### Genetic material, challenge test, and traits

The genetic material used came from a challenge test performed by VESO Vikan Ltd. (Namsos, Norway) on behalf of the Norwegian salmon breeding company Aqua Gen Ltd. (Trondheim, Norway). The Aqua Gen breeding program is large family-based breeding programme with inbreeding control, founded in the 1970's from a base consisting of salmon from 41 different Norwegian rivers. The accepted level of increase in the inbreeding coefficient of the Aqua Gen population is set to 0.5% per generation (Sissel Kjøglum, Aqua Gen, personal communication). Challenge tests for ISA are performed on a routine basis in connection with the Aqua Gen breeding programme, resistance to ISA being part of the breeding goal of Aqua Gen since 1994. In 2000, eight months after first feeding, fish from the 1999 year class of Aqua Gen were transported to VESO Vikan, put into a single tank with 12°C water temperature, acclimatized for nine days, and then intraperitoneally injected with infectious material (ISA strain Glesvaer/2/90). Dead fish were collected every day, and the test was terminated when approximately 50% of the fish overall had died, which was at test day 27. Body weight was measured at the end of the test, implicating that fish were of different ages when they were measured.

The dichotomous trait Test-Period Survival (TPS) was defined as the survival/not survival status of animals at the end of the test period (i.e. day 27). The trait Test-Day Survival (TDS) was defined as survival/not survival status at individual test intervals (i.e. days).

Among the fish that died before the end of the test, 90 (randomly selected) were autopsied to confirm ISA infection. 10% of the animals were tested for cross-infection by other pathogens using bacteriological tests (cross-infection was not detected). Further details on the challenge test can be found in [12].

Within the breeding nucleus, sires were at the time mated to two dams each, producing paternal half-sib family groups each consisting of two full-sib families. Out of a larger number of families tested in the challenge test, 10 such half-sib groups (i.e. 20 full-sib families), and an additional 7 full-sib families were genotyped and used in the present study. The selection of families to be genotyped was based on the distribution of affected versus resistant animals within families, a 50:50 distribution considered optimal. 40 fish from each full-sib family were challenged. Since the study aimed at testing the reproducibility of a putative QTL identified in an earlier study [12], the analysis was done on both i) all genotyped families ('complete data set') and ii) all genotyped families except the two full-sib families ones that were investigated in the earlier study ('restricted data set'). The complete data set consisted of 1053 individuals.

### Microsatellite genotyping

One linkage group (LG) was targeted for investigation in this follow-up study, corresponding to LG1 in [13] and LG8 on the SALMAP Atlantic salmon map (B. Høyheim, unpublished data [39]). Eight microsatellite markers from this linkage group were selected (Table 2). DNA was extracted from muscle tissue, using the DNAeasy Tissue Kit (96 well format) from QIAGEN (Venlo, The Netherlands). Microsatellite PCR was performed in 10 μl reactions containing 1× PCR-buffer with 1.5 mM MgCl_{2}, 0.5 U Taq Gold polymerase (Applied Biosystems, Foster City, CA), 200 μM of each dNTP, 5% dimethylsulphoxide (DMSO), 250 nM of each primer, and 10 ng template. An annealing temperature of 52°C was used on all microsatellites. The electrophoresis was done on a 3730 DNA sequencer from Applied Biosystems, and genotypes were analyzed using GeneMapper 3.0 software (Applied Biosystems, Foster City, CA).

### Linkage analysis

Linkage analysis was done using the program Joinmap 3.0 [27]. For each full-sib family, the data was first split into two sets, containing data on alleles inherited from sires and dams, respectively. Data from all sires were pooled, as were the data from all dams, using the "Combine Groups for Map Integration" command of Joinmap 3.0. Sex-specific maps were then made. The default settings of the program were used for map construction. Since the male recombination rate is close to zero on this linkage group [13], the female map was used for QTL interval mapping. Following construction of the map, the data was checked for double recombinants (indicative of genotype error) using a Visual Basic for Applications (VBA) script running from Microsoft Excel (T. Moen, unpublished). When double recombinants were found, genotypes were checked, re-genotyped, and excluded if ambiguous. After checking for double recombinants and correction of data, the data set contained no double recombinants, supporting earlier findings of complete interference in salmonids [31–34].

