Inbreed1

INBREEDING AND DIVERSITY

Fred Lanting

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 colour 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
When animals are related ‘by blood’, as the expression goes, they share a proportion of their genes in common. It is assumed that the genes shared in common between two related individuals have descended from the same ancestor. If that is true, the genes are termed identical by descent (IBD). That is, genes shared by two related individuals are identical because they have the same origin. Genes may also be what is termed identical in state, which means that the genes at a locus are identical in form, but did not descend from the same ancestor. The coefficient of relationship between two individuals X and Y, RXY, is a measure of pedigree relationship, and may be thought of as either the expected proportion of genes that are IBD between X and Y, or the correlation between the genotypes of X and Y based only on pedigree relationship.
The probability that genes are IBD for two individuals provides the basis for our numerical measure of relationship. We will develop the idea with an example that refers to the pedigree in Figure 1.

Figure 1. A Simple Pedigree
	Sire	Tom
Bob	Jack	Not applicable
	Dam	Not applicable
	Annie	Not applicable

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
The idea of inbreeding is closely tied to that of relationship. Inbreeding may be simply defined as the mating of individuals more closely related than the population average. Another definition often used is that the parents of an inbred individual shared a common ancestor. In Figure 2, Horatio is the product of a sire-dam mating: his dam and paternal grand-dam are one and the same; Emma is the common ancestor. It is hoped that the lovely Emma is exceptional in some character that would warrant her use in this manner, rather than simply a victim of circumstance. The mating of close relatives such as seen here is sometimes called close inbreeding. Since more of an individual’s genes come from the same source, in a sense the gene pool is getting shallower. More formally, homozygosity increases in a population that is inbreeding.

Figure 2. A pedigree demonstrating inbreeding
	Sire	Sire: Edmund
Horatio	Vincent	Dam: Emma
	Dam	Sire: Not applicable
	Emma	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 unfavourable 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
It is necessary to take a moment to stress carefully the differences between coefficients of relationship and coefficients of 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
The advantage of the tabular method of calculating relationship and inbreeding is that it is much simpler to use than the so-called path method. It can become tedious to do by hand if there are a large number of animals in the pedigree you are interested in, but can easily be programmed into a spreadsheet for your computer to deal with. Since we do not know anything about a given offspring, we shall refer to him/her as “X”.

Figure 3. A Mating Between Bob and Victoria
			Sire : Tom
	Sire:	Sire: Jack	Dam : N/A
	Bob	Dam: annie	Sire : N/A
Litter or Dog’s name			Dam : N/A
(“X”) here		Sire:Vincent	Sire : Edmund
	Dam:		Dam: Emma
	Victoria	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
The animals are alphabetized within generation, but this is not necessary. When an individual appears in successive generations, as Emma does, assign her to the group in which she first appears. A given entry in the table is the relationship between the individual at the top of that column and the individual at the far left of that row. Once the table is drawn out, the names should be filled in like this (and we will add more later, below Edmund, in subsequent steps):

Table 3 a.
	Edmund	Emma	Tom	Annie	Tom /N/A Jack	Edm/Emma Vincent	Jack/Anna Bob	Vin/Emma 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’
The first cell in the table corresponds to Edmund’s relationship to himself, which will be 1 unless Edmund is inbred. Since we do not know who the parents of Edmund are, we will assume he is not inbred, and write in a ‘1’. The second cell is the relationship between Edmund and Emma. From the pedigree, we see they are unrelated, and write in a ‘0’; we do this for Tom and Annie as well. To find the relationship of Edmund to Jack, look in the cell for Tom in this row and divide that value by two (because Jack got half of his genes from Tom), which is ‘0’. The procedure for Edmund and Vincent is similar: look at the entry for each parent, divide the number by two, and add them up. For Vincent, we have ½ + 0 = ½. For Bob, we get 0 + 0 = 0, which you can confirm by looking at the pedigree. Victoria is the granddaughter of Edmund, so they share a quarter of their genes in common. For X, we find 1/8 + 0 = 1/8.

Table 3 b.
	Edmund	Emma	Tom	Annie	Tom /N/A Jack	Edm/Emma Vincent	Jack/Anna Bob	Vin/Emma 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.

