To complete the classification, there may be an interactive relationshipbetween
the population and the resource in that the level of the resource influences the rate
of increase of the population, and reciprocally the level of the population’s density
influences the rate of increase of the resource. The dynamics of the animals interact
with the dynamics of the resource, that is the relationship between a herbivore and
its food supply and between a predator and its prey resource. In a reactive relationship,
however, the rate of increase of the animal population reacts to the level of the resource
(as before) but the density of the animals has no reciprocal influence on the rate of
renewal of the resource. The relationships between a scavenger and its food supply
or between a herbivore and salt licks are examples of reactive relationships.
We start by developing a general theoretical framework that applies in principle
to all consumer–resource relationships, regardless of whether they focus on plants
and herbivores, carnivores and their herbivorous prey, or all three.
The origin of consumer–resource theory can be traced directly to the contributions
of two early ecologists: Alfred Lotka and Vito Volterra (Kingsland 1985). Starting
from very different backgrounds, these two men simultaneously developed a similar
framework for thinking about interactions between consumers and their resources
(Lotka 1925; Volterra 1926b), a general framework that is still in common use, albeit
with considerable change in biological details. The framework is a set of mathemat-
ical expressions for simultaneous changes in the density of consumers (denoted here
by N) and their resources (denoted V):
=growth of resource −mortality due to consumption
=growth of consumer due to consumption −mortality
In the case of resources, mortality is largely due to consumption, whereas consumers
experience a constant background level of mortality. For example, one might model
reproduction and mortality by the following equations (Rosenzweig and MacArthur
1963):
=rmaxV 1 −−
=−dN
where rmaxis maximum per capita rate of resource recruitment, Kis resource carry-
ing capacity in the absence of consumers, ais area searched per unit time by con-
sumers, his handling time for each resource item, cis a coefficient for converting
resource consumption into offspring, and dis consumer per capita mortality rate.
The particular form of the equations used in this example is based on the most com-
monly observed patterns. In the absence of consumption (e.g. when N=0), the resource
population has a logistic pattern of growth (see Chapter 8). In other words, the resource
population is self-regulating. Consumption rates and per capita rates of growth by
acVN
1 +ahV
dN
dt
aVN
1 +ahV
D
F
V
K
A
C
dV
dt
dN
dt
dV
dt
CONSUMER–RESOURCE DYNAMICS 197
12.4 Consumer–resource dynamics: general theory
