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Biology 1001 – Laboratory 3
Functional Responses of Predators
PREPARATION
Read this exercise before you come to lab.
Remember to take your lab coat today.
Bring along a calculator, pencils, a ruler and your lab appendix.
In the early 1900’s two mathematical biologists – Alfred Lotka and Vito Voltera – tried show what the effects of numbers of predators and prey were on each other. They were trying to explain a phenomenon that had been seen in several predator prey systems, namely the cycling of predator and prey populations. It is a common idea in studies on predators and prey that their population numbers cycle slightly out of phase with one another.
The simple Lotka-Volterra equations assume that the rate at which predators capture prey (p) is a constant, so numbers of captures each predator makes per unit time is directly proportional to prey density. This is sometimes called a type 1 functional response (see the Figure 1).
There is, however, far more to predator-prey interactions than these simple equations. For example, can we assume predators always take prey in direct proportion to their numbers as the Lotka-Volterra equation would predict? In 1959, a Canadian ecologist named C.S. Holling was studying small mammals feeding on sawfly cocoons and observed that predation is a two-step process: first the prey must be found, then it must be “handled”. Handling time includes all activities required before the next capture, including removal of inedible parts, carrying the prey back to a nest, or eating and digesting the food item. If handling time is long in comparison to searching time, then it can become a limiting factor for a predator’s consumption rate as prey density increases. When plotted against prey density, capture rate levels off in the type 2 response. Holling’s disk equation, so-called because he did simulations in the laboratory involving sandpaper disks, recognizes that predators spend most of their time hunting for food when prey are scarce, but a greater proportion of their time handling food when prey become more abundant. The equation for the type 2 functional response is as follows:
Where:
C = number of prey captured per trial, Th = handling time, A = attack rate of predators, N = population density of prey
There is a third complication – this one being behavioural. For vertebrate predators capable of learning from experience, the most abundant prey may be selected at an even higher frequency than their prevalence in the environment. The least common prey may be ignored altogether. Vertebrate predators often develop a search image for prey with which they have experience. (This is not unlike a phenomenon you may observe in a university cafeteria. If unusual looking food items are presented on a buffet line, they are selected at a lower frequency than food items more familiar to students). If predators form a search image, the functional response curve is S-shaped, due to disproportionately low predation of rare prey. This is called a type 3 functional response. At intermediate prey density, the rate of capture increases rapidly with enhanced predator experience, and then handling time slows the capture rate at very high density. Invertebrate predators such as hunting wasps are less likely to illustrate the S-shaped functional response curve, because most of their predatory behavior is genetically programmed, and not dependent on learning.
In conclusion, predators adjust to their prey over three time scales:
1) Over evolutionary time, predators develop adaptations in structure and behavior to help them capture their prey.
2) Over generations, predator populations fluctuate up and down in response to prey numbers.
3) Over the lifetime of a single predator, handling time and learning affect rates of capture.
SIMULATING FUNCTIONAL RESPONSE OF A PREDATOR
Research Question
How does the functional response of a predator depend on handling time?
Materials (per laboratory group)
20 nuts and bolts
Blind fold
Stopwatch or laboratory timer
Background
In this simulation, a student with eyes closed represents a predator searching for prey. Bolts represent prey, and nuts represent inedible parts of the prey (such as a clam shell or insect wings) that must be removed before the prey can be consumed. Time spent removing the nut from the bolt therefore serves as handling time (Th) in this experiment. The “predator” must search the board with only one finger, pointing straight down, moving across the “habitat”. When a prey item is encountered, it is picked up and “handled” by removing the bolt. Bolt and nut are placed out of the ‘habitat’ and the search resumes, all without peeking!!! Other students in the lab group will time the simulations, count the number of prey “consumed”, and replace the bolts with nuts reattached on the board to maintain a stable prey density.
Procedure
1. Designate one student in your group as the “predator”. With eyes closed, hand the “predator” a bolt with the nut screwed all the way up to the head. Ask the student to remove the bolt from the nut (without spinning the nut around the bolt). After allowing once or twice for practice, conduct a time trial and measure the number of seconds it takes to remove the nut. Then divide the number of seconds by 60 to calculate handling time in minutes. Record this number, to the nearest hundredth of a minute (e.g. 0.54 min/prey), in Data Table 2 (Pg. 5).
