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Dudley Knox Library, KPS
Monterey, CA 93943

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESIS

THE USE OF COMPUTER INTENSIVE STATISTICAL MODELING IN
ESTIMATING THE VARIABILITY OF MARINE FOULING

COMMUNITIES

David L. Martin

June 1983

Thesis Advisor:

E. C, Haderlie

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The Use of Computer Intensive Statistical
Modeling in Estimating the Variability of Marine
Fouling Communities

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Master's Thesis
June 198.3

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David L, Martin

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Naval Postgraduate School
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1». KEY WOROS (Contlnua on reveree aid* II nacaaamry and Idantlty by block number)

Biofouling, Statistics, Variability, Bootstrap Computer Simulations,
Maximum Likelihood

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were then used to determine an appropriate strategy for sampling the
fouling community in Monterey Bay. The results indicate that twenty to
thirty plates are required to resolve ambiguities concerning the mean
percent cover of a group of plates while many more are required to quantify
the variability of the fouling population.

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The Use of Computer Intensive Statistical Modeling
in Estimating the Variability of Marine Fouling Communities

David L. Martin
Lieutenant, United States Navy
B.S., University of Washington, 1976

Submitted in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE IN METEOROLOGY AND OCEANOGRAPHY

from the

NAVAL POSTGRADUATE SCHOOL
June 1983

/M3573

ABSTRACT

The variability of the fouling community in Monterey
Bay was investigated by suspending 100 mild steel plates in
Monterey Harbor. The plates were painted with either a non-
toxic control paint or one of three antifouling paints.
Following the monthly retrieval of a group of these plates,
a census of the fouling organisms was conducted and initial
variability estimates determined. These estimates were used
as inputs for bootstrap computer simulations of the
experiment. The results of the bootstrap simulations were
then used to determine an appropriate strategy for sampling
the fouling community in Monterey Bay. The results indicate
that twenty to thirty plates are required to resolve
ambiguities concerning the mean percent cover of a group of
plates while many more are required to quantify the
variability of the fouling population.

