Derivation of steady state herd productivity using stage-structured population models and mathematical programming

Assessing production efficiency in livestock herds requires the consideration of the effects of herd structure and dynamics on the calculation of efficiency measures. Steady state herd growth models can accommodate for these effects by considering sustained self-recruiting herds, in which herd size and structure are maintained in an equilibrium state over time. Previously published approaches to steady state herd productivity assessment share a number of limitations, e.g., individual animals are classified by their age only; vital parameters such as fecundity, litter size, milk yield, liveweight and liveweight gain are assumed to remain constant throughout the productive lifespan; and the corresponding computer programs lack the capability of choosing the optimal combination of offtake rates across animal classes that leads to a steady state in herd size and structure. In order to refine the concept of steady state herd productivity assessment and improve its flexibility and applicability, a new method of modelling herd dynamics over time and of deriving optimal steady state herd structure and offtake is presented. Herd dynamics are described through a deterministic, stage-structured matrix population model. Stage-structured matrix population models can be generalized to complex life cycles in which individual animals can be classified by several factors other than age. Translating the population dynamics model into a standard non-linear programming problem allows to derive the optimum offtake policy in each stage class. The proposed approach is very general and can easily be applied to a wide range of domestic livestock species and production systems. Combining stage-structured matrix population models with non-linear programming for the determination of optimal steady state herd structure and culling policy removes most limitations of previously published procedures for steady state herd productivity assessment. It is emphasized that the derivation of an optimal culling regime is crucial in comparative studies, in order to obtain a common basis on which alternatives can be compared in terms of a defined production efficiency measure. Biased comparisons may be obtained when using observed or estimated offtake rates for a given management alternative or production system. The reason is that the actual level of productivity achievable under a given management practice is not necessarily identical with the potential productivity achieved when optimal offtake decisions are taken. The choice of culling policy has a great impact on herd dynamics and structure, and needs to be controlled for in comparative assessments.