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.
A third factor that can result in a Type III functional response is the relative abundance of different, alternative prey species. Although a predator may have a strong preference for a certain prey, in most cases it can turn to another, more abundant prey species that provides more profitable hunting. If rodents, for example, are more abundant than rabbits and quail, foxes and hawks will concentrate on rodents.
Ecologists call the act of turning to more abundant, alternate prey switching (Figure 14.9a). In switching, the predator feeds heavily on the more abundant species and pays little attention to the less abundant species. As the relative abundance of the second prey species increases, the predator turns its attention to that species.
The point in prey abundance when a predator switches depends considerably on the predator’s food preference. A predator may hunt longer and harder for a palatable species before turning to a more abundant, less palatable alternate prey. Conversely, the predator may turn from the less desirable species at a much higher level of abundance than it would from a more palatable species.
In a series of laboratory experiments, Roger Hughes and M. I. Croy of the University of Wales (Great Britain) examined prey switching in 15-spined stickleback (Spinachia spinachia) feeding on two prey species: amphipod (Gammarus locusta) and brine shrimp (Aremia spp.). In all experiments, fish showed the sigmoid response to changing relative abundances of prey, typical of switching (Figure 14.9b). The researchers found that a combination of changing attack efficiency and search image formation contributed to the observed pattern of prey switching.
Although simplistic, the model of functional response developed by Holling has been a valuable tool. It allows ecologists to explore how various behaviors—exhibited by both the predator and prey species—influence predation rate and subsequently predator and prey population dynamics. Because the model explicitly addresses the principle of time budget in the process of predation, this framework has been expanded to examine questions relating to the efficiency of foraging, a topic we will return to in Section 14.7.
14.6 Predators Respond Numerically to Changing Prey Density
As the density of prey increases, the predator population growth rate is expected to respond positively. A numerical response of predators can occur through reproduction by predators (as suggested by the conversion factor b in the Lotka–Volterra equation for predators) or through the movement of predators into areas of high prey density (immigration). The latter is referred to as an aggregative response (Figure 14.10). The tendency of predators to aggregate in areas of high prey density can be a crucial feature in determining a predator population’s ability to regulate prey density. Aggregative response is important because most predator populations grow slowly in comparison to those of their prey.
Marc Salamolard of the Center for Biological Studies (French National Center for Scientific Research) and colleagues provide an example of how these two components of numerical response (immigration and increased reproduction) can combine to influence the response of a predator population to changes in prey abundance. Salamolard quantified the functional and numerical responses of Montagu’s harrier (Circus pygargus), a migratory raptor, to variations in abundance of its main prey, the common vole (Microtus arvalis). The researchers monitored variations in the vole population over a 15-year period and the response of the harrier population to this variable food supply. This predatory bird species exhibits a Type II functional response; the per capita rate of predation increases with increasing prey density up to some maximum (see Figure 14.11a). The researchers were able to provide a number of measures relating to the bird’s numerical response. The breeding density of birds increases with increasing prey. This increase in predator density is a result of an increase in the number of nesting pairs occupying the area and represents an aggregative response density (Figure 14.11b). In addition, the mean brood size of nesting pairs (mean number of chicks at fledging) also increased (Figure 14.11c). The net result is an increase in the growth rate of the predator population in response to an increase in the abundance of prey (vole population).
The work of Włodzimierz Je̜drzejewski and colleagues at the Mammal Research Institute of the Polish Academy of Sciences provides an example where the numerical response of the predator population is dominated by reproductive effort. Je̜drzejewski examined the response of a weasel (Mustela nivalis) population to the density of two rodents, the bank vole (Clethrionomys glareolus) and the yellow-necked mouse (Apodemus flavicollis), in Białowieża National Park in eastern Poland in the early 1990s. During that time, the rodents experienced a two-year irruption in population size brought about by a heavy crop of oak, hornbeam, and maple seeds. The abundance of food stimulated the rodents to breed throughout the winter. The long-term average population density was 28–74 animals per hectare. During the irruption, the rodent population reached nearly 300 per hectare and then declined precipitously to 8 per hectare (Figure 14.12).
The weasel population followed the fortunes of the rodent population. At normal rodent densities, the winter weasel density ranged from 5–27 per km2 declining by early spring to 0–19. Following reproduction, the midsummer density rose to 42–47 weasels per km2. Because reproduction usually requires a certain minimal time (related to gestation period), a lag typically exists between an increase of a prey population and a numerical response by a predator population. No time lag, however, exists between increased rodent reproduction and weasel reproductive response. Weasels breed in the spring, and with an abundance of food they may have two litters or one larger litter. Young males and females breed during their first year of life. During the irruption, the number of weasels grew to 102 per km2 and during the crash the number declined to 8 per km2. The increase and decline in weasels was directly related to changes in the rates of birth and death in response to the spring rodent density.
