Dog Size Genetics Theory

I decided to share this before adding it to my Theoretical Dog Genetics guide in case there are still some bugs to work out. If anyone spots logical or mathematical errors feel free to point them out. There is a limit to how realistic this can be, but I seem to be able to keep breeding results within the normal range for breed size.

My theory for a simplified example of how size genetics could work in dogs is based on these sources-

Genetics and the Shape of Dogs: www.americanscientist.org/issu…
AKC: Portuguese Water Dog (building understanding of the effects of IGF1 on size): www.akc.org/breeds/portuguese_…
Big Dog, Little Dog: genetics.thetech.org/original_…
Legacy of the Dog, by Yamazaki Kojima (breed size reference)

Most breeds express the genes II at the IGF1 (insulin-like growth factor-1) locus, giving a possible size range of medium to large. Small breeds express the genes BB, making extreme small size possible. The study found this using the Portuguese Water Dog, which has a female size range of 35-50lbs (calculations are based on female weight and add 15% for males). Both I and B are found in the breed, and have incomplete dominance.

The most likely explanation for the extremes of size is a series of other genes which tell the body to grow a bit bigger or smaller, making accumulative modifications to II, IB, or BB. IGF1 sets limits that the modifications can only take up or down to a certain weight.

Theoretical Calculations

Modifiers- There are 21 pairs that push the weight up or down, or hold the weight stable. They are represented by a +, -, or 0. I theorize that in purebreds these genes tend to be mostly homozygous, keeping a fixed size with a little variation.

Start with:
00/00/00/00/00/00/00/00/00/00/00/00/00/00/00/00/00/00/00/00/00

Larger dogs carry more + modifiers, giving them a number that is positive after every pair is added up. For example, a 174lb Mastiff would have 21 pairs of ++ modifiers acting on II.

Smaller dogs carry more - modifiers, giving them a number that is negative after every pair is added up. For example, a 4lb Chihuahua would have 21 pairs of -- modifiers acting on BB.

I- I set the lower size limit at 35lbs based on the Portuguese Water Dog, and the upper limit at 174.4lbs based on the English Mastiff. The calculation starts at 35lbs and adds 3.4lbs for each + the dog carries which isn’t cancelled out by a -. If end number is negative, subtract 0.01lbs for every -.
174.4 / 171 / 167.6 / 164.2 / 160.8 / 157.4 / 154 / 150.6 / 147.2 / 143.8 / 140.4 / 137 / 133.6 / 130.2 / 126.8 / 123.4 / 120 / 116.6 / 113.2 / 109.8 / 106.4 / 103 / 99.6 / 96.2 / 92.8 / 89.4 / 86 / 82.6 / 79.2 / 75.8 / 72 / 69 / 65.6 / 62.2 / 55.4 / 52 / 48.6 / 45.2 / 41.8 / 38.4 / 35

B- I set the upper size limit at 35lbs based on the Portuguese Water Dog, and the lower limit at 4.3lbs based on the Chihuahua. The calculation starts at 35lbs and subtracts 0.75lbs for each - the dog carries which isn’t cancelled out by a +. If end number is positive, add 0.2lbs for every +.
35 / 34.25 / 33.5 / 32.75 / 32 /31.25 / 30.5 / 29.75 / 29 / 28.25 / 27.5 / 26.75 / 26 / 25.25 / 24.5 / 23.75 / 23 / 22.25 / 21.5 / 20.75 / 20 / 19.25 / 18.5 / 17.75 / 17 / 16.25 / 15.5 / 14.75 / 14 / 13.25 / 12.5 / 11 / 10.25 / 9.5 / 8.75 / 8 / 7.25 / 6.5 / 5.75 / 5 / 4.3

IB- Start with 35lbs.  Add or subtract 0.4lbs per number, depending on whether the final number is positive or negative.

Males- add 15% of weight (0.15 x _lb) to account for sexual dimorphism (based on measurements in Portuguese Water Dog study).

Examples

II
Male Bloodhound, 102.8lbs (without sexual dimorphism, 89.4lbs)
Take blank sequence and randomly make + add up to 15.
00/00/00/++/00/00/00/00/++/+0/00/++/++/00/00/++/00/00/++/++/00= 15

Female Bloodhound, 89.4lbs
00/00/00/++/00/00/00/00/++/+0/00/++/++/00/00/++/00/00/++/++/00= 15

One pair of genes offers a small variation in size. Use www.random.org/integers/?num=2…
+0 x +0

Litter:

Puppy 1= Male, 102.8lbs (without sexual dimorphism, 89.4lbs)
00/00/00/++/00/00/00/00/++/0+/00/++/++/00/00/++/00/00/++/++/00= 15

Puppy 2= Female, 89.4lbs
00/00/00/++/00/00/00/00/++/+0/00/++/++/00/00/++/00/00/++/++/00= 15

Puppy 3= Female, 89.4lbs
00/00/00/++/00/00/00/00/++/0+/00/++/++/00/00/++/00/00/++/++/00= 15

Puppy 4= Male, 110.6lbs (without sexual dimorphism, 96.2lbs)
00/00/00/++/00/00/00/00/++/++/00/++/++/00/00/++/00/00/++/++/00= 17

Puppy 5= Female, 82.6lbs
00/00/00/++/00/00/00/00/++/00/00/++/++/00/00/++/00/00/++/++/00= 13

BB
Male Scottish Terrier, 21.3lbs (without sexual dimorphism, 18.5lbs)
Take blank sequence and randomly make - add up to 22.
0-/--/00/00/--/00/--/00/--/--/00/0-/00/00/--/--/--/00/00/--/--= -22

Female Tibetan Terrier, 29lbs
Take blank sequence and randomly make - add up to 8.
--/00/00/00/00/00/00/--/00/--/00/00/00/00/00/00/00/00/00/00/--= -8

0-/--/00/00/--/00/--/00/--/--/00/0-/00/00/--/--/--/00/00/--/-- X
--/00/00/00/00/00/00/--/00/--/00/00/00/00/00/00/00/00/00/00/--

Litter:

Puppy 1= Female, 23lbs
--/-0/00/00/-0/00/-0/0-/-0/--/00/-0/00/00/-0/-0/-0/00/00/-0/--= -16

Puppy 2= Male, 27.3lbs (without sexual dimorphism, 23.75lbs)
--/-0/00/00/-0/00/-0/0-/-0/--/00/00/00/00/-0/-0/-0/00/00/-0/--= -15

Puppy 3= Female, 23.75lbs
--/-0/00/00/-0/00/-0/0-/-0/--/00/00/00/00/-0/-0/-0/00/00/-0/--= -15

Puppy 4= Male, 26.5lbs (without sexual dimorphism, 23lbs)
--/-0/00/00/-0/00/-0/0-/-0/--/00/-0/00/00/-0/-0/-0/00/00/-0/--= -16

Puppy 5= Male, 27.3lbs (without sexual dimorphism, 23.75lbs)
0-/-0/00/00/-0/00/-0/0-/-0/--/00/-0/00/00/-0/-0/-0/00/00/-0/--= -15