2. While the “predator’s” eyes are still closed, scatter two “prey” (nut and bolt assemblies) onto the poster-board habitat. Your task is to determine how many prey can be captured and handled in a three-minute period. The “predator” searches for prey with one finger touching the board. The “predator” should try to move at a steady pace, and be careful not to touch prey with the whole hand. When a prey item is found, the “predator” picks up the prey, removes the nut from the bolt, places the “eaten” parts off the board, and then continues searching. Record the amount of time from the beginning of the trial that it takes the ‘predator’ to find the first ‘prey’. Put this information into Data Table 1. Student observers should screw the nut back onto the bolt and quietly replace the “prey” item back on the board so that the prey density does not change during the experiment. Record the number of prey taken within a three-minute period (in Data Table 2). If a prey item has been found but not fully processed when time is up, count that bolt as an additional ½ prey consumed.
3. Calculate the “predator’s” attack rate as follows:
a) Multiply the handling time per prey (in minutes) by the number of prey consumed during the three-minute interval. This is total handling time (Th).
b) Subtract total handling time (in minutes) from the total predation time (three minutes) to determine total searching time (Ts).
Ts= 3- Th
For example, if total handling time is 1.2 minutes, then Ts = 3 minutes – 1.2 minutes = 1.8 minutes.
c) Use the following equation to calculate the attack rate for the “predator” in the first trial, which used two prey. The total search time in the denominator is multiplied by 2 because that is the initial prey density.
Attack rate (A) = (# prey consumed)/(2 Ts)
d) Record the attack rate (A) for this “predator” in Data Table 2.
4. Repeat step 2 with the same predator, but with 5 bolts. Then repeat with the densities 10, 15 and 20. Record results for each prey density in the Data Table 2.
5. Allow a second lab group member to take a turn as predator. Measure handling time, record the number of bolts the “predator” is able to “consume” in three minutes at densities 2, 5, 10, 15, and 20. Calculate the attack rate after the first trial, and record all data for the second predator in the second row of data table 2. Allow every member of the laboratory group to take a turn as “predator”. Compute column means based on the number of predators who did the simulation.
6. Calculate average numbers of bolts “eaten” at each of the five densities for your group, and write the means in data table 2. Also calculate a mean handling time, in minutes, for the entire group, and record that grand mean as well.
DATA TABLE 1: Time to first capture (measured in minutes)
Predator # / Prey Density2 / 5 / 10 / 15 / 20
1 / Time (in minutes)=
2
3
4
Mean observed values
DATA TABLE 2: Predator-Prey simulation capture data
Predator # / Prey Density / Handling time (Th) in minutes / Attack Rate (A)(Prey/min)
2 / 5 / 10 / 15 / 20
1 / C=
2
3
4
Mean observed values
Expected Values
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ASSIGNMENT 1
Plot the average time taken to find the first prey at each density. Remember: The dependant variable goes on the y-axis! Think of the type 1 Functional response curve and Lotka-Volterra’s assumptions.
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ASSIGNMENT 2
Using the data that were recorded from the "predator-prey” exercise, plot a functional response curve using the average number of prey captured at each prey density. Assume 0 prey will be caught when prey density is 0. For densities 2-20, plot your mean number of captures per three-minute trial as points on the graph, use smoothing to connect your points to make a curve.
See Appendix page A-3 for help in making graphs.
Compare your curve to the Functional Response curves in the introduction of this lab.
Use the following equation (Holling’s Disk Equation) to calculate an expected number of captures for trials at each of the five prey densities. Put this information into Data Table 2. Draw a dotted line (or use a different shape) to show the expected functional response (on the same graph where you plotted your observed values).
Holling’s Disk Equation:
Where: C = number of prey captured per trial, Th = handling time, A = attack rate of predators, N = population density of prey
After you have constructed your graphs, have an instructor check it.
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ASSIGNMENT 3
Be sure that you can answer the questions on page 7 before you leave the lab today.
Questions
1. Which of the three types of functional response curves showing in Figure 1 does your data plot most resemble? Does this make sense, given the rules of the simulation?
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2. How did your expected functional response curve match the graph of your observations? Propose hypotheses to explain any discrepancies between the two.
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3. If two nuts were placed on each bolt to simulate a prey harder to process and consume, how would you expect the functional response curve to change? Illustrate your answer with a small hand-drawn graph.
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4. What happened to the time taken to find the first prey as density (number of prey) increased? Does this agree with what might be expected from the Lotka-Volterra model?
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