ORIGINAL ARTICLE

New breeding value evaluation of fertility traits in Finnish mink

M. KOIVULA, E. A. MANTYSAARI & I. STRANDEN

MTT Agrifood Research Finland, Biotechnology and Food Research, Biometrical Genetics, FI-31600 Jokioinen, Finland

AbstractLitter size (LS) has been included in the Finnish mink breeding goal for several generations. Still, the phenotypic trend inthe average number of pups per mated female has slightly decreased while animal size (AS) has increased. The aim of thisstudy was to estimate genetic parameters for pregnancy rate (PREG) and felicity (FEL), and their genetic correlations to LSand AS. The estimated heritabilities were low for PREG (0.032) and FEL (0.026). The genetic correlations between LS andPREG (0.34), and LS and FEL (0.53) were clearly positive. Thus, on average females having genetically larger LS havehigher PREG and FEL. The genetic correlation between AS and PREG was low (�0.13), and correlation between AS andFEL was moderate (�0.27) indicating that larger animals are more likely barren or lose their kits during pregnancy or rightafter birth.

Keywords: Fertility, litter size, mink, pregnancy.

Introduction

The main goals in Finnish mink breeding have been

improved fur quality, and increase in body size and

litter size (LS). Consequently, average pelt size has

increased considerably. However, at the same time

the average number of kits per mated female has

slightly decreased in Finland as well as in other

countries (Hansen & Berg, 2007, 2008; Hansen,

2009). Increase in body size may have lead to smaller

LS (Hansen & Berg, 2007, 2008; Hansen, 2009;

Koivula et al., 2009b, 2010). This seems to be a

problem also in other species because when selecting

for body size negative genetic trend has often been

observed in traits measuring reproduction and

survival despite their importance to profitability

(Peura et al., 2007; Goddard, 2009; Koivula et al.,

2009a). One reason is a strong negative genetic

correlation between large animal size (AS) and LS.

For example in minks this correlation has varied

from �0.18 to �0.28, (Lagerkvist et al., 1994;

Rozempolska-Rucinsca, 2004; Peura et al., 2007;

Koivula et al., 2009b, 2010), and in blue foxes

negative correlation has been even higher (�0.36 to

�0.43) (Peura et al., 2007; Koivula et al., 2009a).

Fertility can be measured in many ways. In

Finland, farmers record mink LS at two weeks after

whelping, but also barren females, aborting females

or females losing their kits are recorded in a routine

recording scheme. However, breeding values are

based on LS only, and barren females or females

aborting or losing their kits are not included in the

breeding value evaluation. In blue foxes heritability

of pregnancy rate (PREG) was 0.028 and felicity

(FEL) 0.049, and the genetic correlations between

LS and PREG and LS and FEL were clearly positive

(Koivula et al., 2009a). Thus, it was possible to

include these traits in breeding programmes of

Finnish blue foxes.

The aim of this study was to estimate genetic

parameters for PREG (representing the proportion

of females whelping, i.e. the non-barren females)

and FEL (including both aborting females and

females losing all kits after birth), and their genetic

correlations to LS and AS. In addition, we examined

genetic trends in the traits studied.

Correspondence: M. Koivula, MTT Agrifood Research Finland, Biotechnology and Food Research, Biometrical Genetics, FI-31600 Jokioinen, Finland.

Tel: � 358-40-1960986. Fax: �358-3-4188-3244. E-mail: minna.koivula@mtt.fi

Acta Agriculturae Scand Section A, 2011; 61: 1�6

(Received 14 September 2010; revised 1 November 2010; accepted 2 November 2010)

ISSN 0906-4702 print/ISSN 1651-1972 online # 2011 Taylor & Francis

DOI: 10.1080/09064702.2010.538715

Material and methods

Mink data were obtained from the Finnish Fur

Breeders’ Association. The data had information

from 3.7 million animals. Data for the variance

component estimation were sampled from the full

data. Sampling was done by farm. The complete

pedigree contained about 4.1 million animals from

136 farms. The pedigree had many disconnected

subpopulations, so it had to be pruned with Relax2

(Stranden & Vuori, 2006) to have only informative

animals. In the end, the sample had observations

from 12 farms having 69,441 animals born in years

1998�2006. The pedigree file contained 93,632

animals.