TABLE OF CONTENTS

I . INTRODUCTION 15

A. GENERAL 15

1. Sampling Design 16

2. Previous Research on Fouling Community
Variability 16

B . OBJECTIVE 18

II. METHODS AND MATERIALS 19

A. GENERAL , 19

B. PLATES AND PAINTS 19

1. Priming Procedure 21

2. Painting Procedure 23

C. DEPLOYMENT PROCEDURE 24

D. FOULING COMMUNITY CENSUS AND IDENTIFICATION . . 27

1. Sampling Procedure 27

2. Identification 28

III. STATISTICS 29

A. EXPERIMENTAL DATA 29

1. Percent Cover 29

2. Similarity 29

B. STATISTICAL MODELLING 31

1. Model Alternatives 32

2. Procedure 34

IV. RESULTS 37

A. GENERAL 37

1. Method Verification 37

2. Explanation of Figures 43

B. RESULTS FROM MONTH 2 44

1. Experimental Data 44

2. Computer Simulations 45

C. RESULTS FROM MONTH 3 48

Experimental Data 48

2 . Computer Simulations 50

D. RESULTS FROM MONTH 4 54

1 . Exper imental Data 54

2 . Computer Simulations 56

E. RESULTS FROM MONTH 5 56

1 . Exper imental Data 56

2 . Computer Simulations 59

F. RESULTS FROM MONTH 6 63

1. Experimental Data 63

2. Computer Simulations 65

G. RESULTS FROM MONTH 7 68

1 . Exper imental Data 68

2 . Computer Simulations 68

H. RESULTS FROM MONTH 8 70

1. Experimental Data 70

2 . Computer Simulations 73

I . RESULTS FROM MONTH 9 77

1 . Exper imental Data 77

2. Computer Simulations 77

J. RESULTS FROM MONTH 10 79

1. Experimental Data 79

2 . Computer Simulations 79

K. RESULTS FROM MONTH 11 84

1. Experimental Data 84

2 . Computer Simulations 86

V. CONCLUSIONS AND RECOMMENDATIONS 90

A. DISCUSSION 90

B. RECOMMENDATIONS FOR FURTHER RESEARCH 92

APPENDIX A: MICRON 22 ORGANO METALLIC POLYMER

ANTIFOULING PAINT 94

APPENDIX B: NAVY STANDARD FORMULA 121 RED

VINYL ANTIFOULING PAINT 95

APPENDIX C: NAVY STANDARD FORMULA 170 BLACK

CAMOFLAGE ANTIFOULING PAINT 96

APPENDIX D: ZYNOLYTE EPOXY RUST MATE PAINT 97

APPENDIX E: A DISCUSSION OF THE METHOD OF MAXIMUM
LIKELIHOOD ON ITS INCORPORATION INTO A

MODEL FOR FOULING COVER 98

APPENDIX F: BOOTSTRAP COMPUTER SIMULATIONS 103

APPENDIX G: TABULATED MONTHLY PERCENT COVERAGE VALUES

FOR NON-TOXIC CONTROL SURFACES 107

APPENDIX H: LIST OF THE SESSILE SPECIES IDENTIFIED

BY THE RANDOM POINT CENSUS AND THE MONTHS
THEY WERE PRESENT ON THE NON-TOXIC CONTROL

SURFACES 109

LIST OF REFERENCES Ill

INITIAL DISTRIBUTION LIST 113

LIST OF FIGURES

1. A Diagram of Monterey Bay Showing the Deployment
Site at the Coast Guard Floating Dock 20

2. The Front Side of One of the Experimental Plates . 22

3. A Drawing Showing the Method of Attachment of

the Suspending Cable and Identification Tag 25

4. A Perspective View in Cross Section Showing the
Deployment of the Plates at the Coast Guard Dock . 26

5. Chart Showing the Monthly Mean Similarity Values
for the Control Surfaces (Solid) and the Anti-
fouling Coated Surfaces (Dashed) 39

6. A Diagnostic Plot of the Model With the Ranked,
Normalized Values for the Individual Epsilon
Values Plotted on the Ordinate (Abbreviated as
Z) and the Theoretical Order Statistic Plotted
of the Abscissa. The Dashed Line Indicates
Perfect Correspondence and the Dotted Line is

the Least Squares Best Fit for the Data 41

7. Chart Showing the Arithmetic Mean of the Percent
Fouling Cover From the Experimental Data (Solid)
and the Bootstrap Simulated Mean Percent Cover
(Dashed) 42

8. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces
for Month 2. Dashed Lines Indicate Mean
Similarity Values 46

9. Computer Simulations Using Data From Month 2
Showing the Expected Value of the Mean Percent
Fouling Cover (the Mean of the 200 Individual
Group Simulation Percent Fouling Covers) as a
Solid Line and the 95% Quantile (Dashed) of the
Expected Mean Percent Fouling Cover as a

Function of Increasing Sample Size 47

10. Computer Simulations Using Data From Month 2
Showing: (A) the Percent Fouling Coverage That
One Can Say 90% of the Samples Will Have Fouling
Coverage Less Than or Equal to (With 95% Confi-
dence) ; and (B) the Standard Deviation of Per-
cent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing

Sample Size 49

11. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces
for Month 3. Dashed Lines Indicate Mean
Similarity Values 51

12. Computer Simulations Using Data From Month 3
Showing the Expected Value of the Mean Percent
Fouling Cover (the Mean of the 200 Individual
Group Simulation Percent Fouling Covers) as a
Solid Line and the 95% Quantile (Dashed) of the
Expected Mean Percent Fouling Cover as a

Function of Increasing Sample Size 52

13. Computer Simulations Using Data From Month 3
Showing: (A) the Percent Fouling Coverage That
One Can Say 90% of the Samples Will Have Fouling
Coverage Less Than or Equal to (With 95% Confi-
dence) ; and (B) the Standard Deviation of Per-
cent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing

Sample Size 53

14. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces
for Month 4. Dashed Lines Indicate Mean
Similarity Values 55

15. Computer Simulations Using Data From Month 4
Showing the Expected Value of the Mean Percent
Fouling Cover (the Mean of the 200 Individual
Group Simulation Percent Fouling Covers) as a
Solid Line and the 95% Quantile (Dashed) of the
Expected Mean Percent Fouling Cover as a

