Relationships grow with time: a note of caution about energy expenditure-proxy correlations, focussing on accelerometry as an example

Abstract

Scientists studying the energy expenditure of air-breathing divers are interested in developing a more tractable technique to support their endeavour. Accelerometers instrumented to animals can return a tangible measure of those animals’ activity levels, which in some situations correlates with their metabolic rate. However, I argue that reported evidence for this correlation in semi-aquatic animals while diving is not always as strong as it seems. This is because some analyses have derived a measure of activity level by calculating the sum of accelerometry-based values and compared those data points to measures of summed (total) energy expenditure. These summations mean that time (duration) has been introduced into both sides of the regression equation. This is likely to generate a correlation between body acceleration and energy expenditure even if the two variables are not mechanistically linked because time will correlate with itself. Thus, a strong relationship between a summed measure of energy expenditure and a summed proxy of energy expenditure indicates only that as time passes an animal burns calories. Issues concerning summation of variables in principle extend to other potential proxies of energy expenditure, such as heart rate. I demonstrate the artefactual effect of regressing summed values with analyses of modelled data using ecologically valid parameters. Unless a summed proxy predicts total energy expenditure substantially better than does time alone, there is little evidence upon which to base a claim that body acceleration is suitably predictive of metabolic rate. Clarity about the predictive power of body acceleration to estimate metabolic rate should be sought by simply presenting a graph of the relationship between these raw values. A lay summary is available for this article.