Modeling observed animal performance using the Weibull distribution

Abstract

Understanding how organisms adapt requires linking performance and microhabitat. However, measuring performance, especially maximum performance, can sometimes be difficult. Here we describe an improvement over previous techniques of only considering the largest observed values as maxima. Instead, we model expected performance observations via the Weibull distribution, a statistical approach that reduces the impact of rare observations. After calculating group-level weighted averages and variances by treating individuals separately to reduce pseudoreplication, our approach resulted in high statistical power despite small sample sizes. We fit lizard adhesive performance and bite force data to the Weibull distribution and found it to closely estimate maximum performance in both cases, illustrating the generality of our approach. Using the Weibull distribution to estimate observed performance greatly improves upon previous techniques by facilitating power analyses and error estimations around robustly estimated maximum values.