Behavioral Ecology: Optimal Foraging Introduction

BIOL 101L: Principles of Biology Fall 2008

This week you will complete an experiment designed to quantify the foraging behavior of animals. Using your classmates as experimental subjects, you will test hypotheses about the optimal foraging behavior in patches that differ in quality. The purpose of this lab is to explore a model that describes the behavioral strategies.

Introduction

Animals are constantly faced with decisions about where to look for food and what to eat. Ecologists hypothesize that natural selection favors foragers who maximize their fitness. However, the fitness of wild organisms is usually very hard to measure directly. In ecological studies, fitness is often estimated from an easily measured variable, such as energy gain. In doing so, one assumes that individuals who gain the most energy have the greatest fitness. Accordingly, we define an optimal forager as one that forages in a way that maximizes its net energy gain (i.e., the difference between the energy gained and the energy spent while foraging). Today’s experiment will enable you to test several predictions of an optimal foraging model. This model describes the behavior of animals searching for food in an environment where prey occur in discrete patches. You and your classmates will act as the “foragers” and your “prey” will consist of beans hidden in containers of rice. This scenario mimics natural settings, in which prey are often distributed in patches, whether they are clusters of mussels attacked by a snail, oak trees visited by a squirrel, or herds of wildebeest hunted by lions.

The patchy distribution of prey can influence variables such as the preferred prey or the feeding rate. For instance, prey that are consumed under some conditions may be ignored under other conditions, such as when they are encountered with more valuable types of prey. The density of prey in a patch also can influence the rate and quality of prey that are consumed. For example, a forager in a poor patch (low-density of prey) usually has a lower feeding rate and less pronounced preferences than a forager in a good patch (high-density of prey).

Figure 1 shows a graphical model that predicts the behavior of a forager in a patchy environment. Imagine an animal that travels to a patch and then begins feeding. During the time it spends traveling, the forager’s feeding rate equals zero. Once the forager reaches the patch, its feeding rate rises dramatically. Over time, however, the forager depletes the prey in the patch, and prey become harder and harder to find. Consequently, the time between captures increases, and the average energy intake rate eventually declines. At some point, the forager will probably decide that it’s a good to move to a new patch.

The timing of the decision to leave a patch is interesting, because the forager has several options: it could leave to find a new patch soon after arriving or wait until it has completely exhausted the patch. Remember that ecologists predict that natural selection favors a forager that optimizes its net rate of energy intake. The graphs that follow help us predict that optimal rate. These graphs will probably look complicated at first glance, but they actually depict a fairly logical pattern. You should examine the graphs until you understand them (you can also refer to your lecture notes for additional information). On each graph, time is plotted on the x-axis. Before the forager can begin to gain energy, some time must be spent traveling to a patch. After the forager reaches a patch, it must decide how long to feed there before moving to a new patch. The y-axis of each graph represents the cumulative amount of energy (or prey) obtained in the patch. Start by examining the plot on the left in Figure 2. This plot depicts a “high-quality” patch, in which prey are initially abundant. During the travel time, the forager does not obtain any prey, so its energy intake equals zero. The curved solid line shows that the forager starts to obtain energy at a high rate once it reaches the patch, but over time that rate declines as prey are depleted.

We want to know when the forager should leave this patch to find a new, undepleted patch. In other words, what is the “optimal” time to move to a new patch? Remember that what we want to optimize is the net energy intake, the highest ratio of energy divided by time. Because time is plotted on the x-axis and cumulative energy is plotted on the y-axis, a line through the origin actually represents this ratio. And the steeper the slope of this line, the greater the net rate of energy gain would be. Identifying the steepest possible line between the origin and the curve shows exactly how long an optimally behaving forager should stay in the patch.

A couple of examples should make this idea more clear. Find the points on the curves in Figure 2 labeled early departure. If the forager left at that time, it would have a fairly low net energy

2 intake rate, as shown by the low slope of the dashed line connecting that point to the origin. Similarly, the forager that leaves at the late departure point also has a fairly low net energy/time ratio. The point where the energy/time ratio is maximized is labeled optimal departure. This best possible net energy intake rate is indicated by the steep slope of the solid line connecting this point to the origin.

If every patch were like our example, and if the travel time between patches were always the same, we would now have the answer we want. But different patches have different prey densities, and it is easier to move among some patches than others. The graph at right in Figure 2 depicts one of these alternatives, a low-quality patch with a long travel time. Nonetheless, the optimal solution for the low quality patch should look familiar. For any single patch, the optimal solution is to leave the patch at the point determined by drawing the line through the origin that is tangent to the cumulative energy gain curve.

