Applying survival analysis to managed even-aged stands of ponderosa pine for assessment of tree mortality in the western United States

A critical component of a growth and yield simulator is an estimate of mortality rates. The mortality models presented here are developed from long-term permanent plots in provinces from throughout the geographic range of ponderosa pine in the United States extending from the Black Hills of South Dakota to the Pacific Coast. The study had two objectives: estimation of the probability of a tree survival for the next 5 years and the probability of a tree surviving longer than a given time period (survival trend) for a given set of covariates. The probability of a tree surviving for the next 5 years was estimated using a logistic model regressed on 18 covariates measured 5 years before the last measurement period with 15 smoothing variables (S1–S15) for spatial effects of latitude and longitude surface. The fitted model showed that the probability of survival increased with increasing diameter at breast height (DBH), DBH periodic annual increment (PAIDBH) and increasing plot basal area/number of trees per hectare (PBAH/TPH), and decreased with increasing average of the 5 tallest trees in the plot (AVGHT5) when other selected covariates were included in the model. The probability of a tree surviving longer than a given time period was estimated by fitting the Cox Proportional Hazard model to the last observed survival period regressed on 13 covariates measured at the first measurement period. This probability also increased with increasing DBH and PAIDBH, and decreased with increasing AVGHT5. The Akaike’s Information Criterion (AIC) and graphs of partial residuals were used in the selection of covariates included in the models.

► Two individual tree survival models for ponderosa pine: Logistic and Cox PH models.
► Logistic used spatial smoothing splines for probability of surviving the next five years.
► Cox model estimated the probability of surviving longer than a given time period.
► Survival increased with increasing DBH and PAIDBH and decreased with increasing AVGHT5.
► The models were validated and assessed for goodness of fit.