The analysed traits were the first parity LS,

PREG, FEL and AS. LS was recorded as numbers

of kits alive two weeks after whelping. PREG and

FEL were binary (1/0) traits, value 0 representing

the event when the female was barren or aborted/

lost her kits. Females were scored as pregnant when

she showed visual signs of pregnancy. If pregnancy

was recorded, PREG�1, and also if PREG record

was missing but FEL and LS records exist. If

abortion or kit loss was observed, females were

recorded as FEL�0, similarly if she was recorded

as pregnant and LS was missing. Because all

pregnant females and all females giving birth or

losing kits are not observed, PREG and FEL are

always approximations. Abortion and kit loss after

birth was treated as a single FEL trait, because the

number of observations for aborting females was so

low that it would have been difficult to analyse it as a

separate trait. AS was graded subjectively by the

farmer. The grading scale ranged from 1 (smallest)

to 5 (largest). The recommendation was that the

average AS should be close to 3 within farm and

year.

Restricted maximum likelihood (REML) esti-

mates of (co)variance components were calculated

using DMU software (Madsen & Jensen, 2000). The

multi-trait animal model was:

y�Xb�Wc�Za�e

where y is a vector of observations, b is the vector of

fixed effects, c is the vector of random effect of the

litter in which the female is born, and a is the vector

of random genetic effects for animal and e is the

random residual, and X, W and Z are known

incidence matrices for the fixed and random effects.

Random effects were assumed to be independent

and normally distributed. In particular, c �

N(0;C0�I); a � N (0;G0�A); e � N (0;R0�I)where C0 is common litter effect (co)variance

matrix, G0 is direct additive genetic (co)variance

matrix, A is numerator relationship matrix and R0

residual (co)variance matrix.

The fertility traits were exclusive by nature of their

definition: when PREG had value 0, both FEL and

LS information were missing; when PREG had value

1, and FEL had value 0, then LS was missing. Thus,

LS was observed only when both PREG and FEL

had value 1. Consequently, the residual covariance

between LS and PREG, LS and FEL, and PREG

and FEL was assigned as non-existing (zero) because

these trait combinations are not present in the data,

and thus, cannot be estimated.

Fixed effects for the traits were studied with the

general linear model by excluding random effects

other than the residual (SAS, 2004). Fixed effects

for LS, PREG and FEL were farm�year, time of

birth for animal (three classes: 99�119, 120�140 and

141�160 days from the beginning of the year,

reflecting timing of birth and thus also age of animal)

and number of matings (three classes: 1, 2 or �2

mating/season). Fixed effects for AS were farm�year,

time of birth for animal, sex of animal (three classes:

male, female and unknown) and age of dam (three

class: 1, 2 or �3-years-old).

Heritability (h2) and proportion of common litter

variance (c2) for the traits were calculated as h2�s2

a=(s2a�s2

c �s2e ); and c2�s2

c =(s2a�s2

c �s2e );

where s2a; s2

c and s2e are trait variances of additive

genetic, common litter environment and residual,

respectively. Linear animal model was used to

analyse PREG and FEL, although theoretically a

threshold model would be more appropriate for

analysis of binary data (Gianola, 1982). Heritability

calculated on the observed binary scale varies with

incidence because the amount of variance due to

measurement error depends on the incidence. To

overcome this, heritabilities were converted from the

binary to the continous scale using Dempster and

Lerner (1950) formula:

h2�h201p(1�p)=z2;

where h2 is the heritability in the continuous scale,

h201 is the corresponding heritability calculated on the

binary scale, p is the incidence of affected individuals

in the population, and z is the ordinate of the

standard normal density function on the threshold

corresponding to the incidence p.

In addition to the genetic parameters, genetic

trends for the studied traits were assessed by

examining standardised estimated breeding values

(EBV). EBVs were calculated with MiX99

(Stranden & Lidauer, 1999; Vuori et al., 2006).

The largest subpopulation was used for EBV calcu-

lations. The data included observations from

395,233 animals and the pedigree had 451,643

animals from years 1988�2006 in 59 farms. The

2 M. Koivula et al.

model used in the EBV calculation was the same

as in the variance component analysis but the

variances were the obtained REML estimates.

Breeding values were standardised to year 2003

with mean 100 and SD 10 in order to make

comparison of years and EBVs of different traits

easier.

Results and discussion

Table I gives the number of observations in each trait

pair. Descriptive statistics for LS, PREG, FEL and

AS are given in Table II. The mean LS was 5.47 and

SD was 2.10. Mean PREG was 0.89, indicating that

11% of the young mink females were barren.

