Utilisation and conservation of farm animal genetic resources 175
Chapter 8. Operation of conservation schemes
Box 8.1. Factorial-Minimum-Coancestry mating. Suppose the OC selection of paragraph 2.3 resulted in a contribution of c
i
for animal i: Optimal number of ofspring from sire i = m
i
= 2Nc
i
Optimal number of ofspring from dam j = f
j
= 2Nc
j
where the sum of the m
i
as well as f
i
equals N = the total number of ofspring. A natural mating between a sire and a dam yields n ofspring, where we make n as small as
practically possible to achieve ‘Factorial mating’ as closely as possible. hen the number of matings needed with sire i is M
i
= m
i
n, and with dam j is F
j
= f
j
n, where some rounding
1
of these igures will be required to get the desired total number of matings N
mat
= Nn. he following steps may than be used to assign the minimum coancestry matings:
Step 1: Set up at random a mating table, where Mati,1 denotes the sire of the i-th mating i=1,.., N
mat
and Mati,2 the dam of the i-th mating. Step 2: Use the following algorithm to perform minimum coancestry mating, where K[x,y]
denotes the coancestry kinship between animal x and y:
For k=1,2,3,..etc. Pick at random a mating x 1xN
mat
Pick at random another mating y 1yN
mat
; x ≠y
Set REL
current
⇐ K[Matx,1,Matx,2] + K[Maty,1,Maty,2] Set REL
test
⇐K[Matx,1,Maty,2] + K[Maty,1,Matx,2] Count the number of succesfull swaps: S
k
⇐ S
k-1
If REL
test
REL
current
then Swap the dams of the matings: Matx,2
⇐ Maty,2 Maty,2 ⇐ Matx,2 Set S
k
⇐ S
k
+1 End if
If S
k
== S
k-100
: Finish there were no more successful swaps End for loop
When the algorithm has inished, the Mat-table contains the minimum coancestry matings.
1
For example if m
i
N = 4.459, we round this igure to M
i
= 4. However ater such rounding the sum of the M
i
ΣM
i
may not equal the desired number of matings, N
mat
. If ΣM
i
N
mat
, we give one extra mating to the sires that were rounded down the most. Similarly, if ΣM
i
N
mat
we subtract one mating from the sires that were rounded up the most.
176 Utilisation and conservation of farm animal genetic resources
Theo Meuwissen
2.3. Selection and mating to minimise inbreeding
2.3.1. Optimal Contribution Selection to minimise inbreeding
A robust recommendation for pure conservation programmes is the minimisation of the average kinship, because it minimises inbreeding and maximises allelic diversity
chapter 7. Although the strategies of chapter 7, that minimise sums of squared contributions, will minimise inbreeding, they may sometimes be diicult to apply in
practice, e.g. due to practical reproductive limitations. In such situations and also when the live population goes through a recent severe bottle neck, the family structure can
be very unbalanced. Minimum kinship selection will attempt correct the unbalanced contributions of historical families and minimises the genetic drit. However, whenever
possible, in the long term the conservation strategies of chapter 7 should be re-instated. With minimum kinship selection, a group of parents is selected that minimises:
K
a
= Σ
i
Σ
j
c
i
c
j
K
ij
, where Σ
i
Σ
j
denotes summation over all selection candidates; K
a
is the average kinship of the selected animals; K
ij
is coeicient of kinship between animals i and j; c
i
is the contribution of animal i to the next generation, i.e., c
i
= ½ n
i
N, n
i
is number of ofspring from animal i, and N is total number of ofspring the ½ is because a sire
dam contributes only half of its genes to the ofspring. Also, n
i
= 2Nc
i
gives the number of ofspring a parent should have given its optimal contribution c
i
. he optimal contribution c
i
that minimises K
a
is given in Box 8.2. When the family structure is balanced, minimum kinship selection will result in within family selection.
he genetic drit can be controlled at the DNA level by calculating the kinship conditional on genetic marker information. he markers are used to improve the
coeicient of kinship between the animals in the sense that the kinship is assessed at the DNA level, whereas kinships that are calculated from the pedigree alone are expected
coeicients of kinship of the DNA segments. However, Fernandez
et al. 2005 found no advantage using this approach compared to using the pedigree alone.
2.3.2. Mating
Mating is by Factorial-Minimum-Coancestry mating see Box 8.1 to decide on who is mated to whom, where factorial implies that each mating pair obtains only 1 ofspring
or at least as few as possible ofspring. his mating strategy will to some extend equalise the relationships between the ofspring, such that in the next OC selection round, the
selection of one ofspring does not preclude another due to a high relationship.
Utilisation and conservation of farm animal genetic resources 177
Chapter 8. Operation of conservation schemes
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