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QUANTITATIVE GENETICS |
* USDA, ARS, National Center for Cool and Cold Water Aquaculture (NCCCWA), Kearneysville, WV 25430l; and
Department of Genetics and Biotechnology, University of Aarhus, DK-8830 Tjele, Denmark
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Abstract |
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 Top Abstract INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Key Words: Bayesian analysis • major gene • plasma cortisol • rainbow trout • segregation analysis • stress response
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INTRODUCTION |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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; Wendelaar Bonga, 1997; Barton, 2002; Portz et al., 2006). Disappointingly, studies to date have identified only weak associations between stress response measures and performance traits (e.g., Fevolden et al., 1992; Trenzado et al., 2003; Weber et al., 2008). This failure of altered stress responses, including cortisol responsiveness, to have a consistent effect on performance phenotypes known to be affected by stress may be due in part to the many possible physiological and genetic bases for variation in each measure of stress responsiveness, including cortisol responsiveness.
The main objective of this study was to determine the mode of inheritance of plasma cortisol by using Bayesian methods of complex segregation analysis (CSA) in large full-sib (FS) families. The CSA is a statistical method to determine whether a mixed mode of inheritance of a major gene (MG) and polygenic background effects is consistent with the inheritance of a trait when using only phenotypic data (no marker data are included; Guo and Thompson, 1992; Thaller et al., 1996; Janss et al., 1997). We evaluated whether a mixed model of inheritance including an MG and polygenic background effects was consistent with the inheritance of plasma cortisol. This study provides the basis for designing and carrying out genome-wide linkage scans for stress response QTL in rainbow trout. In addition, markers for genotype variation at the QTL are sought to resolve crude phenotypic measures of stress responsiveness, such as plasma cortisol, into more discrete genotypes, which should associate more strongly with performance traits (e.g., disease resistance) than do the phenotypic measures.
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MATERIALS AND METHODS |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Animals and Measured Traits
The founder NCCCWA population included rainbow trout from 3 different strains (Silverstein et al., 2004). The first parental generation (P0, 2002 spawn) included 100 families that were evaluated for growth performance. From these P0 families, we evaluated the stress response in 64 families. We selected families with high growth performance and low cortisol response (Weber and Silverstein, 2007). High cortisol response is positively correlated with growth; when we looked at the fish that were to be bred based on growth performance, there were few fish with low cortisol. Therefore, we kept some of the low-cortisol fish and bred them so that we had a range in cortisol response beyond that of the selected high-growth fish.
In the second parental generation (P1, 2004 spawn), we generated 111 families, which were evaluated for growth performance and resistance to Yersinia ruckeri. From these P1 families, 60 families were evaluated for stress response when the fish were approximately 130 g of BW by using 4x repeated measurements per fish (Weber et al., 2008). In this P1 generation, we selected families for high growth performance and low cortisol response. From these evaluations on stress response, parents with high and low plasma cortisol response were selected as breeders to produce the FS families evaluated in this study (high x low and low x high families).
Twelve large FS families (F1, 2006 spawn), which included 3 paternal half-sib groups, of rainbow trout (O. mykiss) produced at the NCCCWA were used in this study. The most informative designs for segregation analysis have a collection of medium-sized connected FS families from an outbred population so that the different mating types will be present. By connections between families, the Mendelian segregation of a putative MG can be further confirmed. From each of the FS families, a random sample of 40 siblings per FS family was assessed for plasma cortisol response after a crowding stress. Each individual was measured at 4 time points during this study. The first time evaluation was performed when the fish were approximately 160 g of BW. The subsequent time point evaluations were spaced at approximately 4-wk intervals.
Plasma cortisol response after a crowding stress was measured in each FS family offspring fish at 4 time points by using the protocol outlined below. We recorded BW and length for each of the offspring fish at each sampling period. During the fourth repeated measurement, we recorded the fish that were ripe (<5%), which were those that released milt or eggs when pressure was applied to the abdomen.
