Underpopulation (Allee) effects

The ecologist W. C. Allee (1931) was one of the first to write extensively on the ecological significance of animal aggregations and, because of this, the positive relationship between population density and the reproduction and survival of individuals is often known as the "Allee effect". An Allee or underpopulation effect arises when the per-capita birth rate (B) increases with population density to some maximum value, the reproductive potential of the species, and the death rate (D) remains constant (see figure). The point U where the two rates intersect is an unstable equilibrium because:

  1. When N = U, then births equal deaths, R = 0, and the population remains unchanged.
  2. When N < U, then births are less than deaths, R < 0, and the population declines to extinction.
  3. When N > U, then the births exceed deaths, R > 0, and the population grows continuously.

The equilibrium point U created by the action of +feedback is an unstable or divergent equilibrium, sometimes called a repeller. It is also called a threshold because it separates two quite different kinds of dynamic behavior (growth from extinction),


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©1997 Alan A. Berryman