Functional+Response+Student+Manual

Lab 10: Functional Responses
Developed by M. Smith and J. Kilgore

- Learn and understand the functional response of a predator at varying prey densities - Identify possible factors that cause variation and how these factors could alter the results of your experiment
 * Objectives:**


 * INTRODUCTION**

If you are managing a population of predators or trying to protect a prey species, you might be interested in functional response curves. These curves are mathematical hypotheses that predict the impacts of predators on prey populations. A major component of predator-prey interactions is the response of the predator to changes in prey density. If the prey density increases, we would expect the predator population to respond behaviorally by consuming more prey (i.e., functional response) and eventually increasing in size through reproduction and/or immigration (i.e., numerical response). Foraging is not such a simple enterprise because uncommon prey are more difficult to locate and, once found, a certain amount of time is spent processing the prey before consumption (e.g., removing shells or fur). Functional response models are based on mathematic equations from Lotka and Volterra.

Here are two equations that look at the consumption of prey by a single predator:
 * (Equation 1)**

//Where:// B(V)= Rate of prey eaten by a predator V = Density of the prey population Th = Time spent handling / processing the prey a = Attack rate by the predator

Given a multitude of prey sources, a predator should attempt to minimize energy expenditure for maximal energy gain (i.e., prey) given a particular set of environmental constraints. If seeking out more than one prey source provides more net energy gain than one prey only, the predator should include that second prey source in its diet, according to optimal foraging theory. However, we must first determine the short-term functional response of the predator to determine its feeding success on a particular prey.

The functional response describes an individual predator’s response in terms of food consumption to prey density (Figure 1). Examples abound of regulation of prey populations. Consider Elton’s classic study of Canada lynx regulating snowshoe hare numbers or Hall’s and Mittelbach’s work with foraging of different prey by bluegill sunfish. In this laboratory session, we will explore the functional response of student predators.



Figure 1. Three types of functional responses of predators to increasing prey density expressed as the number of prey consumed. (from Ecological Society of America website)

A **Type I functional response** is expected when predators require little to no time to handle their prey, thus feeding rate increases **linearly** as prey density increases to the point of maximal feeding. In such a response, the predator never gets satiated and can always capture and process more prey as its prey density increases. What types of predators might express a Type I functional response?

A **Type II functional response** occurs when handling time starts to play a strong role in limiting feeding rate at higher prey densities. This means that above a certain density of prey, the predator’s response remains constant (cf. the plateau for the curve II that levels off after a certain prey density) because the predator cannot handle or process prey faster anymore, it has reached its maximum. This is the most common type of functional response observed by ecologists. What types of predators might express a Type II functional response?

A **Type III functional response** is expected when the rate of encounter between predator and prey is not constant and it changes with density. For example, when initial search image recognition and location of prey are reduced or “safe sites” for prey are available at low prey densities. Predators may have switched their prey base until the preferred prey become sufficiently dense, at which time the relative number of safe sites decreases and the predator develops the search image. Feeding rate then increases tremendously until the curve again levels off due to limited processing abilities of the predator. What types of predators might express this type of functional response?

===  ACTIVITY===

As a class, we will determine the functional response of ecology students as predators. The prey will be //Artemia// (a.k.a. brine shrimp or sea monkeys!) and black-eyed peas. Each group will be provided different habitats to be populated with different densities of //prey//.


 * Hand in the 3 graphs with answered questions to your TA at the end of the class section. You will be evaluated on your 3 graphs and your responses to the discussion questions for this lab.**

We will be using the following predator equation:
 * (Equation 1)**

//Where:// B(V)= Number of prey eaten by a predator V = Density of the prey population Th = Time spent handling / processing the prey a = Attack rate by the predator


 * a ****= (detectability) x (area searched) x (prey/unit area)**


 * PART 1**: Choose a group member to be the feeder, the timer, and the recorder. There are 6 dishes with populations of peas. You are given a glass cylinder as your “stomach.” When you are told to “Feed,” you have 30 seconds to get the peas into the cylinder using any method (try to do it as quickly as possible). Record the number of peas that make it into the “stomach” in Table 1, and graph these data on the Graph Page for Part 1.

