On 6/29/06, Henry Baker <hbaker1@pipeline.com> wrote:
Rich, et al:
This is an area of very active research. Do a Google search on Genghis Khan. Recent results claim that 5% of the world's population derives from him or his brothers. (The media claim that this is due to his large sexual appetite; while this probably helped, the truth is that random theory would show that _someone_ would end up with a large number of descendants. A line either dies out within a few generations, or ends up with a huge population; it's actually quite difficult to have only a few descendants for a large number of generations.)
Dawkins' book "The Ancestor's Tale" has some nice discussion about this: if you go back far enough, a person will either be a direct ancestor of the whole human species or will have no descendants. Dawkins also discusses the *titles* Adam and Eve, of the nearest ancestor of all humans whose Y chromosome or mitochondria (since one is passed essentially unchanged along male lines and the other along female lines) we've inherited. They are titles, since the nearest ancestor can jump forward in time a lot when an isolated branch dies out.
Also see David MacKay's (info/coding theorist @ Cambridge) chapter called "Why have Sex? Information Acquisition and Evolution" in his book on Information Theory.
MacKay claims that asexual reproduction yields approx 1 bit per generation due to survival of the fittest, whereas sexual reproduction (with exchange of genes) can yield up to sqrt(G) bits, where G is the total number of bits in the genome. (Human genome is 4-6x10^9 ~ 2^32; and you always wondered what was magic about a 32-bit word...) Note that mitochondrial dna is essentially asexual reproduction, which explains why this dna is reasonably stable from generation to generation.
Slashdot had a good post (they do occur, now and then) on the math of evolution about a year ago: http://tinyurl.com/s3l3z -- Mike Stay metaweta@gmail.com http://math.ucr.edu/~mike