Optimal diet selection, a component of optimal foraging theory, suggests that animals should select a diet that either maximizes energy or nutrient consumption per unit time or minimizes the foraging time needed to attain required energy or nutrients. In this exercise, students simulate the behavior of foragers that either show no foraging preference or demonstrate a foraging preference based on profitability ratios (average energy content of food item, E//average handling time, h). Foragers that optimize their diets consistently acquire more total energy in a timed foraging period. The demonstration is scalable to a full laboratory exercise with statistical analysis and graphing activities.

Optimal foraging theory has major implications for fundamental ecosystem processes such as energy flow and for community interactions such as predator——prey relationships. While the theory has been the target of numerous criticisms (Pyke, 1984; Pierce & Ollason, 1987), it provides an important model for understanding the dynamics of diet selection as well as foraging sites and strategies. A number of excellent laboratory exercises have been published in The American Biology Teacher, including most recently an article by Yahnke (2006). These are primarily field exercises, which are great choices in a laboratory class. However, my General Ecology class unfortunately lacks a laboratory. I needed a quick, in-class activity to supplement my lecture on this topic and to demonstrate the practical application of maximizing the efficiency of energy and nutrient intake in diet selection.

In my classes, I open the discussion of feeding strategies and diet selection by flashing a PowerPoint slide of a plate of white-chocolate-chip macadamia-nut cookies beside a large plate of broccoli. I poll the students in the class as to which they usually prefer. In most cases, only one or two students out of a class of 30 select the broccoli. When asked why they prefer the sugar- and fat-laden cookies to the vitamin- and fiber-rich broccoli, students typically respond that they just like the taste better. Optimal foraging theory suggests a different answer, and it lies in the economic principle of profitability. Fats and sugars do taste good, as the students note; but sugars have the added benefit of providing a rapidly available energy boost, while fats have high caloric density. Such preferences suggest that humans may follow patterns seen in many other species: They may indeed optimize for energy consumption, which may be reflected in dietary preferences (Kaplan & Hill, 1992; Mulder, 2005).

Krebs (2001) summarized the key points of optimal diet selection as maximization of energy or nutrients per unit time and minimization of time required to achieve an acceptable level of daily energy or nutrients. The profitability of a food item can be defined as the ratio

 
formula
(1)

where E is the energy value of the food item and h is the handling time required to process the food item. In order for a food item to be selected, the profitability ratio must be greater than that of alternative items. We can symbolize this as

 
formula
(2)

Switching may occur when the handling time for the preferred item increases because of increased search time (S) to the point that the alternate item becomes more profitable. As an inequality, this can be expressed as

 
formula
(3)

While this theory can be easily presented from the comfortable, seated position of armchair biology, seeing it in simulated action is far more effective and memorable. The exercise presented here can be used as an in-class demonstration or, with only slight modification, it can be used in a laboratory setting.

Materials & Methods

Miller's (1999) exercise on feeding in patchy environments provided a useful foundation for the development of the present simulation. The simulation is based on a simple system in which two kinds of food are available to the forager. Food availability is initially not limiting: there is an ample supply of both food types. The simulation also assumes that the forager can consume an infinite quantity of food and that there is no competition with other foragers.

I use two kinds of beans that are approximately the same size in the simulation. Pinto beans and small white navy beans work well. To facilitate calculations, I assign arbitrary average energy values to each type of bean: pintos have 3 dietary calories each, and navy beans have 4.4. Thus, ostensibly, the navy beans are the more profitable food. However, I wrap each navy bean in a small square of aluminum foil to increase the handling time. For each run, one student serves as a forager and another acts as the official record keeper. The instructor or a third student keeps time with a stopwatch. Using a pair of stainless steel serving tongs, the forager collects beans and places them into a plastic cup. The tongs add a measure of difficulty to the foraging exercise to slow down the process. When the forager picks up a bean, she announces, ““I have a pinto bean!”” or ““I have a navy bean!”” to allow the record keeper to keep track of the particular trial.

There are four trials in the exercise (summarized in Figure 1). In each trial, beans are scattered randomly within a set boundary. I use a hula hoop to serve as the foraging arena. In trial 1, students determine the time to collect and process 10 (or 20) beans and then calculate the handling time per bean in seconds. Profitability is calculated as the ratio of average energy per bean divided by the average handling time in seconds. Trial 2 repeats the process for the wrapped navy beans. To process a navy bean, the forager must unwrap the bean, announce the collection, and then place it into the cup. Comparing the two profitability values, the students can clearly determine which food should be preferred according to the theory.

Figure 1.

Flow of tasks in the simulation of optimal diet selection.

Figure 1.

Flow of tasks in the simulation of optimal diet selection.

Working from the hypothesis that foragers should maximize energy intake per foraging session, students can predict that selecting more profitable food will maximize their energy consumption, whereas eating with no preference will provide less energy per session. Trials 3 and 4 test this hypothesis. In trial 3, the forager selects from an ample supply of both pinto and foil-wrapped navy beans. Using the same rules as before, the forager has 2 minutes to forage methodically along a transect of the feeding arena, consuming the next closest food item without regard to type. In trial 4, the forager again has 2 minutes to feed only on the preferred food item. Students calculate the total energy obtained per trial by multiplying the energy content of a given bean type by the total number of beans collected in the 2-minute period and dividing by 2 to report the energy obtained per foraging-minute.

