From JUDITH MYERS, JAMES SMITH and CHARLES KREBS
Chaos has become a most popular topic in venues ranging from the pages
of New Scientist to conversations at cocktail parties. If the paradigm of
chaos becomes accepted, the population ecologist may appear to be out of
business. If population trends result from purely deterministic processes
that are sensitive to starting conditions and produce chaotic dynamics,
field studies and experiments to predict population trends are doomed to
failure. Therefore, a comment on Robert May’s article (‘The chaotic rhythms
of life’, 18 November 1989) from the perspective of field population ecologists
seems appropriate.
May begins by claiming that ‘until recently most ecologists assumed
that the effects regulating density would, in the absence of other factors,
keep a population at some constant level’. For May’s ‘most ecologists’,
one should perhaps read ‘most mathematical ecologists’. The experiences
of field ecologists and mathematical ecologists are very different.
Field experience shows that it is often extremely difficult to demonstrate
density-dependent relationships. This may be due to measurement problems
or it may indicate realistic biological problems. For example, the quality
of individuals can vary with the the history of the population quite apart
from its density. Therefore, individual animals in increasing populations
can have very different relationships with their predators, parasites, food
plants and diseases at a given density than individuals from declining populations
at the same density.
For plants, relationships between density and survival can change with
moisture and nutrient content of soil, plant distribution, and competitors.
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Therefore, for both plants and animals the effects of density are not
readily captured in simple mathematical expressions. Field ecologists are
not enamoured with equilibria but are impressed by variation. Chaotic behaviour
may result from some simple mathematical expressions, but these expressions
are unlikely to capture realistic population phenomena.
The following points are relevant: (1) Single, unchanging deterministic
processes do not regulate natural populations. Natality and mortality functions
continually change as the genetic and phenotypic composition of populations
shifts with environmental conditions.
(2) Describing patterns of chaotic variation does not identify underlying
mechanisms. Chaotic dynamics may arise in a variety of ways.
(3) Even if the deterministic functions commonly used by mathematical
ecologists to describe population dynamics were realistic, the parameters
necessary for chaotic dynamics are biologically unrealistic.
Nonlinear, deterministic interactions may produce fascinating and counterintuitive
patterns of change in numbers. But, while the emperor’s new clothes may
appeal to physicists, mathematicians and physiologists, perhaps field ecologists
can be excused for a less enthusiastic response.
Judith Myers, James Smith and Charles Krebs Department of Zoology University
of British Columbia
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