The long-standing intermediate disturbance hypothesis suggests that species diversity peaks at intermediate frequencies of environmental perturbation. Previous reviews of the literature come to contrasting conclusions as to the frequency with which this hypothesis holds (Mackey & Currie 2001, Fox 2013, Huston 2014). One reason they reached differing conclusions is that different authors use different analytical methods to test for a humped relationship between diversity and disturbance. Further, one common method for testing for humped relationships in bivariate data—quadratic regression—is biased towards diagnosing any nonlinear concave-down relationship as a hump.
Recently, a new statistical approach, the two-lines test, has been proposed to test for humps in bivariate relationships (Simonsohn 2017). The two-lines test fits separate linear regressions to "low" and "high" values of x, diagnosing a hump when the slopes are (respectively) significantly positive and negative. The breakpoint between "low" and "high" values of x is set via an algorithm that maximizes the power of the test to detect a humped relationship while maintaining the Type I error rate at 0.05. In simulations, the two-lines test is more powerful than previously-proposed techniques for detecting humped relationships in bivariate data. We reanalyzed data from observational and experimental studies of diversity-disturbance relationships using the two-lines test.
Results/Conclusions
We found that humped relationships between diversity and disturbance were rare. In many cases, we failed to find a hump where previous analyses using quadratic regression found one, likely illustrating the propensity of quadratic regression to produce false positives. Contrary to previous suggestions, humped diversity-disturbance relationships are no more common in experiments than in observational studies, even though experiments typically consider a wide range of disturbance rates or levels, and control for or randomize other factors affecting diversity. Our work undermines the case for teaching the intermediate disturbance hypothesis as a general ecological pattern, or for using it to guide management decision-making in the absence of system-specific information. The two-lines test is a promising approach for testing for other hypothesized bivariate relationships, such as between diversity and productivity.