Crowding Stress Challenge and Measurement of Plasma Cortisol
The procedures for the crowding stress challenge followed those described by Weber and Silverstein (2007), as modified from Pottinger and Carrick (1999b). The crowding stress challenge for the parents was described in Weber et al. (2008), and the challenge for the offspring is described here. A total of 480 offspring (40 from each of 12 FS families) were included at the beginning of the study; all hatched within a 14-d span. Fish were reared as individual families. Fish were exposed to an artificial ambient photoperiod and reared in continuous-flow groundwater with an ambient temperature of approximately 11.5 to 13.5°C and a dissolved oxygen content near saturation. The fish from each of the families were placed in 120-L blue polypropylene tanks at approximately 1 mo of age. Seven weeks before the beginning of the experiment, fish were tagged with passive integrated transponder tags (Avid Identification Systems Inc., Norco, CA) and the fish from each family were split into 5 tanks of 8 fish each. The locations of the tanks were determined using a random number-generating program (C++ script written by R. L. Vallejo, unpublished program). Fish in the stress study were fed Zeigler Gold (Zeigler Bros. Inc., Gardners, PA) at 2% of BW/d. The 8 fish from each tank were sampled 4 times at 4-wk intervals beginning September 5, 2004, when the fish were approximately 160 g of BW. Fish were not fed the day of sampling or the afternoon preceding the sampling. Sampling began at 0930 h and finished at 1540 h for 2 d in each sampling period. The fish were returned to different tanks after sampling, and the order for sampling families was changed each sampling period.
For the crowding stress challenge, at 10-min intervals fish from a single family were netted and transferred from a 120-L tank to a 6- or 15-L tank and were left undisturbed for 3 h. Fish were transferred to 6-L tanks in the first sampling period and to 15-L tanks in the remaining sampling periods. All tanks had flow-through water. After 3 h in the crowding tank, the fish were netted and transferred into an anesthesia bath with 100 mg/L of tricaine methanesulfonate (tricaine-S; Western Chemical Inc., Ferndale, WA). Within 5 min of the fish entering the anesthesia, a 0.5-mL sample of blood was collected from each fish by caudal puncture by using heparinized syringes (heparin 10 mg/mL) with 23-gauge needles. Blood samples were centrifuged at 10,000 x g for 10 min at 4°C to separate plasma, and the plasma was stored at –80°C until analyzed for cortisol concentration. Body weight was measured to the nearest 1 g, and fork length was measured to the nearest 0.1 cm, after bleeding. To perform plasma cortisol measurements, the plasma samples were heated to 100°C for 15 min in glutamate buffer (pH 3.3) to denature binding proteins. Plasma cortisol was measured (ng/mL) by tritium RIA according to procedures described by Redding et al. (1984). The assays for the cortisol measurements of the parents used a cortisol antiserum purchased from Esoterix Inc. (cortisol F3-314, lot 345; Esoterix Inc., Calabasas Hills, CA) as validated in the studies mentioned. The assays for the cortisol measurements of the offspring were conducted using cortisol antiserum (R4866; provided by Coralie Monroe, University of California-Davis, School of Veterinary Medicine, Department of Reproduction), which was validated for use in rainbow trout (Barry et al., 1993).
Statistical Analysis of Nongenetic Effects
The analysis included 12 FS families (n = 503 individuals, 23 parents and 480 offspring) with 4 repeated measurements of plasma cortisol per individual. The mean plasma cortisol was 58.08 ± 33.25 ng/mL, with a total of 1,895 data records. As expected, we found that the 4 repeated measurements of plasma cortisol were highly correlated [n = 503 individuals (parents and offspring), Pearson’s r = 0.22 to 0.55, P < 0.0001] using the CORR procedure (SAS Inst. Inc., Cary, NC). Subsequently, we decided to fit a permanent environmental effect in the polygenic and mixed inheritance models used in CSA of plasma cortisol to account for the covariance between the records of an individual (i.e., repeated measurements).
