Fish
Aggression
Background
In
this project, we will be studying the behavior of the Giant Damselfish (Microspathodon dorsalis), which is the
largest damselfish in the Sea of Cortez, growing up to 1 foot long. The Sea of Cortez (or Golfo de California) is
the body of water between the Baja California peninsula and the Mexican state
of Sonora, just south of Arizona. The
data was collected by Professor Jon Moore as part of an undergraduate research
project when he was a student at the University of Arizona.
The
Giant Damselfish lays its eggs in patches (about one foot square) on the sides
of boulders. The nests are defended by
the male fish, who are extremely territorial.
Moore hypothesized that the fish are selective in their defense of their
territory and vary the energy they expend according the species of the
intruding fish. We will test this
hypothesis.
Data
The
data was collected during the summers of 1982 and 1984, from nests on Isle
Coronada, Baja California Sur, in the Sea of Cortez. The species of the intruding fish were identified using
[TFK]. The fish were also classified
according to their diet: (H)erbivorous,
(E)gg-eaters, or (O)ther. The meetings
between the defending and intruding fish were classified (according to Moore's
judgement) as one of the following:
non-interactive: defender ignores intruder
minimal: defender makes a quick turn
towards intruder
moderate: defender chases intruder up to
2 feet from nest
extreme: defender chases intruder more
than 2 feet from the nest, and body contact sometimes occurred
The
table below shows the (combined) results of Moore's observations in 1982 and
1984. Each cell gives the number of
interactions of the given type (column) with the given species (row):
|
Species |
diet |
none |
minimal |
moderate |
extreme |
Total |
|
Barberfish |
E |
2 |
5 |
8 |
2 |
17 |
|
Barspot Cardinalfish |
O |
2 |
0 |
0 |
0 |
2 |
|
Bluechin Parrot |
H |
6 |
10 |
13 |
19 |
48 |
|
Burrito Grunt |
O |
3 |
0 |
0 |
0 |
3 |
|
Clown Hawkfish |
O |
1 |
0 |
0 |
0 |
1 |
|
Cortez
Chub |
H |
2 |
0 |
2 |
1 |
5 |
|
Cortez Damselfish |
H |
555 |
50 |
32 |
4 |
641 |
|
Dog Snapper |
O |
1 |
0 |
0 |
0 |
1 |
|
Fanged Blenny |
O |
4 |
0 |
0 |
0 |
4 |
|
Flag Cabrilla |
O |
12 |
1 |
0 |
0 |
13 |
|
Giant Damselfish |
H |
16 |
5 |
6 |
17 |
44 |
|
Graybar Grunt |
O |
19 |
6 |
0 |
0 |
25 |
|
Gulf Opaleye |
H |
0 |
4 |
0 |
1 |
5 |
|
King Angelfish |
O |
20 |
1 |
3 |
1 |
25 |
|
Leopard Grouper |
O |
33 |
2 |
0 |
0 |
35 |
|
Mexican Goatfish |
O |
3 |
0 |
0 |
0 |
3 |
|
Mexican Hogfish |
O |
82 |
11 |
1 |
0 |
94 |
|
Mutton Hamlet |
O |
5 |
0 |
0 |
0 |
5 |
|
Panama Graysby |
O |
7 |
0 |
0 |
0 |
7 |
|
Rainbow Wrasse |
E |
5 |
9 |
15 |
59 |
88 |
|
Scissortail Damselfish |
O |
0 |
2 |
0 |
0 |
2 |
|
Sergeant Major |
E |
1 |
32 |
89 |
317 |
439 |
|
Sharpnose Puffer |
O |
23 |
8 |
3 |
3 |
37 |
|
Yellow Snapper |
O |
28 |
0 |
0 |
0 |
28 |
|
Yellowtail Surgeonfish |
H |
0 |
0 |
0 |
1 |
1 |
|
Zebra Perch |
H |
0 |
0 |
0 |
23 |
23 |
|
Total |
|
830 |
146 |
172 |
448 |
1596 |
Problems
1.
We
want to perform a significance test on this data. What is the null hypothesis?
What is the alternative hypothesis?
2.
Explain
why you cannot perform a c2 test on this table in its
current form.
In
order to perform a valid c2 test on this table, we need
to compress the data in some reasonable way.
This means we need to refine our original hypothesis. Previous researchers have suggested that the
Giant Damselfish will defend more aggressively against egg-predators and
food-resource competitors (the Giant Damselfish is a herbivore).
3.
Use
the classification of the fish according to diet to construct a new two-way
table with a row each for Herbivores, Egg-eaters and Other. Compute the table of expected counts. Explain why you can you perform a c2 test on your compressed
table.
4.
Perform
a c2 test. What are the degrees of freedom? What is the P-value?
5.
What
can you conclude from the c2 test, and with what
confidence?
6.
Perform
a follow-up analysis of the table, using 2-proportion z-tests. What are your conclusions?
Now
we want to see if there is a greater reaction against food resource competitors
in particular. To do this, ignore the
data for egg predators. You have
probably noticed that by far the largest number of interactions was with the
Cortez Damselfish. The Cortez
Damselfish lives in the same regions as the Giant Damselfish, and so is a
frequent intruder. It might seem
surprising that, although this fish is also a herbivore, it was largely
ignored. However, the Cortez
Damselfish, like the Giant Damselfish, is extremely territorial; one might
conjecture that the Giant Damselfish knows that the Cortez Damselfish has its
own "garden" elsewhere, and so is not really a food competitor.
7.
Construct
a new two-way table of just the herbivores and other species, ignoring the egg
predators and the Cortez Damselfish. Compute the table of expected counts. Explain why you can you perform a c2 test on your compressed
table.
8.
Perform
a c2 test. What are the degrees of freedom? What is the P-value?
9.
What
can you conclude from the c2 test, and with what
confidence?
10.
Perform
a follow-up analysis of the table, using 2-proportion z-tests. What are your conclusions?
11.
Write
a paragraph or two summarizing your conclusions from this project.
References
[TFK] D. Thomson, L. Findley and A. Kerstitch, Reef Fishes of the Sea of Cortez, University of Arizona Press, 1979
You
may do this project as a group of up to 4 people, and turn in one report for
the entire group. Each member of the
group will receive the same grade.
Graded out of 30 points