Modeling the response of tree mortality rates to climate anomalies using non-randomly sampled data that targets unusual mortality events

Background/Question/Methods

Tree mortality rates are principal drivers of the forest carbon cycle and are expected to increase in many regions of the world due to global-change-type drought. Numerous published studies document apparently-drought-induced tree mortality events and associated climate anomalies. These studies provide a wealth of information that could be harnessed to model the responses of mortality rates to climate change and extreme weather conditions. However, quantitative analyses based on mortality events described in the literature pose special challenges, due to potential reporting biases (the tendency for unusual mortality events to be reported in the literature) and sampling biases (the tendency for unusual mortality events to be studied). We derived a maximum likelihood estimator for parameters linking tree mortality rates to climate anomalies (e.g., drought events) using data collected with non-random, “event-based” sampling that preferentially targets times/places with unusually high mortality rates. Here we report results of a computer simulation study designed to test the method. Our test involves: (1) generating artificial data, with noise, assuming a predefined relationship between mortality rate and annual precipitation anomaly; (2) applying the event-based statistical method to simulated data sets representing different sampling strategies (i.e., different proportions of event-based vs. randomly sampled data) and different sample sizes; and (3) comparing the estimated parameter values with the true values.

Results/Conclusions

For all sampling strategies (ranging from 0 to 100% randomly sampled data, as opposed to event-based data), our event-based statistical method was unbiased in that the 95% confidence intervals on the parameter estimates included the true parameter values in about 95% of trials. That is, the event-based method yields unbiased results whether applied to event-based or randomly sampled data. If the starting values in the parameter estimation algorithm were far from the true values, then the event-based approach was robust only if the sampling strategy included at least some randomly sampled data. In practice, this is not an important limitation of the method, because some randomly sampled data (or at least data not targeted at known mortality events) would be available in most applications.  Our results show that published literature on drought-induced mortality, even if it collected with a biased sampling strategy, can be combined with systematic forest inventory data in a quantitative framework to estimate unbiased relationships between tree mortality rates and climate anomalies.