Constraint lines and performance envelopes in behavioral physiology: the case of the aerobic dive limit

Markus Horning

Constraint lines-the boundaries that delimit point clouds in bivariate scattergrams-have been applied in macro-ecology to quantify the effects of limiting factors on response variables, but have not been applied to the behavioral performance and physiological ecology of individual vertebrates. I propose that behavioral scattergrams of air-breathing, diving vertebrates contain informative edges that convey insights into physiological constraints that shape the performance envelopes of divers. In the classic example of repeated cycles of apnea and eupnea in diving, air-breathing vertebrates, the need to balance oxygen consumption, and intake should differentially constrain recovery for dives within or exceeding the aerobic dive limit (ADL). However, the bulk of variance observed in recovery versus dive duration scattergrams originates from undetermined behavioral variables, and deviations from overall stasis may become increasingly apparent at progressively smaller scales of observation. As shown on dive records from 79 Galápagos fur seals, the selection of appropriate time scales of integration yields two distinct recovery boundaries for dive series within and beyond the estimated ADL. An analysis of the corresponding constraint lines is independent of central tendencies in data and avoids violating parametric assumptions for large data sets where variables of interest account for only a small portion of observed variance. I hypothesize that the intercept between these constraint lines represents the effective ADL, and present physiological and ecological considerations to support this hypothesis.