Testing the Ideal Free Distribution Theory on Turtles

William Gardner, Mia Gomez, Rose Hoover, Djimon Mclean

Kaylin Nuñez, Victoria Reis, Manuel Sanchez

Abstract

An experiment was performed to test whether turtles follow the Ideal Free Distribution, which

describes how animals should optimally distribute themselves to maximize their food intake. The

experiment consisted of feeding turtles different amounts of food at different locations near each

other at a pond. The turtles distributed themselves roughly in proportion to the amounts of food.

There was a significant difference between the numbers of turtles at the largest and smallest

sources of food. The results support the hypothesis that turtles can follow the Ideal Free

Distribution.

Introduction

The goal of our experiment was to test if the Ideal Free Distribution theory applies to the

lives of animals such as turtles. Ideal means that each living thing makes the best or optimal

choice for its own wellbeing. Free means that living things are all free to make their own choices

in any given situation. Distribution means that living things place themselves, possibly in

separate groups, in different areas in space. Thus, the Ideal Free Distribution is a theory which

describes the free distribution of living things to a place or area that most benefits their needs.

Scientists have stated that the Ideal Free Distribution can be followed by almost any

living organism. For example, people follow the Ideal Free Distribution in the grocery store

when they choose the shortest available line for the cashier, when choosing rides with shorter

 

lines in theme parks, and when they choose to order food at a restaurant drive-thru versus sitting

down for a meal in the restaurant itself. In each scenario, people distribute themselves in such a

way as to receive the maximum benefit or expend the least amount of time or energy.

Our primary hypothesis is that the Ideal Free Distribution may be applicable to different

habitats with different species of animals. For example, fish in a fish tank experience the Ideal

Free Distribution when they get fed. If the food is sprinkled in different amounts in different

sections of the tank they make a decision of which section to go to. Bumble bees also use the

Ideal Free Distribution when choosing a flower to get nectar out of

(http://www.onlinelibrary.wiley.com/doi/10.1046/j.1365-2435.2002.00644.x/full).

For our experiment, we decided to test if the Ideal Free Distribution theory applies to

turtles. Our null hypothesis is that turtles will not follow a pattern that is related to the

distribution of food. Our alternative hypothesis was that turtles would follow the Ideal Free

Distribution in such a way so that each turtle would receive the maximum amount of food that it

possibly could. We predicted that when turtles are thrown different quantities of food in different

areas of a pond, the highest number of turtles would be observed in the area with the most

amount of food, while the lowest number of turtles would be observed in the area with the least

amount of food. An intermediate number of turtles is expected to be observed in the area with a

medium amount of food (Figure 1).

 

Figure 1. Conceptual diagram of turtles exhibiting the Ideal Free Distribution

Methods

For this experiment, we sampled a man-made freshwater pond on the campus of Florida

International University (FIU) in West Miami (Figure 2). The pond is medium in size and is

home to several species of fish and turtles. The species of turtles included in our experiment

were: Pseudemys nelsoni (Florida red-belly), Trachemys scripta elegans (Red eared slider), and

Apalone ferox (Florida softshell turtle). In the wild, Florida red-bellied turtles are strong

herbivores, preferring aquatic plants, with younger turtles taking in some insects as well. Red-

eared Sliders mostly eat meat and also feed on plants. Florida softshell turtles choose habitats

that are slow-moving bodies of fresh water with mud or sand bottoms and are primarily

carnivorous, feeding on aquatic insects, crustaceans, mollusks, fish, waterfowl, and amphibians.

Figure 3. Study species of turtle used in our experiment.

Trachemys scripta elegans

(Red eared slider)

Apalone ferox

(Florida softshell turtle)

Pseudemys nelsoni

(Florida red-belly)  

 

Figure 2. A map of Miami and FIU pond location. The red star is the location in southern Florida where FIU South is located. To the right is a map of the campus of southern FIU. The red circle represents the pond where the experiment was performed.

