Biases in the estimation of size-dependent mortality models: advantages of a semiparametric approach

Abstract

Mortality rate is thought to show a U-shape relationship to tree size. This shape could result from a decrease of competition-related mortality as diameter increases, followed by an increase of senescence and disturbance-related mortality for large trees. Modeling mortality rate as a function of diameter is nevertheless difficult, first because this relationship is strongly nonlinear, and second because data can be unbalanced, with few observations for large trees. Parametric functions, which are inflexible and sensitive to the distribution of observations, tend to introduce biases in mortality rate estimates. In this study we use mortality data for Abies alba Mill. and Picea abies (L.) Karst. to demonstrate that mortality rate estimates for extreme diameters were biased when using classical parametric functions. We then propose a semiparametric approach allowing a more flexible relationship between mortality and diameter. We show that the relatively shade-tolerant A. alba has a lower annual mortality rate (2.75%) than P. abies (3.78%) for small trees (DBH <15 cm). Picea abies, supposedly more sensitive to bark beetle attacks and windthrows, had a higher mortality rate (up to 0.46%) than A. alba (up to 0.30%) for large trees (DBH ≥50 cm).