Before performing CSA of plasma cortisol, to identify significant predictors of plasma cortisol response, we performed multivariable regression analysis by using 3 linear models (Table 1) that included random (family, animal, sire, and dam) and fixed (tank, time, and ripe) effects and continuous covariates (BW and length) by STEPWISE model selection with the REG procedure of SAS. Model A included all 9 variables; model B included fixed effects and continuous covariates (tank, time, ripe, BW, and length); and model C included fish measurements such as length, BW, and ripe. Overall, the STEPWISE model selection indicated that the effects of time (P < 0.0001), BW (P 
0.0075), length (P 0.0006), and ripe (P = 0.045) on plasma cortisol were significant (Table 1). The fixed effect of tank was a nonsignificant (P > 0.05) predictor of plasma cortisol. Subsequently, we decided to include the variables time, BW, length, and ripe as covariates in the mixed inheritance models used in CSA of plasma cortisol to minimize the variance in the sampled population.
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The pure polygenic model was used to supply an overall quantification of genetic variance for the trait analyzed. The model postulating pure polygenic inheritance was specified as
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permanent environmental variance 
error variance 
and polygenic heritability, defined as 
CSA
Janss et al. (1995) have presented a Bayesian approach for CSA in livestock species. In this study, we used a Bayesian method for CSA implemented in the statistical package iBay, version 1.44 (Janss, 2008).
Mixed Inheritance Model.
For analyses of the presence of MG affecting plasma cortisol, a mixed inheritance model was used with nongenetic effects, the effect of 1 MG, effects of background polygenes, and permanent environmental effects. The mixed inheritance model applied to plasma cortisol was
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The prior distributions for u, p, and e were assumed as follows: polygenic effects were assumed distributed as 
where A is the numerator relationship matrix; permanent environmental effects were assumed distributed as 
where I is the identity matrix; and errors were assumed distributed as 
Specification of the statistical model for the Bayesian approach was completed by specifying the use of uniform prior distributions on 
for nongenetic effects and effects at the major locus, uniform prior distributions on 
for variance components, and uniform prior distributions on [0, 1] for allele frequencies.
The MG effect is assumed to result from segregation at a single locus with 2 alleles (A1,A2). The alleles A1 and A2 are associated with decreased and increased plasma cortisol concentrations, respectively. The frequency of A1 and A2 in the sample population was assumed to be p and q = (1 – p), respectively, under the assumption of the Hardy-Weinberg equilibrium. With 3 genotypes distinguished (A1A1,A1A2,A2A2), genotype means were g' = (–a, d, a), where a and d refer to as the additive and dominant effect, respectively, at the major locus.
The mixed inheritance model included 3 transmission probabilities 
which are defined as the probability that a parent with any of the 3 genotypes (A1A1,A1A2,A2A2) would transmit the allele A1 to its offspring. In the analysis, the mixed inheritance model was analyzed under Mendelian and non-Mendelian assumptions. If Mendelian inheritance was assumed, the transmission probabilities were fixed to 
and 
Under non-Mendelian assumptions (the general and general fixed models described below), the transmission probabilities were given a flat prior for parameter estimation.
Gibbs Sampling.
Statistical inference was based on a Bayesian approach computing marginal posterior densities of the unknown parameters by the Markov chain Monte Carlo (MCMC) method, known as Gibbs sampling (Gelman et al., 2004). The theory and methodology of Bayesian segregation analysis are explained in more detail by Janss et al. (1995), Sorensen (1996), and Janss (2008). The Bayesian approach for CSA allowed the estimation of marginal posterior distributions for nongenetic effects, genotypic values from g' = (–a, d, a), low phenotype allele A1 frequency (p), polygenic variance 
residual variance 
and permanent environmental variance 
for plasma cortisol. On the basis of the MG allele effects (a and d) and the allele frequencies (p and q), the additive 
dominant 
and total MG variance 
were calculated as 
(Falconer and Mackay, 1996). In addition, the proportion of total variance attributable to polygenic effects 
the proportion of total variance attributable to the total effect of an MG 
the proportion of total variance attributable to the additive effect of an MG 
the proportion of total variance attributable to genetic effects 
and the additive effect of an MG expressed in genetic standard deviation units 
were estimated and their marginal posterior distributions were computed.
After exploratory analyses of our data set, the length of each chain was set to 1,200,000 iterations. The first one-half of each chain was discarded (burn-in period of 600,000 iterations) to diminish the effect of the beginning distribution and to allow convergence of the Gibbs sampler (Gelman et al., 2004). On the remaining one-half of the chain (600,000 iterations), a sample was saved from every 10,000 iterations (thinning parameter k = 10,000) to ensure that virtually independent samples were collected. Estimation of posterior distributions of parameters for each model was based on at least 30 replicated Gibbs chains. This Gibbs sampler allowed approximately 1,800 independent samples to be collected per evaluated model.