Function of Increasing Sample Size 57

16. Computer Simulations Using Data From Month 4
Showing: (A) the Percent Fouling Coverage That
One Can Say 90% of the Samples Will Have Fouling
Coverage Less Than or Equal to (With 95% Confi-
dence) ; and (B) the Standard Deviation of Per-
cent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing

Sample Size 58

17. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces
for Month 5. Dashed Lines Indicate Mean
Similarity Values 60

18. Computer Simulations Using Data From Month 5
Showing the Expected Value of the Mean Percent
Fouling Cover (the Mean of the 200 Individual
Group Simulation Percent Fouling Covers) as a
Solid Line and the 95% Quantile (Dashed) of the
Expected Mean Percent Fouling Cover as a

Function of Increasing Sample Size 61

19. Computer Simulations Using Data From Month 5
Showing: (A) the Percent Fouling Coverage That
One Can Say 90% of the Samples Will Have Fouling
Coverage Less Than or Equal to (With 95% Confi-
dence) ; and (B) the Standard Deviation of Per-
cent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing

Sample Size 62

20. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces
for Month 6. Dashed Lines Indicate Mean
Similarity Values 64

21. Computer Simulations Using Data From Month 6
Showing the Expected Value of the Mean Percent
Fouling Cover (the Mean of the 200 Individual
Group Simulation Percent Fouling Covers) as a
Solid Line and the 95% Quantile (Dashed) of the
Expected Mean Percent Fouling Cover as a

Function of Increasing Sample Size 66

22. Computer Simulations Using Data From Month 6
Showing: (A) the Percent Fouling Coverage That
One Can Say 90% of the Samples Will Have Fouling
Coverage Less Than or Equal to (With 95% Confi-
dence) ; and (B) the Standard Deviation of Per-
cent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing

Sample Size 67

23. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces
for Month 7. Dashed Lines Indicate Mean
Similarity Values 69

24. Computer Simulations Using Data From Month 7
Showing the Expected Value of the Mean Percent
Fouling Cover (the Mean of the 200 Individual
Group Simulation Percent Fouling Covers) as a
Solid Line and the 95% Quantile (Dashed) of the
Expected Mean Percent Fouling Cover as a

Function of Increasing Sample Size 71

25. Computer Simulations Using Data From Month 7
Showing: (A) the Percent Fouling Coverage That
One Can Say 90% of the Samples Will Have Fouling
Coverage Less Than or Equal to (With 95% Confi-
dence) ; and (B) the Standard Deviation of Per-
cent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing

Sample Size 72

26. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces
for Month 8. Dashed Lines Indicate Mean
Similarity Values 74

27. Computer Simulations Using Data From Month 8
Showing the Expected Value of the Mean Percent
Fouling Cover (the Mean of the 200 Individual
Group Simulation Percent Fouling Covers) as a
Solid Line and the 95% Quantile (Dashed) of the
Expected Mean Percent Fouling Cover as a

Function of Increasing Sample Size 75

28. Computer Simulations Using Data From Month 8
Showing: (A) the Percent Fouling Coverage That
One Can Say 90% of the Samples Will Have Fouling
Coverage Less Than or Equal to (With 95% Confi-
dence) ; and (B) the Standard Deviation of Per-
cent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing

Sample Size 76

29. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces
for Month 9. Dashed Lines Indicate Mean
Similarity Values 78

30. Computer Simulations Using Data From Month 9
Showing the Expected Value of the Mean Percent
Fouling Cover (the Mean of the 200 Individual
Group Simulation Percent Fouling Covers) as a
Solid Line and the 95% Quantile (Dashed) of the
Expected Mean Percent Fouling Cover as a

Function of Increasing Sample Size 80

31. Computer Simulations Using Data From Month 9
Showing: (A) the Percent Fouling Coverage That
One Can Say 90% of the Samples Will Have Fouling
Coverage Less Than or Equal to (With 95% Confi-
dence) ; and (B) the Standard Deviation of Per-
cent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing

Sample Size 81

32. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces
for Month 10. Dashed Lines Indicate Mean
Similarity Values 82

33. Computer Simulations Using Data From Month 10
Showing the Expected Value of the Mean Percent
Fouling Cover (the Mean of the 200 Individual
Group Simulation Percent Fouling Covers) as a
Solid Line and the 95% Quantile (Dashed) of the
Expected Mean Percent Fouling Cover as a