We performed a total of seven experiments, collecting data over the course of three different

days. The materials used to perform the experiment were: turtle food, 1/2 teaspoon, 1 teaspoon, 1

tablespoon, and a cup to store the food, a timer, and a paper with a pencil to record data. The

time, date, weather conditions, spoon size, and position (left, right, or middle) were recorded at

the start of each experiment.

Eight students were divided into four groups of two each. Three of the groups were

assigned three different spoon sizes at random and told to stand approximately two meters apart.

The fourth group acted as timekeepers, notifying the groups when to get ready, throw food, and

count the number of turtles.

Three of the groups were instructed to toss the assigned amount of food into the pond and

record the number of turtles that came to feed within their assigned area. The timekeepers would

shout “get ready!” when the minute hand reached the “10” on the clock. The other three groups

Figure 4. The materials used in this experiment. At the bottom are the three spoon sizes: ½ tsp, 1 tsp, and 1 tbsp. In the middle are the cups used to store the food. At the top is the bag from which we got our food.

 

would then scoop the food from the cup with their assigned spoon. When the minute hand

reached the “12” on the clock, the time keepers would say “throw food!” and the groups would

toss the food from their spoons approximately one meter away from the shore using an

underhand throwing technique. When the second hand reached the “4” on the clock, the

timekeepers would say “count turtles!” and the other groups would then count the number of

turtles that were eating the thrower’s food in that area. The recorder in each group would record

the number of turtles counted at the end of each trial. The experiment was finished when there

were a total of 17 trials completed. The groups would then rotate and be assigned a spoon at

random for the next experiment.

After each day of performing our experiments, we returned to the University of Miami

and recorded our collected data on the computer. We made scatter plots of all the data obtained

from the 7 experiments. We described our data by using the mean and standard deviation.

Standard deviation is a measure of the amount of variation or dispersion from the set of data.

After each group collected their data, they recorded their data into Microsoft Excel. In that

program, each group graphed the data as a scatter plot and line plot.

Results

We present our results both as a series of seven graphs, representing each of the seven

experiments. Then we present statistical analysis.

 

Table 1

0.5 teaspoons 1 teaspoon 3 teaspoons

mean 7.811966 13.81513 25.09167

S.D. 4.293001

6.303034

7.363316

n 117 121 122

Table 1 shows the mean, standard deviation, and the sample size for each spoon size,

accumulated over all of the trials. The first spoon size was 0.5 tsp, the second spoon size was 1

tsp, and the third spoon size was 1 tbsp (=3 tsp). The results show a pattern: the turtles went to

the largest amount of food; the mean number of turtles was highest for the 3 teaspoon spoon size,

and increased from lowest to highest teaspoon size. The turtles always seemed to go where they

saw the most food, until the food was eaten, and then they would go to the remaining food.

When the food was replenished they would go to the biggest amount.

Table 2

Spoon size (tsp) exp1 exp2 exp3 exp4 exp5 exp6 exp7

mean: 0.5 6.42 8 10.76 8.53 9.24 7.1 4.41

1 14.47 10.65 10.65 18.76 13.65 15.28 10.41

3 21.65 22.61 22.61 26.18 31.29 24.82 20.82

ratio: 0.5 1 1 1 1 1 1 1

1 2.25 1.67 0.99 2.2 1.48 2.15 2.36

3 3.37 3.55 2.1 3.07 3.39 3.5 4.72

 

Table 2 shows the mean number of turtles for each experiment and each spoon size, and

these means converted into ratios. The ideal free distribution is a theory based on ratios, so we

converted our turtle counts into ratios to see if they matched the theory. The data shows that the

largest ratio of turtles went most often to the area where the most food was thrown; the ratio of

turtles for 3 teaspoons was approximately 3.4 times larger than .5 teaspoon and 1.8 times larger

than 1 teaspoon.