Postanalysis and Statistical Inference.
Convergence of the Gibbs sampler was judged by using the approximately 1,800 independent samples generated from 30 chains in ANOVA testing for a significant chain effect. Significant differences between chains indicated that the Gibbs sampler had not converged and that generated samples were not from the correct posterior distribution. Convergence was also tested using the criterion outlined by Gelman et al. (2004). For each unknown parameter in the model, a scale reduction factor 
which involves variance between and within chains, was computed. The 
can be interpreted as the factor by which the scale of the marginal posterior distribution of each variable would be reduced if the simulations were continued in the limit 
The 
should be approximately 1.0 (or at most 1.1) to indicate convergence of the iterative simulation for the unknown parameter.
Statistical inferences were based on summarizing the generated samples in the form of estimated marginal posterior distributions. As features of the marginal posterior distributions, estimated means and SD were computed. Posterior means were used as point estimates for the parameters. Statistical inferences focused on the genetic variance components 
to determine significance of the MG in the model. Judgments were also based on the shapes of estimated posterior distributions of variance components (Janss et al., 1995), where a nonsignificant variance shows a distribution with global mode at 
2 = 0 and a significant variance shows a global mode at 2 > 0. Major gene variance was concluded to be significant when the global mode had a density 20 times larger than the density at 
Once significant MG variance was found, further inferences focused on the effects at the major locus and on estimable functions of allele frequencies. The highest posterior density region at 95% (HPDR95) was also calculated from the marginal posterior distributions for each unknown parameter.
Mode of Inheritance for Plasma Cortisol.
We determined the likely mode of inheritance for plasma cortisol by defining 8 mixed inheritance models and submodels or nested models. The models were categorized into 4 model sets: 1) non-Mendelian (unrestricted 
), which assumes non-Mendelian segregation and which included the general model that maximizes 
(model 1) and the general model with fixed 
(model 2); 2) sporadic, which assumes no genetic effects or the absence of MG and polygenic effects 
and which is equivalent to the assumption of equal transmission probabilities 
(model 3); 3) polygenic, which assumes no MG but a polygenic background (model 4); and 4) Mendelian mixed inheritance of an MG and the polygenic background, which is divided into 4 models: dominance of the cortisol-increasing allele A2; additive; dominance of the cortisol-decreasing allele A1; and codominant (models 5 to 8).
When comparing nested models, the larger model has the advantage of making more sense and fitting the data better but has the disadvantage of being more difficult to understand and compute (Gelman et al., 2004). In the model comparisons, we combined the use of Bayes factors (BF) with approaches that measure the distance of the data to each of the approximate models by comparing nested models. Let 
be the vector of parameters in the smaller model and 
be the additional parameters in the expanded model. We then compared the 2 posterior distributions, p( | y) and p(, | y), along with their predictive distributions for replicated data chains.
The loge of the marginal distribution of the data under each model, loge [p(y|Hi)], is estimated, which is basically the normalization constant for the marginalized posterior density (Janss, 2008). Here, given 2 competing models, H1 and H2, we estimated BF (H2; H1) = p(y|H2)/p(y|H1), which is the ratio of the marginal likelihood under 1 model to the marginal likelihood under a second model (Gelman et al., 2004). In this study, the guidelines provided by Janss (2008) were used to assess the amount of evidence in the data that supported the difference between compared models, BF (H2; H1).
Inference on Transmission Probabilities.
After determining the most likely mode of inheritance for plasma cortisol, we analyzed an MG model under non-Mendelian assumptions, defined as
 | [3] |
and the transmission probabilities 
were given a flat prior for parameter estimation (best-fitting MG model). After running the Gibbs sampler as specified previously, the parameters 
and transmission probabilities 
and 
were estimated from the marginal posterior distributions of the unknown parameters (MG fixed model). For comparison purposes, we also analyzed an MG general model (general fixed model) with all the above parameters treated as unknowns 
and with the polygenic variance set to 
We also analyzed the mixed inheritance model (model 2) to assess the effect of the polygenic background in the estimation of Mendelian transmission probabilities. In this model, the MG additive genetic effect a, MG dominance effect d, allele A1 frequency p, and polygenic variance 
were fixed to values estimated with the most plausible mixed inheritance model for plasma cortisol (best-fitting mixed inheritance model). The unknown parameters were the transmission probabilities 
Inference on Major Locus Genotypes.
