German shepherds and Rottweiler were the two most numerous breeds, constituting over 50% of all tested dogs. The sample was restricted to dogs that had a complete score in all 16 investigated behavioral traits and dogs that had been scored by a judge that had scored at least 9 other dogs. In total, 182 official observers (judges) were involved scoring the dogs for this data set. For the dogs that had been tested twice, only the results from the first test occasion were analyzed. Because no more than 10 Rottweiler and nine German Shepard dogs had been tested more than once, the repeatability was not estimated. Furthermore, because the test occasions were typically separated by 12 months or more for dogs that had been tested twice, the results from a second test could not be expected to be a good repeated measure, owing to the possible learning effect and the possibility of specific training in the intervening period. These criteria resulted in a sample of 5964 German shepherds and 4589 Rottweilers (Table 1). To estimate the genetic correlations and heritabilities, untested relatives to the tested dogs were included to the level of grandparents. As a result, 3646 untested German shepherds and 1255 untested Rottweiler dogs were added to the pedigree files including all tested German shepherds and Rottweilers respectively. The pedigree information was retrieved from the registries of the Swedish Kennel Club.

##### Estimation of genetic correlations and heritability

To estimate the heritability of the 16 scored behavioral traits and the degree to which they are co-inherited (genetic correlations, R_{A}), we analyzed the behavioral traits in all possible pair-wise combinations with a bivariate variance component model. This is a mixed linear model in which the column vector of phenotypic values of *n* individuals (**y**) is expressed in terms of its additive genetic value and other random and fixed effects:

- (1)

where **b**, **a**, **c** and **e** are vectors of fixed effects, additive polygenic effect (breeding values), litter effect and residuals, respectively, with all observations for trait 1 coming first, followed by all for trait 2, and *X*, *Z* and *W* are the corresponding design matrices (Henderson 1984; Mrode 1996). A statistical analysis package (DMU, version 6, release 4) developed for quantitative genetics analysis (Madsen & Jensen 2000) was used to fit the models.

The fixed effects included in **b** were sex, age at test in months (12–25), test version (1 or 2), test year (1989–2001), calendar month of testing (1–12) and judge scoring the dog (1–182). The expectation of random effects were all zero with the following distributions:

where the two traits are indexed by 1 and 2, **A** is the additive relationship matrix including available information on all relationships among all individuals, and **I**_{c} and **I** are identity matrices of sizes equal to number of litters and observations, respectively. The genetic correlation was defined as . The heritability was calculated as , averaging over all 15 bivariate analyses of the behavioral variable. The fixed effects included in the model were selected from a preliminary analysis using a linear model excluding the additive polygenic and litter effects with the GLM procedure (Proc GLM) in the sas software (sas/stat^{®} software, version 8.02, SAS institute Inc., Cary, NC). Typically, three to five of the six fixed effects included in the model had a significant influence on the score of a behavioral trait. The effect of judge was always highly significant (*P* < 0.0001). For German shepherd, the effect of sex was significant for 12 of the 16 behavioral traits, and the effects of age, test, year and month were significant for 11, 2, 15 and 11 of the 16 behavioral traits, respectively. For Rottweiler, the effect of sex, age, test, year and month were significant for 14, 7, 1, 7 and 7 of the 16 behavioral traits, respectively. For simplicity, the same model was used for all behavioral traits. The random factors (direct genetic and litter effects) were selected based on previous model evaluation of DMA personality traits in German Shepard (Strandberg *et al*. 2005).