### Test for non-Mendelian segregation

At each marker, individual parents were tested for a 1:1 segregation of alleles, using a χ^{2} goodness-of-fit test. An overall test statistic was calculated as the sum of χ^{2} test statistics for individual parents. The test was implemented through a Visual Basic-for-Excel script.

### QTL mapping

#### Interval mapping using Haley-Knott regression on test-period survival (TPS-HK)

Interval mapping on TPS was performed using the "Half-sib Analysis" option of QTL Express [28], based on the method of KNOTT *et al*. [29]. A one-QTL model was used, and analysis was performed at every 1 cM. In order to include contributions from both sires and dams, every record was duplicated, and in the duplicates the denomination of parents as sires or dams were switched. Analysis was done with and without body weight as a covariate. Permutation testing and bootstrapping, as implemented in QTL Express, were used to determine chromosome-wise significance levels of the test statistic and confidence intervals for QTL position, respectively. In both cases, the number of iterations was 500. The proportion of phenotypic variance was calculated using the formula 4(1-MS_{full}/MS_{reduced}), where MS is the residual mean square from the regression analysis [28]. The proportion of additive genetic variance explained by the QTL was found by dividing the proportion of phenotypic variance by the estimated heritability h^{2} = 0.19 [11].

#### Interval mapping using the Cox proportional hazard model on test-period survival (TDS-Cox)

A method based on the Cox proportional hazard model was developed for interval mapping of TDS. In the Cox model [14], the hazard function of an individual with covariate vector **x** is the product of an arbitrary (nonparametric) baseline hazard function λ_{0} and a parametric function **e**^{x'β} of **x**. For our application, we used a version of the Cox partial likelihood that accounts for a small number of ties (more than one failure occurring within the same time interval) according to Peto and Peto [30, 18]. A single-QTL model was assumed, with the QTL (Q) being separated by the nearest flanking markers A and B by map distances r_{A} and r_{B}, respectively. At every 1 cM, the maximum log likelihood of the data was calculated under the null hypothesis of no QTL affecting survival and under the alternative hypothesis of a QTL affecting survival during challenge. The log likelihood function was

LogL={\displaystyle \sum _{T\in \{unc.\}}[({\displaystyle \sum _{i\in D(T)}{x}_{i}\beta}})-{d}_{T}(\mathrm{log}\phantom{\rule{0.1em}{0ex}}{\displaystyle \sum _{j\in R(T)}{e}^{{x}_{j}\beta}})]

where {*unc*.} is the set of uncensored time intervals T, i.e. time intervals (days) before the challenge test was terminated; *D*(*T*) is the set of offspring that died within time interval *T*; *d*_{
T
}is the number of offspring in *D*(*T*); *R*(*T*) is the set of offspring at risk at the beginning of time interval *T*; *x*_{
i
}is *P*_{
i
}(*Q*_{1}) - *P*_{
i
}(*Q*_{2}); *P*_{
i
}(*Q*_{1}) and *P*_{
i
}(*Q*_{2}) are the probabilities of animal *i* having inherited one or the other QTL allele from the parent in question; *β* is a regression coefficient. For the calculation of *P*_{
i
}(*Q*_{1}) and *P*_{
i
}(*Q*_{2}), complete interference was assumed, a realistic assumption in salmonids [31–34]. Thus, if QTL allele Q_{1} was assumed to be in coupling phase with marker alleles A_{1} and B_{1}, the probability of Q_{1} being inherited by animals having marker genotypes A_{1}B_{1}, A_{1}B_{2}, A_{2}B_{1}, or A_{2}B_{2} was 1, \frac{{r}_{B}}{{r}_{A}+{r}_{B}}, \frac{{r}_{A}}{{r}_{A}+{r}_{B}}, and 0, respectively. The likelihood ratio test (LRT) statistic was

LRT={\displaystyle \sum _{i=1}^{N}2\left[Log\widehat{L}({H}_{1})-Log\widehat{L}({H}_{0})\right]}

Where *N* is the number of parents, and Log\widehat{L}({H}_{0}) and Log\widehat{L}({H}_{1}) are the maximum log likelihoods under the null- and alternative hypotheses, respectively. Log\widehat{L}({H}_{1}) was found by grid search on *β*. Under H_{0}, *β* was 0. LRT was distributed approximately as χ^{2} with *N* degrees of freedom. The relative risk of animals having inherited one allele from the parent in question versus animals having inherited the other allele was \frac{{e}^{{\beta}_{Q}}}{{e}^{-{\beta}_{Q}}}. The interval mapping was implemented in a Visual Basic-for-Excel program.