The strategy followed was first to determine the best-fitting mixed inheritance model for plasma cortisol. We then analyzed the mixed inheritance model (model 2) under Mendelian assumptions 
The parameters a, d, p, and polygenic variance 
were fixed to the values estimated for the best-fitting mixed inheritance model. This allowed the estimation of the MG locus genotype of individuals for the predetermined MG model. The software iBay, version 1.44 (Janss, 2008) internally stores the genotype as the genotype number 1, 2, or 3 (1 = A1A1, 2 = A1A2, 3 = A2A2). During cycles of the MCMC, one of these values will be selected for every genotype and averaged over several MCMC cycles. This produces a genotype estimate that is a fractional number. The resulting estimate will be close to 1 when the genotype is most likely "1" and close to 3 when the genotype is most likely "3." Genotype estimates around 2 are somewhat ambiguous because this can correspond to a likely heterozygote, but also to a relatively inaccurate genotype that has been averaged. Thus, to safeguard against this potential drawback, we estimated the accuracy (R) for the posterior mean of a genotype (gi) or predicted the MG locus genotype, defined as
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RESULTS |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Inferences for a polygenic model were obtained for the full data set using the polygenic inheritance model (model 1). Analysis of the 30 Gibbs chains with virtually 60 independent samples per chain indicated good convergence; the scale reduction factor reached 
for all the variance components and for the heritability estimate of plasma cortisol (Table 2). The posterior means of variance components and polygenic heritability are presented in Table 2. The estimated SD of the marginal posterior distributions of these variance components indicated that these estimates were significant. The estimated polygenic variance and heritability suggest that there is a reasonable amount of genetic variance for plasma cortisol in the population under study. The polygenic heritability estimate of 
was significant and likely was different from zero, as suggested by the HPDR95 boundaries of 0.18 and 0.35, respectively.
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A summary of estimated marginal posterior means for variance components and major locus parameters using nongenetic, polygenic, and mixed inheritance models of plasma cortisol is presented in Table 3. Comparing the loge [p(y|Hi)] of the tested models, we could not reject the hypothesis of no polygenic background [model tested: 1 vs. 2; BF (H2; H1) = 0.0]. However, there was strong evidence to support the polygenic background or polygenic heritability model when compared with the sporadic or nongenetic effects model [model tested: 4 vs. 3; BF (H2; H1) = 11.8]. These model comparisons and results of Table 2 support the contribution of polygenic background effects in plasma cortisol variation.
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the estimated transmission probabilities were closer to the expected Mendelian proportions (model 2). This indicates that there was genetic transmission of plasma cortisol, but this trait might have a complex mode of inheritance and might be controlled by more than 1 MG. Third, all the mixed inheritance models were rejected (model tested: 5 to 8 vs. 1), which suggests a lack of statistical support for a purely Mendelian transmission of 1 MG and polygenic background in the inheritance of plasma cortisol. Although the hypothesis of mixed inheritance of 1 dominant cortisol-decreasing allele A1 and polygenic background (model 7) was rejected [model tested: 7 vs. 1; BF (H2; H1) = –1.8], model 7 had one of the best loge [p(y|Hi)] estimates among the mixed inheritance models (models 5 to 8). Furthermore, according to the guidelines provided by Janss (2008) for judging the difference between 2 competing models, model 1 was only marginally better than model 7.
When comparing model 7 with the second best-fitting mixed inheritance model of 1 additive MG and a polygenic background (model 6), according to the guidelines proposed by Janss (2008), there was substantial evidence in favor of the mixed inheritance model 7 [model tested: 7 vs. 6; BF (H2; H1) = 3.3]. Definitely, the mixed inheritance models 5 and 8 could be ruled out because they had the worst loge [p(y|Hi)] estimates among the 4 mixed inheritance models. Overall, these results suggest that the inheritance of plasma cortisol might be controlled by 1 or more dominant cortisol-decreasing MG alleles and polygenic background effects in the sampled population.
