Size as an example of additive inheritance

Sheltie breeders, as a group, tend to be hung up on size. We have reason to be. The breed was produced by mixing large and small breeds, few if any of which were in the size range we accept as correct today (13" to 16", with preference for 15" and up). Size, however, is not a simple genetic trait. At a minimum, it depends on the genetic codes for growth hormones, the genes that dictate when and how much growth hormone is produced, probably genes that code for receptor proteins that respond to growth hormones, genes that control bone shape and angulation between bones, and other genes affecting various metabolic processes. We don't even know the whole list, or how to determine what makes a particular dog large or small. In some cases the gene for larger size would be dominant, in some cases recessive, in some cases the dog heterozygous at a particular locus would be intermediate is size. It is, however, possible to use a very simple model to explain some of the oddities of Sheltie size. Remember this is a greatly simplified model! The real situation is almost certainly more complicated. We may even have a few genes for correct size hidden in there somewhere!

Suppose we assume we have four loci affecting size. Assume also that each locus has two alleles, one derived from the Collie part of our breed's ancestry, and the other from the original small island Sheltie (remember that at one time 12" was pushed as the maximum height) and toy breeds crossed in late in the 19th Century. We'll call these loci f, i, j, and k. The alleles for large size will be f+, i+, j+ and k+; those for small size will be f-,i-, j-, and k-. The size of the dog will be a base of 15" plus 3/4 times the sum of the "+" genes minus 3/4 times the sum of the "-" genes. A dog with all "+" genes, for instance, would be 21" tall, while a dog with all "-" genes would by 9" tall.

Suppose a breeder, breeding fairly close within her own line and related dogs, winds up with a consistent size genotype of f+f+ i+i+ j-j- k-k-. All gametes will be f+i+j-k-. All puppies will have the same size genotype as their parents, and will be 15" tall. But she's had to inbreed quite a bit, and she is looking for an outcross that will give her back what she's lost without sacrificing her predictable size.

She finds another breeder, again breeding fairly closely within her own line, who also gets all 15" Shelties, and whose line is strong for exactly the traits she needs. Breeder A breeds her best bitch to breeder B's best stud dog, and breeder B, who is missing a couple of things A has managed to fix, breeds her own bitch to a stud from breeder A's lines. The puppies arrive, grow up, and all are 15".

Then two of these 15" pups, from litters level in size stemming from strains level in size, are bred to each other. The result could easily be puppies all over the map in size. What happened?

Breeder B had a consistent size genotype of f-f- i-i- j+j+ k+k+, and her dogs consistently produced f-i-j+k+ gametes. The uniformly in -size puppies from the strain cross, then, all had the genotype f+f-i+i-j+j-k+k- and could produce any of 16 types of gamete, ranging from f+i+j+k+ to f-i-j-k-. I'm not going to try to draw a 16 x 16 Punnett square, but the expected size distribution in 256 puppies is:

1- 9 inch (all -)
8- 10 1/2 inch (7 -, 1 +)
28- 12 inch (6-, 2+)
56- 13 1/2" (5-, 3+)
70- 15" (4+, 4-)
56- 16 1/2" (5+, 3-)
28- 18" (6+, 2-)
8- 19 1/2" (7+. 1-)
1- 21" (all +)

If we assume some minor size genes as well, so the various categories are smeared out somewhat, the results don't look too unfamiliar. Note that if you breed the 16 1/2" but do not breed the 13 1/2", the result will be a gradual loss of - genes, and an overall upward creep in height. Also, there is no way to look at a 15" dog and determine whether it is fully heterozygous ( f+f-i+i-j+j-k+k-) or homozygous ( f-f- i-i- j+j+ k+k+, for instance) It's not as simple as breeding only from in-size dogs with in-size littermates!

How about genes for correct size? Could we have an additional allele, f, i, j, k at each locus, with ffiijjkk dogs being uniformly 15", and dogs with 7 normal genes and one + gene being 15 3/4"? It would certainly be nice, as then we'd just have to eliminate the + and - genes to have a breed that breeds true for size. It would be a slow process, if only because dogs with the alleles for correct size would so easily be confused with dogs with a balance of + and - genes. Given the background of our breed, though, the source of such genes for correct size is an open question. Most of our breed's ancestors were larger or smaller than 13" to 16". The standard advice on breeding for size, though, is to breed to correct size, which is based on the unstated assumption that the alleles f, i j and k exist.

Other complications undoubtedly occur. The hypothetical small and large genes may differ in their effect - f+ might contribute more to oversize than j- does to undersize, for instance. There may be additional loci that have a dominant-recessive effect - NN or Nn might add 2" to the height while nn would allow the fjkl loci to control size. On the other hand, QQ or Qq might allow the fjkl loci to control size while qq would be 2" less than the fjkl size. The important thing to remember is that size is based on more than one gene pair, and as a result can do some very strange things.

Genetics index page

updated March 8, 2010