Function of Increasing Sample Size 83

34. Computer Simulations Using Data From Month 10
Showing: (A) the Percent Fouling Coverage That
One Can Say 90% of the Samples Will Have Fouling
Coverage Less Than or Equal to (With 95% Confi-
dence) ; and (B) the Standard Deviation of Per-
cent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing

Sample Size 85

35. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces
for Month 11. Dashed Lines Indicate Mean
Similarity Values 87

36. Computer Simulations Using Data From Month 11
Showing the Expected Value of the Mean Percent
Fouling Cover (the Mean of the 200 Individual
Group Simulation Percent Fouling Covers) as a
Solid Line and the 95% Quantile (Dashed) of the
Expected Mean Percent Fouling Cover as a

Function of Increasing Sample Size 88

37. Computer Simulations Using Data From Month 11
Showing: (A) the Percent Fouling Coverage That
One Can Say 90% of the Samples Will Have Fouling
Coverage Less Than or Equal to (With 95% Confi-
dence) ; and (B) the Standard Deviation of Per-
cent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing

Sample Size 89

ACKNOWLEDGMENT

I express my sincere gratitude and appreciation to
Distinguished Professor Eugene C. Haderlie for his guidance
and many excellent suggestions during the course of this
study, to Professor Donald P. Gaver who designed the
probabilistic model used to quantify the fouling community
variability, to Professor Patricia Jacobs for both her
critical review of the thesis and her patience in
instructing a biologist in the many complexities of modern
statistical analysis, and finally to my wife whose support
and understanding made the successful completion of this
project possible.

I. INTRODUCTION

A. GENERAL

The term biofouling refers to the settlement,
attachment, and growth of marine organisms on surfaces
that man puts into the ocean. This process has a profound
impact on naval operations due to the fouling of ships
hulls, rudders, salt water piping systems, sonar domes,
and the fouling and biodeter ioration of harbor or pier
structures. This problem has been estimated to cost the
Navy several hundred million dollars a year (Woods
Hole, 1952; Fisher et al,1975) due in part to increased fuel
requirements caused by the greater frictional drag of
fouled ships hulls, the increased repair or replacement
cost of piping and machinery damaged by fouling organisms,
and the need to expend funds to continually remove the
fouling organisms from vessels.

The principal method used to combat the problem of
biofouling on the hulls of ships has been the application
of antifouling paints. In general, such paints contain any
of several metallic compounds which, as they leach out of
the paint matrix, are toxic to fouling organisms.

The testing of antifouling paints prior to their
release for general use involves the use of sampling assay
techniques. In simple terms, a number of substrates are

painted with the paint to be tested and are deployed in the
sea for some arbitrary length of time. Following the
retrieval of these substrates, they are compared with non-
toxic control surfaces that have been exposed for the same
length of time and the efficacy of the antifouling paint in
preventing the settlement of fouling organisms is
ascertained.

1. Sampling Design

The proper number of plates to deploy for the
testing of antifouling paints, or for that matter, the
study of fouling organisms in general, has always been
somewhat arbitrary. This is because the proper number of
plates to deploy to sample the fouling population is a
direct function of the degree of variability within the
population. Despite the great volume of fouling research
that has been conducted, the study and quantification of
this variability has only very recently been attempted.

2. Previous Research on Fouling Community Variability
Most of the information dealing with the

variability of biofouling communities has been collected
within the past decade and is often somewhat contradictory.
This contradiction is sometimes caused by the particular
descriptors of the fouling community (percent cover,
species counts, etc.) the researchers used in the analysis
of its variability.

Research concerning the variability of small
numbers of panels suspended for only one month off the
Florida coast (Mook,1976) showed very little variability in
species count. These results should be interpreted
cautiously however due to the short time of immersion.

Similar research conducted in North Carolina
(Sutherland, 1974) using a more extensive series of panels
suggested that the development of the fouling community was
extremely variable. This research supported the conclusion
of earlier studies in California (Boyd, 1972) which also
found significant fouling community variability.