Evidence of Major Genes Affecting Plasma Cortisol
The estimated marginal posterior mean, PSD, and left and right HPDR95 for variance components and MG parameters of plasma cortisol for all of the evaluated models, with the exception of the polygenic and sporadic models, are presented in Table 4.
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for plasma cortisol is presented in Figure 1. The 
is significant because the HPDR95 for its variance does not include 0 (Table 4). Similarly, the posterior distribution of additive variance attributable to the MG 
and the polygenic variance 
for plasma cortisol (Figure 1) are significant because the HPDR95 for both variances do not include 0 (Table 4). The posterior mean and PSD for the additive effect â are –41.7 ng/mL and 4.8, respectively. The additive effect â in genetic SD units was aGSD = 0.96 ± 0.05, which suggests that this is a relatively large MG with a significant effect. The posterior distribution of â is presented in Figure 2, and it is clearly significant because its HPDR95 does not include 0 (Table 4). Finally, the posterior mean of the dominant cortisol-decreasing allele frequency was 
(Table 4), which is also significant because its HPRD95 does not include 0 (Figure 3).
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Partial dominance can be rejected, because the HPDR95 for the difference between the additive effect and the absolute dominance effect 
covers 0, so complete dominance of the A1 allele can be accepted (data not shown).
In Table 4, we also present results on within- and between-chain variances, the effective number of samples, and the scale reduction factor 
for each estimated scalar parameter within each model evaluated. These results indicate that mixing and convergence of the MCMC iterations are very good for all the mixed inheritance models. However, for the general and general fixed models, we acknowledge that the convergence for several parameters is still problematic. Approximate convergence was reached only for 5 of 13 and 2 of 7 parameters in the general and general fixed models, respectively.
Inference on Transmission Probabilities
For further validation of evidence on MG for plasma cortisol, transmission probabilities were estimated by fitting MG and mixed inheritance models in the BSA (Table 5). For the best-fitting MG model and the best-fitting mixed inheritance model, the left-right bounds of HPDR95 for the first and last transmission probability do not overlap. It is interesting to note that the transmission probabilities resembled Mendelian transmission more closely when fitting a general fixed model 
Under this model, the posterior mean (and PSD) transmission probabilities were 0.98 (0.01), 0.70 (0.28), and 0.05 (0.05), respectively. For this general fixed model, the left-right bounds of HPDR95 for the first and last transmission probabilities clearly do not overlap.
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for the best-fitting MG and best-fitting mixed inheritance models (Table 5). However, approximate convergence of the simulated iterations was reached for only 1 of 3 of the transmission probabilities when fitting the general fixed model (Table 5). Overall, because 2 of the transmission probabilities do not overlap, an environmental hypothesis for the inferred mixture distribution for plasma cortisol can be rejected. In this case, there is proof of a genetic transmission of some kind in the inheritance of plasma cortisol, although it may not be strictly Mendelian. The distortion can be of genetic origin (i.e., the MG may be X-linked), the MG can have multiple alleles, or the true model can be digenic, and this can result in an apparent distortion in the Mendelian transmission when the data are fitted using an autosomal biallelic model. Thus, it can be accepted that a simple autosomal dominant gene is not the most plausible mode of inheritance for plasma cortisol.
Inference on Major Gene Genotypes
The BSA enabled estimation of the posterior probability of major locus genotypes for each pedigree member. Here, we present only the predicted major locus genotypes for parents of each family (Table 6) when using the most plausible mixed inheritance model for plasma cortisol (dominant cortisol-decreasing allele A1 and polygenic effects) from the BSA (Table 3). The predicted major locus genotypes suggested that we had 4 F1 intercross families (18, 58, 60, and 125) and 1 backcross family (126), although the genotype of the dam in family 126 had low accuracy. In the F1 intercross families, siblings with high accuracy for the predicted genotype can be identified and brother-sister can be mated to generate F2 families for mapping QTL for stress response. Based on the inferred likely mode of inheritance of plasma cortisol in the sampled population, it will be most efficient to intercross siblings from the F1 intercross families with homozygous individuals for the cortisol-increasing allele A2 to generate backcross families that can be used in QTL mapping for stress response in this rainbow trout population. We also noticed that there was a significant correlation of the posterior mean of a genotype with the plasma cortisol mean in parents (r = 0.85, P = 0.0001; data not shown). This indicates high correspondence between the plasma cortisol phenotypes of the parents and their predicted major locus genotypes.
