A flexible sigmoidal model relating crop yield to weed relative leaf cover and its comparison with nested models

Abstract

A flexible sigmoidal model relating crop yield to relative leaf cover of weed was derived. The model was shown to embody a hyperbolic, a symmetric sigmoidal and an asymmetric logistic model as special cases. Data from field experiments conducted in 1996 and 1997 on maize in competition with various weed infestation conditions were used to validate the model. A high accuracy was observed for yield description, and the four parameters of the model were estimated easily using a non‐linear regression procedure. When compared with other (nested and restricted) models, a better fit of the data was obtained than with the symmetric sigmoidal and the asymmetric logistic models. Rejection of the null hypothesis of hyperbolic yield response was observed in only 1 out of 16 cases, meaning that both the hyperbolic and the flexible sigmoidal models have comparable yield‐descriptive capacities. The increased complexity because of the extra (fourth) parameter in the flexible sigmoidal model may favour the use of the hyperbolic model by most investigators. Failure of the sigmoidal model to outperform the hyperbolic model was primarily due to the weak sigmoidal yield response (sigmoidal response parameter δ close to unity) and the relatively small sample sizes. However, when the model is to be embedded in a decision‐support computer program, larger sample sizes are required and the flexible sigmoidal model may be more appropriate in such situations. The high flexibility of the model may allow the detection of special cases, and thus minimize the risk of a wrong decision.