INBREEDING AND DIVERSITY - PART 2


Author:

Return to Part 1

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 labor. Look ahead to the completed Table 3e, 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 – Annie = 0;  Emma – Jack = 0/2 = 0;  Emma – X = 0/2 + 3/8;  Emma – Vin = 0/2 + ½;  Emma – Vic = ½ + ¼;  Emma – Bob = 0/2 + 0/2 = 0                                
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 Table3:                     
Table 3 c.

 

Edm.

Emma

Tom

Annie

Tom
Jack

Edm/Emma
Vincent

Jack/An
Bob

Vin/Em
Victoria

Bob/Vic
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.

 

Edm.

Emma

Tom

Annie

Tom
Jack

Edm/Emma
Vincent

Jack/An
Bob

Vin/Em
Victoria

Bob/Vic
X

Edmund

1

0

0

0

0

½

0

¼

1/8

Emma

0

1

0

0

0

½

0

¾

3/8

Tom

0

0

1

0

½

0

¼

0

1/8

Annie

0

0

0

1

0

0

½

0

¼

Jack

0

0

½

0

1

0

½

0

¼

Vincent

½

½

0

0

0

1

0

¼

3/8

Bob

0

0

¼

½

½

0

1

0

½

Victor

¼

¾

0

0

0

¾

0

1 + ¼

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.

 

 

Edm

 

Emma

 

Tom

 

Annie

Tom
Jack

Ed/Em
Vincent

Jack/An
Bob

Vin/Em
Victoria

Bob/Vic
X

Edmund

1

0

0

0

0

½

0

¼

1/8

Emma

0

1

0

0

0

½

0

¾

3/8

Tom

0

0

1

0

½

0

¼

0

1/8

Annie

0

0

0

1

0

0

½

0

¼

Jack

0

0

½

0

1

0

½

0

¼

Vincent

½

½

0

0

0

1

0

¾

3/8

Bob

0

0

¼

½

½

0

1

0

½

Victoria

¼

¾

0

0

0

¾

0

1 + ¼

5/8

X

1/8

3/8

1/8

¼

¼

3/8

½

5/8

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


Litter or Dog’s name (“Y”) here

Sire: Bill

Sire: Jack

Sire: Tom

Dam: N/A

Dam: Lisa

Sire: Tom

Dam: N/A

Dam: Victoria

Sire: Vincent

Sire: Edmund

Dam: Emma

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

 

 

Edm

 

Em

 

Tom

Tom
Lisa

Tom/n.a.
Jack

Edm/Em
Vincent

Jack/Lisa
Bill

Vinc/Em
Victoria

Bill/Vic
Y

Edmund

1

0

0

0

0

½

0

¼

1/8

Emma

0

1

0

0

0

½

0

¾

3/8

Tom

0

0

1

½

½

0

½

0

¼

Lisa

0

0

½

1

¼

0

5/8

0

5/16

Jack

0

0

½

¼

1

0

5/8

0

5/16

Vincent

½

½

0

0

0

1

0

¾

3/8

Bill

0

0

½

5/8

5/8

0

1 + 1/8

0

9/16

Victoria

¼

¾

0

0

0

¾

0

1 + ¼

5/8

Y

1/8

3/8

¼

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.

Continue to Part 3

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.

All Things Canine  consulting division, Willow Wood Services. Tel.: 256-498-3319  Mr.GSD[at]netscape.com
Also use this address for inquiries regarding judging or lecturing schedule and availability.

Canine Hip Dysplasia and Other Orthopedic Problems
It covers all joints plus many bone disorders and includes genetics, diagnostic methods, treatment options, and the role that environment plays. This highly-acclaimed book is a comprehensive (nearly 600 pages!), amply illustrated, annotated, monumental work that is suitable as a coffee-table book, reference work for breeders and vets, as well as a study adjunct for veterinary students, for the dog trainer and the general dog owner of any breed.

The Total German Shepherd Dog
This is the expanded and enlarged second edition, a “must” for every true GSD lover. It is an excellent alternative to the “genetic history” by Willis, but less technical and therefore suitable for the novice, yet very detailed to be indispensable for the reputable GSD breeder. Chapters include not only such topics as: History and Origins, Modern Bloodlines, The Standard, etc., but also topics of great value to owners of any other breed, such as Anatomy, Nutrition, Health and First Aid, Parasites and Immunity, Basics of Genetics, Reproduction, Whelping, The First Three Weeks, Four to Twelve Weeks, and a Trouble-shooting Guide.

Conflict: Life, Love and War Volume I – a “War and Peace”-size novel of love, war, joy, suffering, and the meaning of life. Ask about it.

Click here to purchase books by Fred Lanting


The views and opinions expressed on this web site are solely those of the original authors and other contributors. These views and opinions do not necessarily represent those of SiriusDog.com, the staff, and/or any/all contributors to this site.

Categories