Adding The Row ‘Emma’
Now that we have added a second row to form a column, a comment is in order that will greatly reduce your labour. Look ahead to the completed Table 3 e, for a moment. If you draw a diagonal line down the matrix from the cell Edmund-Edmund to the cell X-X, the numbers above that line will be the same as the numbers below that line. The diagonal is darkly shaded in the completed table in Table 3 e (step 4 of this Bob-Victoria breeding exercise). The shaded upper-right “triangle” in the completed table can be flipped around the diagonal axis to fill in the lower part of the table. The row for Edmund contains exactly the same entries as the column for Edmund. So to get started, we copy the entry from Edmund-Emma into Emma-Edmund, which is ‘0’. The rest of the entries follow as in step (1):

Emma – Tom = 0	Emma – X = 0/2 + 3/8	Emma – Bob = 0/2 + 0/2 = 0	Emma – Annie = 0
Emma – Vin = 0/2 + ½	Emma – Jack = 0/2 = 0	Emma – Vic = ½ + ¼

Since Emma is “related to herself” (“has the same genes” is another way of saying this) by a factor of one, look across her row and see who else she is related to. To Vincent, it is 1 (herself as one of the parents) divided by 2 (since she is only one of the two parents.) In the same way, relationship to Victoria is calculated by dividing 1.5 (½ for Vincent’s R value and 1 for her own as Victoria’s dam) by 2, to give the ¾ you see in the table. Emma has no relation to Bob because she has no relation to his parents Jack or Annie (therefore 0/2 in each case).

And now, back to where we were, in the early stages of constructing that coefficient of inbreeding Table 3:

Table 3 c
	Edmund	Emma	Tom	Annie	Tom Jack	Edmund/Emma Vincent	Jack/Annie Bob	Vincent/Emma Victoria	Bob/Victoria X
Edmund	1	0	0	0	0	1/2	0	1/4	1/8
Emma	0	1	0	0	0	1/2	0	3/4	3/8

We continue to build our table. Remember that for convenience more than anything else, we put the oldest ones on the left, and X, the Bob-Victoria pup, on the right.

Rows ‘Tom’ through ‘Victoria’

The next six rows were filled in as outlined in steps (1) and (2) above. Note that the values in the triangle below the diagonal are the same as in the upper triangle, flipped around the diagonal. When we look at Victoria’s pedigree, though, we see something that requires special attention. We said earlier that we can use the tabular method to find inbreeding coefficients, and Victoria is inbred (on Emma).

Table 3 d.
	Edmund	Emma	Tom	Annie	Tom/N/A Jack	Edmund/Emma Vincent	Jack/Annie Bob	Vincent/Emma Victoria	Bob/Victoria X
Edmund	1	0	0	0	0	1/2	0	1/4	1/8
Emma	0	1	0	0	0	1/2	0	3/4	3/8
Tom	0	0	1	0	1/2	0	1/4	0	1/8
Annie	0	0	0	0	1	0	1/2	0	1/4
Jack	0	0	1/2	0	1	0	1/2	0	1/4
Vincent	1/2	1/2	0	0	0	1	0	3/4	3/8
Bob	0	0	1/4	1/2	1/2	0	1	0	1/2
Victoria	1/4	3/4	0	0	0	3/4	0	1 1/4	5/8

In the entry Victoria-Victoria, we see that the entry is 1 + ¼. Where did the ¼ come from and what does it mean? The 1 is Victoria’s relationship to herself in the absence of inbreeding. When an animal is inbred, or if you are not sure if an animal is inbred, you determine the coefficient of inbreeding from the table entry that corresponds to the relationship between its two parents. Victoria’s parents, Vincent and Emma, have a coefficient of relationship of ½. If we divide by 2, we get the ¼ in the table entry. Victoria is the most linebreed/inbred dog in this chart.

We can write the formula out more formally as: FAnyDog = ½ (RSire-Dam). To show that this works the way we assert it does, we’ll also find Bob’s coefficient of inbreeding: FBob = ½ (RVincent-Emma), and ½ of (0) is 0. Examination of Bob’s pedigree confirms that his coefficient of inbreeding is 0.

Row ‘X’
We are then left with only one row left to fill in, that belonging to X. If we fill out this last row as we have filled out all of the others, we will see that X is not inbred, despite the fact that his dam was. The fact that this is so may not come as much of a surprise because it is clear from the pedigree that Bob’s line is unrelated to Victoria’s.

