Development of a structural growth curve model that considers the causal effect of initial phenotypes

Growth curves have been widely used in genetic analyses to gain insights into the growth characteristics of both animals and plants. However, several questions remain unanswered, including how the initial phenotypes affect growth and what is the duration of any such impact. For beef cattle production in Japan, calves are procured from farms that specialize in reproduction and then moved to other farms where they are fattened to achieve their market/purchase value. However, the causal effect of growth, while calves are on the reproductive farms, on their growth during fattening remains unclear. To investigate this, we developed a model that combines a structural equation with a growth curve model. The causal effect was modeled with B-splines, which allows inference of the effect as a curve. We fitted the proposed structural growth curve model to repeated measures of body weight from a Japanese beef cattle population (n = 3831) to estimate the curve of the causal effect of the calves' initial weight on their trajectory of growth when they are on fattening farms.

Maternal and reproduction farm effects explained 26% of the phenotypic variance of initial weight at fattening farms. The structural growth curve model was fitted to remove the effects of these factors in growth curve analysis at fattening farms. The estimated curve of causal effects remained at approximately 0.8 for 200 d after the calves entered the fattening farms, which means that 64% of the phenotypic variance was explained by the initial weight. Then, the effect decreased linearly and disappeared approximately 620 d after entering the fattening farms, which corresponded to an average age of 871.5 d.

The proposed model is expected to provide more accurate estimates of genetic values for growth patterns because the confounding causal factors such as maternal and reproduction farm effects are removed. Moreover, examination of the inferred curve of the causal effect enabled us to estimate the effect of a calf's initial weight at arbitrary times during growth, which could provide suitable information for decision-making when shifting the time of slaughter, building models for genetic evaluation, and selecting calves for market.