THE principle that allows an opera singer鈥檚 shrill tones to shatter fine
crystal can drive flour beetle populations to dizzying heights, according to a
new mathematical model. The equations show how rhythmic swings in habitat size
and in beetle life cycles create a 鈥渞esonance鈥�. The result may point to ways of
boosting production of some farmed animals, such as fish.
Flour beetles (Triboleum castaneum) survive indefinitely in bottles
if they receive fresh flour regularly. Varying the amount of flour would be
expected to have adverse effects on the beetles as they try to cope with the
varying habitat size. 鈥淭here鈥檚 a tenet in biology that says fluctuating habitats
are not good,鈥� says Jim Cushing, a mathematician at the University of Arizona in
Tucson.
But lab studies have shown that if the amount of flour is regularly varied
above and below a given average, the population can sometimes end up
dramatically higher than in bottles that contain the same average amount of
flour all the time. Bob Costantino, a beetle expert at the University of Rhode
Island in Kingston, says this has puzzled his research group for more than a
decade. 鈥淲e didn鈥檛 understand it at all,鈥� he says.
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Now Cushing and his colleague Shandelle Henson have explained the puzzle by
adapting equations that describe population changes in the wild to the beetle
cultures. They found that if the frequency of habitat variations matched natural
fluctuations in the beetle population, they could create a 鈥渞esonance鈥�. This
would boost population growth, much as a soprano can hit the resonant pitch of a
crystal goblet and concentrate vibrations in the glass.
鈥淧opulations have a propensity to oscillate on their own,鈥� Cushing says. The
main force driving natural fluctuations in flour beetle populations鈥攁nd
those of many other insects鈥攊s cannibalism. Both larvae and adults eat
unhatched eggs and smaller larvae. And according to Costantino, the denser the
population, the higher the rate of cannibalism.
Cushing and Henson accounted for the variation of cannibalism with habitat
size in their equations. 鈥淭hen it all fell into place,鈥� says Constantino. The
equations predicted that for the population to grow rapidly, the flour volume
should be high when the number of eggs and larvae is at its peak, making
cannibalism low. Two weeks later, when the bottles contain mostly pupae and
adults, far less flour would suffice. The results appear in the current
Journal of Mathematical Biology (vol 36, p 201).
Costantino speculates that it may be possible to adapt the beetle model to
fish cultures at hatcheries, to produce more fish for the same average volume of
water as farms now use.
