### Estimation of genetic relationship

Genetic covariance matrices between all animals present in the dataset were estimated with three methods. First approach (pedigree based method - PB) was based on the additive relationship matrix calculated from pedigree. Second method computed similarity between individuals as a correlation coefficient between allelic states using 90 SNP markers from chromosome 1 (SNP based method - SNPL). For this purpose the method of Loiselle [4] was used as implemented in software package SPAGeDi 1.2g [2], which computes relationship as a_{ij} = Σ1[ Σa(Σc_{i}Σc_{j}(*x*_{1cia} - *p*_{1a})(*x*_{1cja} - *p*_{1a})/Σc_{i}Σc_{j}1) + Σa(*p*_{1a}(1 - *p*_{1a})/(*n*_{1} - 1)) ] / ΣlΣa (*p*_{1a}(1 - *p*_{1a})) where x_{1cia} is an indicator variable (x_{1cia} = 1 if the allele on chromosome *c* at locus *l* for individual *i* is *a*, otherwise x_{1cia} = 0), p_{1a} is the frequency of allele *a* at locus *l* in the reference sample, *n*_{1}is the number of alleles defined in the sample at locus *l* (the number of individuals times the ploidy level minus the number of missing alleles), and Σc_{i} stands for the sum over the homologous chromosomes of individual *i*. Here, the term involving (*n*_{1} - 1) is a sampling bias correction. The program calculates the pair wise relationship between animals i and j (a_{ij}) leaving the diagonal elements blank (a_{ii}), thus selfcoancestry had to be estimated as: F_{k} = 1 + 0.5*a_{ij}, where a_{ij} is relationship between parents i and j of individual k.

The third method used MCMC (Markov Chain Monte Carlo simulations) to estimate genetic relationship between animals for a selected number of 39 SNP markers from chromosome 1, with minor allele frequency above 0.1 (selected SNP method - SNPC). This limitation was imposed due to time-extensive properties of the MCMC method. Software package Citius[5, 6] was used to apply the MCMC method to calculate multilocus genotype probabilities and to analyse genes shared identical by descent (IBD). IBD matrices were calculated in 9 points along the analysed fragment of chromosome 1. Afterwards they were averaged into one G-matrix, that was used for further computations.

### Estimation of variance components and breeding values

Variance components were estimated separately for each time point (0, 132, 265, 397, 530), with ASREML [7] using the following model:

*y*_{
i
} = *μ* + *a*_{
i
} + *e*_{
i
}

Where: y_{i} - analysed trait a_{i} - random additive genetic effect of animal i; e_{i} - random residual effect.

The covariance structure was specified as:

*and*

where:
- additive genetic variance,
- residual variance, G - genetic relationship matrix, I – identity matrix.

The analysis was performed with three types of genetic covariance matrices (G) based on: pedigree (PB method), and SNP markers (methods SNPL and SNPC).

Quadratic regression of predicted breeding values on time, extracted from ASREML, in the first five time points was applied to estimate least square regression coefficients for each animal. Subsequently, the estimated regression coefficients were used topredict the unknown breeding values in the 6

^{th} time point (time 600) using the following formula:

where: y_{600,i} is the breeding value in time point 600;
,
, *and,*
are least square regression coefficients, estimated for animal i.