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

Authors: Dustin J Marshall, Michael Bode and Craig R White

Published in: The Journal of Experimental Biology, volume 216 (June 2013)


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 PO2 or Pc). For almost 30 years, the principal way in which Pc has been estimated has been via piecewise ʻbroken stickʼ 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 Pc. 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 Pc, and also suggest that this approach might be more appropriate for a range of physiological studies that use BSR currently.

Full paper

Marshall DJ, Bode M, White CR (2013) Estimating physiological tolerances – a comparison of traditional approaches to nonlinear regression techniques. The Journal of Experimental Biology, 216 (12), 2176–2182 PDFPDF 562 KB doi:10.1242/jeb.085712

The biogeography of marine invertebrate life histories

Authors: Dustin J Marshall, Patrick J Krug, Elena K Kupriyanova, Maria Byrne and Richard B Emlet

Published in: Annual Review of Ecology, Evolution and Systematics, volume 43, pp. 97–114, doi: 10.1146/annurev-ecolsys-102710-145004


Biologists have long sought to identify and explain patterns in the diverse array of marine life histories. The most famous speculation about such patterns is Gunnar Thorson’s suggestion that species producing planktonic larvae are rarer at higher latitudes (Thorson’s rule). Although some elements of Thorson’s rule have proven incorrect, other elements remain untested.

With a wealth of new life-history data, statistical approaches, and remote-sensing technology, new insights into marine reproduction can be generated.

We gathered life-history data for more than 1,000 marine invertebrates and examined patterns in the prevalence of different life histories. Systematic patterns in marine life histories exist at a range of scales, some of which support Thorson, whereas others suggest previously unrecognized relationships between the marine environment and the life histories of marine invertebrates.

Overall, marine life histories covary strongly with temperature and local ocean productivity, and different regions should be managed accordingly.

Full paper

Marshall DJ, Krug PJ, Kupriyanova EK, Byrne M, Emlet RB (2012) The biogeography of marine invertebrate life-histories. Annual Review of Ecology, Evolution and Systematics, 43: 97–114 External linke-print doi: 10.1146/annurev-ecolsys-102710-145004