Supplemental Item 4.
In order to estimate the effects of filtering on the speed and acceleration data, we performed additional analyses on the same subset of taxa (O. chelifer, O. erythrocephalus, and O. haematodus) used in the experimental-error calculations. Two types of spline curves were fit to the data (cubic and quintic; Walker, 1998) in addition to 1st order (linear) curve, and both 2-point and 3-point differentiation methods were used, resulting in a total of 6 combinations of analytical methods. This was done by modifying the original tracking code using the Matlab Spline Toolbox. This code is available upon request from the authors.
Effects of differentiation methods and spline curve combinations on speed calculations can be seen in Fig. S1A. The maximum speeds calculated via 3-point differentiation were consistently lower than their 2-point differentiated counterparts in 8 of 9 combinations, by an average of 4.03%. Fitting a spline curve and finding the maximum resulted in small differences which were, on average, higher for spline-based estimates than for controls (linear estimates).
With respect to acceleration (S1B), notable effects were seen for both use of splines and differentiation method. 3-point differentiation resulted in values that were always lower than the respective value from 2-point differentiation, regardless of species or spline order. The average difference between 2-point and 3-point differentiation was 31.7%. Estimating maximum acceleration from a spline curve resulted in a greater average value than from linear estimates in all cases except for the quintic spline fit to the 3-point differentiated curve for O. haematodus, which was slightly lower (0.4%) than the linear estimate.
Due to the very large differences (>30%) seen between 2-point and 3-point differentiation results for acceleration, the 2-point method was preferred, as using the 3-point method could result in artifactually low accelerations. As the spline-fit based estimates were generally higher than those of the raw (linear) estimates (example seen in Figure S2), these did not provide a reasonable solution to the potential problem of systematic overestimation by selection of points of greatest acceleration, and linear estimates were used. Thus the 2-point differentiated, linear fit data were used throughout the paper.
Figure S1. A. Differences in mean (+/- s.d.) speed using 2 differentiation methods (2-point and 3-point) and 3 spline-fit techniques (linear, cubic, and quintic) in three representative species. B. Differences in mean (+/- s.d.) acceleration using same combinations of filters.
Figure S2. Absolute accelerations of jaws during 2-jaw strike, demonstrating that spline-fit maxima (black arrows) frequently exceed measured maximum data values (red arrows). Circles represent measured data points, solid lines represent quintic spline curves fit to data.