184
See also: Predator–prey equations 44–49 ■ Non-consumptive effects of predators
on their prey 76–77 ■ The Verhulst equation 164–165 ■ Metapopulations 186–187C
haos theory—the idea that
predictions are limited by
time and the nonlinear
nature of behavior—took hold in the
1960s. American meteorologist
Edward Lorenz observed the effect
in weather patterns, and described
it in 1961. Since then, the theory
has been applied to many sciences,
including population dynamics.Chaotic populations
In the 1970s, Australian scientist
Robert May became interested in
animal population dynamics, and
worked on a model to forecast
growth or decline over time. This
led him to the logistic equation.
Devised by Belgian mathematician
Pierre-François Verhulst, this
equation produces an S-shaped
curve on a graph—showing
population growing slowly at first,
then rapidly, before tapering off
into a state of equilibrium.
May experimented with
Verhulst’s formula to create the
“logistic map,” which showed
the population trends on a graph.
Although it created predictablepatterns at the lowest rates of
growth, May found that the logistic
equation produced erratic results
when the growth rate was equal to
or above 3.9. Instead of producing
repeating patterns, the map
plotted trajectories that appeared
completely random. May’s work
showed how a simple, constant
equation could produce chaotic
behavior. His logistic map is now
used by demographers to track and
predict population growth. ■IN CONTEXT
KEY FIGURE
Robert May (1936–)BEFORE
1798 Thomas Malthus argues
that human populations will
increase at an ever-faster rate,
inevitably causing suffering.1845 Belgian demographist
Pierre-François Verhulst argues
that checks to population
growth will increase in line
with population growth itself.AFTER
1987 Per Bak, Chao Tang, and
Kurt Wiesenfeld, a research
team in New York, describe
“self-organized criticality”—
elements within a system
interacting spontaneously
to produce change.2014 Japanese ecologist
George Sugihari uses a chaos
theory approach called empirical
dynamic modeling to produce
a more accurate estimate of
salmon numbers in Canada’s
Fraser River.POPULATION DYNAMICS
BECOME CHAOTIC
WHEN THE RATE OF
REPRODUCTION SOARS
CHAOTIC POPULATION CHANGE
Chaos: when the present
determines the future, but
the approximate present
does not approximately
determine the future.
Edward LorenzUS_184-185_Chaotic_population_change_Macro-ecology.indd 184 12/11/18 6:25 PM