Quantifying flow-assistance and implications for movement research.

The impact that flows of air and water have on organisms moving through these environments has received a great deal of attention in theoretical and empirical studies. There are many behavioral strategies that animals can adopt to interact with these flows, and by assuming one of these strategies a researcher can quantify the instantaneous assistance an animal derives from a particular flow. Calculating flow-assistance in this way can provide an elegant simplification of a multivariate problem to a univariate one and has many potential uses; however, the resultant flow-assistance values are inseparably linked to the specific behavioral strategy assumed. We expect that flow-assistance may differ considerably depending on the behavioral strategy assumed and the accuracy of the assumptions associated with that strategy. Further, we expect that the magnitude of these differences may depend on the specific flow conditions. We describe equations to quantify flow-assistance of increasing complexity (i.e. more assumptions), focusing on the behavioral strategies assumed by each. We illustrate differences in suggested flow-assistance between these equations and calculate the sensitivity of each equation to uncertainty in its particular assumptions for a range of theoretical flow conditions. We then simulate trajectories that occur if an animal behaves according to the assumptions inherent in these equations. We find large differences in flow-assistance between the equations, particularly with increasing lateral flow and increasingly supportive axial flow. We find that the behavioral strategy assumed is generally more influential on the perception of flow-assistance than a small amount of uncertainty in the specification of an animal's speed (i.e. <5 ms(-1)) or preferred direction of movement (i.e. <10°). Using simulated trajectories, we show that differences between flow-assistance equations can accumulate over time and distance. The appropriateness and potential biases of an equation to quantify flow-assistance, and the behavioral assumptions the equation implies, must be considered in the context of the system being studied, particularly when interpreting results. Thus, we offer this framework for researchers to evaluate the suitability of a particular flow-assistance equation and assess the implications of its use.