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Table 2 Genetic parameters and genetic correlations (±their approximate standard error) between intercept and slope obtained from the random regression models for daily growth coefficient (DGC) when the intercept was placed either in the low or high temperature environment

From: Thermal sensitivity of growth indicates heritable variation in 1-year-old rainbow trout (Oncorhynchus mykiss)

Parameter

Intercept environment

LowT

HighT

\(\widehat{\sigma }_{{a, {\text{int}}}}^{2}\)

0.190 (0.063)

0.130 (0.043)

\(\widehat{\sigma }_{{e, {\text{int}}}}^{2}\)

0.221 (0.041)

0.156 (0.028)

\(\widehat{\sigma }_{{a, {\text{sl}}}}^{2}\)

0.005 (0.002)

0.005 (0.002)

\(\widehat{\sigma }_{{P, {\text{Total}}}}^{2}\)

0.354

0.354

\(h_{\text{int}}^{2}\)

0.463 (0.123)

0.455 (0.120)

\(h_{\text{TS}}^{2}\)

0.244

0.244

Co-heritability of TS

−0.284 (0.124)

0.197 (0.141)

\(r_{{{\text{G}}({\text{int}},{\text{sl}})}}\)

−0.643* (0.147)

0.376 (0.214)

  1. \(\widehat{\sigma }_{{a, {\text{int}}}}^{2}\) = genetic variance of DGC at the intercept point; \(\widehat{\sigma }_{{e, {\text{int}}}}^{2}\) = residual variance of DGC at the intercept point; \(\widehat{\sigma }_{{a, {\text{sl}}}}^{2}\) = genetic variance of the reaction norm slope; \(\widehat{\sigma }_{{P, {\text{Total}}}}^{2}\) = total phenotypic variance of DGC across environments; \(h_{\text{int}}^{2}\) = heritability of DGC at the intercept \((\widehat{\sigma }_{{a, {\text{int}}}}^{2} /\widehat{\sigma }_{{P, {\text{int}}}}^{2} )\), where \(\widehat{\sigma }_{{P, {\text{int}}}}^{2}\) is the phenotypic variance of DGC; co-heritability of TS \(\left( {\frac{{6\widehat{\sigma }_{{a, {\text{int}}, {\text{sl}}}} }}{{\widehat{\sigma }_{{a, {\text{int}}}}^{2} + \widehat{\sigma }_{{e, {\text{int}}}}^{2} }}} \right)\), where \(\widehat{\sigma }_{{a, {\text{int}}, {\text{sl}}}}\) is the additive genetic covariance between the intercept and slope
  2. \(h_{\text{TS}}^{2}\) = heritability of the slope \(\left( {\frac{{\widehat{\sigma }_{{a, {\text{sl}}}}^{2} \times \widehat{\sigma }_{a, X}^{2} }}{{\widehat{\sigma }_{{P, {\text{Total}}}}^{2} }}} \right)\), where \(\widehat{\sigma }_{{a, {\text{sl}}}}^{2} \times \widehat{\sigma }_{a, X}^{2}\) is the additive genetic variance of the slope multiplied by the variance of environmental values \(X\), respectively; \(r_{{{\text{G}}({\text{int}}, {\text{sl}})}}\) = genetic correlation between the intercept and slope \(\left( {\frac{{\widehat{\sigma }_{{a_{{{\text{int}}, {\text{sl}}}} }} }}{{\sqrt {\widehat{\sigma }_{{a, {\text{int}}}}^{2} \times \widehat{\sigma }_{{a, {\text{sl}}}}^{2} } }}} \right)\)
  3. * Estimate that is significantly different from 0 (95% CI does not include zero)
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Genetics Selection Evolution

ISSN: 1297-9686