Estimating physiological tolerances - a comparison of traditional approaches to nonlinear regression techniques

Traditionally, physiologists have estimated the ability of organisms to withstand lower partial pressures of oxygen by estimating the partial pressure at which oxygen consumption begins to decrease (known as the critical P-O2 or P-c). For almost 30 years, the principal way in which P-c has been estimated has been via piecewise 'broken stick' regression (BSR). BSR was a useful approach when more sophisticated analyses were less available, but BSR makes a number of unsupported assumptions about the underlying form of the relationship between the rate of oxygen consumption and oxygen availability. The BSR approach also distils a range of values into a single point with no estimate of error. In accordance with more general calls to fit functions to continuous data, we propose the use of nonlinear regression (NLR) to fit various curvilinear functions to oxygen consumption data in order to estimate P-c. Importantly, our approach is back-compatible so that estimates using traditional methods in earlier studies can be compared with data estimates from our technique. When we compared the performance of our approach relative to the traditional BSR approach for real world and simulated data, we found that under realistic circumstances, NLR was more accurate and provided more powerful hypothesis tests. We recommend that future studies make use of NLR to estimate P-c, and also suggest that this approach might be more appropriate for a range of physiological studies that use BSR currently.