ABSTRACT
Holzmann et al. (2006) have described, inter alia, the application of HMMs with circular state-dependent distributions to the movement of larvae of the fruit fly Drosophila melanogaster. It is thought that locomotion can be largely summarized by the distribution of speed and direction change in each of two episodic states: ‘forward peristalsis’ (linear movement) and ‘head swinging and turning’ (Suster et al., 2003). During linear movement, larvae maintain a high speed and a low direction change, in contrast to the low speed and high direction change characteristic of turning episodes. Given that the larvae apparently alternate thus between two states, an HMM in which both speed and turning rate are modelled according to two underlying states might be appropriate for describing the pattern of larval locomotion. As illustration we shall examine the movements of two of the experimental subjects of Suster (2000) (one wild larva, one mutant) whose positions were recorded once per second. The paths taken by the larvae are displayed in Figure 11.1.
First we examine the univariate time series of direction changes for the two larvae; then in Section 11.5 we shall examine the bivariate series of speeds and direction changes.
