An experiment that was conducted by gause in the 1930s with paramecium clearly demonstrated

CHAPTER 14

Smith, T. M., & Smith, R. L. (2015). Elements of Ecology (9th ed.). Boston, MA: Pearson.

14.1 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 (dN/dt = 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 cNprey, 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 (cNprey) and the number of predators (Npred), or (cNprey)Npred. 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 (dNprey/dt) 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 dNpred, 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 (cNprey), 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 (cNprey), or b(cNprey). The total birthrate for the predator population is then the product of the per capita birthrate, b(cNprey), and the number of predators, Npred: b(cNprey)Npred. 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 (dNprey/dt = rNprey). As the predator population increases, prey mortality increases until eventually the mortality rate resulting from predation, (cNprey)Npred, is equal to the inherent growth rate of the prey population, rNprey, and the net population growth for the prey species is zero (dNprey/dt = 0). We can solve for the size of the predator population (Npred) 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 (Nprey), and the y-axis represents the predator population (Npred). The prey zero-growth isocline is independent of the prey population size (Nprey) and is represented by a line parallel to the x-axis at a point along the y-axis represented by the value Npred = r/c. For values of Npred below the zero-growth isocline, mortality resulting from predation, (cNprey)Npred, is less than the inherent growth rate of the prey population (rNprey), 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, (cNprey)Npred, is greater than the inherent growth rate of the prey population (rNprey) 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 (dNpred/dt = 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 (Nprey) 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 (Nprey). 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 (Npred) and is represented by a line parallel to the y-axis at a point along the x-axis (represented by the value Nprey = d/bc). For values of Nprey to the left of the zero-growth isocline (toward the origin) the rate of birth in the predator population, b(cNprey)Npred, is less than the rate of mortality, dNpred, 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 Nprey 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 Nprey and Npred 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 (Nprey, Npred) 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 Nprey and Npred 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 Nprey and Npred 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 Nprey and Npred 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.

14.3 Predator–Prey Interaction Results in Population Cycles

The graphical analysis of the combined dynamics of the predator (Npred) and prey (Nprey) populations using the zero-growth isoclines presented in Figure 14.2c reveal a cyclical pattern that represents the changes in the two populations through time (Figure 14.3a). If we plot the changes in the predator and prey populations as a function of time, we see that the two populations rise and fall in oscillations (Figure 14.3b) with the predator population lagging behind the prey population. The oscillation occurs because as the predator population increases, it consumes more and more prey until the prey population begins to decline. The declining prey population no longer supports the large predator population. The predators now face a food shortage, and many of them starve or fail to reproduce. The predator population declines sharply to a point where the reproduction of prey more than balances its losses through predation. The prey population increases, eventually followed by an increase in the population of predators. The cycle may continue indefinitely. The prey is never quite destroyed; the predator never completely dies out.

How realistic are the predictions of the Lotka–Volterra model of predator–prey interactions? Do predator–prey cycles actually occur, or are they just a mathematical artifact of this simple model? The Russian biologist G. F. Gause was the first to empirically test the predictions of the predator–prey models in a set of laboratory experiments conducted in the mid-1930s. Gause raised protozoans Paramecium caudatum (prey) and Didinium nasutum (predator) together in a growth medium of oats. In these initial experiments, Didinium always exterminated the Paramecium population and then went extinct as a result of starvation (Figure 14.4a). To add more complexity to the experimental design, Gause added sediment to the oat medium. The sediment functioned as a refuge for the prey, allowing the Paramecium to avoid predation. In this experiment the predator population went extinct, after which the prey hiding in the sediment emerged and increased in population (Figure 14.4b). Finally, in a third set of experiments in which Gause introduced immigration into the experimental design (every third day he introduced one new predator and prey individual to the populations), the populations produced the oscillations predicted by the model (Figure 14.4c). Gause concluded that the oscillations in predator–prey populations are not a property of the predator–prey interactions suggested by the model but result from the ability of populations to be “supplemented” through immigration.

In the mid-1950s, the entomologist Carl Huffaker (University of California–Berkley) completed a set of experiments focused on the biological control of insect populations (controlling insect populations through the introduction of predators). Huffaker questioned the conclusions drawn by Gause in his experiments. He thought that the problem was the simplicity of the experiment design used by Gause. Huffaker sought to develop a large and complex enough laboratory experiment in which the predator–prey system would not be self-exterminating. He chose as the prey the six-spotted mite, Eotetranychus sexmaculatus, which feeds on oranges and another mite, Typhlodromus occidentalis, as predator. When the predator was introduced to a single orange infested by the prey, it completely eliminated the prey population and then died of starvation, just as Gause had observed in his experiments. However, by introducing increased complexity into his experimental design (rectangular tray of oranges, addition of barriers, partially covered oranges that functioned as refuges for prey, etc.) he was finally able to produce oscillations in predator–prey populations (Figure 14.5).

