Test Ideal Free Distribution on Turtles at FIU Ponds

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.
Pond near bridge
Fig.1 Map of FIU south campus.
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
Highest
Lowest
Average
1 Tsp
8
0
2.67
1 Tbsp
8
2
2.4375
½ Tbsp
9
0
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).
Figure 3a. Results of Experiment 2
Figure3b. Histogram of experiment 2
Table 2. Data from Experiment #2
Teaspoon ½ Teaspoon ½ Tablespoon Spoon size
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 4a. Results of Experiment 3
Figure. 4b Histogram of experiment 3
Table 3. Results of Experiment 3
Spoon size
Highest
Lowest
Average
Teaspoon
3
0
1.1
½ Teaspoon
4
1
2.8
½ Tablespoon
3
0
1.2
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
at the feeding site for the 1/2 teaspoon was 7 and the smallest number of turtles was 0. The mean
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).
Table 4. Results of Experiment 4
Spoon size Highest Lowest Average Teaspoon 6 0 3.3 ½ Teaspoon 7 0 2.9 Figure 5a. Results of Experiment 4.
½ Tablespoon 9 2 4.6 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
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 for the ½ teaspoon was 1.05. For the
teaspoon, the largest number of turtles for a given count was 8, the lowest amount was 0 and the
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 6a. Results of Experiment 5.
Figure 6b. Histogram of Experiment 5.
Table 5. Results of Experiment 5
Spoon Size Highest Lowest Average ½ teaspoon 3 0 1.05 Teaspoon 8 0 2.9 ½ tablespoon 7 2 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
number of turtles over the whole period of 16 minutes for the ½ teaspoon was 1.9. For the
teaspoon, the largest number of turtles for a given count was 13, the lowest amount was 3 and the
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 7a. Results of Experiment 6.
Figure 7b. Histogram of Experiment 6
Table 6. Results of Experiment 6
Spoon size Lowest Highest Average ½ teaspoon 4 0 1.9 Teaspoon 13 3 2.9 ½ tablespoon 7 2 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.