From "The Miniature Schnzauzer", Anne Paramoure Eskrigge, 1975.

     How do the dog's 78 chromosomes act to transmit inherited characteristics and what accounts for individual differences? The answer is linked with the fact that the offspring, like his parents, still has 78 chromosomes instead of double that number. Naturally, if he received the whole 78 from each parent he would have 156. The next generation would have 312, and so on indefinitely. This does not happen because of what is known as reduction division.

     In ordinary cell division the chromosomes divide lengthwise, as if they were sliced down the middle. In reduction division, however, the chromosome pairs separate, one of each pair going into one half of the cell nucleus and the other member of each pair going into the other half of the nucleus. The nucleus itself then proceeds to divide, leaving each half with 39 chromosomes, one of each kind. In the case of the male, each half becomes a sperm and is ready to fertilize an egg when mature. In the case of the female, however, there is further division and the parts of the divided cell are not of equal size. The smaller portion, called the polar body, does not contain sufficient nutritive material to nourish the fertilized egg until it is firmly implanted in the uterus. Consequently, in each division the polar cell is discarded and excreted from the body. With it go the 39 chromosomes which separated from their opposite numbers remaining in the egg proper. Thus half the chromosomes carried by the bitch are discarded before fertilization, whereas in the male all 78 chromosomes are to be found-in one half or the other of the dividing sperm cell and may be passed on to the next generation.

     The key to this matter of chromosome division lies in the fact that so far as scientists have been able to determine it is pure chance how the chromosomes line up before the cell division, and consequently the two halves of the dividing cells may contain chromosomes derived from either grandparent in varying proportions and are not alike. This sounds more complicated than it is, as you can easily test for yourself.

     Suppose you take two sets of counters (red and white poker chips would do nicely) and number each color from one to 39. Mix them together in a bowl and then draw out one at a time. Arrange them in two piles, with the first of each pair of numbers in one pile and the second in the other. When all have been drawn you will have chips numbered 1-39 in each pile, but they will not be the same color. If the red chips represent chromosomes that were derived from the sire and the white chips those derived from the dam, the two mixed piles represent the two halves of the germ cell, in the reduction division, each of which will become a sperm. As you look at the piles you may find that you have 20 red chips and 19 white chips in one pile and 19 red chips and 20 white chips in the other. You might theoretically have 39 red in one and 39 white in the other, but that is considerably less likely than a bridge hand of 13 spades. Probably you would have something between these two extremes.

     Now put your chips back in the bowl and try again. Whatever your first result, this time it will be different. Even if by any remote chance you came out with the same number of each color you would find that the chips were grouped differently when you looked at the numbers on them. For instance, if you had only one red chip in a pile, you could still have any one of the 39 red chips, making 39 different possible groupings of I and 38. If you had two red chips, any number could be paired with any of the other 38, and so on. At the same time, the other pile could also vary. If the first pile contained red chip number I and 38 white chips, the second pile would of course contain the other 38 red chips, but it might contain any one of the 39 white chips without changing the overall numbers. A few trials will show that the possible combinations are almost unlimited. A mathematician could figure out the chance of any particular combination coming up; in human beings (who have only 48 chromosomes instead of 78-24 pairs, that is) the chance of a specific chromosome combination occurring is one in 16,777,216.

     In the case of the bitch, with only a few eggs maturing at one time, in contrast to the millions of sperms produced by the male, the number of variations possible in a given litter would be drastically reduced. The chance of any given combination appearing would be only half as great, however, because half of the chromosomes actually inherited would be discarded with the polar body.

     Going back now to our colored chips, suppose we go a step further. Let us take another pair of colors, say blue and yellow, and number them from1 to 39 as before. They represent the chromosomes of the bitch, while the red and white chips represent the chromosomes of the dog to whom she is to be mated. Separate your blue and yellow chips as you did the red and white ones. Discard one pile (as the polar body is discarded) and arrange the other 39 in order. (Chance decides which chromosomes go into the polar cell, so it does not matter which pile you choose in this case.) Now take your two piles of red and white chips, representing the stud dog's chromosomes and arrange each of them in line, one on each side of the bitch's blue and yellow. Each line of red and white represents one of the many possible combinations of chromosomes in the sperm of a particular dog. Whichever group was combined with the ones from the bitch would give a different result even without considering the endless possible variations.