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DISCUSSION |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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The results from this study clearly support a familial transmission and evidence of segregating MG for stress response, a potentially economically important trait in rainbow trout. The results from BSA for plasma cortisol provided significant statistical evidence supporting the view that at least 1 MG with a dominant cortisol-decreasing allele and polygenic background effects is likely underlying the genetic variation of stress response in the sampled population.
The estimated magnitude of the MG effect in genetic SD units was aGSD = 0.96 ± 0.05 when assuming a mixed inheritance model of an MG dominant cortisol-decreasing allele and polygenic background effects in BSA (dominant A1 model). These results suggest that there must be genes of relatively large effect for stress response segregating in the sampled population, which might explain approximately 63% of the total stress response variance.
It is clear from these results that the stress response in rainbow trout is hereditary and is influenced by genetic factors transmitted from parents to offspring. The results obtained here indicate that stress response is likely determined by the interplay of one or more dominant cortisol-decreasing MG, a large number of minute-effect additive polygenes, environmental factors, and their interactions. This study also supports the importance of polygenic effects in the genetic variation of stress response in the studied population. The magnitude of the polygenic background effect had an average of 
which is slightly smaller than those previously reported in rainbow trout (Weber et al., 2008).
The implications of poor convergence observed for several parameters estimated with general and general fixed models are minimal for the conclusions drawn in this study. Poor mixing of the MCMC is a potential problem for the fit of MG models; mixing refers to the possibility of the Markov chain moving through the parameter space. For the genotypes, this implies that the chain should be able to make transitions between different genotypic configurations (Janss, 2008). Because multiple chains were run and compared and because the general model was still marginally better than the best-fitting mixed inheritance model 7, lock-up of Gibbs chains in subspaces of the parameter space likely did not occur. Further, the evidence to support significant MG and polygenic effects and variance components was based on analysis of marginal posterior distributions of polygenic and mixed inheritance models that had very good mixing and convergence in the MCMC computations.
The results presented here support a pedigree-based linkage analysis approach for the discovery of the underlying MG or QTL for crowding stress response in rainbow trout and other farm animals that might have similar models of mixed inheritance. There have been few reports of evidence for MG and QTL for stress response as measured by cortisol responsiveness in other animal species. Buitenhuis et al. (2003) detected suggestive QTL for stress response on GGA5 and GGA18 in laying hens. Desautes et al. (2002) reported highly significant gene effects for poststress cortisol concentration and a significant effect for basal cortisol concentration at the end of the q arm of chromosome 7 in pigs. Ousova et al. (2004) proposed that the corticosteroid-binding globulin gene (Cbg) might be the causal gene of a QTL associated with cortisol concentrations, fat deposition, and muscle content in a pig intercross. Solberg et al. (2006) identified 3 significant and 2 suggestive QTL for plasma cortisol response to a 10-min restraint stress when using divergent inbred rat strains for several hypothalamic-pituitary-adrenal axis measures. Kadarmideen and Janss (2007) detected an MG with an additive effect of 86 ng/mL of cortisol in pigs divergently selected for stress response.
Gibbs sampling allows the use of looped pedigrees, the incorporation of many relationships, and the ability to circumvent the intrinsic problems in marginalizing a joint distribution with respect to both discrete and continuous parameters (Hasstedt, 1982). Because of these advantages, Gibbs sampling has also been used in maximum likelihood approaches to segregation analysis (Guo and Thompson, 1992). The Bayesian approach in combination with Gibbs sampling, as used in this study, provides more flexibility and accuracy than a maximum likelihood approach. For instance, in the estimation of means, they are straightforwardly included in the Gibbs chains and treated as nuisance parameters, yielding a REML-type approach by accounting for uncertainty originating from the estimation of these fixed effects (Janss et al., 1997); accounting for such uncertainty removes bias in the estimation of variance components. However, we are aware of the risk of predicting incorrect genetic models when using methods of segregation analysis that are usually not robust to violations of assumptions (Lynch and Walsh, 1997). Ultimately, the molecular approach will allow confirmation or rejection of the presence of a Mendelian locus (Jarvik, 1998).
