Bugs That Count
Missing a Beat
The synchronization of cicada emergence is impressive, but not
perfect. There are always at least a few clueless unfortunates who
turn up a year early or a year late. Four–year accelerations
and retardations are also common. Evidently, the year–counting
mechanism can go awry. How much error can the system tolerate before
synchronization is lost entirely?
Several authors have proposed that Magicicada periodicity
evolved during the Pleistocene epoch, as a response to the
unfavorable and uncertain climate of glacial intervals. Conditions
have changed dramatically since the glaciers retreated, and so it
seems unlikely that the same selective pressures are still working
to maintain synchronization. What does maintain it? Before
considering more complicated hypotheses, it seems worthwhile to ask
whether periodicity could have survived as a mere vestigial
carryover, without any particular adaptive value in the current
environment. If the timekeeping device is never reset, how
accurately would it have to work to maintain synchronization over
the 10,000 years or so since the end of the Pleistocene?
The answer depends in part on what kinds of errors can disrupt the
counting. The simplest model allows individual cicadas to make
independent errors. Each year, each cicada has some small likelihood
of either failing to note the passage of the year or interpolating a
spurious extra year. Under this model, the error rate needs to be
kept below 1 in 10,000.
The weakness of this model is the assumption that cicadas would make
independent errors. If all the cicadas are trying to read the same
chemical signal in the tree sap, errors could be strongly
correlated. In a bad year with a short growing season, the signal
might never reach the threshold of detection for many individuals. A
double oscillation is also a possibility, for example if the trees
are defoliated by predators and then put out a second growth of leaves.
An error model that allows for such correlations works like this: A
cicada's probability of correctly recording the passage of a year
depends on the strength of the xylem signal, which varies randomly
from year to year but is the same for all the cicadas. If the signal
is very strong, almost everyone detects it correctly. If the signal
is extremely feeble, nearly all miss it. Although this latter
event must be counted as a timekeeping error, it does not break
synchronization; instead it retards the entire population by a year.
What spoils synchronization is an ambiguous signal, one in the gray
area where half the cicadas detect it and the other half don't. This
splits the population into two groups, which will mature and emerge
a year apart. Four or five such splittings over 10,000 years would
be enough to wipe out synchronization.
A drawback of this error model is that it depends on two variables,
which are hard to disentangle: the frequency of ambiguous signals in
the xylem and the cicada's acuity in reading those signals. If the
signal is usually near the extremes of its range, then even with a
crude detector, the population will almost always reach a consensus.
If ambiguity is common, then the insect's decision mechanism needs
to be finely tuned. I have experimented with tree–ring data as
a proxy for the distribution of xylem–signal amplitudes, but
the results were not much different from those with a random distribution.
The cicadas' response to the signals is defined by an S–shaped
curve. If the curve is infinitely steep—a step
function—then the probability of registering a tick of the
clock is exactly 0 up to some threshold and exactly 1 above the
threshold. As the curve softens, the transitional region where
probabilities are close to ½ gets broader.
Running the simulation, it turns out that synchronization survives
only if the response curve is very steep indeed, with a vanishingly
narrow region of ambiguity. For ease of analysis, suppose we are
merely trying to synchronize the clocks of two cicadas that each
live for 10,000 years. To a first approximation, they remain in
phase only if they agree on the interpretation of the signal every
year throughout the 10,000–year interval. For a
90–percent chance of such uninterrupted agreement, the
probability of agreement each year must be at least 0.99999.
Is such accuracy plausible in a biological mechanism? Could
periodicity really be a historical relic, without adaptive
significance today? Probably not, but the models are too simplistic
to support quantitative conclusions. Nevertheless, the idea of
timekeeping errors introduced by ambiguities in environmental
signals may well have a place in the biology of cicadas. Suppose
there is a north–south gradient in signal amplitude; then
somewhere along the gradient there must be a zone of ambiguity.
Forty years ago, Richard D. Alexander and Thomas E. Moore of the
University of Michigan, Ann Arbor, pointed out that broods tend to
be arranged like shingles from north to south, with each brood
emerging one year later than the one above. It's a pattern that
might have been generated by successive population–splitting
events like those in the model.