test ideal free distribution on turtles at fiu pondstest ideal free distribution on turtles at fiu...

Test Ideal Free Distribution on Turtles at FIU Ponds

By: Team Crush (Veronica Junco, Erika Blandon, Gina Gonzalez, Etienne Chenevert,

Nicholas Cummings, Gaby Materon and Vince Pinon)

Abstract:

The purpose of this experiment was to test the theory of Ideal Free Distribution (IFD).

The research group studied turtle behavior to understand how IFD relates with turtles obtaining

food resources. The research team conducted the experiment in ponds at the south campus of

Florida International University. Turtle food was distributed at different rates at three feeding

stations separated by 2 meters. At one minute intervals food was dispersed, and after ten seconds,

the number of turtles was recorded in three different areas of the same pond. The experiment was

statistically relevant and the null hypothesis of random distribution of turtles at the feeding

stations was rejected. However, there were some environmental factors that negatively impacted

our final results.

Introduction:

Ecology is the study of plants and animals in their environment. Among the

characteristics of animals and plants are their distribution patterns. IFD is a theory describing the

way in which animals distribute themselves among several patches of resources under certain

circumstances. In particular, IFD states that if animals are free to move where they want,

individual animals will ideally congregate in various patches proportionately to the amount of

resources available.

The three words ‘‘ideal’’, ‘‘free’’, and ‘‘distribution’’ have the following definitions:

Ideal means that the animals or people have made an optimal choice of all their possible choices

that they could not improve their fitness (such as the amount of food available to them) by

moving someplace else. The word ‘‘free’’ means that animals or people have made their own

free choices and no one has obligated them to do it. Consider the following example: There are

three cats and three different types of cat food. Suppose there is tuna in one area, normal cat food

in another, and chicken in the third area. If there are three cats and one cat likes to eat tuna, the

other one would likes to eat normal cat food, and the last one likes to eat chicken, the cats would

be free if each of them makes their own choice of what to feed on without anyone obligating

them to eat one thing or another. This is free-decision making based on adequate resources being

provided.

The word ‘‘distribution’’ refers to how the individual animals locate themselves across an

area of land or water. Consider this example: There are three trees; one has ten mangos, second

one has fifteen mangos, and third one has five mangos. There are six monkeys and the question

is how they will distribute themselves among the total number of mangos. If the monkeys

distribute themselves freely and ideally, in the tree with five mangos there would be one monkey

eating those five mangos. In the tree with fifteen mangoes there would be three monkeys eating

them. In the third tree with ten mangoes there would be two monkeys eating them. From this

calculation you can tell that each monkey will be eating five mangos.

In experiments like the ones we will be introducing, the IFD has been tested on various

animals in nature or in artificial conditions. Four examples are mentioned here. Milinski (1979)

studied 6 stickleback fish feeding on two patches with different amounts of food. The

sticklebacks distributed themselves according to an IFD. In another example, Sokolowski et al.

(1999) performed experiments on humans competing for money and found that the humans

distributed themselves in a way consistent with the IFD. In another experiment, Abrahams

(1989) studied 10 female and 10 male guppies, in which he examined foraging on food at two

separate feeders. Both groups of fish conformed to the predictions of the ideal free distribution

theory.

There have been studies where animal behavior does not conform to the IDF model, but

show the Ideal Despotic Distribution model, or IDD. In a study performed by Beckmann and

Berger (2003) on a black bear population, the results were such that the black bears had no

freedom to choose. The experiment showed that there was one dominant bear that chose the best

supply for itself resulting in an IDD. This distribution pattern is not as commonly seen as the

IDF model for the feeding behavior patterns of the majority of animal species.

Materials and Methods:

To do this experiment, we first selected a pond to perform experiments on IFD. We

performed experiments at three ponds at FIU: the “Bridge Pond”, the “Duck Pond” and

the”‘Ewa Alona Pond”. The Bridge Pond was approximately 710m2, the Duck Pond

approximately 530m2, and the Ewa Alona pond was about 1.256m2 (Figure 1). The research

team chose the ponds by first checking to see if they had any turtles. The team also checked to

make sure that the ponds didn’t have any ducks present. This was an important factor as the

ducks were extremely aggressive and tended take the turtles’ food. These experiments were

performed during the first three weeks of the Research in Ecology (RIE) course, from 9:30am to

10:30am on the dates June 17, 20, 22, and 24. During all of the experiments the weather was hot

and sunny.

