Decision errors in evaluating tipping points for ecosystem resilience

When an ecosystem reaches tipping points for selected indicators, resilience to further changes in external drivers can decrease, regime shifts can occur that diminish the capacity of the ecosystem to provide ecosystem services, and the ecosystem is more vulnerable to collapse. Evaluating tipping points for resilience using crisp decision rules can result in decision errors about whether or not resilience has been compromised. The source and nature of those errors are described and a fuzzy decision rule is proposed for evaluating resilience. Decision errors are evaluated for four cases. Cases 1 through 3 (or case 4) derive conditions for evaluating decision errors when there is a single (or multiple) indicator(s). The primary sources of decision errors for the four cases are discrepancies between measured (or established) and true values of the indicators (or tipping points) and using a crisp decision rule to reach conclusions about whether or not resilience has been compromised. A fuzzy decision rule, based on fuzzy TOPSIS, is proposed that evaluates the extent to which an ecosystem is resilient. Although crisp decision rules provide unambiguous conclusions about resilience, those conclusions can be faulty, particularly when measured indicators and established tipping points deviate substantially from their true values. In contrast, the conclusions from the fuzzy decision rule are less susceptible to the decision errors and, hence, faulty decisions.