Scientists, biologists and mathematicians have built a model circuit to simulate the internal compass mechanisms monarch butterflies use to navigate the 4,000 km journey from Canada to Mexico each year. The model takes into account the two cues butterflies use for migratory navigation: the horizontal position of the sun and time of day.

In June 2014, scientists at the University of Massachusetts Medical School and Worcester Polytechnic Institute identified a sort of solar compass in the antennas of North American monarch butterflies. The clock mechanism was the first clue that monarch butterflies depend on sunlight for navigational orientation.

Azimuth neurons—light-sensitive neurons in monarchs’ eyes—help the butterflies keep track of the sun’s ever-changing position during the day.

Eli Shlizerman is an assistant professor in the departments of applied mathematics and electrical engineering at the University of Washington. He and his team created the neuronal model system to simulate how these cues interact to form a “time-compensated sun compass that directs flight.”

According to their study, the “remarkable ability of monarch butterflies to migrate for thousands of miles while keeping the southerly direction suggests that they possess a neural circuit capable of integrating time of day and the sun’s position into a compass useful for navigation.” The model, therefore, was designed to match the firing rate of monarchs’ time indicators with signals derived from azimuth neurons to illustrate butterflies’ angular position control.

According to how it’s wired, the circuit controls signals that “tell the system if a correction is needed to stay on the correct course,” said Shlizerman in an interview with the BBC. “For me this is very exciting – it shows how a behaviour is produced by the integration of signals.”

The model circuit was published on April 14, 2016 in the open access journal Cell Reports.