#### QTL mapping using Variance Component analysis on Test-Period Survival (TPS-VC-lin)

1. For each putative QTL position on the chromosome segment, calculate the (co-) variance matrix associated with the QTL. This matrix is also called the G or IBD (identical by descent) matrix, and has elements *ij* = Prob(QTL alleles *i* and *j* are IBD). We used the LOKI package [36] to calculate the IBD matrix from the marker information.

2. For each putative QTL position in step 1, construct a model to estimate QTL variance and other parameters, then test for the presence of a QTL.

The model was *s*_{
i
}= *μ*+ *u*_{
i
}+ *v*_{
ip
}+ *v*_{
im
}+ *e*_{
i
}where *s*_{
i
}is the phenotype of animal i, 0 for affected and 1 for resistant; *μ* is the overall mean; *u*_{
i
}is the polygenic effect for animal *i*; *v*_{
ip
}is the effect of the paternal QTL allele for animal *i*; *v*_{
im
}is the effect of the maternal allele of animal *i*; and *e*_{
i
}is a random residual. The random effects *u*, *v*, and *e* are assumed to be distributed as follows: *u* ~ N(0, σ_{u}^{2}**A**), *v* ~ N(0, σ_{v}^{2}**G**), *e* ~ N(0, σ_{e}^{2}**I**), where σ_{u}^{2}, σ_{v}^{2}, and σ_{e}^{2} are the polygenic variance, the additive QTL variance of one allele, and the residual variance, respectively. **A** is the additive genetic relationship matrix, **G** is the IBD matrix described above. Parameters σ_{u}^{2}, σ_{v}^{2}, and σ_{e}^{2} were estimated using the ASREML statistical package [37], which also calculated the likelihood of the above model. The LRT test statistic was calculated as twice the difference between the likelihoods of the model fitting the QTL and without fitting the QTL (without *v*_{
ip
}and *v*_{
im
}). LRT has approximately a χ^{2} distribution with one degree of freedom. Analysis points were at mid-marker values.

#### QTL mapping using Variance Component analysis on Test-Period Survival with logit link (TPS-VC-logit)

This method is very similar to the method above, but accounts for the binary nature of the *s*_{
i
}data in Step 2 of the VCs analysis, by using a Generalised Linear Model (GLM) with the logit link function [37], i.e. *Logit*(*s*_{
i
}) = *μ* + *w*_{
i
}+ *u*_{
i
}+ *v*_{
ip
}+ *v*_{
im
}. The goodness-of-fit of generalised linear models is measured by their Deviance [38], and a Deviance Ratio Test-statistic (DRT) was calculated as the difference in deviance between a model fitting the QTL and a model without fitting the QTL. The analysis was performed by ASREML [37], which also calculated the deviance. DRT has also approximately a χ^{2} distribution with one degree of freedom.

#### QTL mapping using Variance Component analysis on Test-Day Survival (TDS-VC-lin)

Following [16], Survival scores (*S*_{
ij
}) were given for each animal *i* and day *j* so that *S*_{
ij
}= 1 if the fish survived day *j*, *S*_{
ij
}= 0 if the fish died at day j, *S*_{
ij
}='missing' if the fish was not alive on day *j*, and thus could not show whether it would survive day j or not. The 2-step variance component mapping approach was used also here, where the model used in step 2 was: *S*_{
ij
}= *μ*+ *day*_{
j
}+ *u*_{
i
}+ *v*_{
ip
}+ *v*_{
im
}+ *e* ij, where the fixed effect *day*_{
j
}accounts for the differences in survival probabilities between days. The likelihood ratio test was calculated as above.

#### QTL mapping using Variance Component analysis on Test-Day Survival with logit link (TDS-VC-logit)

This method is very similar to TDS-lin, but the binary nature of the data is accounted for by a GLM using the logit link function, i.e. the model is: *Logit*(*S*_{
ij
}) = *μ*+ *w*_{
i
}+ *day*_{
j
}+ *u*_{
i
}+ *v*_{
ip
}+ *v*_{
im
}. The Deviance Ratio Test was calculated as for the TPS-logit model.