INBREEDING AND DIVERSITY PART 1


Author:

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

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

  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.

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

 

Bob

Sire:
Jack

Sire:
Tom

Dam:
Not applicable

Dam:
Annie

Sire:
Not applicable

Dam:
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

 

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

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

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

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

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’

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

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.

Continued in PART 2

Fred Lanting The Total German Shepherd Dog Canine Hip Dysplasia and Other Orthopedic Problems Conflict: Life, Love and War

Fred Lanting 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 as one of only two SV breed judges in the US. He presents seminars and consults worldwide on such topics as Gait-&-Structure, HD and Other Orthopedic Disorders, and The GSD. He conducts annual non-profit sightseeing tours of Europe, centered on the Sieger Show (biggest breed show in the world) and BSP.

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