So the remaining worry concerned the chance that the slave factor had told the truth-in which case what were the chances of a bad cross? How many ways could such artificially produced zygotes recombine unfavorably?
Sheffield tried to set up the problem while cursing the lack of sufficient data, plus the fact that the only real computer in the ship was the piloting computer, which could not be programmed for a genetics problem. He wished Libby were aboard. Andy would have stared at the bulkhead a few minutes, then come up with answers definite where possible and expressed in probability percentages where not.
A genetics problem, even with all pertinent data (many thousands!), was too unwieldy to solve without computer assistance.
Well, try some simplified illustrative problems and see what insight could be gained.
Primary assumption: Llita and Joe were "mirror twins"- genetically complementary zygotes from the same parent zygotes.
Control assumption: They were unrelated other than being part of the home planet's gene pool. (An extreme assumption, as slaves from the same area were likely to derive from a much smaller gene pool, which might be still further reduced by inbreeding. But this "most favorable normal breeding pattern" was the correct control against which he must measure.)
Simplified example: Test one gene site-call it site 187 of the twenty-first chromosome-for reinforcement, masking, or elimination, of an assumed "bad" gene, under each assumption.
Arbitrary assumption: Since this site might hold an unfavorable gene-or two, or none-in its gene pair, assume that the chance was exactly the same for both primary and control assumptions, and even-i.e., 25 percent no bad gene in the pair at the site, 50 percent one bad gene, 25 percent two bad genes-an extreme condition since, over the generations, reinforcement (two bad genes at one site) tended toward non-survival, either lethal or reducing a zygote's ability to compete. Never mind; make it even for both of them-there were no data on which to base any better assumption.
Wups! If a bad reinforcement was visibly demonstrated, or could be shown by tests, such zygotes would not be used. A scientist competent to attempt this experiment would use specimens as "clean" in a genetic sense as possible-free of all the hundreds (thousands now?) of identifiable hereditary defects; the primary assumption should include this subsidiary assumption.
These young people were free of any defect Sheffield could detect in a shipboard examination-which enhanced the probability that this horsethief had told the truth and these exhibits were sober records of an exotic and successful experiment in gene manipulation.
Sheffield now tended to believe that the experiment had taken place-and wished that he had the resources of a major Howard Clinic, say the one on Secundus, to give these kids a genetic going-over that he was not equipped to do aboard ship and not qualified to do in any case.
One nagging doubt lay in how he had acquired these kids. Why had that gonif been so anxious to sell? If they were what the exhibits claimed? Why sell them when breeding the two created complements back together was the next step of the experiment?
Well, perhaps the kids knew but he bad not asked the right questions. Certain it was that they had been brought up to believe that such was their proper destiny; whoever planned this had induced in the kids from earliest childhood a pair-bond stronger than most marriages, in Sheffield's long experience. More than any of his own- (Except one, except one!)
Sheffield put it out of his mind and concentrated on the theoretical consequences.
At the selected site, each parent zygote had been assumed to have three possible states or gene pairs in probability 25-50-25.
Under the control assumption, parents (diploid zygotes) both male and female would show this distribution at the selected site:
25% good-good ("clean" at that site)
25% good-bad (bad gene masked but could be transmitted)
25% good-bad (bad gene masked but could be transmitted)
25% bad-bad (bad reinforcement-lethal or disabling)
But under his modified primary assumption Sheffield assumed that the priest-scientist would discard bad stock as displayed in zygotes-which would eliminate the fourth group ("bad-bad") and leave a parent-zygote distribution for this site of:
33-1/3% good-good
33-1/3% good-bad
33-1/3% good-bad
Such culling gave marked improvement over the original random-chance situation and meiotic division would produce gametes (both sperm and ova) in this incidence:
Good, four out of six, and
Bad, two out of six-
-but with no way to detect the bad genes without destroying the gametes carrying them. Or so Sheffield assumed, while stipulating that the assumption might not be true forever. But to protect Llita (and Joe) it was necessary that his assumptions be pessimistic within the limits of available data and knowledge-i.e., that a bad gene could be spotted only as reinforcement in a zygote.
Sheffield reminded himself that the situation was never as black-and-white as was implied by "good-dominant" and "bad-recessive"-these descriptions were less complex than the real world they were used to image. A characteristic exhibited by an adult zygote was prosurvival or contrasurvival only in terms of what and when and where-and also in terms of more than one generation. An adult who died saving its progeny had to be counted a prosurvival whereas a cat that ate her own young was contrasurvival no matter how long she lived.
In the same vein, a dominant gene sometimes was of no importance one way or the other-e.g., brown eyes. Just as its corresponding recessive when paired and thereby reinforced to produce blue eyes gave the zygote exhibiting it no measurable disadvantage. The same was true of many other in-heritable characteristics-hair patterns, skin color, et cetera.
Nevertheless this description-good-dominant, bad-recessive-was in essence correct; it synopsized the mechanisms by which a race conserved its favorable mutations and destroyed (eventually) its unfavorable mutations. "Bad-dominant" was almost a contradiction in terms, as a thoroughly bad mutation which was dominant killed itself off (along with the unfortunate zygote inheriting it) in one generation, either lethal in womb or so damaging to the zygote that it failed to reproduce.
But the usual weeding process involved bad-recessives. These could remain in the gene pool until one of two events happened, each controlled by the blind laws of chance: Such a gene could pair with a gene like it when sperm fertilized ovum and thereby eliminate itself by eliminating the zygote-hopefully before birth, or-tragically-after birth. Or this bad-recessive might be eliminated by chromosome reduction at meiosis and the result would be a healthy baby who did not carry this bad gene in its gonads-a happy outcome.
Both these statistical processes slowly weeded out bad genes from the race's gene pool.
Unfortunately the first of these processes often produced babies viable but so handicapped they needed help to stay alive-sometimes needing economic help, born losers, who never managed to support themselves; sometimes needing plastic surgery or endocrine therapy or other interventions or supports. When Captain Aaron Sheffield had been practicing medicine (on Ormuzd and under another name), he had gone through stages of increasing frustration over these poor unfortunates.
At first he had tried to practice therapy by the Hippocratic Oath-or close to it; he was by temperament unable to follow any man-made rule blindly.
Then he had had a period of temporary mental aberrance during which he had sought a political solution to what he saw as a great danger: reproduction by defectives. He tried to persuade his colleagues to refuse therapy to hereditary defectives unless they were sterile or sterilized or willing to accept being sterilized as a precondition for receiving therapy. Worse yet, he had attempted to include in the definition of "hereditary defective" those who displayed no stigmata save that they had never managed to be self-supporting--on a planet not overcrowded and which he himself had selected centuries earlier as nearly ideal for human beings.