Table 3 e.
	Edmund	Emma	Tom	Annie	Tom/N/A Jack	Edmund/Emma Vincent	Jack/Annie Bob	Vincent/Emma Victoria	Bob/Victoria X
Edmund	1	0	0	0	0	1/2	0	1/4	1/8
Emma	0	1	0	0	0	1/2	0	3/4	3/8
Tom	0	0	1	0	1/2	0	1/4	0	1/8
Annie	0	0	0	0	1	0	1/2	0	1/4
Jack	0	0	1/2	0	1	0	1/2	0	1/4
Vincent	1/2	1/2	0	0	0	1	0	3/4	3/8
Bob	0	0	1/4	1/2	1/2	0	1	0	1/2
Victoria	1/4	3/4	0	0	0	3/4	0	1 1/4	5/8
X	1/8	3/8	1/8	1/4	1/4	1/8	1/2	3/8	1

We will now present a pair of brief examples to demonstrate two important ideas. The first point is that a table like the one above can be easily extended to answer “What-if…?” type questions about future matings. The second is that two inbred parents can produce offspring that are not inbred as long as the parents do not share a common ancestor. We will use the pedigree presented in Figure 4 for this example.

Figure 4. A Mating Between Bill and Victoria
			Sire : Tom
	Sire:	Sire: Jack	Dam : N/A
	Bill	Dam: Lisa	Sire : Tom
Litter or Dog’s name			Dam : N/A
(“Y”) here		Sire:Vincent	Sire : Edmund
	Dam:		Dam: Emma
	Victoria	Dam: Emma	Sire : N/A
			Dam : N/A

The sire of Y, Bill, is the product of a half-sib mating, while the dam, Victoria, is the product of a dam-son mating. The completed table of relationships and inbreeding coefficients is:

Table 4
	Edmund	Emma	Tom	Annie	Tom/N/A Jack	Edmund/Emma Vincent	Jack/Annie Bob	Vincent/Emma Victoria	Bob/Victoria X
Edmund	1	0	0	0	0	1/2	0	1/4	1/8
Emma	0	1	0	0	0	1/2	0	3/4	3/8
Tom	0	0	1	0	1/2	0	1/4	0	1/8
Annie	0	0	0	0	1	0	1/2	0	1/4
Jack	0	0	1/2	0	1	0	1/2	0	1/4
Vincent	1/2	1/2	0	0	0	1	0	3/4	3/8
Bob	0	0	1/4	1/2	1/2	0	1	0	1/2
Victoria	1/4	3/4	0	0	0	3/4	0	1 1/4	5/8
Y	1/8	3/8	1/4	5/16	5/16	3/8	9/16	5/8	1

Both parents of Y are inbred (FBill = 1/8 and FVictoria = ¼), but as they do not share a common ancestor.

FY = 0. This example emphasizes a point made earlier: inbreeding is dependent on relationship. In small breeds, it often happens that there are a few very influential individuals to whom most of the population is related. These elevated levels of relationship can make it difficult to plan matings free of inbreeding.

Let us say, for the sake of argument, that we are thinking about mating Emma to Y because we are using her in a linebreeding program. The goal of linebreeding, usually connoting a “milder” form of inbreeding, is to maintain a high degree of relationship and similarity to a desirable individual, and is usually carried out by mating that individual recurrently. The pedigree in Figure 5 outlines a possible linebreeding scheme based on the repeated use of Emma as a dam. The paternal side of the pedigree is the same as shown in Figure 4.
Figure 5. A Linebreeding Scheme based on Emma

Z
Offspring linebred on Emma

			Sire :Tom
	Sire:	Sire: Jack	Dam : N/A
	Bill	Dam: Lisa	Sire : Tom
Litter or Dog’s name			Dam : N/A
(“Y”) here		Sire:Vincent	Sire : Edmund
	Dam:		Dam: Emma
	Victoria	Dam:Emma	Sire : N/A
			Dam : N/A

Z's Dam: Emma (rest of Emma's pedigree not applicable

The first thing we do is add a column and a row to the table that we will fill in with coefficients of relationship between Z, the offspring of Emma and Y, and the rest of the dogs in the pedigree. We can also fill in the Z-Z cell because we already know the relationship between Y and Emma is 3/8, giving Z a coefficient of inbreeding of 3/16 (18.75%). The normal procedure is then followed to complete the table, which is presented below.

