Most behaviors such as making tea are not stereotypical but have an obvious structure. However, analytical methods to objectively extract structure from non-stereotyped behaviors are immature. In this study, we analyze the locomotion of fruit flies and show that this non-stereotyped behavior is well-described by a Hierarchical Hidden Markov Model (HHMM). HHMM shows that a fly's locomotion can be decomposed into a few locomotor features, and odors modulate locomotion by altering the time a fly spends performing different locomotor features. Importantly, although all flies in our dataset use the same set of locomotor features, individual flies vary considerably in how often they employ a given locomotor feature, and how this usage is modulated by odor. This variation is so large that the behavior of individual flies is best understood as being grouped into at least three to five distinct clusters, rather than variations around an average fly.

Mechanisms that control movements range from navigational mechanisms, in which the animal employs directional cues to reach a specific destination, to search movements during which there are little or no environmental cues. Even though most real-world movements result from an interplay between these mechanisms, an experimental system and theoretical framework for the study of interplay of these mechanisms is not available. Here, we rectify this deficit. We create a new method to stimulate the olfactory system in Drosophila or fruit flies. As flies explore a circular arena, their olfactory receptor neuron (ORNs) are optogenetically activated within a central region making this region attractive to the flies without emitting any clear directional signals outside this central region. In the absence of ORN activation, the fly's locomotion can be described by a random walk model where a fly's movement is described by its speed and turn-rate (or kinematics). Upon optogenetic stimulation, the fly's behavior changes dramatically in two respects. First, there are large kinematic changes. Second, there are more turns at the border between light-zone and no-light-zone and these turns have an inward bias. Surprisingly, there is no increase in turn-rate, rather a large decrease in speed that makes it appear that the flies are turning at the border. Similarly, the inward bias of the turns is a result of the increase in turn angle. These two mechanisms entirely account for the change in a fly's locomotion. No complex mechanisms such as path-integration or a careful evaluation of gradients are necessary.

Most behaviors such as making tea are not stereotypical but have an obvious structure. However, analytical methods to objectively extract structure from non-stereotyped behaviors are immature.In this study, we analyze the locomotion of fruit flies and show that this non-stereotyped behavior is well-described by a Hierarchical Hidden Markov Model (HHMM). HHMM shows that a fly's locomotion can be decomposed into a small number of locomotor features, and odors modulate locomotion by altering the time a fly spends performing different locomotor features. Importantly, although all flies in our dataset use the same set of locomotor features, individual flies vary considerably in how often they employ a given locomotor feature, and how this usage is modulated by odor. This variation is so large that the behavior of individual flies is best understood as being grouped into at least 3-5 distinct clusters, rather than variations around an average fly. that the behavior of different flies represents variations around an "average" fly. Rather, our data is most consistent with the idea that flies employ 3-4 different strategies, at a minimum, to explore a small circular arena and a similar number in their response to odors. 65 Results Rationale for the choice of HHMM as the model and the model architectureWe model the locomotion of wild-type flies exploring a circular arena 28 whose center (odorzone) consists of a fixed concentration of odor ( Figure 1A). The arena and the experimental procedure is detailed in an earlier manuscript 28 . Briefly, locomotion of each of the 34 flies in our 70 dataset was measured 3 minutes before an odor (apple cider vinegar or ACV) was turned on, and 3 minutes during the presence of ACV. Sample trajectories are shown in Figure 1B. Inspired by past success at modeling animal trajectories using Hidden Markov Model (HMM), we attempted to model the fly's locomotion using a HMM 17 26 . HMM creates discrete states based on a time series of observables such as position, speed or acceleration. The 75 advantage of using HMMs in modeling locomotion is well described in earlier studies 17 . Briefly, instantaneous measures of an observable are variable; therefore, behavioral states inferred by simple thresholding applied to instantaneous measures of the observables are likely to be more erroneous. HMM remedies this problem by inferring states based not only on the value of the observable at the current time point but also on the previous and following time points and 80 allows a more accurate determination of state (this idea is well-explained in Figure 2 in ref 17).In this study, we use observables that describe the change of position as a function of time, and hence our analysis will focus on behavioral states in the velocity space. The most commonly used representation of locomotion in the velocity space is instantaneous speed and angular speed.But, as noted by others 17 , because it is difficult to measure angular speed accurately at low 85 speeds (see methods for details), we fit the model to two othe...

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