Pick almost any location within the eastern United States — say, Columbus Ohio. Every 13 or 17 years, because the soil warms in springtime, vast swarms of cicadas emerge from their underground burrows singing their deafening song, take flight and mate, producing offspring for the following cycle.
This noisy phenomenon repeats all around the eastern and southeastern US as 17 distinct broods emerge in staggered years. In spring 2024, billions of cicadas are expected as two different broods — one which appears every 13 years and one other that appears every 17 years — emerge concurrently.
Previous research has suggested that cicadas emerge once the soil temperature reaches 18°C, but even inside a small geographical area, differences in sun exposure, foliage cover or humidity can result in variations in temperature.
Now, in a paper published within the journal Physical Review E, researchers from the University of Cambridge have discovered how such synchronous cicada swarms can emerge despite these temperature differences.
The researchers developed a mathematical model for decision-making in an environment with variations in temperature and located that communication between cicada nymphs allows the group to return to a consensus concerning the local average temperature that then results in large-scale swarms. The model is closely related to at least one that has been used to explain ‘avalanches’ in decision-making like those amongst stock market traders, resulting in crashes.
Mathematicians have been captivated by the looks of 17- and 13-year cycles in various species of cicadas, and have previously developed mathematical models that showed how the looks of such large prime numbers is a consequence of evolutionary pressures to avoid predation. Nevertheless, the mechanism by which swarms emerge coherently in a given 12 months has not been understood.
In developing their model, the Cambridge team was inspired by previous research on decision-making that represents each member of a gaggle by a ‘spin’ like that in a magnet, but as an alternative of pointing up or down, the 2 states represent the choice to ‘remain’ or ’emerge’.
The local temperature experienced by the cicadas is then like a magnetic field that tends to align the spins and varies slowly from place to position on the size of lots of of metres, from sunny hilltops to shaded valleys in a forest. Communication between nearby nymphs is represented by an interaction between the spins that results in local agreement of neighbours.
The researchers showed that within the presence of such interactions the swarms are large and space-filling, involving every member of the population in a variety of local temperature environments, unlike the case without communication through which every nymph is by itself, responding to each subtle variation in microclimate.
The research was carried out Professor Raymond E Goldstein, the Alan Turing Professor of Complex Physical Systems within the Department of Applied Mathematics and Theoretical Physics (DAMTP), Professor Robert L Jack of DAMTP and the Yusuf Hamied Department of Chemistry, and Dr Adriana I Pesci, a Senior Research Associate in DAMTP.
“As an applied mathematician, there may be nothing more interesting than finding a model able to explaining the behaviour of living beings, even in the best of cases,” said Pesci.
The researchers say that while their model doesn’t require any particular technique of communication between underground nymphs, acoustical signalling is a probable candidate, given the ear-splitting sounds that the swarms make once they emerge from underground.
The researchers hope that their conjecture regarding the role of communication will stimulate field research to check the hypothesis.
“If our conjecture that communication between nymphs plays a task in swarm emergence is confirmed, it would supply a striking example of how Darwinian evolution can act for the advantage of the group, not only the person,” said Goldstein.
This work was supported partially by the Complex Physical Systems Fund.
