Jay Lush, father of modern animal breeding, stated that variation is the raw material with which breeder works.  The focus of this article is on the use of variation and measures of variation, in making breeding decisions.  It includes the related ideas of relationship and inbreeding, as well as systems of mating that make use of these ideas. The use of crossbreeding to introduce genetic variation into small populations will also be explained. Our goal is to provide some practical tools for genetic management and decision-making.

Most breeders keep records (pedigrees) of their animals and their animals’ performance. Information such as litter size, milk production, and slaughter weight are collected when such information is of importance.  The more information we have, the more informed and accurate our decisions become.  This chapter will show us how to use the information at our disposal to make good decisions.  As dog breeders, we are most concerned with breeding animals that typify breed standards for physical appearance, temperament, mental acuity, and similar traits. However, in most cases we only have pedigree information and a small number of recorded traits on which to base our decisions. While scientists now understand the genetic basis for moderately complex traits such as coat color and pattern, research in other species suggests that there is little or no significant genetic component to such indicators of performance as success in the show ring, The dog breeder, then, is often at a loss for accurate sources of information about performance traits he is interested in. We shall show how to make the most of what is available.

Relationship

1. the expected proportion of genes that are IBD between X and Y, or
2. the correlation between the genotypes of X and Y based only on pedigree relationship.

Figure 1.   A Simple Pedigree

This pedigree says that Jack and Annie are the sire and dam of Bob. When Bob was conceived, half of his chromosomal complement was paternal in origin, and half was maternal.  If you then sample one of Bob's genes at random, the probability that it is identical to one of Jack's genes is 50%, or 0.5.  If we extend that sample to include the whole of Bob's genotype, we find that the relationship between Bob and Jack, denoted RBJ , is 0.5.  Similarly, the probability that a gene drawn at random from Bob is identical to a gene drawn at random from Tom is 0.25.  This line of reasoning can be extended to find the definitions of some familiar degrees of relationship (Table 1).
 
 

Table 1.  Some Common Coefficients of Relationship
Relationship	RXY
Parent-offspring	0.5
Full sibs (siblings)*	0.5
Half sibs*	0.25
Grandparent-grandchild	0.25
Great grandparent-grandchild	0.125
*(Full sibs share both parents; half sibs share only a single parent.)

Equations have been developed for determining the relationships between any two related individuals, and may be found in a text on basic animal breeding.  In the simplest case, the relationship between two individuals that are only related through a single line of descent is (½)n, where n is the number of steps between the two in the pedigree.  For example, there is a single step between parent and offspring, so RXY = (½)1 = ½.  In the case of half-sibs, there are two steps in the pedigree: one from the first offspring to the common parent and one from the common parent to the second offspring. This gives us RXY = (½)2 = ¼.  This method was used to obtain the coefficients of relationship in Table 1.  When inbreeding is involved, the resulting equations are very tedious to work with. A simple method that is suitable for small pedigrees will be presented later in the piece.

Inbreeding and Relationship

Figure 2.   A pedigree demonstrating inbreeding
 
 

Horatio	Sire: Vincent	Sire: Edmund
		Dam: Emma
	Dam: Emma	Sire: Not applicable
		Dam: Not applicable

Inbreeding is a double-edged sword: it has both beneficial and detrimental effects.  The most useful feature of inbreeding is an effect called prepotency, which is the ability of an individual to produce offspring whose performance is very much like their own. Inbred individuals are homozygous at more loci than the population average, and they produce fewer types of gametes, resulting in fewer types of zygote at fertilization. For example, inbred and non-inbred individuals may have the following genotypes:

Inbred	AABbcc
Non-inbred	AaBcCc

The inbred individual can only produce two types of gamete: ABc or Abc. The non-inbred individual, on the other hand, can produce eight different gametes (ABC, ABc, AbC, Abc, aBC, aBc, abC and abc). Prepotency is particularly useful if a parent is homozygous for a dominant allele, which each offspring will receive with certainty. However, it is really only of great value if the trait is simply-inherited (under the control of a single pair of genes) or highly heritable.  When a trait is complicated in its genetic control, or the environment is much more influential than genetics, any effects of prepotency are overwhelmed.

Two types of problems generally arise when inbreeding is practiced in a population: an increase in the occurrence of deleterious recessive traits, and inbreeding depression.  When inbred animals mate, the level of homozygosis in the population increases. This leads to a higher probability that deleterious alleles will appear in the same individual. In the German Shepherd Dog, somewhat common “simple”-recessive traits include long coat, progressive retinal atrophy and pituitary dwarfism.  Other problem traits such as hip dysplasia (HD) are polygenic, and not as sensitive to homozygosis (homozygosity) at individual loci, but are also expected to increase with higher levels of inbreeding. Inbreeding depression is a decrease in quality or performance of inbred animals that is due to the expression of unfavorable genes affecting polygenic traits. The traits most affected are traits such as fertility and survivability, which have a negative effect on lifetime health and performance. Close inbreeding should be carefully avoided to prevent such problems. In livestock breeding, 6.25% is often used as an upper limit for an acceptable level of inbreeding in a population. This is not always the case, and should not automatically be assumed as a limit for dogs, but is a good starting point to consider.