Although the presence of a clear mode of inheritance will facilitate the genetic dissection of stress response in the rainbow trout, response in terms of plasma concentrations of cortisol is likely affected by several physiological factors, which complicate identification of genes contributing to the phenotype. As an example, our previous studies suggest that poststressor plasma cortisol was not affected by BW or length per se, but was due instead to the association between growth performance and cortisol responsiveness (Weber and Silverstein, 2007). Support for this interpretation comes from the observation that, although BW more than tripled over the 3-mo sampling period in the current study, mean plasma cortisol concentrations did not increase (mo 1 = 65.4, 2 = 50.3, 3 = 53.6, 4 = 59.4 ng/mL). The interpretation that BW per se does not affect poststressor cortisol concentrations was also drawn in studies of European lines of rainbow trout (Pottinger and Carrick, 1999a). Although treating BW and length as covariates may have caused us to misidentify genes that contribute to both stress responsiveness and growth performance in the current study, we chose to use a more simplified model to focus on identifying genes affecting stress response independent of growth characteristics. Once these stress response loci have been identified, we can attempt the complex task of identifying genes associated with the interaction of stress responsiveness and growth performance.
When mixed inheritance of an MG and polygenic background is supported, the investigator may wish to estimate the major locus genotype of particular pedigree members (i.e., QTL genotype of the parents). This is a common problem with studies of complex diseases in humans and livestock species, where pedigrees are gathered on the basis of extreme disease phenotypes. Under a mixed inheritance model, extreme individuals in some families will result from having extreme major locus genotypes, whereas in other families they will result from having extreme polygenic values (Lynch and Walsh, 1997). The information on predicted major-locus genotypes for pedigree members can be used in the design of efficient QTL mapping studies. This information on mode of inheritance of the studied trait and predicted major-locus genotypes can enable the identification of genetic mapping families (e.g., F2 intercross and BC families), and the identification of F1 intercross families from which the siblings can be sister-brother mated to generate large F2 intercross or backcross mapping families. Thus, when attempting to dissect complex traits in outbred populations, we advocate early use of CSA to avoid the pain of realizing later that only a fraction of the families already genotyped on hundreds of markers are indeed informative for QTL mapping.
We are currently generating large F2 intercross families by mating siblings from the F1 intercross families identified in this study. These F2 families will be used in genome-wide linkage scans for QTL affecting stress response in the NCCCWA rainbow trout broodstock. Assembly of these mapping resources provides a tool for eventually elucidating the genetic basis of variation in stress response and identifying QTL to provide more specific markers of possibly distinct stress response genotypes for phenotype association studies, for physiological studies of stress responsiveness, and possibly for selective breeding.
This study is the first of its kind in that no research so far has investigated stress response in rainbow trout by using a crowding stress paradigm to detect evidence of an MG for stress response by using Bayesian methods of CSA. The results from performing CSA support the view that one or more MG dominant cortisol-decreasing alleles and a large number of additive polygenes are likely underlying the genetic variation of plasma cortisol in the sampled rainbow trout families. These findings support a pedigree-based linkage analysis approach (and genome-wide association scans if tools and reagents are available) to the discovery of the underlying MG or QTL for stress response variation in rainbow trout.
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3 Present address: 5601 Sunnyside Ave, Rm 4-2106, Beltsville, MD 20705.
2 Corresponding author: roger.vallejo{at}ars.usda.gov
Received for publication November 5, 2008. Accepted for publication July 6, 2009.
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total major gene variance 
and additive genetic variance attributable to the major gene 
from Bayesian segregation analysis of plasma cortisol in rainbow trout broodstock. A mixed inheritance model of a major locus with a dominant cortisol-decreasing allele A1 and polygenic effects was used in the Bayesian segregation analysis with the computer program iBay, version 1.44 (Janss, 2008
