Modelling the probability of microhabitat formation on trees using cross‐sectional data

Context: Tree-related microhabitats (TreMs), such as trunk cavities, peeled bark, cracks or sporophores of lignicolous fungi, are essential to support forest biodiversity because they are used as substrate, foraging, roosting or breeding places by bryophytes, fungi, invertebrates and vertebrates. Biodiversity conservation requires the continuous presence of TreMs in a forest. However, little is known about their dynamics. Moreover, we usually have only cross-sectional TreM data (observations of many trees at a single time), making it difficult to estimate TreM formation rates. Method: This study adapted the methods of survival and reliability analysis to model the rate of TreM formation per unit of diameter increment as a function of tree diameter at breast height (DBH). We tested three variants of this model: the TreM formation rate independent of, proportional to or increasing nonlinearly with DBH. We calculated the likelihood of the models, considering cross-sectional observations either of TreM presence/absence or TreM number on trees of different sizes. We calibrated the models in six subnatural montane forests dominated by European beech (Fagus sylvatica) and silver fir (Abies alba) - in the French Pyrenees. Assuming an annual DBH increment value, the annual formation rate of TreMs was predicted both at the level of the tree and at the level of the forest stand. Results: This method provides a coherent framework to model the probability that a TreM forms on a tree during a unit growth step and produces realistic predictions of TreM accumulation on trees. TreM formation accelerated as trees grew for A. alba but not for F. sylvatica. The TreM formation rate was twice as fast on F. sylvatica as on A. alba. We estimated a formation of 0.82-1.28 TreMs/ha per year and 0.5-0.9 TreM-bearing trees/ha per year in the subnatural forests studied. Synthesis and applications: This method makes rigorous modelling of the formation of TreMs possible during the growth of trees and forest stands. The quantitative evaluation of TreM fluxes will help to design forest biodiversity conservation strategies favouring the development and temporal continuity of TreMs.