The work of Mark O’Donoghue and colleagues at the University of British Columbia (Canada) provides an example of a numerical response of a predator population in which there is a distinct lag between the prey and predator populations. The researchers monitored populations of Canadian lynx (Lynx canadensis) and their primary prey, the snowshoe hare (Lepus americanus) at a site in the southwest Yukon Territory, Canada, between 1986 and 1995. During this time, the lynx population increased 7.5-fold in response to a dramatic increase in the number of snowshoe hares (Figure 14.13a). The abundance of lynx lagged behind the increase in the hare population, reaching its maximum a year later than the peak in numbers of snowshoe hares. The increase in the lynx population eventually led to a decline in the hare population. The decline in the number of lynx was associated with lower reproductive output and high emigration rates. Few to no kits (offspring) were produced by lynx after the second winter of declining numbers of hares. High emigration rates were characteristic of lynx during the cyclic peak and decline, and low survival was observed late in the decline. The delayed numerical response (lag) results in a cyclic pattern when the population of lynx is plotted as a function of size of the prey population (Figure 14.13b), as was observed in the analysis of the Lotka–Volterra model in Section 14.2 (see Figure 14.2c).
14.7 Foraging Involves Decisions about the Allocation of Time and Energy
Thus far, we have discussed the activities of predators almost exclusively in terms of foraging. But all organisms are required to undertake a wide variety of activities associated with survival, growth, and reproduction. Time spent foraging must be balanced against other time constraints such as defense, avoiding predators, searching for mates, or caring for young. This trade-off between conflicting demands has led ecologists to develop an area of research known as optimal foraging theory . At the center of optimal foraging theory is the hypothesis that natural selection favors “efficient” foragers, that is, individuals that maximize energy or nutrient intake per unit of effort. Efficient foraging involves an array of decisions: what food to eat, where and how long to search, and how to search. Optimal foraging theory approaches these decisions in terms of costs and benefits. Costs can be measured in terms of the time and energy expended in the act of foraging, and benefits should be measured in terms of fitness. However, it is extremely difficult to quantify the consequences of a specific behavioral choice on the probability of survival and reproduction. As a result, benefits are typically measured in terms of energy or nutrient gain, which is assumed to correlate with individual fitness.
One of the most active areas of research in optimal foraging theory has focused on the composition of animal diets—the process of choosing what to eat from among a variety of choices. We can approach this question using the framework of time allocation developed in the simple model of function response in Section 14.5, where the total time spent foraging (T) can be partitioned into two categories of activity: searching (Ts) and handling (Th). Here we will define the search time for a single prey (per capita search time) as ts, and the handling time for a single captured prey as th (capital letters refer to total search and handling time during a given period of hunting or feeding, T).
For simplicity, consider a predator hunting in a habitat that contains just two kinds of prey: P1 and P2. Assume that the two prey types yield E1 and E2 units of net energy gain (benefits), and they require th1th1 and th2th2 seconds to handle (costs). Profitability of the two prey types is defined as the net energy gained per unit handling time: E1/th1E1/th1 and E2/th2E2/th2 . Now suppose that P1 is more profitable than P2: E1/th1> E2/th2P2: E1/th1> E2/th2 . Optimal foraging theory predicts that P1 would be the preferred prey type because it has a greater profitability.
This same approach can be applied to a variety of prey items within a habitat. Behavioral ecologist Nicholas B. Davies of the University of Cambridge examined the feeding behavior of the pied wagtail (Motacilla alba) in a pasture near Oxford, England. The birds fed on various dung flies and beetles attracted to cattle droppings. Potential prey types were of various sizes: small, medium, and large flies and beetles. The wagtails showed a decided preference for medium-sized prey (Figure 14.14a). The size of the prey selected corresponded to the prey the birds could handle most profitably (E/th; Figure 14.14b). The birds virtually ignored smaller prey. Although easy to handle (low value of th), small prey did not return sufficient energy (E), and large prey required too much time and effort to handle relative to the energy gained.
The simple model of optimal foraging presented here provides a means for evaluating which of two or more potential prey types is most profitable based on the net energy gain per unit of handling time. As presented, however, it also implies that the predator always chooses the most profitable prey item. Is there ever a situation in which the predator would choose to eat the alternative, less profitable prey? To answer this question, we turn our attention to the second component of time involved in foraging, search time (ts).
