A novel algorithm for robust estimation of ants' speed on convoluted trajectories derived from their gait pattern

Accurate measurements of travel distance and the corresponding speed are crucial for the analysis of animal movements. Particularly, the trajectories of ants were used in numerous behavioral studies. However, measurements of travel distance involve the dilemma of setting the proper time window: Estimates from a short time window are vulnerable to spatial errors in observation, while estimates from a long time window lead to an underestimation of the travel distance. To overcome these difficulties, we propose a novel algorithm that successively interpolates two consecutive points of an ant's trajectory for a given time window by embracing the alternating tripod gait and other gait patterns of ants. We demonstrate that this algorithm is more reliable compared with the conventional method of travel distance estimation based on the sum of the consecutive straight-line displacement (SLD). After obtaining speed estimates for a range of sampling time windows, we applied a fitting method that can estimate the actual speed without prior knowledge of spatial error distribution. We compared results from several methods of speed estimation extracted from the empirical and simulated data of ant trajectories. The accuracy of our algorithm was comparable with or much higher than the accuracy of the sum over the consecutive SLD with optimal window length. Hence, subjective selection of the sampling time window can be avoided by using the proposed algorithm. We provide software that enables empirical scientists to utilize the proposed methods rather than the conventional SLD method of distance and speed estimation.