Utilisation and conservation of farm animal genetic resources 163
Chapter 7. Genetic contributions and inbreeding
approximation for overlapping generations can be made by deining the mating ratio to be the total number of breeding dams entering the breeding system per generation
= L, see Box 7.4 for information on generation intervals divided by the total number of breeding males entering the breeding system per generation. he value of ΔF is
relatively insensitive to the mating ratio above 5, so there is little to be gained from further separating out mating ratios.
Note again the major impact that mass selection can have, and the danger of assumptions that selection is random or within families when it is not so. However this should
be put into perspective: a mass selection will deliver much faster rates of gain than strict within-family selection, particularly when litter sizes are small; b mass selection
has a relatively benign impact on ΔF when compared to simple truncation selection in similar-sized schemes using breeding values estimated from BLUP or classical sib-
indices as shown in Figure 7.4.
his justiies the recommendations: if using mass selection, and optimum contributions is not an option, use Table 7.2
to guide the size of scheme necessary to achieve Ne ≥ 50; if the breeding scheme is suiciently sophisticated to use evaluation methods such as
BLUP, then it is both desirable and achievable to implement optimum contribution methodology, and to ensure Ne ≥ 50.
• •
Table 7.2. he minimum number of sires to be used per generation to achieve an efective population size of 50 or more, for diferent mating ratios and expected family sizes, and
assuming discrete generations. he values for mass selection further assume h
2
= 0.4. All assume that family sizes have a Poisson distribution prior to selection. he values for random
and within family selection are independent of the expected family size. Estimates are based upon: equation 6 of Bijma et al. 2000 for mass selection; 8M
-1
1+d
-1
for random selection, Wright1969; 16M
-1
1½+½d
-1
for within family selection, Gowe et al. 1959.
Mating ratio Lifetime ofspring Random
selection Within family
selection 4
8 12
16 20
36 5 or more
21 23
25 27
28 30
15 10
4 to 5 21
25 27
28 29
32 16
11 3 to 4
23 26
28 30
31 35
17 11
2 to 3 25
29 32
34 36
40 19
11 1 to 2
31 38
43 46
48 55
25 13
164 Utilisation and conservation of farm animal genetic resources
John Woolliams
References
Avendaño, S., J.A. Woolliams and B. Villanueva, 2004. Mendelian sampling terms as a selective advantage in optimum breeding schemes with restrictions on the rate of inbreeding. Genetical Research 83: 55-64.
Bijma, P. and J.A. Woolliams, 2000. Prediction of rates of inbreeding in populations selected on best linear unbiased prediction of breeding value. Genetics 156: 361-373.
Bijma, P., J.A.M. van Arendonk and J.A. Woolliams, 2000. A general procedure for predicting rates of inbreeding in populations undergoing mass selection. Genetics 154: 1865-1877.
FAO. 1998. Secondary Guidelines for the National Farm Animal Genetic Resources Management Plans: Management of Small Populations at Risk. FAO, Rome, Italy.
Fernandez J., M.A.Toro and A. Caballero, 2003. Fixed contributions designs vs. minimization of global coancestry to control inbreeding in small populations. Genetics 165: 885-894.
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