	Edmund	Emma	Tom	Annie	Tom/N/A Jack	Edm/Emma Vincent	Jack/Ann Bob	Vinc/Emma Victoria	Bob/Vict X	Y/Emma
Edmund	1	0	0	0	0	1/2	0	1/4	1/8	1/16
Emma	0	1	0	0	0	1/2	0	3/4	3/8	11/16
Tom	0	0	1	0	1/2	0	1/4	0	1/8	1/8
Annie	0	0	0	0	1	0	1/2	0	1/4	5/32
Jack	0	0	1/2	0	1	0	1/2	0	1/4	5/32
Vincent	1/2	1/2	0	0	0	1	0	3/4	3/8	7/16
Bob	0	0	1/4	1/2	1/2	0	1	0	1/2	9/32
Victoria	1/4	3/4	0	0	0	3/4	0	1 1/4	5/8	11/16
Y	1/8	3/8	1/4	5/16	5/16	3/8	9/16	5/8	1	11/16
Z	1/16	11/16	1/8	5/32	5/32	7/16	9/32	11/16	11/16	1+3/16

The shaded row and column contain coefficients of relationship between Z and the other dogs in the pedigree. We can clearly see that relationships between these animals are rising quickly because of the ties back to Emma in three out of four generations. Many breed societies have rules that dictate how frequently the same animal may appear in a pedigree, perhaps four times in six generations, and those rules are based on this idea. However, you can now see that the influence of such an individual depends quite a lot on just where in the pedigree the repeat appearances are. A more sensible rule might be that animals with a coefficient of inbreeding beyond a certain threshold will not be issued papers. A second approach would be to restrict the average relationship to influential members of the breed. The American Jersey Cattle Club publishes what they call a coefficient of kinship (K) on their pedigrees. That number represents the average relationship between the pedigreed individual and a set of the most influential sires in the Jersey breed. A disadvantage of this approach, however, is that K cannot be computed using the tabular method or other simple technique, and can vary considerably depending on the definition of the “most influential” group.

Introducing Genetic Variation through Crossbreeding
Breeds small in numbers (such as the Shiloh, certainly the Chinook and Klee Kai) are sometimes faced with the need or temptation to introduce genetic variation from an outside source to keep their population viable. This is typically done using crosses between the breed’s base (small gene pool) and another breed deemed to be suitable. The decision of what breed to outcross with can be based on anatomical conformation, behavior, or some other characteristic important to the base breed. A concern is often to limit the influence of the new breed to maintain an acceptable level of “purity”, or breed composition. An approach to calculating the outcome of matings between base and outcross animals will be presented and discussed.
Outcrossing may be used to take advantage of a phenomenon erroneously known as “hybrid vigor”, more properly heterosis. The idea is that a cross between two populations that have each become relatively homozygous will produce offspring that are heterozygous at many loci. Research has shown that such crosses are often much heartier, healthier and productive than either of the parental lines. Heterosis is an effect dog breeders have known about and taken advantage of for many years.

[Note: technically, a hybrid is a cross between two species, such as horse X jackass, or bison X cattle; crossbred dogs or dog-wolf matings do not produce true hybrids. But we should recognize that the word is used, and consider the context, even though a wolf is just another breed of dog.]

A tabular approach can be used to determine levels of breed composition. By breed composition, we mean the percentage of base and outcross breeds in the improved population. For example, if you were to cross populations of German Shepherds and Labradors, the composition of the resulting breed would be 50% GSD and 50% Labrador. Rules for acceptable matings are often based on distance between the outcross and current generation of individuals, and the tabular method to be presented can be used to determine if breed association rules are based on sound genetic ideas or breeder preferences.

We are going to use as the basis for this discussion a question posed to the author regarding breed composition and association rules. The situation is as follows: because of concerns about small population size, a breed association wishes to outcross for a single generation to bring in some new genetic variation. The outcross individuals will be used only for a single generation, and matings between composite (mixed) individuals will only be allowed if they are a certain distance apart in generations from the outcross. The club rules as they currently stood stated that:

(A): 2, 3 and 4 may only mate with 5 and 6, and

(B): 5 and 6 may only mate with 2, 3, 4, 5, and 6.

Those numbers refer to distance, in generations, from the outcross event. A ‘1’ would be the offspring of the limited-numbers breed and the introduced “outcross” breed. We will use the pedigree in Figure 6 as the basis for our discussion.

Figure 6. Seven Generations From an Outcrossing Event
#'s refer to							Outcross
generations