Average FEL was 0.96, indicating that 4% of females

getting pregnant lost or aborted their kits. Mean AS

was 4.06 in the current data. The recommendation

given to grader is that the average for AS should be

close to three within a farm�year. However, the

mean 4.06 shows that higher scores are commonly

used. Males comprised 30% of the graded indivi-

duals, their average of AS being 4.60, females

average AS was 3.82, and that with unknown sex

(3.5% of the individuals) 3.97.

Proportion of litter variance was low for PREG

and FEL (0.0032 and 0.0009, respectively). Thus,

littermates do not have great impact on these traits.

For the LS the c2 was 0.07 and AS 0.03. Koivula

et al. (2009b) suggested that litter effects were larger

than maternal heritabilities for litter size and animal

size. This implies that it is important to estimate also

environmental effects common to littermates for

these traits.

Heritability (h2) and litter variance proportion (c2)

for the traits are in Table III. Heritability estimate of

LS was 0.11. In other studies heritability for LS in

mink has varied from 0.02 to 0.20 (Berg, 1993;

Lagerkvist et al., 1994; Rozempolska-Rucinsca,

2004; Koivula et al., 2009b, 2010). Thus, the

obtained heritability estimate in this study is within

the range reported for mink. Heritability estimates for

LS in other fur animals have also been similar to those

for mink. In blue fox, heritability estimates of LS

have varied from 0.03 to 0.17 (Kenttamies, 1996;

Wierzbicki & Jagusiak, 2006; Peura et al., 2007;

Koivula et al., 2009a), for raccoon dog LS heritability

has been 0.08 (Slaska, 2002).

The heritabilities estimated on the observed bin-

ary scale for the PREG and FEL were low, 0.032

and 0.026, respectively. Because of the low herit-

ability, genetic change in PREG and FEL will be

expected to be slow. In the underlying continuous

scale (Dempster & Lerner, 1950), the heritability

estimates were higher, 0.092 for PREG and 0.046

for FEL. The results suggest some benefit for using a

threshold model over a linear model so that the

binary nature of the response variable in PREG and

FEL is accounted. However, the low heritability

suggests that both models give the same ranking of

animals (Meijering & Gianola, 1985; Hoeschele,

1988; Foulley et al., 1990).

Reproductive traits like PREG and FEL have been

studied in other production animals as well. In other

species heritability estimates for traits similar to

PREG and FEL in mink have varied considerably.

In blue fox, heritability of PREG and FEL were

0.029 and 0.049 (estimated on continuous scale),

respectively (Koivula et al., 2009a). Heritability

estimates from threshold models for heifer PREG

have ranged from 0.13 to 0.66 (Evans et al., 1999;

Bormann et al., 2006; Eler et al., 2006). In pig,

heritability estimate of return rate has been 0.03 with

a threshold model (Holm et al., 2005), and in sheep

heritability estimate of fertility (ewes lambing per

ewes joined) has been 0.02, estimated on continuous

scale (Brash et al., 1994). Thus, the heritability

estimates of mink fertility traits are similar to

estimates from other species, although estimates

from the linear model depend on frequency and

are not directly comparable to threshold model

estimates.

The genetic correlations between the traits are in

Table IV. The genetic correlation between AS and

LS was antagonistic (�0.26). This result is sup-

ported by the earlier studies in mink (Lagerkvist

et al., 1993, 1994; Rozempolska-Rucinsca, 2004;

Koivula et al., 2009b), and blue fox (Peura et al.,

2007; Koivula et al., 2009a). Negative correlation

between body size and reproduction is seen also in

Table I. Number of observations in each trait pair in multi-trait

analysis. Pregnancy rate (PREG), felicity (FEL), first parity litter

size (LS) and animal size (AS).

PREG FEL LS, no AS, score

PREG 50,200

FEL 45,154 45,154

LS, no 40,523 40,523 40,523

AS, score 21,756 19,421 15,961 40,983

Table II. Number of observations (n), mean and standard

deviation (SD) for the pregnancy rate (PREG), felicity (FEL),

first parity litter size (LS) and animal size (AS).

