# Predation Takes a Variety of Forms.

The broad definition of predation as the consumption of one living organism (the prey) by another (the predator) excludes scavengers and decomposers. Nevertheless, this definition results in the potential classification of a wide variety of organisms as predators. The simplest classification of predators is represented by the categories of heterotrophic organisms presented previously, which are based on their use of plant and animal tissues as sources of food: carnivores (carnivory—consumption of animal tissue), herbivores (herbivory—consumption of plant or algal tissue), and omnivores (omnivory—consumption of both plant and animal tissues); see Chapter 7. Predation, however, is more than a transfer of energy. It is a direct and often complex interaction of two or more species: the eater and the eaten. As a source of mortality, the predator population has the potential to reduce, or even regulate, the growth of prey populations. In turn, as an essential resource, the availability of prey may function to regulate the predator population. For these reasons, ecologists recognize a functional classification, which provides a more appropriate framework for understanding the interconnected dynamics of predator and prey populations and which is based on the specific interactions between predator and prey.

In this functional classification of predators, we reserve the term *predator*, or *true predator*,
for species that kill their prey more or less immediately upon capture.
These predators typically consume multiple prey organisms and continue
to function as agents of mortality on prey populations throughout their
lifetimes. In contrast, most herbivores (grazers and browsers) consume
only part of an individual plant. Although this activity may harm the
plant, it usually does not result in mortality. Seed predators and
planktivores (aquatic herbivores that feed on phytoplankton) are
exceptions; these herbivores function as true predators. Like
herbivores, parasites feed on the prey organism (the host) while it is
still alive and although harmful, their feeding activity is generally
not lethal in the short term. However, the association between parasites
and their host organisms has an intimacy that is not seen in true
predators and herbivores because many parasites live on or in their host
organisms for some portion of their life cycle. The last category in
this functional classification, the parasitoids, consists of a group of
insects classified based on the egg-laying behavior of adult females and
the development pattern of their larvae. The parasitoid attacks the
prey (host) indirectly by laying its eggs on the host’s body. When the
eggs hatch, the larvae feed on the host, slowly killing it. As with
parasites, parasitoids are intimately associated with a single host
organism, and they do not cause the immediate death of the host.

In this chapter we will use the preceding functional classifications,
focusing our attention on the two categories of true predators and
herbivores. (From this point forward, the term *predator* is used
in reference to the category of true predator). We will discuss the
interactions of parasites and parasitoids and their hosts later,
focusing on the intimate relationship between parasite and host that
extends beyond the feeding relationship between predator and prey (Chapter 15).

We will begin by exploring the connection between the hunter and the hunted, developing a mathematical model to define the link between the populations of predator and prey. The model is based on the same approach of quantifying the per capita effects of species interactions on rates of birth and death within the respective populations that we introduced previously (Chapter 13, Section 13.2). We will then examine the wide variety of subjects and questions that emerge from this simple mathematic abstraction of predator–prey interactions.

**14.2 Mathematical Model Describes the Interaction of Predator and Prey Populations**

In the 1920s, Alfred Lotka and Vittora Volterra turned their attention from competition (see Section 13.2) to the effects of predation on population growth. Independently, they proposed mathematical statements to express the relationship between predator and prey populations. They provided one equation for the prey population and another for the predator population.

The population growth equation for the prey population consists of two components: the exponential model of population growth (d*N*/d*t* = *rN*; see Chapter 9)
and a term that represents mortality of prey from predation. Mortality
resulting from predation is expressed as the per capita rate at which
predators consume prey (number of prey consumed per predator per unit
time). The per capita consumption rate by predators is assumed to
increase linearly with the size of the prey population (Figure 14.1a) and can therefore be represented as *cN*prey, where *c* represents the capture efficiency of the predator, defined by the slope of the relationship shown in Figure 14.1a. (Note that the greater the value of *c*,
the greater the number of prey captured and consumed for a given prey
population size, which means that the predator is more efficient at
capturing prey.) The total rate of predation (total number of prey
captured per unit time) is the product of the per capita rate of
consumption (*cN*prey) and the number of predators (*N*pred), or (*cN*prey)*N*pred.
This value represents a source of mortality for the prey population and
must be subtracted from the rate of population increase represented by
the exponential model of growth. The resulting equation representing the
rate of change in the prey population (d*N*prey/d*t*) is:

dNprey/dt=rNprey−(cNprey)NpreddNprey/dt=rNprey−(cNprey)Npred

The equation for the predator population likewise consists of two
components: one representing birth and the other death of predators. The
predator mortality rate is assumed to be a constant proportion of the
predator population and is therefore represented as *dN*pred, where *d*
is the per capita death rate (this value is equivalent to the per
capita death rate in the exponential model of population growth
developed in Chapter 9).
The per capita birthrate is assumed to be a function of the amount of
food consumed by the predator, the per capita rate of consumption (*cN*prey), and increases linearly with the per capita rate at which prey are consumed (Figure 14.1b). The per capita birthrate is therefore the product of *b*,
the efficiency with which food is converted into population growth
(reproduction), which is defined by the slope of the relationship shown
in Figure 14.1b, and the rate of predation (*cN*prey), or *b*(*cN*prey). The total birthrate for the predator population is then the product of the per capita birthrate, *b*(*cN*prey), and the number of predators, *N*pred: *b*(*cN*prey)*N*pred. The resulting equation representing the rate of change in the predator population is:

dNpred/dt=b(cNprey)Npred−dNpreddNpred/dt=b(cNprey)Npred−dNpred

The Lotka–Volterra equations for predator and prey population growth therefore explicitly link the two populations, each functioning as a density-dependent regulator on the other. Predators regulate the growth of the prey population by functioning as a source of density-dependent mortality. The prey population functions as a source of density-dependent regulation on the birthrate of the predator population. To understand how these two populations interact, we can use the same graphical approach used to examine the outcomes of interspecific competition (Chapter 13, Section 13.2).

