Accounting for variability among individual pigs in deterministic growth models

Abstract

Inclusion of variation in deterministic nutritional models for growth by repeating simulations using different sets of parameters has been performed in literature without or with only hypothetic consideration of the covariance structure among parameters. However, a description of the structure of links among parameters describing individuals is required to generate realistic sets of parameters. In this study, the mean and covariance structure of model parameters describing feed intake and growth were analyzed from 10 batches of crossbred gilts and barrows. Data were obtained from different crossbreeds, originating from Large White × Landrace sows and nine sire lines. Pigs were group-housed (12 pigs/pen) and performance testing was carried out from 70 days of age to ∼110 kg BW. Daily feed intake (DFI) was recorded using automatic feeding stations and BW was measured at least every 3 weeks. A growth model was used to characterize individual pigs based on the observed DFI and BW. In this model, a Gompertz function was used to describe protein deposition and the resulting BW gain. A gamma function (expressing DFI as multiples of maintenance) was used to express the relationship between DFI and BW. Each pig was characterized through a set of five parameters: BW70 (BW at 70 days of age), BGompertz (a precocity parameter) PDm (mean protein deposition rate) and DFI50 and DFI100 (DFI at 50 and 100 kg BW, respectively). The data set included profiles for 1288 pigs for which no eating or growth disorders were observed (e.g. because of disease). All parameters were affected by sex (except for BW70) and batch, but not by the crossbreed (except for PDm). An interaction between sex and crossbreed was observed for PDm (P < 0.01) and DFI100 (P = 0.05). Different covariance matrices were computed according to the batch, sex, crossbreed, or their combinations, and the similarity of matrices was evaluated using the Flury hierarchy. As covariance matrices were all different, the unit of covariance (subpopulation) corresponded to the combination of batch, sex and crossbreed. Two generic covariance matrices were compared afterwards, with (median matrix) or without (raw matrix) taking into account the size of subpopulations. The most accurate estimation of observed covariance was obtained with the median covariance matrix. The median covariance matrix can be used, in combination with average parameters obtained on-farm, to generate virtual populations of pigs that account for a realistic description of mean performances and their variability.