The materials in this experiment were the following: three empty coffee cups to hold

the fish food in, three spoons of different sizes (teaspoon, ½ teaspoon, and ½ tablespoon) to

disperse the food to the turtles at different pond sites, Koi and Goldfish food, notebook paper,

and pencil. In most cases we used the 1/2 teaspoon, the teaspoon and the 1/2 tablespoon. In one

experiment we used the 1/2 teaspoon, 1 teaspoon and tablespoon. We carried out our experiment

for no more than 25 minutes per experiment. Team members positions were varied for each day

of data collection.

Fig.1 Map of FIU south campus.

Pond near bridge Ewa Alona Duck pond

The team was divided into three groups with two students at each of the feeding sites. Each

group had a different spoon size to feed the turtles; the groups were separated by two meters.

Typically, the left side had the smallest spoon, the middle had the medium-sized spoon, and the

right side had the biggest spoon. Each group had a coffee cup that held the mix of koi and

goldfish food. Each team filled the spoon with fish food from our cup and waited for the time

keeper to say “throw” at 1 minute intervals. When the command was given, the researchers

threw the food about 1 meter away from us into the pond. After 10 seconds the time keeper said

“count” and the number of turtles by each distribution group. This procedure was repeated for

twenty consecutive minutes.

After data collection the team would go to the computer lab and enter the information on

an Excel spreadsheet. Data was combined and graphs were devised to compare results. The

statistical T-test was used to test the significance of the data obtained.

Results:

The experiments were performed at three FIU ponds for four days from 6/17/11 -6/24/11.

Each experiment was performed around 9:00 am.

Experiment #1. The date for experiment #1 was performed on 6/17/11. We did this

experiment in the morning around 9:00.The results are shown in Figure 2 and Table 1. The

largest number of turtles recorded at a given count for the teaspoon was 8, the lowest was 0, and

the mean (over the whole period of 25 minutes) number of turtles over the experiment was 2.67.

For the tablespoon, the highest number of turtles over a given count was 8, the lowest was 2, and

the mean over the whole 20 minutes was 2.4375. Finally, the ½ tablespoon results were that the

highest number of turtles over a given count of turtles was 9, the lowest was 0, and the mean

number of turtles over the whole 20 minutes was 4.8. The T-test shows that there is a significant

difference between ½ tablespoon and 1 tablespoon (p<0.01). And there is also a significant

difference between the tablespoon and the teaspoon (p<0.01). But there is no difference between

the ½ tablespoon and the teaspoon (p=0.24).

Figure 2a. Results of Experiment 1

Figure 2b Histogram of Experiment 1 (Change to be like Figure 3b)

Table 1. Data from Experiment #1

Spoon size 1 Tsp 1 Tbsp ½ Tbsp Highest 8 8 9 Lowest 0 2 0 Average 2.67 2.4375 4.8

Experiment #2. We performed Experiment 2 on the morning of June 20. The results are

shown in Figure 3 and Table 2 and are as follows: The largest number of turtles for a given count

at the feeding site for the 1/2 teaspoon was 3 and the smallest number of turtles was 0. The mean

number of turtles over the whole period of 16 minutes was 1.11 turtles. For the teaspoon, the

largest number of turtles for a given count was 6, the lowest amount was 0 and the mean over the

whole 16 minutes was 2.5 turtles. The ½ tablespoon results yielded the largest number of turtles

with 6 turtles for a count, the lowest was 0, and the mean number of turtles over the whole 16

minutes was 2.27 turtles. T-test shows that there a significant difference between ½ teaspoon and

one teaspoon (p<0.01). T-test shows that there is no significant difference between 1 teaspoon

and ½ tablespoon (p=0.71). T-test shows that there a significant difference between ½ teaspoon

and ½ tablespoon (p<0.01).