In the absence of predators (or at low predator density), the prey population grows exponentially (d*N*prey/d*t* = *rN*prey).
As the predator population increases, prey mortality increases until
eventually the mortality rate resulting from predation, (*cN*prey)*N*pred, is equal to the inherent growth rate of the prey population, *rN*prey, and the net population growth for the prey species is zero (d*N*prey/d*t* = 0). We can solve for the size of the predator population (*N*pred) at which this occurs:

cNpreyNpred=rNpreycNpred=rNpred=rccNpreyNpred=rNprey cNpred=r Npred=rc

Simply put, the growth rate of the prey population is zero when the
number of predators is equal to the per capita growth rate of the prey
population (*r*) divided by the efficiency of predation (*c*).

This value therefore defines the zero-growth isocline for the prey population (Figure 14.2a). As with the construction of the zero-growth isoclines in the analysis of the Lotka–Volterra competition equations (see Section 13.2, Figure 13.1), the two axes of the graph represent the two interacting populations. The *x*-axis represents the size of the prey population (*N*prey), and the *y*-axis represents the predator population (*N*pred). The prey zero-growth isocline is independent of the prey population size (*N*prey) and is represented by a line parallel to the *x*-axis at a point along the *y*-axis represented by the value *N*pred = *r*/*c*. For values of *N*pred below the zero-growth isocline, mortality resulting from predation, (*cN*prey)*N*pred, is less than the inherent growth rate of the prey population (*rN*prey),
so population growth is positive and the prey population increases, as
represented by the green horizontal arrow pointing to the right. If the
predator population exceeds this value, mortality resulting from
predation, (*cN*prey)*N*pred, is greater than the inherent growth rate of the prey population (*rN*prey)
and the growth rate of the prey becomes negative. The corresponding
decline in the size of the prey population is represented by the green
arrow pointing to the left.

Likewise, we can define the zero-growth isocline for the predator
population by examining the influence of prey population size on the
growth rate of the predator population. The growth rate of the predator
population is zero (d*N*pred/d*t* = 0) when the rate of predator increase (resulting from the consumption of prey) is equal to the rate of mortality:

b(cNprey)Npred=dNpredbcNprey=dNprey=dbcb(cNprey)Npred=dNpred bcNprey=d Nprey=dbc

The growth rate of the predator population is zero when the size of the prey population (*N*prey) equals the per capita mortality rate of the predator (*d*) divided by the product of the efficiency of predation (*c*) and the ability of predators to convert the prey consumed into offspring (*b*). Note that these are the two factors that determine the per capita predator birthrate for a given prey population (*N*prey). As with the prey population, we can now use this value to define the zero-growth isocline for the predator population (Figure 14.2b). The predator zero-growth isocline is independent of the predator population size (*N*pred) and is represented by a line parallel to the *y*-axis at a point along the *x*-axis (represented by the value *N*prey = *d*/*bc*). For values of *N*prey to the left of the zero-growth isocline (toward the origin) the rate of birth in the predator population, *b*(*cN*prey)*N*pred, is less than the rate of mortality, *dN*pred,
and the growth rate of the predator population is negative. The
corresponding decline in population size is represented by the red arrow
pointing downward. For values of *N*prey to the right of the
predator zero-growth isocline, the population birthrate is greater than
the mortality rate and the population growth rate is positive. The
increase in population size is represented by the vertical red arrow
pointing up.

As we did in the graphical analysis of competitive interactions (see Section 13.3, Figure 13.2),
the two zero-growth isoclines representing the predator and prey
populations can be combined to examine changes in the growth rates of
two interacting populations for any combination of population sizes (Figure 14.2c).
When plotted on the same set of axes, the zero-growth isoclines for the
predator and prey populations divide the graph into four regions. In
the lower right-hand region, the combined values of *N*prey and *N*pred
are below the prey zero-isocline (green dashed line), so the prey
population increases, as represented by the green arrow pointing to the
right. Likewise, the combined values lie above the zero-growth isocline
for the predator population so the predator population increases, as
represented by the red arrow pointing upward. The next value of (*N*prey, *N*pred)
will therefore be within the region defined by the green and red arrows
represented by the black arrow. The combined dynamics indicated by the
black arrow point toward the upper right region of the graph. For the
upper right-hand region, combined values of *N*prey and *N*pred
are above the prey isocline, so the prey population declines as
indicated by the green horizontal arrow pointing left. The combined
values are to the right of the predator isocline, so the predator
population increases as indicated by the vertical red arrow pointing up.
The black arrow indicating the combined dynamics points toward the
upper left-hand region of the graph. In the upper left-hand region of
the graph, the combined values of *N*prey and *N*pred are
above the prey isocline and to the left of the predator isocline so both
populations decline. In this case, the combined dynamics (black arrow)
point toward the origin. In the last region of the graph, the lower
left, the combined values of *N*prey and *N*pred are below the
prey isocline and to the left of the predator isocline. In this case,
the prey population increases and the predator population declines. The
combined dynamics point in the direction of the lower left-hand region
of the graph, completing a circular, or cyclical, pattern, where the
combined dynamics of the predator and prey populations move in a
counterclockwise pattern through the four regions defined by the
population isoclines.