Trait n Mean SD

PREG 50,200 0.89 0.30

FEL 45,154 0.96 0.20

LS, no 40,523 5.47 2.10

AS, score 40,983 4.06 0.72

New breeding value evaluation of fertility traits 3

practise because phenotypic LS has somewhat de-

creased at the same time as AS has increased

(Figure 1). The negative genetic correlation between

AS and PREG was low (�0.13), and between AS

and FEL moderate (�0.27), indicating that large

animals will more likely lose their kits during

pregnancy or immediately after birth. Similar inter-

action has been observed in blue foxes (Koivula

et al., 2009a), and in Holstein�Friesian cows where

larger animals tend to be relatively less fertile than

smaller animals (Haile-Mariam et al., 2004).

The genetic correlations between LS and PREG,

and LS and FEL were 0.33 and 0.53, respectively.

Thus, females having genetically larger LS have

lower risk to be barren or abort/lose their kits. The

positive genetic correlation is favourable when selec-

tion goal is to increase LS: the results from our study

indicate that selection for increased LS could in-

crease the PREG or decrease kit loss. Similar

correlation has also been observed in pigs, where

genetic correlation between return rate of gilts and

number of piglets born alive in the first litter was

�0.22 (Holm et al., 2005). The genetic correlation

between PREG and FEL was positive (0.46).

Despite reasonably high genetic correlation be-

tween LS and other fertility traits and between

PREG and FEL, correlations were clearly less than

1. Therefore, LS, PREG and FEL are undoubtedly

different traits, and accuracy of fertility evaluations

will increase when more traits are included into the

breeding programme. Females without LS observa-

tion are expected to gain more than females with LS

observation from including PREG and FEL infor-

mation into genetic evaluation. A simple example

illustrates this. Assume phenotypic selection. If

female has no LS observation, accuracy of EBV

increases from zero to 0.11 when PREG and FEL

observations are available. For a female with a LS

observation, accuracy increases from 0.33 to 0.34. In

practice, increase in accuracy is not as large because

no relationship information was accounted in the

calculations. Note that LS was observed only for

animals for which PREG and FEL had value 1, i.e.

female was pregnant and did not lose/abort all kits. A

similar consecutive relationship exists for PREG and

FEL. Thus, some model assumptions are violated,

Table IV. Estimated genetic correlations (rg) between the first

parity litter size (LS), pregnancy rate (PREG), felicity (FEL) and

animal size (AS) with standard errors, and phenotypic (rp)

correlations with AS.

rg rp

Trait FEL LS AS AS

PREG 0.4690.13 0.3490.08 �0.1390.09 �0.02

FEL 0.5390.08 �0.2790.10 �0.05

LS �0.2690.06 �0.05

R2 = 0.54

R2 = 0.59

4.2

4.4

4.6

4.8

5.0

5.2

5.4

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

Birth year

Mea

n li

tter

siz

e, n

o

3.0

3.4

3.8

4.2

4.6

Mea

n a

nim

al s

ize,

sco

re

Figure 1. Phenotypic trend and coefficient of determination R2 in litter size (--j--) and animal size (score, 1�5) (--I--) by birth year in

Finnish mink

Table III. Estimated additive genetic variance (s2a); litter variance (s2

c ); phenotypic variance (s2p ); and proportion of litter variance (c2) and

heritability (h2) with standard error for the first parity litter size (LS), pregnancy rate (PREG), felicity (FEL) and animal size (AS).

Trait s2a s2

c s2p c2 h2

PREG 0.0028 0.0032 0.0877 0.0490.006 0.0390.01

FEL 0.0010 0.0009 0.0398 0.0290.007 0.0390.01

LS 0.4683 0.0704 4.2789 0.0290.008 0.1190.01

AS 0.0617 0.0296 0.3271 0.0990.006 0.1990.01

4 M. Koivula et al.

or at least interpretation of genetic correlation

parameters is not as straightforward as described.

The standardised breeding value estimates for LS,

PREG and FEL show similar trends between years

1988 and 2001 (Figure 2). Genetic trends were

negative during 1988�2001 for all the fertility traits.

After 2002 the genetic trend for LS has been slightly

positive, but still decreasing for PREG and FEL.

PREG and FEL have not been included in the

breeding programme and selection for better LS has

not improved other fertility traits. The genetic trend

for AS has been positive (Figure 2). Increase in AS

was also clear in the phenotypic trend (Figure 1).

The phenotypic trend in LS has been decreasing but

lately the decrease seems to have ceased. Thus, it

seems that in spite of the negative genetic correlation

between AS and LS, there has been genetic im-

provement in LS, although this is not as clearly seen

in phenotypic trend.

