Mating crosses of white pine trees

data("hanover.whitepine")

Format

A data frame with 112 observations on the following 4 variables.

rep: replicate
female: female parent
male: male parent
length: epicotyl length, cm

Details

Four male (pollen parent) White Pine trees were mated to seven female trees and 2654 progeny were grown in four replications, one plot per mating in each replication. Parent trees were sourced from Idaho, USA. The data are plot means of epicotyl length.

Becker (1984) used these data to demonstrate the calculation of heritability.

Source

Hanover, James W and Barnes, Burton V. (1962). Heritability of height growth in year-old western white pine. Proc Forest Genet Workshop. 22, 71--76.

Walter A. Becker (1984). Manual of Quantitative Genetics, 4th ed. Page 83.

References

None

Examples

# \dontrun{
  
  library(agridat)
  data(hanover.whitepine)
  dat <- hanover.whitepine

  libs(lattice)
  # Relatively high male-female interaction in growth comared
  # to additive gene action. Response is more consistent within
  # male progeny than female progeny.
  # with(dat, interaction.plot(female, male, length))
  # with(dat, interaction.plot(male, female, length))
  bwplot(length ~ male|female, data=dat,
         main="hanover.whitepine - length for male:female crosses",
         xlab="Male parent", ylab="Epicotyl length")
  
  # Progeny sums match Becker p 83
  sum(dat$length) # 380.58
#> [1] 380.58
  aggregate(length ~  female + male, data=dat, FUN=sum)
#>    female male length
#> 1    F193  M17  15.87
#> 2    F195  M17  14.49
#> 3    F197  M17  18.89
#> 4    F201  M17  11.93
#> 5    F203  M17  16.61
#> 6    F204  M17  12.82
#> 7    F208  M17  15.91
#> 8    F193  M19  12.49
#> 9    F195  M19  10.95
#> 10   F197  M19  10.39
#> 11   F201  M19  11.02
#> 12   F203  M19  15.90
#> 13   F204  M19   9.94
#> 14   F208  M19  10.78
#> 15   F193  M22  16.94
#> 16   F195  M22  12.80
#> 17   F197  M22  14.06
#> 18   F201  M22  15.01
#> 19   F203  M22  12.92
#> 20   F204  M22  13.65
#> 21   F208  M22  14.58
#> 22   F193  M58  14.52
#> 23   F195  M58  14.28
#> 24   F197  M58  13.94
#> 25   F201  M58  12.41
#> 26   F203  M58  11.63
#> 27   F204  M58  11.78
#> 28   F208  M58  14.07
  
  # Sum of squares matches Becker p 85
  m1 <- aov(length ~ rep + male + female + male:female, data=dat)
  anova(m1)
#> Analysis of Variance Table
#> 
#> Response: length
#>             Df  Sum Sq Mean Sq F value    Pr(>F)    
#> rep          3  1.8218  0.6073  3.0299   0.03406 *  
#> male         3 12.3538  4.1179 20.5460 5.393e-10 ***
#> female       6  6.4977  1.0829  5.4032 9.740e-05 ***
#> male:female 18 13.4609  0.7478  3.7312 2.266e-05 ***
#> Residuals   81 16.2344  0.2004                      
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
  
  # Variance components match Becker p. 85
  libs(lme4)
  libs(lucid)
  m2 <- lmer(length ~ (1|rep) + (1|male) + (1|female) + (1|male:female), data=dat)
  #as.data.frame(lme4::VarCorr(m2))
  vc(m2)
#>          grp        var1 var2    vcov  sdcor
#>  male:female (Intercept) <NA> 0.1369  0.3699
#>       female (Intercept) <NA> 0.02094 0.1447
#>         male (Intercept) <NA> 0.1204  0.3469
#>          rep (Intercept) <NA> 0.01453 0.1205
#>     Residual        <NA> <NA> 0.2004  0.4477
  ##         grp        var1 var2    vcov  sdcor
  ## male:female (Intercept) <NA> 0.1369  0.3699
  ##      female (Intercept) <NA> 0.02094 0.1447
  ##        male (Intercept) <NA> 0.1204  0.3469
  ##         rep (Intercept) <NA> 0.01453 0.1205
  ##    Residual        <NA> <NA> 0.2004  0.4477
  
  # Becker used this value for variability between individuals, within plot
  s2w <- 1.109
  
  # Calculating heritability for individual trees
  s2m <- .120
  s2f <- .0209
  s2mf <- .137
  vp <- s2m + s2f + s2mf + s2w  # variability of phenotypes = 1.3869
  4*s2m / vp # heritability male 0.346
#> [1] 0.3460956
  4*s2f / vp # heritability female 0.06
#> [1] 0.06027832
  2*(s2m+s2f)/vp # heritability male+female .203
#> [1] 0.203187
  # As shown in the boxplot, heritability is stronger through the
  # males than through the females.
# }