124 Utilisation and conservation of farm animal genetic resources
Herwin Eding and Jörn Bennewitz
3.3.2. Maximum Variance Total
he maximum variance total or MVT core set Bennewitz and Meuwissen, 2005 does not maximise the genetic variance within a hypothetical, but maximises the total
genetic variance within and between the populations. he optimised contributions to an MVT core set are calculated through:
¸¸ ¹
· ¨¨
© §
1
K 1
K 1
D K
1 D
K c
1 1
1 1
mvt
4 4
1 =
mvt mvt
mvt
Kc c
D c
where D = diagK is a vector of size equal to the number of populations containing the diagonal elements of K. he genetic diversity in this set is calculated as:
¸¸ ¹
· ¨¨
© §
1
K 1
K 1
D K
1 D
K c
1 1
1 1
mvt
mvt mvt
mvt
Kc c
D c
2 1
+ =
S D
MVT
As before, D
MVT
S is the total amount of genetic diversity relative to the genetic diversity in the founder population.
D
MVT
is expressed in terms of trait mean variance, and not of total genetic variance
,
and the MVT core set will sometimes produce diversity estimates larger then 1, indicating that the variance in the core set is more then
the variance present in the hypothetical founder. his is due to evaluating the variance in separate populations. According to genetic theory, the additive genetic variance lost
due to inbreeding within a population doubles the additive genetic variance gained between populations:
¸¸ ¹
· ¨¨
© §
1
K 1
K 1
D K
1 D
K c
1 1
1 1
mvt
K
mvt mvt
mvt
Kc c
D c
total within
total
G Var
f G
Var f
G Var
2 1
herefore results of D
MVT
1 are not contradictory to standard genetic theory. he MVT core set places more emphasis on populations that have high within population
kinship, but low between population kinships. It tends to value small populations that are distinct from the rest of
S. MVT maximises the total variance, including the variance between populations, for quantitative traits. Higher contributions are theoretically
given to breeds with more diverse phenotypes. hus the variance is maximised in such a way that it would be easier for breeders to focus on a speciic set of traits from the
MVT core set.
4. Genetic distances, kinships and conservation decisions
Being proportional to the time span since divergence, genetic distances create the impression of increasing diversity between two populations, even when there is no
Utilisation and conservation of farm animal genetic resources 125
Chapter 5. Measuring genetic diversity in farm animals
change in the actual genetic diversity in terms of allelic diversity or coeicient of kinships. he mean kinship within a population can be written as:
5.4. Genetic distances, kinships and conservation decisions
i ij
i
f f
f
hat is: the mean within population kinship is the sum of the mean kinship of the founder of
f
xy
and the increase in within population kinship since ission ∆ f
x
. he total distance between a pair of populations
i and j is determined by two distances: the distance between each population and the most recent common ancestor of
i and j i.e. the founder of the pair
i, j; Eding and Meuwissen, 2001:
Box 5.6. Example of MVO and MVT core sets.
As an illustration to the diferences between MVO and MVT we present the results from Dutch cattle populations. A contour plot of the kinship matrix of this small set was given in Figure 5.1.
he kinship matrix was estimated using the Weighted Log-linear Model and bootstrapping over loci and individuals Bennewitz and Meuwissen, 2005.
he most striking diference is the diference in valuation of the Heck population. he Heck population in the Netherlands was started from a very limited number of founder animals. Within
the population animals are highly related to each other. Nevertheless, the genetic background of the breed mostly East and South European breeds; Felius, 1995 is relected in a low mean kinship
between this population and all others. he MVO gives the Heck population moderate priority, as it is inbred to a degree that exceeds that of all other populations. he MVT, on the other hand,
puts high value on the Heck population being so distinct form the rest of the population.
MVO MVT
Limousine 0.304
0.169 Holstein Friesian
0.229 0.209
Dutch Red Pied 0.115
0.028 Dutch Friesian
0.086 0.004
Heck 0.072
0.267 Galloway
0.051 0.139
Improved Red Pied 0.049
0.133 Blonde d’Aquitaine
0.039 Belgian Blue
0.032 0.002
Dutch Black Belted 0.021
0.049
126 Utilisation and conservation of farm animal genetic resources
Herwin Eding and Jörn Bennewitz
j i
j i
ij j
ij i
ij j
i
F +
F f
+ f
= j
di, f
f +
f f
= f
f +
f =
j i,
d |
2
Essentially the distance between i and j is determined by the increase in kinships or the
amount of inbreeding since the founder of i and j. Given that f
ij
remains unchanged ater population ission, an increase in distance between
i and j can only be caused by an increase in
f
i
andor an increase in f
j
. his means that in this case an increase in distance can only occur if the inbreeding coeicient in
i andor j increases. In other words, given that
f
ij
remains constant ater population ission, an increase in distance is associated with a loss of within population genetic diversity.
A larger genetic distance is only related to a larger diversity if the within population kinships are equal. If within population kinships vary, a larger distance may lead to
lower diversity, as the following example illustrates: Suppose there is a phylogenetic tree as given in Figure 5.2. In this igure the similarity scores are given within and between
breeds. Nei’s genetic distances between A,B A,C and B,C are given in the table. Mean kinship coeicients calculated from the similarities are also given.
If two populations were chosen for conservation based on these distances, the choice would be the pair A,B as they have the largest distance between them and seem the
furthest apart. However, both the within and between population kinship is smaller and consequently the conserved diversity larger, when the pair A,C or B,C is
chosen for conservation instead of A,B.
0.30 0.35
A 0.75
B 0.65
C 0.40
Nei’s D
A B
Kinship
A B
C B
0.30
A
0.64
C 0.26
0.23 B
0.07 0.50
C 0.00
0.00 0.14
Figure 5.2. Example of a phylogenetic tree between breeds A, B and C, and calculated Nei’s genetic distances and mean kinship coefcients.
