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My question is simple:

Given that evolution is described by random genetic mutations allowing certain members of a species to gain a reproductive advantage over others that coexist in the particular environment- I am curious- single genetic mutations do not seem to really explain complex morphic changes such as the length of a giraffes neck. Instead it appears it must be a compilation of many such mutations. So what are the statistics for mutations? How long does it really take for so many to favorably compile? How does this compare with the reproductive time of the species?

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This is a good question but I’d remove / rephrase the last paragraph since it’s unnecessarily inflammatory and not actually accurate: most arguments for natural selection entirely take this into account (but it’s usually implied in mutation rates, rather than explicit). –  Konrad Rudolph Jun 18 '12 at 7:32
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just to clarify, evolution by natural selection is based on heritable variation that produces a reproductive advantage. Evolution is simply a change in the allele frequency of a population over time and does not require natural selection. –  KennyPeanuts Jun 18 '12 at 13:59

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You might have a look at the E. coli long-term evolution experiment lead by Lenski. They've traced over 50 thousand generations of E. Coli and measured how they evolved when growing in a minimal growth medium. Since these E. Coli reproduce asexually and do not trade genes via bacterial conjugations, the only genetic changes over time come from mutations. Since they keep frozen samples of earlier generations, it's possible to test exactly what changed and when (and even to go back in time and rerun the experiment again). The experimenters estimate that there were hundreds of millions of mutations during the first 20K generations. Of those 20K, approximately 100 reached fixation (that is, where everything without those mutations died), and of those there were between 10 and 20 beneficial mutations. During those 20K generations the fitness (measured by how quickly the population grew when introduced to a new media) grew by 70%. Later studies have looked directly at the DNA and identified the precise mutations which lead to important increases in fitness.

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Here's a paper on that experiment which includes a summary of the project and also a particularly stunning example of a trait that evolved due to a combination of more than one point mutation: pnas.org/content/105/23/7899.full –  Noah Snyder Jun 17 '12 at 23:09
    
This is such a fantastic experiment. It must have been a hard slog for so many doctoral candidates endlessly curating E. coli cultures, reminiscent of Morgan's fly boys. –  Richard Smith Jun 18 '12 at 15:04

The rate of mutation has been studied since the early 1900s, which is when your question was put to rest in a prescient paper by JBS Haldane (1949). Essentially the answer is that it varies a lot between organisms and environmental conditions, but for any given gene a mutation occurs once in about 50,000 sexual replications. That is equivalent to, in a human, several hundred new mutations in each person born. Impressively, Haldane's calculations have since been confirmed by a variety of other methods (e.g. Nachman & Crowell, 2000; Xue et al., 2009).

Faster rates of evolution have been recorded in other organisms, and there have been many, many studies looking at the rate of increase in sizes of the whole body or of particular organs of a wide variety of animals and plants.

For example, Azevedo et al. (2002) look at the rate of mutations affecting size (trying to select for decrease in body size) in C. elegans, and found mutations affecting size occured at a rate of ~0.0025 per haploid genome per generation.

In another example, with a result more definite regarding your question, Keightley (1998) investigated the rate of change in average body weight under conditions of selection for increased body size, over 50 generations in mice. They recorded an average increase of 0.23-0.57% body weight per generation from new mutations. That's pretty huge, and demonstrates how rapidly a complex trait can change by mutation under selection.

I wrote a small piece of python code to calculate the increase after x generations at the same rate (the formula is very simple)...

initial = 1
rate = 0.35
generations = 1000
result = initial * (1.0 + rate) ** generations
print result
>>>20.10655586861808

Thus if we assume that approximately the average rate found in the mouse study (0.35%) could be the rate at which giraffes' necks might increase under strong selection, after 1000 generations the mean neck length would be over 20 times the original length. A low estimate for wild giraffe longevity is around 20 years, thus for giraffe necks to increase around 20x might take 20,000 years. Of course this basic estimate is making a whole lot of assumptions, but the point is that rates of mutation are actually very high, easily enough to explain the diversity of traits we see in the world.

References

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wow- that's a really good answer. So these rates of mutation that are studied- in particular the Haldane paper- they represent mutations in the genome that are passed on to the offspring or just random mutations that occur in individual cells throughout the collective body? –  c-design Jun 17 '12 at 18:35
    
okay i reread- nevamind the above.. –  c-design Jun 17 '12 at 18:38
    
Yes, they represent mutations that are passed on to the offspring. –  Richard Smith Jun 17 '12 at 19:03

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