     Now look at the 78 chips which represent the fertilized egg resulting from the mating of dog A and bitch B as above. They will include all four colors. The red chips will be from the stud's sire, which we will call S, and the white from his dam, which we will call T. The blue will be from the bitch's sire, J, and the yellow from her dam, K. Well, how do they divide up? Since 39 is an odd number, you cannot possibly get exactly 25 percent from each of the four grandparents, as a widely held theory proclaims. The nearest you could come to this would be 20 each from two and 19 each from the other two (and even that would give various possible combinations such as 20 red and 20 yellow, 20 red and 20 blue, with their corresponding opposites). Whatever your result, take the whole 78 chips, of the four different colors, and divide them into two piles as you did with each pair of colors in the beginning. Either pile of 39 chips which results will represent one of the possible combinations -of chromosomes inherited by a puppy from the mating of dog A to bitch B. What color proportions do you have now? How many reds have come down from grandsire S? How many from grandsire J?  How many from each of the two granddams? Already you may find that one of them is not represented at all! In that case, of course, one or more of the others would have a heavier representation.

     Now suppose that the previous combination of 78 chips in the four different colors were as even as is mathematically possible, that is to say, two groups of 20 and two of 19. An even division (not likely to occur in actual fact, but representing an average) could give three groups with 10 chips of one color in each 39, and one group of 9. If you continue to divide in this manner and figure the average number of chromosomes derived from any single ancestor in a given generation, you will find that by the seventh generation the odds are 4 to 3 against a given descendant inheriting any chromosome at all from him! Naturally, in that case the dog would inherit more than the average number from some other ancestor. The only case in which one can be sure (granted that the pedigree has been accurately kept) that a dog has inherited at least one chromosome from an ancestor several generations back is the Y chromosome, which is necessarily passed from father to son and so must have been inherited in turn from each ancestor back in the direct male line, no matter how remote. Perhaps this explains the tendency which is found in all breeds of dogs which I have studied, as well as in other animals such as race horses and cattle, for one male line to gradually oust all others, which in time come to appear only through female descendants. However, the Y chromosome has very few genes and it is believed that these are relatively unimportant.

Generation	# potential	Aver Chromosomes  Odds against receiving
		  ancestors	from each	  even one chromosome
1st (parents)	  2		39			
2nd		  4		19-20		
3rd 		  8		 9-10
4th 		 16		 4-5
5th 		 32		 2-3
6th 		 64		 1-2
7th		128    (at least 50 ancestors will  4 to 3					
       			will be unnrepresented)
8th		256 				    8 to 3
9th		512				    5 to 1	
10th	       1024				   10 to 1

     The table above shows the average number of chromosomes that a puppy will derive from any ancestor in a given generation back to the 10th. This would compare with the human generations back to 1620 A.D.

     There is a further point to remember, however. Purebred dogs are all more or less inbred. (If they were not, there would come a point when the mathematical number of ancestors would work out to more than the number of dogs existing at that time.) Every time a dog or bitch appears in a pedigree an additional time, the probability that the descendant carries chromosomes derived from him or her is increased. So if a full brother and sister were mated, the puppies would average half their chromosomes from each of their common grandparents, in which case they would be as closely related as regards the number of chromosomes as they would be to their own parents. On the other hand, if both the sperm and the egg in a brother- sister mating actually happened to include more than the average number of chromosomes from the same grandparent, the resulting puppy might carry more than 39 chromosomes from that grandparent, and so could be more closely related than to his own sire or dam. Say the sire's sperm had 30 of his sire's chromosomes and only 9 of his dam's. Say the dam's egg also had 30 of her sire's chromosomes. Then the fertilized egg would have 60 out of 78 chromosomes from the double grandsire, and only 18 from the double granddam. The offspring of half-brother and sister, with only one parent in common, could also receive just as many chromosomes from the double grandparent as in the above case, but the remaining chromosomes would necessarily be derived from two other grandparents.

     From all this it should be clear why even litter brothers and sisters can carry entirely different chromosomes and in consequence can be entirely different in color, size, or any characteristic which is determined or influenced by the genes in the chromosomes. Also, it should be plain that the closer the inbreeding the more likely it is that two dogs will carry similar chromosomes derived from a common ancestor.