Records of matings and of phenotypic variables were kept in a pedigree of the shrimp Penaeus vannamei. The variables recorded were as shown in Table 9.10, and the first and last few rows of the spreadsheet holding the data are presented in Table 9.11: the full data set is held in the file ‘shrimp pedigree.xls’ (www.wiley.com/go/mixed modelling). (Data reproduced by kind permission of Dr Shaun Moss, Director, Shrimp Department, Oceani Institute, Hawaii, USA.) The variable of economic interest is the weekly growth rate.

(a) Consider whether any of the variables studied should be modelled as fixedeffect terms when estimating the genetic and residual components of variance of the weekly growth rate.

(b) Fit a mixed model to the data, taking account of the pedigree structure. Obtain estimates of the genetic and residual components, and estimate the heritability of the weekly growth rate. 330 Beyond mixed modelling Table 9.10 Variables recorded in a pedigree of the shrimp Penaeus vannamei. Name of variable Description Kid identifier of the shrimp Ksire identifier of the male parent Kdam identifier of the female parent SEX M = male; F = female F coefficient of inbreeding, relative to the founders of the pedigree WeekGro weekly growth rate, post-larva to harvest, (grams) Brood brood identifier, useful for the recognition of maternal effects when a female had more than one brood of full-sibs CGU contemporaneous group seq a database reference DD degree days accumulated during the growth period; this will be the same for all members of a brood and contemporaneous group Table 9.11 Pedigree and phenotype data from shrimps of the species Penaeus vannamei. A B C D E F G H I J 1 Kid Ksire Kdam SEX F WeekGro Brood CGU seq DD 2 17 1 6 M 5120 3 18 2 7 M 5121 4 19 3 9 M 5122 5 28 4 10 M 5473 . . . . . . 268 68533 63411 10166 M 0.02 1.52 101723411 34 22904 972 269 68547 63411 10166 F 0.02 1.22 101723411 34 22917 972 270 68571 63411 10166 F 0.02 1.72 101723411 34 22939 972 271 69500 11966 63406 M 0.03 1.54 634071966 34 25533 972 272 69528 11966 63406 F 0.03 1.45 634071966 34 25559 972 273 69545 11966 63406 F 0.03 1.43 634071966 34 25574 972 274 69676 11966 63391 M 0.02 1.29 633921966 34 25691 972 275 69712 11966 63391 F 0.02 1.38 633921966 34 25724 972 276 69718 11966 63391 F 0.02 1.41 633921966 34 25730 972

(c) Compare graphically the phenotypic value of the weekly growth rate for each individual and the estimated genetic effect on this variable.