There he dug out everything the slave factor had offered as proof of the alleged odd genetic heritage of Llita and Joe, and gave each item intense study. He was looking for clues to truth or falsity of the allegation that they were "mirror twins"-complementary diploids having the same mother and father. From such clues he hoped to estimate the probability of unfavorable gene reinforcement in any child Llita and Joe might have.

The problem seemed to divide into three (simplified) cases:

The two might be no relation to each other. Chance of a bad reinforcement: slight.

Or they might be the usual sort of brother and sister. Chance of bad reinforcement: too high to be ignored.

Or they might be (as alleged) zygotes resulting from complementary gametes-all genes conserved at reduction-division but with no duplication. In this case the chance of unfavorable reinforcement would be-what?

Let that wait. First assumption, that they were no relation but simply raised together from babyhood-no special hazard, forget it.

Second assumption, that they might be full siblings of the usual sort. Well, they did not look like it-but, more important, that scoundrel had set up a most elaborate "store" for such a swindle, and had used publicly the name of a bishop to back him up. The Bishop might be just as crooked (likely-he knew that priesthood too well!)-but why be so careless when slave babies were so cheap?

No, even if he assumed a swindle, there was no reason to expect an unnecessary risk in a setup so elaborate. So forget that, too: Llita and Joe were not sister and brother' in the ordinary sense-although they might have shared the same host-mother's womb. The latter, if true, was of no genetic significance.

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.