Speciation with hybrid breakdown:
The camel was domesticated in Bactria in what is now modern Afghanistan some time before 4,000 years ago. I had read in a good source not many years ago that the modern two humped Bactrian camel resembled the wild sort but that the single humped dromedary had only evolved after the camel had been brought to Egypt. I now read that the two both exist in the wild, and so it is not clear to me how many generations they have been separated.
I understand from an informal source that people who keep camels traditionally have milked them after they gave birth, delaying another pregnancy so that the generation time of the camel was about 7 years. That would mean that the number of generations that separated the one humped and two humped was something like 500. That would be a very interesting number to have, because if one crosses a Bactrian with a dromedary, the offspring are fertile. But if one follows them for a few generations, the line eventually dies out from infertility. This is called “hybrid breakdown.” As a first guess, it would suggest that they were fairly recently the same species and that we would know at least for camels, how many generations of separation it took for a single species to turn into two. I know of no other kind of mammal in which such an estimate can be made.
One wonders why hybrid breakdown should happen, and as far as I know there is no widely accepted mathematical model for speciation (until perhaps the one I have talked about is recognized) much less a model for hybrid breakdown.
So let us see what we can do.
I tried to demonstrate hybrid breakdown with the program used to develop the numbers on the Main Page of this site. If you will remember, in that program, each individual in a population had two chromosomes that never exchanged information except indirectly. Each chromosome kept all of its gene sites, sometimes modified by mutations, when the chromosome was passed on to an offspring.
There is another program that is quite similar but contains some more variables that can be introduced. This other program can be set so that every gene is passed on at random without regard to any other gene. It was as if every gene had its own chromosome. Using this program I prepared 2 populations that had developed under the following conditions:
1,000 generations. 12 offspring per mating pair. Initial population size of 100. Maximum permitted population size of 200. 400 pairs of sites subject to recessive lethal mutation at a rate of 2 per 40,000 sites per generation. 100 pairs of genes tuned to each other. Random assortment of all genes. 16 detuning mutations per 4,000 sites per generation. A chance of losing 50 one thousandths of an offspring per generation per unit of detuning. Then I took one member at random from each of the two populations and attempted to create a new population with the pair, using the same parameters.
In each of 10 consecutive runs, the population survived for 1,000 generations, always with more than 200 offspring for the 100 mating couples. I saved 200 individuals (their files, of course) out of the last generation of the last run. I then did 10 runs, in each of which I elected two individual files at random and attempted to establish a new population using the same parameters except that the number of generations was limited to 100. All 10 populations died out after 1, 1, 1, 1, 1, 5, 1, 1, 1 and 2 generations. You may remember that this program counts dying in the first generation as a 1. The usual program counts it as a 2.
Each of the crosses that never made it past the first generation are simply an example of speciation. However one of the crosses had at least one offspring in the first generation, rather like a mule, and one cross went 5 generations before dying out. I remember that in the past I have been able to demonstrate a more frequent occurrence of this and demonstrate longer runs before dying out. I have never been able to demonstrate anything of the sort using the usual program.
The usual program does produce speciation. Just produce two populations that have been run according to the usual parameters limiting the population size to 200 and carry each out to 2,000 generations. Taking a pair at random from either of the two resulting final populations and running them under the same conditions will establish a new equally stable population, bar the occasional infertile couple. Taking one from each of the final populations will always result (almost always, since there is such a large random component to this) in infertility in the first generation.
Thus the first program, in which there is no chromosome effect, demonstrates speciation with hybrid breakdown but nothing else of interest. The usual program demonstrates speciation and more than a dozen more interesting effects that can be verified with real world evidence that is massive. So where is the truth?
It is often said that the truth lies somewhere in between. In this case that seems to be so. We know that there are chromosomes, and we know that there are more than two chromosome pairs in higher animals. We also know that in many animals there is recombination, in which the chromosomes of a pair break and rejoin to form two new ones, each with all the same gene sites but with the actual forms of the genes for one chromosome coming from one parental chromosome on one side of the splice and from the other on the other side of the splice, the matched chromosome being the reciprocal.
It ought to be possible, if laborious and of limited interest, to create a far more complex program that could combine elements of both and demonstrate all the effects.
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