has a beneficial mutation it will spread throughout the population, so the argument from the probabilistic contingency(or independent joint probability) is clearly wrong. Can we please stop this silliness now?
p.s. The genetic shotgun bacteria is crazy neat, if I remember all the details. As I remember it, the wild type naturally uses special plasmids to insert genes into a plant that it is attacking. These inserted genes basically cause tumors in the plant that happen to be very tasty for the bacteria. When they use it for genetic engineering, the tumor plasmids are replaced with whatever gene they want to insert. Since the bacteria was savaging the plant anyway, it never evolved much specificity to insertion, so tons of copies of the gene end up in all sorts of places. Sometimes it does what they want, sometimes it does something different, sometimes the plants just die. But they run a few iterations and normally end up with a variant that does what they want, which they select for. Then they add another gene. Do this enough and you can insert all the enzymes in an entire pathway.