Quantifying Ecology 14.2 A Simple Model of Optimal Foraging
Faced with a variety of potential food choices, predators make decisions regarding which types of food to eat and where and how long to search for food. But how are these decisions made? Do predators function opportunistically, pursuing prey as they are encountered, or do they make choices and pass by potential prey of lesser quality (energy content) while continuing the search for more preferred food types? If the objective is to maximize energy intake (energy gain per unit time), a predator should forage in a way that maximizes benefits (energy gained from consuming prey) relative to costs (energy expended). This concept of maximizing energy intake is the basis of models of optimal foraging.
Any food item has a benefit (energy content) and a cost (in terms of time and energy involved in search and acquisition). The benefit–cost relationship determines how much profit a particular food item represents. The profitability of a prey item is the ratio of its energy content (E) to the time required for handling the item (th), or E/th.
Let us assume that a predator has two possible choices of prey, P1 and P2. The two prey types have energy contents of E1 and E2 (units of kilojoules [kJ]) and take th1th1 and th2th2 seconds to handle. The searching time for the two prey types are ts1ts1 and ts2ts2 in seconds. We will define P1 as the most profitable prey type (greater value of E/th).
As the predator searches for P1, it encounters an individual of P2. Should the predator capture and eat P2 or continue to search for another individual of P1? Which decision—capture P2 or continue to search—would be the more profitable and maximize the predator’s energy intake? This is the basic question posed by optimal foraging theory, and the solution depends on the search time for P1.
The profitability of capturing and eating P2 is E2/th2E2/th2 and the profitability of continuing the search, capturing, and eating another individual of P1 is E1/(th1+ts1)E1/(th1+ts1) . Notice that the decision to ignore P2 and continue the search carries the additional cost of the average search time for P1, ts1ts1 . Therefore, the optimal solution, the decision that will yield the greater profit, is based on the following conditions:
If:
E2/th2>E1/(th1+ts1)E2/th2>E1/(th1+ts1)
then capture and eat P2.
If:
E2/th2<E1/(th1+ts1)E2/th2<E1/(th1+ts1)
then ignore P2 and continue to search for P1.
Therefore, if the search time for P1 is short, the predator will be better off continuing the search; if the search time is long, the most profitable decision is to capture and consume P2.
The benefit–cost trade-off for the optimal choice in prey selection is best understood through an actual example. David Irons and colleagues at Oregon State University examined the foraging behavior of glaucous-winged gulls (Larus glaucescens) that forage in the rock intertidal habitats of the Aleutian Islands, Alaska. Data on the abundance of three prey types (urchins, chitons, and mussels) in three intertidal zones (A, B, and C) are presented in the table. Mean densities of the three prey types in numbers per m2 are given for the three zones. Average energy content (E), handling time (th), and search time (ts) for each of the three prey types are also listed in the table.
In feeding preference experiments, where search and handling time were not a consideration, chitons were the preferred prey type and the obvious choice for maximizing energy intake. However, the average abundance of urchins across the three zones is greater than that of chitons. As a gull happens upon an urchin while hunting for chitons, should it capture and eat the urchin or continue to search for its preferred food? Under conditions of optimal foraging, the decision depends on the conditions outlined previously. The profit gained by capturing and consuming the urchin is E/th = (7.45 kJ/8.3 s), or 0.898. In contrast, the profit gained by ignoring the urchin and searching, capturing, and consuming another chiton is E/(th + ts) = [24.52 kJ/(3.1 s + 37.9 s)] or 0.598. Because the profit gained by consuming the urchin is greater than the profit gained by ignoring it and continuing the search for chitons, it would make sense for the gull to capture and eat the urchin.
What about a gull foraging in intertidal zone A that happens upon a mussel? The profit gained by capturing and eating the mussel is (1.42/2.9), or 0.490, and the profit gained by continuing the search for a chiton remains [24.52 kJ/(3.1 s + 37.9 s)] or 0.598. In this case, the gull would be better off ignoring the mussel and continuing the search for chitons.
We now know what the gulls “should do” under the hypothesis of optimal foraging. But do they in fact forage optimally as defined by this simple model of benefits and costs? If gulls are purely opportunistic, their selection of prey in each of the three zones would be in proportion to their relative abundances. Irons and colleagues, however, found that the relative preferences for urchins and chitons were in fact related to their profitability (E/th); mussels, however, were selected less frequently than predicted by their relative value of E.
1. How would reducing the energy content of chitons by half (to 12.26 kJ) influence the decision whether the gull should capture and eat the mussel or continue searching for a chiton in the example presented?