Figure3b. Histogram of experiment 2

Table 2. Data from Experiment #2

Spoon size Teaspoon ½ Teaspoon ½ Tablespoon Highest 6 3 6 Lowest 0 0 0 Average 2.5 1.11 2.27

Experiment #3. We performed experiment #3 on the morning of Monday, June 20, 2011.The

results are shown in Figure 4 and Table 3. In this experiment, we used the teaspoon, the ½

teaspoon, and the ½ tablespoon. For this experiment, the highest number of turtles for a given

count for the ½ teaspoon was 3, the lowest is 0 and the average over the whole period of 20

minutes was 1.1. For the teaspoon, the highest number of turtles recorded at a given count was 4,

the lowest was 1, and the average was 2.8. And the ½ tablespoon highest was 3, the lowest was

0, and the average was 1.2. T-test proved that there was a significant difference between the ½

teaspoon and the teaspoon (p<0.01). There is also a significant difference between the teaspoon

and the ½ tablespoon (p<0.01). But there is no significant difference between the ½ teaspoon and

the ½ tablespoon (p=0.87).


Figure. 4b Histogram of experiment 3

Table 3. Results of Experiment 3


Experiment #4. We performed Experiment 4 on the morning of June 22. The results are

shown in Figure 5 and Table 2 and are as follows. The largest number of turtles for a given count


number of turtles over the whole period of 16 minutes for the ½ teaspoon was 2.9. For the

teaspoon, the largest number of turtles for a given count was 6, the lowest amount was 0 and the

mean over the whole 16 minutes was 3.3. The ½ tablespoon results yielded the largest number of

turtles with 9 turtles for a count, the lowest was 2, and the mean number of turtles over the whole

20 minutes was 4.6. T-test shows that there was no significant difference between ½ teaspoon

and one teaspoon (p=0.43). T-test shows that there was a significant difference between 1

teaspoon and ½ tablespoon (p<0.01). T-test shows that there was a significant difference between

½ teaspoon and ½ tablespoon (p<0.01).



Figure 5a. Results of Experiment 4.

Figure 5b. Histogram of experiment 4

Experiment #5. We performed Experiment #5 on the morning of June 22. The results are

shown in Figure 6 and Table 5and are as follows: The largest number of turtles for a given count




mean was 2.9. The ½ tablespoon results yielded the largest number of turtles with 7 turtles for a

count, the lowest was 2, and the mean number of turtles was 4.6. T-test shows that there a

significant difference between ½ teaspoon and one teaspoon (p<0.01). T-test shows that there a

significant difference between 1 teaspoon and ½ tablespoon (p<0.01). T-test shows that there a

significant difference between ½ teaspoon and 1/2 tablespoon (p<0.01).


Figure 6b. Histogram of Experiment 5.


Spoon Size ½ teaspoon Teaspoon ½ tablespoon Highest 3 8 7 Lowest 0 0 2 Average 1.05 2.9 4.6

Experiment #6. We performed Experiment #6 on the morning of June 24. The results are

shown in Figure 7 and Table 5 and are as follows. The largest number of turtles for a given count

at the feeding site of the 1/2 teaspoon was 4 and the smallest number of turtles was 0. The mean



mean was 2.9. The ½ tablespoon results yielded the largest number of turtles with 7 turtles for a

count, the lowest was 7. T-test shows that there a significant difference between ½ teaspoon and

one teaspoon (p<0.01). T-test shows that there is no significant difference between 1 teaspoon

and ½ tablespoon (p=0.20). T-test shows that there a significant difference between ½ teaspoon

and 1/2 tablespoon (p<0.01).


Figure 7b. Histogram of Experiment 6


Spoon size ½ teaspoon Teaspoon ½ tablespoon Lowest 4 13 7 Highest 0 3 2 Average 1.9 2.9 7

Discussion and Conclusions:

The hypothesis we tested in these experiments is that, if the turtles are fed in different

sites in the ponds, close enough that they can move back and forth between those sites easily,

they will distribute themselves in proportion to the amount of food being supplied in the different

sites. This is called the Ideal Free Distribution (IFD). We realized that turtles wouldn’t follow the

hypothesis precisely. But, we still found general consistency between our results and what is

expected from the (IFD). On average, the two larger spoon sizes attracted the most turtles, and

usually the largest spoon size had the most turtle activity. The smallest spoon (always the

leftmost of the three feeding sites excluding experiment #1) had the fewest of turtles on average.

We learned several things that could make this experiment more accurate in the future.

First, we noticed that the middle site (where the teaspoon was used) tended to attract more turtles

than we expected from the IFD. This may be due to the turtles recognizing that the middle

feeding site was a good place to be even though most food was thrown in the right-hand side.