Traits measuring reproduction and survival may

show a negative genetic trend in spite of their

importance to profitability (Goddard, 2009). This

occurs due to inbreeding depression and selection

for other correlated traits. To overcome this pro-

blem, fertility traits as well as other fitness traits

should be included in the breeding objectives and

the selection index. Genetic trends for the fertility

traits in the Finnish mink population have been

negative although fertility through LS has been

included in the breeding goal for several generations.

Only since year 2002 the genetic trend for LS has

been slightly positive. However, in Finland basically

whole fur animal breeding programmes operate on

farm level and farmers are responsible for final

breeding selection. Thus, farmers may also decide

themselves if they want to weight more or less

fertility traits and less AS. The most important

reason to the negative trends is the antagonistic

genetic correlation between AS and the fertility

traits, and selection for large AS. When selection

mainly focuses on increasing AS, the genetic level of

LS and the other fertility traits will probably

decrease. However, phenotypic impact may not be

very dramatic because heritabilities of the fertility

traits are quite low.

Conclusions

PREG and FEL are new fertility traits to the Finnish

mink breeding evaluation where LS has been the

only measure for fertility. Negative genetic correla-

tions were estimated between the three studied

fertility traits and AS. These antagonistic relation-

ships would be reasonable to take into account in

breeding value evaluations by using a multi-trait

model. Including the new fertility traits into the

breeding programme would make selection of breed-

ing animals with good fertility more reliable.

References

Berg, P. (1993). Present knowledge about heritability of different traits

in mink, NJF Utredning/Rapport 90, NJF Workshop Viborg,

Denmark. 10 pp.

Bormann, J. M., Totir, L. R., Kachman, S. D., Fernando, R. L., &

Wilson, D. E. (2006). Pregnancy rate and first-service

conception rate in Angus heifers. Journal of Animal Science,

84, 2022�2025.

Brash, L. D., Fogarty, N. M., & Gilmour, A. R. (1994).

Reproductive performance and genetic parameters for Aus-

tralian Dorset sheep. Australian Journal of Agricultural

Research, 45, 427�441.

Dempster, E. R. & Lerner, I. M. (1950). Heritability of threshold

characters. Genetics, 35, 212�236.

Eler, J. P., Ferraz, J. B. S., Balieiro, J. C. C., Mattos, E. C., &

Mourao, G. B. (2006). Genetic correlation between heifer

pregnancy and scrotal circumference measured at 15 and 18

months of age in Nellore cattle. Genetics and Molecular

Research, 5, 569�580.

Evans, J. L., Golden, B. L., Bourdon, R. M., & Long, K. L.

(1999). Additive genetic relationships between heifer preg-

nancy and scrotal circumference in Hereford cattle. Journal

of Animal Science, 77, 2621�2628.

Foulley, J. L., Gianola, D., & Im, S. (1990). Genetic evaluation

for discrete polygenic traits in animal breeding. In D. Gianola

and K. Hammond (eds.) Advances in statistical methods for

genetic improvement of livestock, pp. 361�410. Berlin, Heidel-

berg: Springer-Verlag.

Gianola, D. (1982). Theory and analysis of threshold characters.

Journal of Animal Science, 54, 1079�1096.

Goddard, M. (2009). Fitness traits in animal breeding programs.

In J. van der Werf, H.-U. Graser, R. Frankham, & C. Gondro

(eds.) Adaptation and fitness in animal populations, evolutionary

and breeding perspectives on genetic resource management, pp.

41�52. Netherlands: Springer.

Haile-Mariam, M., Bowman, B. J., & Goddard, M. E. (2004).

Genetic parameters of fertility traits and their correlation

with production, type, workability, liveweight, survival index,

and cell count. Australian Journal of Agricultural Research, 55,

77�87.

91

93

95

97

99

101

103

105

Birth year

Ind

ex

LS Preg Fel AS

19981988 1990 1992 1994 1996 2000 2002 2004 2006

Figure 2. Average genetic level by birth year according to mean

standardised estimated breeding value for the first parity litter size

(LS), pregnancy rate (PREG), felicity (FEL) and animal size (AS)

in Finnish blue fox

New breeding value evaluation of fertility traits 5

Hansen, B. K. (2009). Litter size and kit survival. Scientifur, 33,

19�21.

