Quantifying the effects of drought and insect outbreaks on tree mortality rates using imperfect data

Background/Question/Methods

Tree mortality rates may increase in the future due to global-change-type drought, which may affect mortality rates directly and/or make trees more susceptible to insect outbreaks and other biotic mortality agents. Anecdotal evidence suggests that these changes are already underway. However, there is little quantitative understanding of how drought, insects, and other environmental drivers affect tree mortality rates. These quantitative relationships are critical both for understanding observed patterns in tree mortality rates, and for testing and improving terrestrial carbon cycle models that are used to project the future state of the Earth system. The availability of national-level systematic forest inventories and remote-sensing products are both increasing, and these data should allow relationships between tree mortality rates and environmental drivers to be quantified. However, errors in environmental driver variables (e.g., uncertainty in meteorological history and the spatial-temporal distribution of insect outbreaks) introduce bias into statistical analyses that ignore these errors. In most cases, driver errors bias statistical models towards detecting weaker effects than those that occur in reality. Similarly, model-data fusion (“data-assimilation”) with carbon cycle models is biased in the presence of driver errors. I used computer simulations to (1) demonstrate the biases that result when errors in climate and insect-outbreak data are ignored; and (2) explore potential solutions to this problem.

Results/Conclusions

For a variety of non-linear statistical models, driver errors cause the estimated effects of climate anomalies and insect outbreaks on tree mortality rates to be weaker than the true effects if driver errors are ignored. The problem is particularly severe if there are interactions between drought and insect outbreaks. Analytical Measurement Error Models are an effective and computationally cheap solution to the driver-errors problem, but are only appropriate for cases that are linear-in-parameters with normal error structures. Bayesian hierarchical models (BHMs), in which driver variables are assumed to be random samples from a probability distribution, are also an effective solution, and have no restrictions in terms of functional forms. However, BHMs are computationally expensive, and are therefore inconvenient for data exploration. Finally, if driver errors can be minimized by data-aggregation (e.g., if climate errors are large at the scale of individual forest inventory plots, but small at the scale of 1-degree grid cells), and if effects of drivers on mortality rates are linear at the scale of aggregation, then standard statistical methods are unbiased when applied to aggregated data.