These early experiments show that predator–prey cycles can result from the direct link between predator and prey populations as suggested by the Lotka–Volterra equations (Section 14.2), but only by introducing environmental heterogeneity—which is a factor not explicitly considered in the model. As we shall see as our discussion progresses, environmental heterogeneity is a key feature of the natural environment that influences species interactions and community structure. However, these laboratory experiments do confirm that predators can have a significant effect on prey populations, and likewise, prey populations can function to control the dynamics of predators.

14.4 Model Suggests Mutual Population Regulation

The Lotka–Volterra model of predator–prey interactions assumes a mutual regulation of predator and prey populations. In the equations presented previously, the link between the growth of predator and prey populations is described by a single term relating to the consumption of prey: (cNprey)Npred. For the prey population, this term represents the regulation of population growth through mortality. In the predator population, it represents the regulation of population growth through reproduction. Regulation of the predator population growth is a direct result of two distinct responses by the predator to changes in prey population. First, predator population growth depends on the per capita rate at which prey are captured (cNprey). The relationship shown in Figure 14.1a implies that the greater the number of prey, the more the predator eats. The relationship between the per capita rate of consumption and the number of prey is referred to as the predator’s functional response . Second, this increased consumption of prey results in an increase in predator reproduction [b(cNprey)], referred to as the predator’s numerical response .

This model of predator–prey interaction has been widely criticized for overemphasizing the mutual regulation of predator and prey populations. The continuing appeal of these equations to population ecologists, however, lies in the straightforward mathematical descriptions and in the oscillatory behavior that seems to occur in predator–prey systems. Perhaps the greatest value of this model is in stimulating a more critical look at predator–prey interactions in natural communities, including the conditions influencing the control of prey populations by predators. A variety of factors have emerged from laboratory and field studies, including the availability of cover (refuges) for the prey (as in the experiments discussed in Section 14.3), the increasing difficulty of locating prey as it becomes scarcer, choice among multiple prey species, and evolutionary changes in predator and prey characteristics (coevolution). In the following sections, we examine each of these topics and consider how they influence predator–prey interactions.

14.5 Functional Responses Relate Prey Consumed to Prey Density

The English entomologist M. E. Solomon introduced the idea of functional response in 1949. A decade later, the ecologist C. S. Holling explored the concept in more detail, developing a simple classification based on three general types of functional response (Figure 14.6). The functional response is the relationship between the per capita predation rate (number of prey consumed per predator per unit time, Ne) and prey population size (Nprey) shown in Figure 14.1a. How a predator’s rate of consumption responds to changes in the prey population is a key factor influencing the predator’s ability to regulate the prey population.

In developing the predatory prey equations in Section 14.2, we defined the per capita rate of predation as cNprey, where c is the “efficiency” of predation, and Nprey is the size of the prey population. This is what Holling refers to as a Type I functional response . In the Type I functional response, the number of prey captured per unit time by a predator (per capita rate of predation, Ne) increases linearly with increasing number of prey (Nprey; Figure 14.6a). The rate of prey mortality as a result of predation (proportion of prey population captured per predator per unit time) for the Type I response is constant, equal to the efficiency of predation (c), as in Figure 14.6b.

The Type I functional response is characteristic of passive predators, such as filter feeders that extract prey from a constant volume of water that washes over their filtering apparatus. A range of aquatic organisms, from zooplankton (Figure 14.7a) to blue whales, exhibit this feeding bahavior. Filter feeders capture prey that flow through and over their filtering system, so for a given rate of water flow over their feeding apparatus, the rate of prey capture will be a direct function of the density of prey per volume of water.

The Type I functional response is limited in its description of the response of predators to prey abundance for two reasons. First, it assumes that predators never become satiated, that is, the per capita rate of consumption increases continuously with increasing prey abundance. In reality, predators will become satiated (“full”) and stop feeding. Even for filter feeders, there will be a maximum amount of prey that can be captured (filtered) per unit time above that it can no longer increase regardless of the increase in prey density (see Figure 14.7a). Secondly, even in the absence of satiation, predators will be limited by the handling time, that is, the time needed to chase, capture, and consume each prey item. By incorporating the constraint of handling time, the response of the per capita rate of predation (Ne) to increasing prey abundance (Nprey) now exhibits what Holling refers to as a Type II functional response . In the Type II functional response, the per capita rate of predation (Ne) increases in a decelerating fashion, reaching a maximum rate at some high prey population size (see Figure 14.6a). The reason that the value of Ne approaches an asymptote is related to the predator’s time budget (Figure 14.8; for a mathematical derivation of the Type II functional response, see Quantifying Ecology 14.1).

