Methods for estimating peak physiological performance and correlating performance measures

Abstract

Estimates of animal performance often use the maximum of a small number of laboratory trials, a method which has several statistical disadvantages. Sample maxima always underestimate the true maximum performance, and the degree of the bias depends on sample size. Here, we suggest an alternative approach that involves estimating a specific performance quantile (e.g., the 0.90 quantile). We use the information on within-individual variation in performance to obtain a sampling distribution for the residual performance measures; we use this distribution to estimate a desired performance quantile for each individual. We illustrate our approach using simulations and with data on sprint speed in lizards. The quantile method has several advantages over the sample maximum: it reduces or eliminates bias, it uses all of the data from each individual, and its accuracy is independent of sample size. Additionally, we address the estimation of correlations between two different performance measures, such as sample maxima, quantiles, or means. In particular, because of sampling variability, we propose that the correlation of sample means does a better job estimating the correlation of population maxima than the estimator which is the correlation of sample maxima.

Conflict, compensation, and plasticity: Sex‐specific, individual‐level trade‐offs in green anole (Anolis carolinensis) performance

“…Taken together, these results illustrate the value and importance of expanding our performance measurement methodology to consider multivariate variation beyond maximum performance (Careau & Wilson, 2017a;Head et al, 2012).…”

“…Performance trade-offs can be difficult to detect because researchers overwhelmingly employ performance measurement protocols that focus on obtaining single "personal best" measures of maximum performance (Adolph & Pickering, 2008;Head, Hardin, & Adolph, 2012;Losos, Creer, & Schulte, 2002) and consequently do not allow for the rigorous statistical estimation of both within-and amongindividual (co)variation (Brommer, 2013;Dingemanse & Dochtermann, 2013;Houslay & Wilson, 2017). Careau and Wilson (2017a) used simulations to show that although within-individual performance variation can mask performance trade-offs among different individuals, these among-individual trade-offs are recovered by the use of multivariate mixed-models (MMM) that partition variation in performance both among and within individuals.…”

Performance trade-offs and individual quality in decathletes

“…Repeatability in our data varies between 0.81 and 0.86 for all events except 1500 m speed (0.77), which is relatively high but also computed from the best performances for each outdoor track season. Because our data are sample maxima (and not sample means), standard corrections for correlation attenuation would also likely contain some unknown error (Head et al, 2011). Even if we had estimated sample mean performances for each individual, a standard correction may not be applicable to the quality-free correlations that we attempt to interpret as these are missing the component correlation due to a global (quality) factor and we do not know how the bias is decomposed and distributed across multiple components.…”

Performance, Personality, and Energetics: Correlation, Causation, and Mechanism

“…Ability of an individual to conduct a task when maximally motivated. Best performances by individuals from a series of measurements are often analyzed, but this may not be the optimal approach from a statistical perspective (Head et al 2012). Arnold (1983) specified that a performance trait should preferentially be ecologically relevant and phylogenetically interesting.…”