There is a mathematical measure of inbreeding that is similar to that used for relationship.  The coefficient of inbreeding (denoted FX  where “X” is the name of the individual in question), is the probability that two genes taken at random from an individual are identical by descent.  FHoratio in Figure 2 is 0.25 (25%), which implies that genes are IBD (identical by descent) at 1 of every 4 of his loci. Such a high degree of inbreeding is almost certainly undesirable. Equations to predict the inbreeding coefficient of any individual (given a pedigree) have been derived, but we shall not discuss those here. Coefficients of inbreeding for some common matings are presented in Table 2, and you can see the similarity to Table 1. The method mentioned earlier for calculating relationships in small pedigrees also yields the coefficients of inbreeding for all animals in the pedigree.

Table 2.    Coefficients of Inbreeding for Some Common Matings
 
 

Mating	FX
Parent-offspring	0.25
Full sibs (siblings)	0.25
Half sibs	0.125
Grandparent-grandchild	0.125

You may now be anxious to point out that all members of a breed, and perhaps even a species, are related to one another. This potential problem has long been recognized, and to get around it, we define what is called a genetic base. This base is simply an arbitrary population that is assumed to be non-inbred. For example, the base might be assumed to be all dogs born in 1950. It must therefore be emphasized that FX has meaning as a measure of inbreeding only relative to a base population. If we defined Vincent and Emma’s generation as the base in Figure 2, then Horatio would have a coefficient of inbreeding of zero. The idea is not that inbreeding never occurred before that point, but that it occurred far enough back in time that it would not have a significant influence on the current population if inbreeding is avoided or carefully managed in the future. To illustrate the point, the average relationship between an individual and an ancestor eight generations back in their pedigree is only about 0.00391 (0.391%).

Comparing Relationship and Inbreeding

RXY     measures the proportion of an animal’s genes that are identical by descent to those of a second animal; relationships can exist in the absence of inbreeding.

FX      measures the proportion of an individual’s genes that are identical by descent to one another; remember that inbreeding does not exist in the absence of relationship.

It may help to think of relationship as a characteristic of a pair of individuals, while inbreeding is a characteristic of an individual. As will be demonstrated in an example later, two unrelated, inbred individuals may be mated to produce an individual that is not inbred. It is simple to understand this if the differences between inbreeding and relationship are kept firmly in mind.

The Tabular Method for Calculating Relationship and Inbreeding

Figure 3.   A Mating Between Bob and Victoria

Litter or Dog’s name (“X”) here	Sire: Bob	Sire: Jack	Sire: Tom
			Dam: N/A
		Dam: Annie	Sire: N/A
			Dam: N/A
	Dam: Victoria	Sire: Vincent	Sire: Edmund
			Dam:Emma
		Dam:Emma	Sire: N/A
			Dam: N/A

The first step is to set up the pedigree containing the individuals of interest. A common situation might be the examination of a mating between Victoria, a full sister of Horatio, and the Bob of the example in Figure 3 above.  We shall refer to the offspring of this mating as “X”.  This pedigree will be used to demonstrate how to easily figure out coefficients of relationship and inbreeding.

We are going to construct a table with as many rows and columns as there are unique animals in the pedigree. In Figure 3 there are ten animals, but Emma appears twice, so we will construct a 9-by-9 table. The animals in the pedigree should be ordered by generation from oldest to youngest. For example, we would order X’s pedigree like this:

Edmund, Emma, Tom, Annie, Jack, Vincent, Bob, Victoria, X

Table 3 a.

	Edmund	Emma	Tom	Annie	Tom/ N/A Jack	Edm/Emma Vincent	Jacl/An Bob	Vin/Em Victoria	Bob/Vic X
Edmund

In some cells, such as Jack’s, there are two or three names. The lower names, which I have highlighted in boldface, are the animals the columns correspond to. The upper animals are the parents of that animal. We need this information close at hand to fill in the table.  There will also be a row for each dog in the pedigree; the table has been abbreviated here in step 1 to save space. We will demonstrate how to fill in the table, one row at a time, in a series of four steps. I have used some abbreviations in the table to save space: Edm is Edmund;  Em is Emma;  Ann is Annie; etc.

The Row ‘Edmund’

Table 3 b.

	Edmund	Emma	Tom	Annie	Tom/ N/A Jack	Edm/Emma Vincent	Jacl/An Bob	Vin/Em Victoria	Bob/Vic X
Edmund	1	0	0	0	0	1/2	0	1/4	1/8

If you are confused or uncertain about the value you have calculated for an entry, look at the pedigree. If you have a large number, but there are many steps between the two animals, you may have made an arithmetical error.  The number in the cell should always make sense when compared to the pedigree.

Fred Lanting is an internationally respected show judge, approved by many registries as an all-breed judge, has judged numerous countries’ Sieger Shows and Landesgruppen events, and has many years experience with SV. He presents seminars and consults worldwide on such topics as Gait-&-Structure, HD and Other Orthopedic Disorders, Anatomy, Training Techniques, and The GSD. Fred lives part of the year in Alabama, actively trains in schutzhund, and breeds for occasional litters. He invites all to join his annual non-profit Sieger Show and sightseeing tour.

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