Why are there Chromosomes. I have said that it is a fairly easy matter to prove that an animal with chromosomes can carry more genetic information than one in which all the genes are handled independently. This seems idle, since we know there are chromosomes, but since I have done the calculations, I shall offer them now.
When I first started working on a computer model to simulate the change in population growth with various population sizes, I ignored chromosomes. I reckoned that genes were scattered over many chromosomes, and even within a chromosome the genes were scattered, and there was a process we used to call “crossing over” and which is now more commonly called “recombination.” What happens during ordinary cell division, or mitosis, is that the entire nuclear DNA content of a cell is replicated. One complete copy, give or take rare errors, goes to one daughter cell and the other copy goes to the other daughter cell.
Now excluding the sex chromosomes, each chromosome in a nucleus has a twin that is similar in many ways, carrying the same set of genes in the same order but with slight differences between copies of the two genes on the two different chromosomes. When preparing gametes, egg and sperm for reproduction, the process is a more complicated one called meiosis. The unique step in meiosis is that each pair of chromosomes matches up. Then they sort of twist around each other and break and reattach. When they pull apart, each now has the same genes in the same order, but it has some genes from one or the original pair and some from the other. The cell then undergoes two divisions and the result is egg and sperm each with only one of each kind of chromosome, ready for the fertilization event that will bring the number of chromosomes back to normal in a fertilized egg or zygote. If that cell can successfully divide and do so often enough to establish an embryo, then a new individual is on the way.
A large chromosome will have many sites of crossing over during any meiotic event. So I reasoned that it was unlikely that genes tuned to each other would be regularly inherited together, and I dismissed chromosomes from my computer model.
I plugged away for a less than enjoyable year creating the model and then testing it. The house became littered with burned out computers. I would set calculations running and get up in the middle of the night to check them. I tried an enormous number of approaches. In effect I was wandering around lost in a roughly 17 dimensional space. I do not recommend the experience. I did not record the number of psychosomatic ailments I was subject to; maybe it was one per dimension or so. You know, nausea, dry heaves, can’t eat, can’t stop eating, can’t sleep, can’t wake up, the creepy crawlies, and so forth.
And I came up with nothing. I had hard evidence that population size and fertility could be negatively correlated, but the program never budged. I once even had a computer burn out and start giving me spurious negative correlations.
About the best I was able to do was this. Figure 1 shows a set of runs showing growth rate against population size using that program that ignored chromosomes.
Figure 1. Each point represents the average of 10 simulations lasting up to 1,000 generations with 8 offspring per couple, initial population 100, maximum population the independent variable, 8 recessive lethal mutations per 40,000 gene pairs per generation with 400 gene pairs, 100 sets of genes fine tuned to each other inherited with 50% likelihood of being inherited together, 16 mutations per 4,000 elements, each producing a 40 per 1,000 chance of eliminating an offspring. Horizontal axis is population size. Vertical axis is the average number of offspring in the final generation per member of maximum population size, again assuming extinct populations have zero offspring per member. The mutation burden is very high.
It looks rather promising, we see the familiar extinction at a low population size followed by a maximum that then falls rapidly and tends to level off. But it is totally unrealistic. Under these conditions everything goes extinct. It may be that somebody with a more systematic approach can show this and still have a viable population. I look forward to that.
Then I wrote a new program that hooked everything up on chromosomes, and it was like the light coming on. Everything clicked as you can see from the 16 proofs on the Main Page of this site. (Actually it’s 17. Can you find the other?)
So here in figure 2 is an example of a set of runs of populations of sizes ranging from 20 to 2,000 done with the program that has the genes arrayed on chromosomes, just one pair as in the calculations presented before. The actual parameters used for the calculations are given in the caption. I shall not repeat them here.
Figure 2.
Figure 2. Each point represents the average of 10 simulations lasting up to 1,000 generations with 8 offspring per couple, initial population 100, maximum population the independent variable, 80 recessive lethal mutations per 100,000 gene pairs per generation with 100 gene pairs, 100 sets of genes fine tuned to each other inherited together, 400 mutations per 100,000 elements, each producing a 40 per 1,000 chance of eliminating an offspring. Horizontal axis is population size. Vertical axis is the average number of offspring in the final generation per member of maximum population size, again assuming extinct populations have zero offspring per member.
There are two things to notice. First, over a substantial range, there is, yes, actually an advantage that a larger population has over a smaller one, and this advantage persists over a large range. That is because this set of calculations was heavily weighted toward recessive lethal mutations compared with mutations that detune genes against each other. So yes, it is possible to construct a model that conforms with received wisdom. It just doesn’t conform with reality. This is the classical situation where it is said that the population needs to be “invigorated by an infusion of new blood.” Bold prose. Dead wrong in real life.
But the key thing is that with the chromosomes in play, the same parameters that produced a disaster without chromosomes produces viable populations (if only at large population sizes).
The proof is not perfect. Don’t bother with repeating the arithmetic. There are 4 times as many sites subject to recessive lethal mutations in the model without chromosomes but only ¼ the mutation rate.
So the proof could be refined, but there is no urgency in that. We know that chromosomes exist. Furthermore, they just about have to. Consider a cell undergoing meiosis or even mitosis in which every gene had to be handled separately. It would be like coaxing 20,000 flies to land on your hand at the same time. They would all get in each others way.
So I rest the case that our invocation of chromosomes in the model is valid.
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