How many ancestors does my dog have?
. . . seems like a weird question, doesn't it?
And it has a weird answer.
Your dog, provided she is normal, has 78 chromosomes, in 39 pairs. 39 chromosomes came from her mother, of course, and 39 from her father -- you know that for sure. These paired up in your bitch so that we have 39 pairs of chromosomes in her cells. When we say 'pairs' what we mean is 'homologous pairs', which is to say, pairs of chromosomes which physically look the same and carry on them the same genes. Alleles on a single pair of chromosomes may vary -- one might say "be white-spotted" and another "don't be white-spotted" -- but they will belong to the same gene controlling the same basic trait ("be either spotted or not-spotted").
If we line all the canine chromosomes up in pairs and take a picture of them, we have the canine 'karyotype', which looks like this:
On this karyotype, two X chromosomes and two Ys are shown. Actually, a dog would have one X and one Y and a bitch would have two X chromosomes, for a total of 78 chromosomes.
When you breed your bitch, she will pass 39 chromosomes on to her puppies, one of each pair -- you also know that for sure. But which chromosome of each pair will be passed along to any given puppy is a matter of chance. Still, she will definitely give half of her chromosome to each puppy, thus being related by 50% to each one. Her own parents will be related to her offspring by 25%, half of her relatedness. Or average.
On average? Yes, just on average. Bethesda (let us say) will definitely give 39 chromosomes to her daughter Chloe, but those 39 could have been inherited from her mother, Athena, or her father, Apollo. On average, about half of the chromosomes passed to Chloe will be from Athena and about half from Apollo, but that's only an average. In fact, obviously one grandparent or the other must be overrepresented in the grandpuppies -- 39 can't be cut in half evenly, after all. In fact, there's no reason at all to expect any given puppy to get equal inheritances from each grandparent. It's theoretically possible that Bethesda will pass on to Chloe only those chromosomes which she inherited from Athena and none from Apollo. Not likely, but possible. In that case, Chloe is not related to Apollo by 25%, which is the expected average relatedness between granddaughter and grandfather. She isn't related to Apollo at all. Strange, but true.
Let's see how this would work via a diagram:
Athena (AABBCC) x Apollo (aabbcc)
Bethesda (AaBbCc) x Zephyr (ÂÂßßČČ)
Chloe (AÂBßCČ)
Chloe, as we see, must get half of her mother's chromosomes and half of her father's. But there is no telling which of Bethesda's chromosomes Chloe will get. In this case, getting all of the chromosomes that originally belonged to Athena is as simple as flipping heads three times in a row. In real dogs, getting all the maternal grandmother's chromosomes and none of the maternal grandfather's would be like flipping 39 heads in a row -- not at all likely, but not impossible in theory. In the example above, Chloe has a relatedness of 50% to her mother, a relatedness of 50% to her father, a relatedness of 50% to her grandmother Athena, and a relatedness of 0 to her grandfather Apollo. If you were hoping to carry on Apollo's characteristics, too bad! His entire potential genetic contribution has been lost.
Or has it?
In theory, no dog can have more than 78 unique ancestors, because it only has 78 chromosomes. Of the 512 ancestors shown in a nine-generation pedigree, most must have vanished, because there's not room for that many ancestors' chromosomes in the pedigree.
Or is there?
A phenomenon called 'crossing over' occurs during meiotic cell division, when gametes -- that is, sperm and egg cells -- are being formed. In crossing over, the chromosomes of each pair -- the A's, let us say, or the B's -- wrap around each other and trade bits. This phenomenon is mentioned, briefly, in a few genetic books written for the dog breeder, but its importance is not emphasized. But it is very important. It's not like only a few tiny fragments are traded here and there -- crossing over thoroughly combines the genetic contribution from each chromosome, making 'hybrid' chromosomes before the chromosomes assort into their various egg or sperm cells. Just how much crossing over takes place between each pair of chromosomes, and just which bits of DNA are traded back and forth, is highly variable, but it's generally quite a bit.
Instead of giving Chloe an A, Bethesda gave her a chromosome that was a lot A but also partly a. Instead of just handing on Athena's B, Bethesda gave Chloe a chromosome that was mostly B but also contained bits of Apollo's b chromosome. And so forth. What Chloe therefore got in the end was a lot of the genes from her grandmother Athena, but also some from her grandfather Apollo.
Your dog has more than 78 ancestors. We figure ancestry in average percentages because there's no other way to do it, but isn't it interesting to reflect that out of the 512 ancestors in that nine-generation pedigree, it's possible that not a single dog's genetic contribution has been entirely lost?
Incidentally, because a parent is always related by 50% to each offspring, but siblings are only related by 50% on average to each other, it is not true (as I have seen stated) that a brother-sister breeding is a closer inbreeding than a father-daughter breeding. Instead, a brother-sister breeding will sometimes be closer than a parent-offspring breeding and sometimes be less close. Only a parent-offspring breeding will reliably be exactly 50% (yes, I know, except in the case of weird genetic mishaps such as trisomies or uniparental disomies).