Of TITAN and straw men: an appeal for greater understanding of community data

Cuffney and Qian (2013) performed numerous simulations to demonstrate potential flaws in Threshold Indicator Taxa Analysis (TITAN), a method for interpreting taxon contributions to community change along novel environmental gradients. Based on their simulations, they concluded that: 1) TITAN is not an effective method for detecting different types of statistical thresholds in trend lines, 2) permutation results in highly significant p-values even for splits that are not thresholds, and 3) coincident change points may arise as an artifact of inaccuracies, imprecision, and systematic bias in both change-point estimation and TITAN's bootstrap. The critique raises some important concerns, but because of significant misunderstanding, it is based on analyses that violate basic assumptions of both TITAN and indicator species analysis (IndVal), and thus, constitutes a straw man that cannot be used to evaluate their performance. We demonstrate that the critique: 1) fundamentally misrepresents TITAN's primary goals; 2) simulates taxon abundances based on unrealistic statistical models that fail to represent important empirical patterns present in Cuffney and Qian's own published data sets (i.e., negative binomial distributions, frequent absences a function of the predictor); 3) tests TITAN's ability to identify breaks in trend lines distorted by log-transformation that do not match the greatest change in the simulated response, leading to misinterpretation of expected and previously documented behavior by TITAN as errors; 4) misinterprets TITAN's use of p-values while ignoring diagnostic indices of purity and reliability for identifying robust indicator taxa; and 5) asserts that bootstrapped change-point quantiles in TITAN are too narrow despite published results to the contrary. Last, in contrast to the claim that change-point synchrony may be an artifact of the technique, we show that: 6) analysis of published data using completely independent methods (i.e., scatterplots of abundance data or generalized additive models) also reveals synchrony in the nonlinear decline of numerous taxa in corroboration of TITAN and its underlying conceptual model. Thus, Cuffney and Qian have not identified any serious limitations of TITAN because their critique is based on misinterpretation of TITAN's assumptions and primary objectives. However, their critique does highlight the need for clarification of the appropriate uses, potential misuses, and limitations of TITAN and other methods for ecological analysis.