Uncovering genetic information from commercial forest plantations—making up for lost time using “Breeding without Breeding”

Abstract

An application of “Breeding without Breeding” (BwB) is proposed to uncover or extract genetic information from existing plantations, using pedigree reconstruction and BLUP to predict breeding values and identify genetically superior individuals. The focus is on the use of the methodology at the initiation of an operational breeding program to circumvent the first cycle of breeding and testing, but it could also have application in more advanced tree improvement programs. A simulation study was done to examine different sizes of three conceptual populations used in the BwB approach, and to compare the genetic gains achieved using that approach with those that would have been achieved with a full-sib breeding and testing strategy if it had been started years before. The BwB approach is based on pedigree reconstruction with a relatively small number of trees (from 1,200 to 3,600), comprised of a randomly selected sub-population of size N _R = 600 to 3,000, and a top-phenotype sub-population of size N _T = 600 (pre-selected out of 5,940 to 23,760 trees on the basis of phenotype alone). With the reconstructed pedigree, a combined REML/BLUP analysis of phenotypic data is done to predict breeding values, and a linear optimization is done to make the final selections to maximize gain while constraining relatedness to a given effective population size N _e = 5, 10, or 20. Results indicate that the BwB strategy can achieve substantial levels of genetic gain, equivalent to 80 to 98 % of the gain that could have been achieved using a full-sib strategy.

Appendix: accuracy of prediction (r â,a) for phenotypic, within-family, and mid-parent + within-family selection

• 1. Define a = f + w

  where a = overall genetic value, f = midparent genetic value, and w = within-family genetic value, and Var (a) = σ ² _A , Var $(f)=1/2{\sigma}_A^2$, and Var $(w)=1/2{\sigma}_A^2$

• 2. Define â = $\widehat{f}$ + ŵ

  where â = predicted genetic value, $\widehat{f}$ = predicted mid-parent genetic value, and ŵ = predicted within-family genetic value.

• 3. The accuracy of prediction is defined as

  $$ {r}_{\widehat{\mathrm{a}},\mathrm{a}}={\left[Var\left(\widehat{a}\right)/Var(a)\right]}^{1/2} $$

• 4. For mass selection based on phenotypic value y,

  $$ \widehat{a}={h}^2S, $$

  where h ² = heritability = Var(a) / Var(y), and S = phenotypic deviation of y, and accuracy of prediction = [Var(â) / Var(a)]^1/2 = h (Falconer 1981; Hodge and White 1992). So if h ² = 0.15, then r _â,a = 0.39.

• 5. Assuming infinite testing (number of tests, number of crosses, number of progeny), then mid-parent genetic values f will be predicted without error, that is, accuracy of prediction = 1.00. ${r}_{\widehat{f},f}=1.00={\left[Var\left(\widehat{f}\right)/Var(f)\right]}^{1/2},$therefore Var($\widehat{f}$) = Var(f) = $1/2{\sigma}_A^2$

• 6, For within full-sib family selection based on within full-sib family phenotypic deviation S _w ,

  $$ \widehat{w}={h}_w^2{S}_w, $$

  where h ² _w  = within-family heritability = $1/2{\sigma}_A^2$ / [Var(y) − $1/2{\sigma}_A^2$].

  If h ² = 0.15, h ² _w  = 0.075 / [1.00–0.075] = 0.081. As above, accuracy of prediction equals the square root of the heritability, so accuracy of prediction = h _w  = [Var(ŵ)/Var(w)]^1/2

  $$ \begin{array}{c}\hfill \mathrm{V}\mathrm{a}\mathrm{r}\left(\widehat{w}\right)={h}_w^2\;\mathrm{V}\mathrm{a}\mathrm{r}(w)\hfill \\ {}\hfill =0.081\ 1/2{\sigma}_A^2\hfill \\ {}\hfill =0.0405{\sigma}_A^2\hfill \end{array} $$

• 7, Now assume offspring selection (equivalent to mid-parent selection + within-family selection), with h ² = 0.15, and with infinite progeny testing.

  $$ \begin{array}{l}\widehat{a}=\widehat{f}+\widehat{w}\\ {}\begin{array}{c}\hfill \mathrm{V}\mathrm{a}\mathrm{r}\left(\widehat{a}\right)=\mathrm{V}\mathrm{a}\mathrm{r}\left(\widehat{f}\right)+\mathrm{V}\mathrm{a}\mathrm{r}\left(\widehat{w}\right)\hfill \\ {}\hfill =1/2{\sigma}_A^2+0.0405{\sigma}_A^2\hfill \\ {}\hfill =0.5405{\sigma}_A^2\hfill \end{array}\end{array} $$

  The accuracy of selection would then be

  $$ \begin{array}{c}\hfill {r}_{\widehat{\mathrm{a}},\mathrm{a}}=\left[\mathrm{V}\mathrm{a}\mathrm{r}\left(\widehat{a}\right)/\mathrm{V}\mathrm{a}\mathrm{r}{(a)}^{1/2}\right]\hfill \\ {}\hfill =\left[0.5405{\sigma}_A^2/{\sigma}_A^2\right]\hfill \\ {}\hfill =0.7352\hfill \end{array} $$

• 8, Thus, with h ² = 0.15, the theoretical maximum accuracy of prediction for offspring selection from full-sib families (mid-parent selection + within-family selection) is r _â,a = 0.7352.