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