纽约大学数学建模课笔记

纽约大学数学建模课笔记:You have probably heard the cicadas sing a lazy summer afternoon in the coun-
tryside. You may not be aware though, that cicadas spend most of their life
underground, coming out only for about two weeks, during which they sing,
reproduce and die. Most surprising in this respect are two species of cicadas
that live in the Eastern and Southern United States. These cicadas spend re-
spectively seventeen and thirteen years underground. Then they emerge all at
once, in areas hundreds of miles wide, within a couple of days. They lay eggs
in trees; these eggs fall to the ground and, when new cicadas are born in the
form of nymphs, the nymphs enter the ground and attach themselves to roots.
There they slowly develop over the next thirteen or seventeen years (thirteen
in the South, seventeen in the Eastern United States), until within a couple of
days they are all out again to repeat the cycle. Thus there are “cicada years”,
rare events that take place every so many years that they come each time as
a surprise: suddenly there are myriads of holes in the ground, and cicadas all
around singing and mating.
The strange behavior of these periodic cicadas requires an explanation. Why
do they wait so long to come out? And why do they do it all at once? A
plausible answer [1] involves a mechanism called predator satiation. The idea is
the following: When the cicadas are out, predators –particularly birds– feed off
them. If the cicadas emerged frequently, these birds would prosper; so much in
fact that they could drive the cicadas to extintion. By emerging at very long
intervals, the cicadas make sure that no birds will make a living off them; at
most every third or fourth generation of birds will have a formidable banquet
once in their life. Moreover, when the cicadas come out, they do it by the
millons. Thus even if the birds manage to eat a few, there will always be very
many left to perpetuate the species; hence the name predator satiation.
This mechanism also explains the need for such precise synchronization: if
a cicada emerges too early or too late, it will make a sure prey for the waiting
birds. By coming at the same time as everybody else, it reduces significantly
the probability of ending up devoured.