Results

Table 1 is a comparison of the handling-time trials for pinto and navy beans, summarizing the results from five different classes. Mean values from the five trials were used to calculate profitability ratios for each food type. Mean handling times were 3.83 seconds//bean (SE = 0.26) for the pinto trial and 11.92 seconds//bean (SE = 1.44) for the navy bean trial (Figure 2). Although the average energy contained per bean was greater for the navy beans, the handling time reduced the profitability significantly: the averages for the five trials returned profitability ratios of 0.78 for pintos and only 0.34 for navy beans. According to optimal foraging theory, a clear preference should be shown for the pintos.

Table 1.

Results of trials 1 and 2: calculation of handling time (in seconds) and profitability ratios.

Results of trials 1 and 2: calculation of handling time (in seconds) and profitability ratios.
Results of trials 1 and 2: calculation of handling time (in seconds) and profitability ratios.
Figure 2.

Sample figure showing results of handling time experiments from five groups.

Figure 2.

Sample figure showing results of handling time experiments from five groups.

Using the baseline profitability values from trials 1 and 2, it was predicted that a foraging trial with no preference for food type would yield lower total energy consumption per unit time than one in which the more profitable food was preferred. Table 2 summarizes the results of five runs of trials 3 and 4. Comparing the results of the no-preference and preferred foraging trials, it is evident that foraging for the preferred food does indeed increase total energy consumption (Figure 3). Although roughly equal amounts of energy were consumed for the two food items in trial 3, the greater handling time (and decreased profitability) of the navy beans caused a decline in overall energy consumption. The data from these trials indicate that selectively feeding on preferred food types resulted in a 2.27-fold increase in energy consumption compared with indiscriminant foraging.

Table 2.

Results of trials 3 and 4: total energy (dietary calories) consumed per foraging minute with no preference vs. selective foraging for preferred food.

Results of trials 3 and 4: total energy (dietary calories) consumed per foraging minute with no preference vs. selective foraging for preferred food.
Results of trials 3 and 4: total energy (dietary calories) consumed per foraging minute with no preference vs. selective foraging for preferred food.
Figure 3.

Energy consumption per foraging minute (±± SE) for a no-preference feeding strategy versus an energy-optimizing feeding strategy.

Figure 3.

Energy consumption per foraging minute (±± SE) for a no-preference feeding strategy versus an energy-optimizing feeding strategy.

Discussion

Optimal foraging theory provides a framework for understanding a key aspect of energy flow in ecosystems. It focuses the process on the active forager and elucidates rules by which organisms select food to efficiently meet their metabolic requirements. The principles presented in this simulation make clear why cookies are more popular than broccoli (beyond taste alone): they pack more energy into a smaller package. If an average white-chocolate-chip macadamia-nut cookie has 177 dietary calories and a 1-cup serving of broccoli has 43 dietary calories, it would take 4.12 cups of broccoli to provide the same amount of energy. Needless to say, it takes significantly longer to process (e.g., cut and chew) the broccoli. Of course, it is overly simplistic to say that humans optimize on the basis of energy alone (Kaplan & Hill, 1992). Other factors such as protein content and even social activities affect diet selection in studies of more primitive human cultures. However, the core principle of optimization is still evident in humans.

The simulation I have presented here is indeed a simple one: it has only a few parameters, such as limited food choice, and it assumes that encounters with food items are random and that the forager can consume an infinite amount of food. Of course, nature provides far more variation than can be tested in a short simulation. But, as with any model system, it shows a principle and gives a starting point for understanding a phenomenon. This simulation accurately and reliably produces results that support the fundamental premises of optimal diet selection.

Demonstrating the principles of optimal diet selection sets the stage for a discussion of how organisms may select their food and why this is important in the greater scheme of ecosystem processes. I have used this simulation successfully as an in-class demonstration for 3 years in a sophomore//upper division General Ecology class as well as in presentations for middle school students visiting campus for the annual science career day. The concept is equally accessible to both audiences, and, not surprisingly, both types of students correctly draw similar conclusions when provided with only a minimum of introductory discussion and definition of terms, which makes it an excellent addition to an inquiry-based learning program.

Another key benefit of using a simulation such as this is that it provides an opportunity to integrate math into the biology classroom. Many biology students tend to resist using math outside of a math class. Depending on how the instructor chooses to set up the simulation, she may choose to walk the students through the calculations or she may instruct them to find specific values and let them determine the best route to find the solutions. Obviously, the latter would work better in a laboratory with enough time for trial-and-error inquiry. Using the simulation in a laboratory also allows the pooling of results from several groups, thus providing greater confidence in the results and a larger data set with which to work. Students can calculate descriptive statistics from the pooled class data and then graph the results. For example, using a Student's t-test for means and testing the handling-time data against the null hypothesis that there is no difference in handling times between the two kinds of beans yields a two-tailed t-test value of ——5.53 (p≤≤0.001); this would indicate that the two handling-time averages are significantly different.

Additional questions may arise from the simulation. For example:

  1. 1. Why are some organisms sit-and-wait predators if there is benefit to seeking out a preferred food type? One approach to this question would be to consider that many sit-and-wait predators are poikilotherms, for which the energetic demands of active hunting would likely negate any benefit derived from that energy-expensive activity.

  2. 2. What type of organism best fits the optimal foraging model with respect to optimal diet selection? Here, you might want to think about specialists and generalists with respect to foraging. Organisms that are specialists may tend to optimize their diet selections more than generalists.

  3. 3. What is the role of satiation in determining the optimal diet? The present model system assumes that the forager can eat an infinite number of food items —— that is, satiation is not a factor. However, in the real world, most species tend to feed until they have met their nutritional needs. This may tend to put less pressure on the prey resource, thus moderating the necessity and frequency of the predator's switching of prey items.

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