Abstract:
The question of how environmental and genetic factors interact to place limits on the
dynamics of biological populations has been a matter of debate throughout the 20th century (for
review, see Turchin 1995; Mueller & Joshi 2000). History is replete with examples of
uncontrollable population expansions and crashes, and often unsuccessful interventions to
impose artificial regulation. However, a range of studies examining the stability of laboratory
and natural populations have found relatively stable dynamics in terms of constancy stability,
more often than not (Hassell et al. 1976; Thomas et al. 1980; Mueller & Ayala 1981b; Turchin &
Taylor 1992; Ellner & Turchin 1995). A theory which has gained acceptance over the past
century is that the dynamics of biological populations are regulated via density-dependent
mechanisms (Turchin 1995). This idea in its basic form arose with the logistic model of
population growth, proposed in 1838 by the French mathematician Pierre-François Verhulst.
(Verhulst 1838)
Verhulst proposed the “logistique” model of population growth in response to the
logarithmic model suggested by Malthus (1798). In Malthus' model, population regulation could
only occur by density-independent factors, loosely categorized under “natural causes,” “misery”
and “vice.” Here, an exponentially growing population would swiftly outstrip its resources and
crash. Verhulst's logistic model, on the other hand, introduced an alternative, very elegant theory
with far-reaching implications: he suggested that populations might demonstrate self-regulation,
through an inverse relationship between growth rates and population density. These ideas were
picked up by mainstream ecology 80 years later, when Verhulst's logistic model was
rediscovered and expanded upon by Pearl & Reed (1920). It was later applied to multi-species
models of predator-prey conflict and competition by Lotka (1925) and Volterra (1926).