There is one further complication. Imagine that the forager moves among many patches of varying quality. Considering all these patches together, there is an average energy gain curve for the environment as a whole, with an associated tangent line that gives the optimal net energy intake rate across all patches. This is shown as the solid line in Figure 4. In this situation—when the forager wants to maximize its return across all patches, not just in one patch—the best time to leave a given patch is when the intake rate drops below this optimal rate for the environment as a whole. Once again, this point can be determined by drawing a line tangent to the curve for the individual patch. Note that this tangent line does not necessarily run through the origin; instead, it is the point on the curve where the tangent has this environment-wide optimal slope. In the two example curves below, these points are indicated by dashed tangents — note that the slopes of these tangents are the same as that of the environment-wide optimal net gain. What does all this mean? In summary, this model of foraging behavior predicts that an optimal forager should leave each individual patch when its intake rate drops below the average optimal energy gain rate averaged across all patches. In high-quality patches with lots of prey, it may take the forager a long time to deplete the patch to this average rate. The average rate will be reached more quickly in lower-quality patches. In the worst patches, this average might not be reached even at the beginning of the foraging bout, and the forager should leave these very low-quality patches immediately. The amount of time needed to travel to the patch also is important, because it affects the net energy gain rate for that patch.

The most important–and least intuitive–concept to grasp from your examination of these graphs is that when considering the environment as a whole instead of considering individual patches in isolation, the forager should leave each patch when it reaches the same optimal energy intake rate, regardless of the initial quality of each patch, or how long it took to deplete them to that level. This optimal rate shared by all patches is called the ‘marginal value,’ and this now-famous model was correspondingly termed the “Marginal Value Theorem” by Eric Charnov (1976), the ecologist who developed it.

Given our theoretical scenario that assumes there are many randomly distributed patches with different prey densities, this model enables us to make four explicit predictions:

1. Foragers should capture more prey in patches of high prey density than in patches of low prey density.

2. Foragers should remain longer in patches of high prey density than in patches of low prey density.

3. Foragers should catch more prey per unit time in dense prey patches than in sparse patches.

4. Foragers should leave each patch when the intake rate for that patch has declined below the average rate for the environment as a whole, and the intake rate at departure should thus be similar across all patches. A simple way to test this is by comparing the “giving-up-time” across patches of different density. Giving-up-time (or “GUT”) is the amount of time that passes between the forager finding its last food item and its decision to leave the patch.

4 Optimal Foraging Experiment

You and your classmates will act as the foraging animals, and each of you will forage for dried beans (your prey) mixed into bins of uncooked rice (prey patches). You will forage in a total of three patches with variable but undisclosed numbers of prey. Your objective as an optimal forager is to maximize the net rate at which you find beans (not to find as many beans as possible). Therefore, you must decide when to leave each patch.

You will forage by using one hand to search for beans hidden in the rice. When you find a bean, you must raise that hand above your head and shout “found one!” to mimic handling time (the time it would take you to eat the prey if you were really a foraging animal—actually eating our beans is not recommended), and then place the bean in a separate cup. You will also incur some traveling time as you move between patches. Although minimizing your travel times will help you maximize your net rate of prey intake, please be careful in running between patches. All patches must be equidistant so that the travel time between each patch is the same.

Before starting, you will have a practice trial of one minute of foraging in a prey patch with the average environmental density of beans. This trial run will help you gauge the optimal rate you are shooting for in the patches with variable prey density.

Each forager will be observed by a recorder (with a data sheet) and a timer (with a stopwatch) who together will record:

1) the time (to the nearest second) at which your foraging started 2) the time at which each patch is reached 3) the time at which each patch is left 4) the time at which each bean is captured 5) the time at which your foraging ended

The recorder should fill out an individual data sheet (a blank data sheet is at the end of this chapter) as each student runs through the optimal foraging course. Your lab instructor will ask for volunteers to help reset the patches for each forager.

5 Data Analysis

1. Calculate the following values from your individual data sheet:

6 2. The blank graph below provides axes to graph your individual cumulative gain curve for each patch. See Figure 1 for an example of a cumulative gain curve. You should plot each patch on the same graph (i.e., put the three curves on this single set of axes).

3. Your TA will prepare three graphs on the board on which you and your classmates will plot your pooled data. Once you have completed the calculations above, add your own data to the following plots:

A) Number of beans found (y-axis) as a function of patch density (x-axis) B) Time spent in patch (y-axis) versus patch density (x-axis) C) Capture rate (y-axis) versus patch density (x-axis) D) GUT (y-axis) versus patch density (x-axis)

7 4. After examining the class data plotted on the board and your own cumulative gain curve, answer the following questions:

Which analyses tested which of the four specific predictions derived from the model (p. 5)? In which cases do the experimental data seem to support those predictions?

Examine your own gain curves. Based on your curves, do you think you left each patch too early, too late, or at an optimal time?

The GUT versus patch density plot is especially important, because it relates directly to the Marginal Value Theorem. Do the data for your class suggest that this theorem applies to the behavior of humans in this experiment? Explicitly justify the rationale for your answer.

Describe a natural situation where you might expect animals to behave this way? When might you expect animals to behave otherwise?

8 Optimal Foraging Lab — Individual Data Sheet

Instructions for Recorder and Timer: Start the stopwatch when the forager is told to travel to the first prey patch. The start time thus equals 0 seconds. Record all later times as the number of seconds that have elapsed since this start time. It is also your responsibility to record the absolute number of beans in each of the three patches. Be sure that you don’t pass this information along to the forager until after their foraging bouts have been completed.