1. Chapter 11 Inbreeding When the parents of an individual share one or more common ancestors, the individual is inbred. Inbreeding is unavoidable in small populations as all individuals become related by descent over time.

2. The consequence of matings between relatives is that offspring have an increased probability of inheriting alleles that are recent copies of the same DNA sequence. These recent copies of the same allele are Identical by DescentAutozygous referred to as Identical by Descent or Autozygous. F The inbreeding coefficient (F) is used to measure inbreeding.

3. As F is a probability, it ranges from 0 to 1. Identity by descent is related to, but distinct from homozygosity. Individuals carrying two alleles identical by descent are homozygous. However, not all homozygotes carry alleles that are identical by descent -- homozygotes include both autozygous and allozygous types.

4. Inbreeding decreases heterozygosity and increases homozygosity thus altering genotypic ratios from that expected based on Hardy- Weinberg expectations. However, inbreeding does NOT change allele frequencies. The reduction in heterozygosity due to inbreeding is directly related to the inbreeding coefficient.

5. We can estimate the level of inbreeding by comparing observed (H o ) heterozygosity with expected (H e ) under random mating as follows: F = 1 - (H e /H o ) Effects of population size on the level of inbreeding can be determined by considering the probability of identity by descent in the idealized randomly mating population.

6. NOT When the initial population is NOT inbred (F 0 = 0), the inbreeding coefficient in any subsequent generation t is: F t = 1 - [1 - 1/2N e ] t Thus, inbreeding accumulates with time in all closed finite populations at a rate dependent upon their population size.

7. If population sizes fluctuates among generations, as occurs in real populations, the expression for the inbreeding coefficient at generation t is: F t = 1 -  [1 - (1/2N ei )] i=1 t Where N ei is the effective size of the i th generation.

8. Indirect Estimates of Inbreeding Coefficients In most populations, levels of inbreeding are unknown. However, an estimate of the average inbreeding can be obtained from the effective inbreeding F e coefficient (F e ): F e = 1 - (H t /H 0 )

9. Gray wolves became established on Isle Royale in about 1949 during an extreme winter when the lake froze.

10. The wolf population is assumed to have been started by a single pair of individuals. Population rose to about 50 in 1980. Population crashed to 14 in 1990.

11. Decline could have been due to: reduced availability of prey disease deleterious effects of inbreeding combination of factors Suggested that the island population must be inbred due to the low number of founders. All individuals have the same rare mtDNA haplotype.

12. DNA fingerprint data suggests that island wolves are as similar as sibs in a captive population of wolves. Allozyme heterozygosity, based on 25 loci, was 3.9% for Isle Royale wolves compared to 8.7% for a captive population. F e = 1 - (H island /H mainland ) = 1 - (0.39/0.87)= 0.55

13. Thus, this endangered island population is highly inbred. Gray wolves suffer reproductive fitness due to inbreeding -- the Isle Royale population has smaller litters and poor juvenile survival!

14. Pedigree Path Analysis Pedigree Path Analysis -- Once a pedigree of an X individual (say “X”) is obtained, we can calculate F X its inbreeding coefficient, F X. Step I Step I: Draw the pedigree so that the common ancestors appear only once. A common ancestor is any individual related to both parents of X, the individual for whom we wish to determine F X. If there are no common ancestors, then F X = 0

15. A Step II Step II: Determine the inbreeding coefficient. If there is no pedigree information on the common ancestors, it is often assumed to be non-inbred If the common ancestor is inbred, then its inbreeding coefficient, F CA, must be calculated before calculating F X Calculate F CA as you would F X as described below. Once F CA is determined, F X can be calculated.

16. Step III Step III: Look for loops in the pedigree A loop is a path that runs from X, through one parent, to the common ancestor, through the other parent, and back to X without going through any individual more than once. Determine the number of steps in each path.

17. Step IV Step IV: Calculate the contribution of each loop to the inbreeding coefficient. The contribution of each loop to F X is determined as follows: (1/2) i X (1 + F CA ) Where F CA is the inbreeding coefficient of the common ancestor and i is the number of steps in each loop as defined in step III.

18. Step V Step V: Sum the contribution of each loop. The summation of all the contributions will be the inbreeding coefficient of individual X.

19. Example I: Half-Sib Matings X ABAC DE Pedigree A DE X Path

20. A DE X LoopF CA iContribution to F X D - A - E0.03(1/2) 3 X (1 + 0.0) F X = 0.125

21. Example 2 -- Full-Sib Mating A BAB X

22. AB X CD LoopF CA iContribution to F X A C--A--D0.03(1/2) 3 X (1+0.0) = 0.125 B C--B--D0.03(1/2) 3 X (1+0.0) = 0.125 F X = 0.25

23. ABCDEFGHIJKLMNOABCDEFGHIJKLMNO WHAT IS F O ?

24. ABCDEFGHIJKLMNOABCDEFGHIJKLMNO P

25. ACDGHKLMACDGHKLM What is F M ?

26. ACDGHKLMACDGHKLM Loop F CA i A K-G-C-A-D-H-L0.07(1/2) 7 0.0078 A K-H-C-A-D-G-L0.07(1/2) 7 0.0078 A K-G-D-A-C-H-L0.07(1/2) 7 0.0078 A K-H-D-A-C-G-L0.07(1/2) 7 0.0078 C K-G-C-H-L0.05(1/2) 5 0.0313 D K-G-D-H-L0.05(1/2) 5 0.0313 A [C-A-D0.03(1/2) 3 0.125] G K-G-L0.1253(1/2) 3 X (1.125)0.1406 H K-H-L0.1253(1/2) 3 X (1.125)0.1406 F M = 0.375