A not so random walk

A mathematical model suggests that, for fruit flies at least, there is no such thing as an average walk.

Image credit: NASA / Dominic Hart (CC BY-NC 2.0)

Many behaviors that we perform everyday, including something as familiar as making a peanut-butter sandwich, consist of a sequence of recognizable acts. These acts may include, for example, holding a knife and opening a jar. Yet often neither the sequence nor the individual acts are always performed in the exact same way. For example, there are many ways to hold a knife and there are many ways to open a jar, meaning neither of these actions could be called “stereotyped”.

A lack of stereotypy makes it difficult for a computer to automatically recognize the individual acts in a sequence. This same problem would apply to other common behaviors, such as walking around somewhere you have not visited before. While we easily recognize it when we see it, walking is not a stereotyped behavior. It consists of a series of movements that differ between individuals, and even in the same individual at different times. So how can someone automatically recognize the individual acts in a non-stereotyped behavior like walking?

To begin to find out, Tao et al. developed a mathematical model that can recognize the walking behavior of a fruit fly. Existing recordings of fruit flies walking were analyzed using a type of mathematical model called a Hierarchical Hidden Markov Model (often shortened to HHMM). Such models assume that there are hidden states that influence the behaviors we can see. For example, someone’s chances of going skiing (an observable behavior) depend on whether or not it is winter (a hidden state).

The HHMM revealed that the seemingly random wanderings of a fly consist of ten types of movement. These include the “meander”, the “stop-and-walk”, as well as right turns and left turns. Exposing the flies to a pleasant odor – in this case, apple cider vinegar – altered how the flies walked by changing the time they spent performing each of the different types of movement. All flies in the dataset used the same ten movements, but in different proportions. This means that each fly showed an individual pattern of movement. In fact, the differences between flies are so great that Tao et al. argue that there is no such thing as an average walk for a fruit fly.

The model represents a complete description of how fruit flies walk. It thus provides clues to the processes that transform an animal’s sensory experiences into behavior. But it also has potential clinical applications. Similar models for human behaviors could help reveal behaviors that are abnormal because of disease. Normal behaviors also show variability, and some diseases increase or decrease this variability. By making it easier to detect these changes, mathematical models could support earlier diagnosis of medical conditions.