Hansen, B. K. & Berg, P. (2007). Low kit survival � consequences

of selection for high body weight. Scientifur, 31, 104

Hansen, B. K. & Berg, P. (2008). Reduced litter size and percent

kits alive is a consequences of selecting for high body weight.

Scientifur, 32, 15.

Hoeschele, I. (1988). Comparison of ‘‘maximum a-posteriori

estimation’’ and ‘‘quasi best linear unbiased prediction’’

with threshold characters. Journal of Animal Breeding and

Genetics, 105, 327�361.

Holm, B., Bakken, M., Vangen, O., & Rekaya, R. (2005). Genetic

analysis of age at first service, return rate, litter size, and

weaning-to-first service interval of gilts and sows. Journal of

Animal Science, 83, 41�48.

Kenttamies, H. (1996). Genetics and environmental factors

affecting fertility traits in foxes. Animal Production Review

Applied Science, 27, 63�66.

Koivula, M., Mantysaari, E. A., & Stranden, I. (2009a). New

fertility traits in breeding value evaluation of Finnish blue

fox. Acta Agriculturae Scandinavica. Section A � Animal

Science, 59, 131�136.

Koivula, M., Stranden, I., & Mantysaari, E. A. (2009b). Direct

and maternal genetic effects on first litter size, maturation

age, and animal size in Finnish minks. Journal of Animal

Science, 87, 3083�3088.

Koivula, M., Stranden, I., & Mantysaari, E. A. (2010). Genetic

and phenotypic parameters of age at first mating, litter size

and animal size in Finnish mink. Animal, 4, 183�188.

Lagerkvist, G., Johansson, K., & Lundeheim, N. (1993). Selection

for litter size, body weight and pelt quality in mink (Mustela

vison): Experimental design and direct response of each trait.

Journal of Animal Science, 71, 3261�3272.

Lagerkvist, G., Johansson, K., & Lundeheim, N. (1994). Selection

for litter size, body weight, and pelt quality in mink (Mustela

vison): Correlated responses. Journal of Animal Science, 72,

1126�1137.

Madsen, P. & Jensen, J. (2000). A user’s guide to DMU, a package

for analyzing multivariate mixed models, Mimeo 22 p. Tjele,

Denmark: Danish Institute of Agricultural Sciences (DIAS).

Meijering, A. & Gianola, D. (1985). Linear versus nonlinear

methods of sire evaluation for categorical traits: A simulation

study. Genetics Selection Evolution, 17, 115�132.

Peura, J., Stranden, I., & Mantysaari, E. A. (2007). Genetic

parameters for Finnish blue fox population: Litter size, age at

first insemination and pelt size. Agricultural and Food Science,

16, 136�146.

Rozempolska-Rucinsca, I. (2004). Genetic background of perfor-

mance and functional traits in mink. Electronic Journal of

Polish Agricultural Universities, Animal Husbandry. Accessed

3 September 2010, available at: http://www.ejpau.media.pl/

volume7/issue2/animal/art-03.html

SAS. (2004). Statistical analysis system. Release 9.1 ed. Cary, NC:

SAS Institute.

Slaska, B. (2002). Genetic and environmental factors of raccoon

dog reproduction traits. Electronic Journal of Polish

Agricultural Universities, Animal Husbandry. Available at:

http://www.ejpau.media.pl/volume5/issue2/animal/art-06.html

(Accessed 3 September 2010)

Stranden, I. & Lidauer, M. (1999). Solving large mixed models

using preconditioned conjugate gradient iteration. Journal of

Dairy Science, 82, 2779�2787.

Stranden, I. & Vuori, K. (2006). RelaX2: Pedigree analysis

program. In Proceedings of the 8th world congress on Genetics

Applied to Livestock Production. 13�18 August, 2006, Belo

Horizonte, MG, Brazil, CD-ROM communication No.

27-30.

Vuori, K., Stranden, I., Lidauer, M. & Mantysaari, E. A. (2006).

MiX99-Effective solver for large and complex linear mixed

models. In Proceedings of the 8th world congress on Genetics

Applied to Livestock Production. 13�18 August, 2006, Belo

Horizonte, MG, Brazil, CD-ROM communication No.

27-33.

Wierzbicki, H. & Jagusiak, W. (2006). Breeding value evaluation

in Polish fur animals: Estimates of (co)variances due to direct

and litter effects for fur coat and reproduction traits. Czech

Journal of Animal Science, 51, 39�46.

6 M. Koivula et al.