Table 1. Data table for capturing peas.
 * (Equation 1)**


 * |||||||||||| **Pea Density** ||
 * || 1 || 3 || 5 || 10 || 20 || 40 ||
 * *** captured ||  ||   ||   ||   ||   ||   ||

Observed Response Curve for Part 1:




 * Discussion Questions:**


 * 1) **What type of functional response curve did the data indicate? Did this fit with your expectations? Provide explanations as to why or why not.**


 * 1) **What part of the general predator equation does** NOT **affect the shape of this functional response the most?**

PART 2**: In Part 2 the feeder will be given 30 seconds to catch as many //Artemia// as possible and place them in the stomach container. Have one group member set-up one of the six densities of shrimp in the large plastic bowl (either 1, 3, 5, 10, 20, or 40 //Artemia//). Do not let the “predator” know the density of //Artemia// being tested (randomize the order of the densities you test).** Change this so that the class is given 30 second bouts and timers record intervals for handling time

Prior to Part 2, you need to develop your predictions.
 * Predators must follow some rules of predation:**
 * ¨ Predators cannot move until they are given the command “FEED” (given by the timer).**
 * ¨ The predator will have 30 seconds to locate as many prey as they can and use only the feeding apparatus (pipette) they’ve been given.**
 * ¨ Predators can only pick up one //Artemia// at a time and must place this in the “stomach” before catching another.**


 * 1) What are some potential limiting factor(s) for the predator?


 * 1) How will these limiting factors impact the predator’s response with respect to the prey densities?


 * 1) What type of functional response can be expected based on these limitations? Draw the expected graph, and provide a brief explanation.



After a “predator” has finished the set of densities, have a different group member become the predator and sample the six densities of shrimp again. Do this for both Part 2 and 3. Graph the two lines of the two predators on the graph “Observed Response Curve for Part 2”

(Equation 2)


 * Table 2: data table for trial 2 (no background) for each prey density**

Density ||
 * |||||||||||| Prey
 * Predator || 1 || 3 || 5 || 10 || 20 || 40 ||
 * 1 ||  ||   ||   ||   ||   ||   ||
 * 2 ||  ||   ||   ||   ||   ||   ||
 * Average ||  ||   ||   ||   ||   ||   ||

Observed Response Curve for Part 2:




 * 1. Where does handling time start to affect the shape of this graph (try comparing to the curve from Part 1)?**

PART 3**: Once your group finishes collecting data for Part 2, set up the six densities of Artemia in the six containers provided (the densities are labeled on the bottom of the container. Then graph and answer the questions for Part 2. This will give the Artemia time to settle into the new habitat. In Part 3, we will create a more complex habitat for //Artemia//. Add the abiotic variables provided in the lab to your habitat. Before starting trial two, however, you must develop your predictions for this trial:**
 * 2. Since there is no replacement of prey, the density of prey changes over the course of the experiment. How does this impact the conclusions you reach in your experiment?**


 * 1) How will the abiotic variables affect the predator’s foraging?


 * 1) How will this abiotic factor impact the predator’s response with respect to the prey densities?


 * 1) What type of functional response curve can be expected based on these limitations? Draw the expected graph, and provide a brief explanation.



(Equation 3)
 * Table 3: data table for trial 2 (with background) for each prey density**

Density ||
 * |||||||||||| Prey
 * Predator || 1 || 3 || 5 || 10 || 20 || 40 ||
 * 1 ||  ||   ||   ||   ||   ||   ||
 * 2 ||  ||   ||   ||   ||   ||   ||
 * Average ||  ||   ||   ||   ||   ||   ||

Observed Response Curve for Part 3:**



Discussion Questions:


 * 1) Did the background affect the “predator’s” ability to find prey differently at different densities? What density did it affect the most and in what way did it change the shape of the curve.


 * 1) So far we have been talking about how many prey the predator catches (so looking at the situation through the benefit of the predator). Instead if we looked at it through the prey’s eyes, under what conditions is the relative risk of the prey minimized? When is the risk the highest? (Determine for each type of curve)