2. Because the gulls do not have the benefit of the optimal foraging model in deciding whether to select a prey item, how might natural selection result in the evolution of optimal foraging behavior?
Alternate View
| Prey Type | Density Zone A | Density Zone B | Density Zone C | Energy (kJ/individual) | Handling Time (s) | Search Time (s) |
| Urchins | 0.0 | 3.9 | 23.0 | 7.45 | 8.3 | 35.8 |
| Chitons | 0.1 | 10.3 | 5.6 | 24.52 | 3.1 | 37.9 |
| Mussels | 852.3 | 1.7 | 0.6 | 1.42 | 2.9 | 18.9 |
Suppose that while searching for P1, the predator encounters an individual of P2. Should it eat it or continue searching for another individual of P1? The optimal choice will depend on the search time for P1, defined as ts1ts1 . The profitability of consuming the individual of P2 is E2/th2E2/th2 ; the alternative choice of continuing to search, capture, and consume an individual of P1 is E1/(th1+ts1)E1/(th1+ts1) , which now includes the additional time cost of searching for another individual of P1 (ts1ts1 ). If E2/th2>E1/(th1+ts1)E2/th2>E1/(th1+ts1) , then according to optimal foraging theory, the predator would eat the individual of P2. If this condition does not hold true, then the predator would continue searching for P1. Testing this hypothesis requires the researcher to quantify the energy value and search and handling times of the various potential prey items. An example of this simple model of optimal prey choice is presented in Quantifying Ecology 14.2.
A wealth of studies examines the hypothesis of optimal prey choice in a wide variety of species and habitats, and patterns of prey selection generally follow the rules of efficient foraging. But the theory as presented here fails to consider the variety of other competing activities influencing a predator’s time budget and the factors other than energy content that may influence prey selection. One reason that a predator consumes a varied diet is that its nutritional requirements may not be met by eating a single prey species (see Chapter 7).
14.8 Risk of Predation Can Influence Foraging Behavior
Most predators are also prey to other predatory species and therefore face the risk of predation while involved in their routine activities, such as foraging. Habitats and foraging areas vary in their foraging profitability and their risk of predation. In deciding whether to feed, the forager must balance its potential energy gains against the risk of being eaten. If predators are about, then it may be to the forager’s advantage not to visit a most profitable, but predator-prone, area and to remain in a less profitable but more secure part of the habitat. Many studies report how the presence of predators affects foraging behavior. In one such study, Jukka Suhonen of the University of Jyväskylä (Finland) examined the influence of predation risk on the use of foraging sites by willow tits (Parus montanus) and crested tits (Parus cristatus) in the coniferous forests of central Finland. During the winter months, flocks of these two bird species forage in spruce, pine, and birch trees. The major threat to their survival is the Eurasian pygmy owl (Glaucidium passerinum). The owl is a diurnal ambush, or sit-and-wait hunter, that pounces downward on its prey. Its major food is voles, and when vole populations are high, usually every three to five years, the predatory threat to these small passerine birds declines. When vole populations are low, however, the small birds become the owl’s primary food. During these periods, the willow and crested tits forsake their preferred foraging sites on the outer branches and open parts of the trees, restricting their foraging activity to the denser inner parts of spruce trees that provide cover and to the tops of the more open pine and leafless birch trees.
14.9 Coevolution Can Occur between Predator and Prey
By acting as agents of mortality, predators exert a selective pressure on prey species (see Chapter 12, Section 12.3). That is, any characteristic that enables individual prey to avoid being detected and captured by a predator increases its fitness. Natural selection functions to produce “smarter,” more evasive prey (fans of the Road Runner cartoons should already understand this concept). However, failure to capture prey results in reduced reproduction and increased mortality of predators. Therefore, natural selection also produces “smarter,” more skilled predators. As characteristics that enable them to avoid being caught evolve in prey species, more effective means of capturing prey evolve in predators. To survive as a species, the prey must present a moving target that the predator can never catch. This view of the coevolution between predator and prey led the evolutionary biologist Leigh Van Valen to propose the Red Queen hypothesis. In Lewis Carroll’s Through the Looking Glass, and What Alice Found There, there is a scene in the Garden of Living Flowers in which everything is continuously moving. Alice is surprised to see that no matter how fast she moves, the world around her remains motionless—to which the Red Queen responds, “Now, here, you see, it takes all the running you can do, to keep in the same place.” So it is with prey species. To avoid extinction at the hands of predators, prey must evolve means of avoiding capture; they must keep moving just to stay where they are.
