Combining time trends in multiple metrics for identifying persistent changes in population processes or environmental stressors.
Metrics have become a standard way for summarizing environmental monitoring results. Different metrics react differently to natural variations and human-induced stressors. We suggest that combined analysis of time trends in selected biological metrics allows identification of biological processes (e.g. individual growth, mortality or recruitment) that have changed (increased or decreased) persistently. Alternatively, time trends in the abundance of sensitive species could indicate changes in environmental stressors. We calculate the joint likelihood of time trends in three metrics and use it to evaluate the evidence in the data for different combinations of metric time trends. A simulation study provides guidelines for interpreting log-likelihood differences. We illustrate the approach for identifying biological process changes for three North Sea fish stocks (cod Gadus morhua, lesser-spotted dogfish Scyliorhinus canicula and whiting Merlangius merlangius) using metrics derived from international bottom-trawl survey data for the period 1997-2008. Over the period, a decrease in recruitment and several simultaneous process changes were most likely for cod, while a recruitment increase, mortality decrease and several process changes were most likely for lesser-spotted dogfish. No significant persistent process changes were found for whiting. Synthesis and applications. The likelihood approach offers a way of combining monotonic time trends in multiple metrics for identifying persistent changes in exploited populations or environmental stressors, given suitable metric time series and tables for interpreting joint time trends. For data rich fish populations, the proposed method can supplement analytical stock assessments. For many other populations with no fisheries-dependent data, it offers a way to identify population changes, which will be crucial for implementing the ecosystem approach to fisheries management and the European marine strategy framework directive.