Furthermore, we learned that the way we throw the food can also affect the number of the

turtles in the area. That is because the turtles can see how much food is thrown into a particular

site and even the way it is thrown; far, close, clumsily or accurately. The spoon size is important

in many ways, because it affects the amount of food thrown into the pond. We learned that the

position of the feeding station affects the number of turtles attracted. Several factors to take into

consideration may include the water current, the turtles’ perception (if it sees the food being

thrown), and direction of the incoming turtles. Sometimes the food washed away to the left or

right because of water currents and the turtles (fish or ducks) fins moving the water. Sometimes,

the “throwers” would over-fill the spoon and throw it clumsily; interrupting the pattern of food

availability. In addition, the “throwers” would sometimes throw the food in too soon or too late.

Also, sometimes the “counters” would count the turtles too late or too early, and that caused the

number of turtles to be wrong in our data.

We think the turtles are good animals to test on because you can see them afloat on the

water and it’s not that hard to count them. Another good reason to use turtles as our animals to

test on is because the turtles aren’t very fast at swimming and is easier to count them then other

animals. In addition, the turtles we tested on were not easily frightened.

In our experiments we also saw that fish would eat the food that was being distributed.

That was also one of the things that made the experiment less accurate because when the big fish

appeared, they would scare turtles away. The small fishes would also eat the food that sank into

the bottom of the pond. The big fishes also distracted us when they were jumping in the air. Our

experimenting group also saw that some turtles would stay on the bottom and also eat the food

that sank too. For example, when we threw food we saw that some turtles would come up from

the bottom of the pond and go back down. In our experiment we also had some confusion,

because when it was time to count the turtles; while we were counting, the turtles would move

from one site to another so it made it tricky for us to see what site was site the turtle was eating

in.

Many times, there wouldn’t be that much wind coming, so it would be easier to throw

the food at a certain direction (and not have to throw it at a certain angle so it can go in the

correct direction). But there were water currents because there was a fountain making the water

flow to the right. So the food from the left sites food would travel to the right. In addition that

would make the right or middle side have more food. There was also a better chance that the

right side had more turtles because its spoon size was the largest: but the water current or turtles

swimming made the food go to the middle.

Keeping time is also very important also in this experiment. The reason on why the

timekeeper was very important in this experiment is is that he tells “exactly’’ when to throw. It

is best for the timekeeper to give a ‘countdown’ so the teams know how many seconds are left

before the team needs to throw. If you are planning to do this experiment, we recommend that

you to do all the steps correctly, so that the results can be accurate. The most important is; be

consistent. In particular, always throw exactly when the timekeeper says ‘throw’. One good tip

(mentioned earlier) is to keep track of the seconds you have before time is called. The person

who is tracking the time (in our case was Vicente) should do a ‘countdown’ when there are five

seconds left before the next throw. That’s something the time keeper should do. In addition, you

should throw the food correctly, not too far or to close it should be, a yard away. Also if you are

planning to do this experiment, we suggest that you also pay close attention to your turtles; keep

notes on what they’re doing. That may help you understand why or why not the turtles come to

your feeding site. Another thing you should see is the weather. It is very important because the

turtles are more expected to come when it is sunny. than when it is raining because they may go

and hide. It is very important to also keep calm when experimenting; because it can send some

turtles further, and it is better to be calm anyway.

Acknowledgements:

We would like to recognize Dr. DeAngelis, Jiang Jiang, Tony Gustitus, Mrs. Melissa Martin, Mr.

Dwight Williams, Dr. Kremples, HHMI, and all those who supported our project.

References:

1) Milinski, M. 1979. An evolutionarily stable feeding strategy. Z. Tierpsychol. 51:36-40.

2) Sokolowski, M.B.C, F.Tonneau, E.Freixa Baque. 1999. The Ideal Free Distribution in

Humans: An Experimental Test. Psychonomic Bulletin and Review. 6:157-161.

3) Abrahams, M. V. 1989. Foraging guppies and Ideal Free Distribution: The influence of

information o patch choice. Ethology 82:116-126.

4) Beckman, J. P. and J. Berger. 2003. Using black bears to test ideal free distribution

models experimentally. Journal of Mammology 84:594-606.

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