We can think of the total amount of time that a predator spends feeding as T. This time consists of two components: time spent searching for prey, Ts, and time spent handling the prey once it has been encountered, Th. The total time spent feeding is then: T = Ts + Th. Now as prey abundance (Nprey) increases, the number of prey captured (Ne) during the time period T increases (because it is easier to find a prey item as the prey become more abundant); however, the handling time (Th) also increases (because it has captured more prey to handle), decreasing the time available for further searching (Ts). Handling time (Th) will place an upper limit on the number of prey a predator can capture and consume in a given time (T). At high prey density, the search time approaches zero and the predator is effectively spending all of its time handling prey (Th approaches T). The result is a declining mortality rate of prey with increasing prey density (see Figure 14.6b). The Type II functional response is the most commonly reported for predators (see Figure 14.7b).

Holling also described a Type III functional response , illustrated in Figures 14.6a and 14.7c. At high prey density, this functional response is similar to Type II, and the explanation for the asymptote is the same. However, the rate at which prey are consumed is low at first, increasing in an S-shaped (sigmoid) fashion as the rate of predation approaches the maximum value. In the Type III functional response, mortality rate of the prey population is negligible at low prey abundance, but as the prey population increases (as indicated by the upward sweep of the curve), the mortality rate of the population increases in a density-dependent fashion (Figure 14.6b). However, the regulating effect of predators is limited to the interval of prey density where mortality increases. If prey density exceeds the upper limit of this interval, then mortality resulting from predation starts to decline.

Quantifying Ecology 14.1 Type II Functional Response

The Type I functional response suggests a form of predation in which all of the time allocated to feeding is spent searching (Ts). In general, however, the time available for searching is shorter than the total time associated with consuming the Ne prey because time is required to “handle” the prey item. Handling includes chasing, killing, eating, and digesting. (Type I functional response assumes no handling time below the maximum rate of ingestion.) If we define th as the time required by a predator to handle an individual prey item, then the time spent handling Ne prey will be the product Neth. The total time (T) spent searching and handling the prey is now:

Relationship between the density of prey population (x-axis) and the per capita rate of prey consumed (y-axis) for the model of predator functional response presented above that includes both search (Ts) and handling (Th = Neth) time (T = Ts + Th). At low prey density, the number of prey consumed is low, as is handling time. As prey density increases, the number of prey consumed increases; a greater proportion of the total foraging time (T) is spent handling prey, reducing time available for searching. As the handling time approaches the total time spent foraging, the per capita rate of prey consumed approaches an asymptote. The resulting curve is referred to as a Type II functional response.

T=Ts+(Neth)T=Ts+(Neth)

By rearranging the preceding equation, we can define the search time as:

Ts=T−NethTs=T−Neth

For a given total foraging time (T), search time now varies, decreasing with increasing allocation of time to handling.

We can now expand the original equation describing the type I functional response [Ne – (cNprey)Ts] by substituting the equation for Ts just presented. This includes the additional time constraint of handling the Ne prey items:

Ne=c(T−Neth)NpreyNe=c(T−Neth)Nprey

Note that Ne, the number of prey consumed during the time period T, appears on both sides of the equation, so to solve for Ne, we must rearrange the equation.

Ne=c(NpreyT−NpreyNeth)Ne=c(NpreyT−NpreyNeth)

Move c inside the brackets, giving:

Ne=cNpreyT−NecNpreythNe=cNpreyT−NecNpreyth

Add NecNpreythNecNpreyth to both sides of the equation, giving:

Ne+NecNpreyth=cNpreyTNe+NecNpreyth=cNpreyT

Rearrange the left-hand side of the equation, giving:

Ne(1+cNpreyth)=cNpreyTNe(1+cNpreyth)=cNpreyT

Divide both sides of the equation by (1+cNpreyth),(1+cNpreyth), giving:

Ne=cNpreyT(1+cNpreyth)Ne=cNpreyT(1+cNpreyth)

We can now plot the relationship between Ne and Nprey for a given set of values for c, T, and th. (Recall that the values of c, T, and th are constants.)

Several factors may result in a Type III response. Availability of cover (refuge) that allows prey to escape predators may be an important factor. If the habitat provides only a limited number of hiding places, it will protect most of the prey population at low density, but the susceptibility of individuals will increase as the population grows.

Another reason for the sigmoidal shape of the Type III functional response curve may be the predator’s search image , an idea first proposed by the animal behaviorist L. Tinbergen. When a new prey species appears in the area, its risk of becoming selected as food by a predator is low. The predator has not yet acquired a search image—a way to recognize that species as a potential food item. Once the predator has captured an individual, it may identify the species as a desirable prey. The predator then has an easier time locating others of the same kind. The more adept the predator becomes at securing a particular prey item, the more intensely it concentrates on it. In time, the number of this particular prey species becomes so reduced or its population becomes so dispersed that encounters between it and the predator lessen. The search image for that prey item begins to wane, and the predator may turn its attention to another prey species.