Estimating long-term tree mortality rate time series by combining data from periodic inventories and harvest reports in a Bayesian state-space model

Tree mortality is a complex process that exhibits great spatio-temporal variability. Long term mortality data is needed to understand this demographic parameter and how it is related to biotic, climatic, and anthropogenic disturbances. Here, we propose a Bayesian state-space model to estimate tree mortality time series in managed forests, where tree mortality is expressed as the annual proportion of the dead volume over the growing stock volume in a forest stand (subsequently, volume mortality rate). We argue that the volume mortality rate is an informative measure of tree mortality; and our simulations and field data suggests that the volume mortality rate is a good proxy of the demographic sense annual mortality rate (i.e. based on the number of trees), though the quality of the approximation depends on the particular management scheme. The proposed Bayesian state-space model combines two types of data: annual dead volumes from harvest reports and total growing stock volumes from periodic inventories. We illustrate the performance of the Bayesian state-space model using data simulated with an individual based and spatially explicit forest dynamic model (Samsara2). Then, we apply the Bayesian state-space model to field data from four forests in the French Alps and recover, unprecedented, century long, time series of annual volume mortality rate at the scale of a forest stand (10. ha) within each forest. We advocate the use of forest management data for future research, since temperate forests are managed in many countries since decades, thus many other unexploited data sets must exist.