Mathematics and Biology

Exploitation interactions
Curious features of population cycles

 
Math Awareness Month 1999

Causes of the cycles

lthough the cycles of boreal mammal populations have been known for centuries, and despite the fact that determining their cause has engaged many scientists for seven decades at least, today scientists do not agree on the causes underlying this most singular phenomenon.


First known depiction of lemmings, shown here falling from the sky. 
From Olaus Magnus (1555), Historia de Gentibus, Roma.

The image above is from a sixteenth century manuscript. It shows lemmings raining out of the clouds and swarming upon the land.  Two weasels are shown with lemmings in their mouths.  Fur merchants had observed the connection between lemming cycles and the abundance of fur-bearing animals long before it came to the attention of clerics and then scientists.

The following is a partial catalog of the many, sometimes strange hypotheses that have been put forward to explain the lemming and/or hare cycles:

     
  1. Diseases wipe out the small mammals when their densities get too great.
  2. Some unknown climactic factor might be controlling the growth and death of the populations.
  3. Sunspot cycles (~11 yr) are responsible for driving the cycles of snowshoe hares.
  4. The alignments of certain celestial bodies exert their influences over the animals.
  5. At high densities, the little creatures go mad and start killing each other or stop reproducing.
Each of these hypotheses has been refuted.  Nowadays, it is safe to say that scientists agree that exploitation of one form or another is at the heart of the cycles, although they disagree regarding who is the exploiter and who the exploited.


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