Figure 5 shows a scatter plot of the mean number of turtles for each of the seven

experiments, at each treatment trial. The means were consistently higher for the spoon with 3

teaspoons of food. From Table 1, we know that the standard deviation is higher for the 3

teaspoon spoon (7.36) than the other treatment levels, 0.5 (4.29), and 1 (6.3). The means of three

teaspoon group are about 3 times greater than .5 teaspoons.

0  

5  

10  

15  

20  

25  

30  

35  

0   0.5   1   1.5   2   2.5   3   3.5  

MEA

N  #  OF  tURT

LES  PE

R  EX

PERIMEN

T  

SPOON  SIZE  

Figure  5.  Scatter  plot  of  the  mean  number  of  turtles  vs.  spoon  size.  

 

Figure  7.  The  bottom  figure  shows  the  number  of  turtles  that  went  to  each  scoop  size  for  all  the  experiments  combined.    

Num

ber  o

f  turtle

s  

Figure  6.  Plots  of  data  on  number  of  turtles  versus  time  for  seven  experiments.  The  data  displayed  in  the  top  figures  show  the  results  of  seven  experiments  that  were  performed  over  3  days  in  the  FIU  pond.  

 

Discussion

The goal of our experiment was to find out if turtles would follow the Ideal Free Distribution.

We set up three feeding stations, with different amounts of food, and let the turtles choose which

pile they wanted to go to. Our null hypothesis was that there would be no difference in the

amount of turtles that would come to each area. Our alternative hypothesis was that more turtles

would come to the area that has the most food than to the area that has the least and medium

amounts of food. To test these hypotheses, we conducted 7 experiments with 17 trials in each.

Our results led us to accept our alternative hypothesis because the mean number of turtles at the

1 tbsp. (3tsp) station (25 turtles) was significantly greater than the number of turtles at the other

two stations. A non-parametric statistical test supported these differences, and the results were

significant. There was also a difference between the mean number of turtles at the 1tsp (13.8)

and the 0.5 tsp (7.8) station, though the difference was not statistically significant.

Experimental conditions were not always perfect. During the experiment, a few

unexpected events occurred that may have affected or altered the results. For example, many

Figure 8. A student tossed the spoon into the FIU south pond

 

turtles would come and aggressively fight with other turtles to get more food. Also, the larger

turtles would come and scare away many of the smaller turtles. Some of the turtles would also

stray away from the food; we believed that this was because the area in which they were trying to

feed might have been too crowded, or that some of the turtles just weren’t interested or hungry.

Another possibility is that some of the turtles couldn’t see all the possible choices of feeding

areas, or the people who were tossing the food might have thrown it in such a way that the turtles

weren’t able to access it. Another error that occurred during the experiment was the accidental

tossing of a measuring spoon into the pond (Figure 8). This affected the data obtained for that

group’s experiment and thus the overall results. Another factor was that several large fish started

to eat the food, causing there to be less food for the turtles (Figure 9).

In conclusion, we accept our alternative hypothesis, and reject our null hypothesis. Our

experiment could have been better if there were no other variables that changed the outcome of

the experiment, such as the fish that ate the turtle’s food, and the tossing of the spoon that caused

the student to miss trials in their experiment.

Figure 9. The fish ate food and scared the turtles off, which interfered with the experiment

 

The results show animal behavior and it displays that it can be useful because it may

help to protect the rare turtles that are endangered. Scientists can use all the data to see and test if

it is right and see if this will help.

Acknowledgements

We appreciate the help given by Gabriella Perez, Simeon Yurek, and Dr. Donald

DeAngelis. They really helped this experiment run smoothly. We appreciate being able to use

FIU South pond and their turtles. We are grateful for the funding provided by the Howard

Hughes Foundation. We also thank our teachers, Ms. Susna Attilus, Ms. Carneasha Parks, and

especially Ms. Maria Licona. We would like to thank Dr. Michael Gaines and Dr. Dana

Krempels for organizing the Research in Ecology Program.