title: Interpreting experimental data on egg production--applications of dynamic differential equations.
abstract: This contribution focuses on applying mathematical models based on systems of ordinary first-order differential equations to synthesize and interpret data from egg production experiments. Models based on linear systems of differential equations are contrasted with those based on nonlinear systems. Regression equations arising from analytical solutions to linear compartmental schemes are considered as candidate functions for describing egg production curves, together with aspects of parameter estimation. Extant candidate functions are reviewed, a role for growth functions such as the Gompertz equation suggested, and a function based on a simple new model outlined. Structurally, the new model comprises a single pool with an inflow and an outflow. Compartmental simulation models based on nonlinear systems of differential equations, and thus requiring numerical solution, are next discussed, and aspects of parameter estimation considered. This type of model is illustrated in relation to development and evaluation of a dynamic model of calcium and phosphorus flows in layers. The model consists of 8 state variables representing calcium and phosphorus pools in the crop, stomachs, plasma, and bone. The flow equations are described by Michaelis-Menten or mass action forms. Experiments that measure Ca and P uptake in layers fed different calcium concentrations during shell-forming days are used to evaluate the model. In addition to providing a useful management tool, such a simulation model also provides a means to evaluate feeding strategies aimed at reducing excretion of potential pollutants in poultry manure to the environment.
authors: Centre for Nutrition Modelling, Department of Animal and Poultry Science, University of Guelph, Guelph, ON, N1G 2W1, Canada. jfrance@uoguelph.ca
authors: J
authors: J
authors: France
authors: S
authors: S
authors: Lopez
authors: E
authors: E
authors: Kebreab
authors: J
authors: J
authors: Dijkstra
mesh_terms: D000822:Animal Husbandry; D000818:Animals; D002118:Calcium / Q000008:administration & dosage / Q000378:metabolism; D003198:Computer Simulation; D005260:Female; D008954:Models, Biological; D010063:Ovum / Q000502:physiology*; D010758:Phosphorus / Q000008:administration & dosage / Q000378:metabolism; D011200:Poultry / Q000502:physiology*; D012098:Reproduction; D012107:Research Design
chemical_list: D010758:Phosphorus; D002118:Calcium