Threshold indicator taxa analysis (TITAN): A simple method for identifying and interpreting biodiversity thresholds

We introduce Threshold Indicator Taxa ANalysis (TITAN) as a simple method of identifying and interpreting biodiversity and community thresholds along an environmental gradient.  TITAN is based on indicator species analysis (IndVal), a widely accepted method for identifying indicator taxa among levels of a categorical variable.  In TITAN, we extend principles of IndVal to identify the value of a continuous variable, x, resulting in the optimal partitioning of sample units to the left and right of x based on normalized indicator values (z) for individual taxa and additive response of all indicator z scores (sum(z)) at the community level.  Negatively responding taxa (z–) are distinguished from those responding positively (z+) to yield taxa-specific threshold distributions as well as cumulative threshold responses of declining (sum(z–)) and increasing (sum(z+)) subsets of the community.  Resampling procedures are used to measure indicator purity and uncertainty surrounding thresholds.  We illustrate the advantages of TITAN using a simulated data set and by retrospectively analyzing two aquatic macroinvertebrate community data sets spanning a watershed urbanization gradient in Maryland and a phosphorus gradient in the Florida Everglades, USA.  We contrast TITAN with a complementary method, multivariate regression trees, to acknowledge similarities while illustrating differences that arise when considering taxa-specific responses.