Modelling of discontinuous relationships in biology with censored regression

Discontinuous relationships between variables are common in biological data. Discontinuities can sometimes give the appearance of curvilinearity, which suggests the data should be analyzed with nonlinear models. Here we show that often a more meaningful analysis can be obtained with censored regression techniques. In a censoring model all points below (or above) a certain threshold are observed only by the value of the threshold (e.g., a baseline temperature). We illustrate the method with an example from plant reproductive biology: plant reproductive mass is never negative but becomes positive only after some ''capacity'' to flower reaches a threshold. The vegetative mass at which the threshold is reached and the relationship between reproductive mass and vegetative mass above the threshold are estimated from data. Using censored regression with real and simulated data shows that apparent curvilinearity suggested by models that do not account for censoring can be an artifact.