Studies conducted in Hawaii (Schoener et al,1978)
and in Massachusetts (Osman,1977) found that fouling
community variability based on species counts was
relatively low. This conclusion was echoed by a study which
analyzed the variability of identical panels in terms of
total percent cover, species count, and inter-panel
similarity indices (Schoener and Greene, 1980). The results
of the study indicated that approximately ten replicate
panels were sufficient to resolve to a high degree of
confidence, the mean value of these descriptors.

As is evident, there is wide disparity between the
various studies conducted to date on what the variability
of the biofouling community at various locations truly is.
Before meaningful antifouling paint test procedures can be

developed, proper sampling techniques based on the
quantification of fouling community variability must be
devised.

B. OBJECTIVE

The primary objective of this thesis was to determine
the variability of the biofouling community in Monterey
Bay. Once this had been completed, the development of a
appropriate sampling strategy based on this variability
could be accomplished. This information was to be provided
to the David Taylor Naval Ship Research and Development
Center so that modifications to present antifouling test
procedures could be undertaken as required.

II. METHODS AND MATERIALS

A. GENERAL

The experiment consisted of deploying one-hundred (100)
mild steel plates, each painted with one of four vinyl or
epoxy based paints, in Monterey Harbor (Figure 1) for
periods of up to 11 months and determining the variability
of the resulting fouling communities that settled. Three of
the paints used in the study contained antifouling
compounds while the fourth ( the control surface ) did not.
The fouling community structure on each plate was deter-
mined destructively (the plates were not redeployed after
study) by microscopic analysis and the fouling population
and makeup were determined.

B. PLATES AND PAINTS

The one-hundred plates used in this study were
fabricated from low carbon, mild (structural) steel with
dimensions 25.4cm x 30.5cm x .16cm . A small (.64cm) hole
was drilled approximately 1.3 cm down from the midpoint of
the top edge (one of the edges with the lesser dimension)
of the plates to allow for the attachment of the suspending
line for deployment. Additionally, a small (.32cm x 2cm)
groove was milled through the plate approximately 6.5cm to
one side of the drilled hole for the attachment of the

Figure 1. A Diagram of Monterey Bay Showing the Deployment
Site at the Coast Guard Floating Dock.

identification tag. For consistent reference, the front of
the plate was chosen as that side which would face the
observer when the plate was held vertically with the dril-
led hole at the top and the identification groove to its1
left (Figure 2).

The four paints used in the experiment were:

1. MICRON 22; a commercially available antifouling
paint containing bis ( tr ibutyltin) oxide and cuprous
thiocyanate as the antifouling agents (Appendix A).

2. Navy Standard Formula 121 Red Vinyl Antifouling
Paint; the discontinued U.S. Navy antifouling paint
containing cuprous oxide as the antifouling agent
(Appendix B) .

3. Navy Standard Formula 170 Black Camoflage Vinyl
Antifouling Paint; the currently used standard
antifouling paint of the U.S. Navy containing
bis ( tr ibutytin) oxide and tributyltin fluoride as the
antifouling agents (Appendix C) .

4. Zynolyte Epoxy Rust Mate; a commercially
available non-toxic corrosion resistant epoxy based paint
used as the control surface (Appendix D) .

Allplates were sandblasted then primed and painted in
accordance with label directions.

1. Priming Procedure

The priming procedure consisted of first applying
one coat of Navy Standard Formula 117 'Green Wash Primer'
to both sides of all plates with a 5cm latex rubber brush
and allowing this to dry for twenty-four hours. This was
followed by the application of two coats of Navy Standard
Formula 119 'Red Lead' to both sides of all plates using a
7.6cm nylon paint roller. The first coat of Formula 119 was

E
u

6
ro

Figure
Plates.

2. The Front Side of One of the Experimental

allowed to dry for forty-eight hours before the second coat
was applied, and an additional forty-eight hours drying
time was allowed prior to painting with the vinyl or epoxy
paints.

2. Painting Procedure

All painting was accomplished using 7.6cm nylon
paint rollers. The plates were divided into four groups
(A,B,C, and D) of twenty-five plates each and labelled and
painted as follows:

1. Plates Al through A25 were painted on both sides
with one coat of MICRON 22 antifouling paint.

2. Plates Bl through B25 were painted on both sides
with one coat of Navy Standard Formula 121 Antifouling
Paint.

3. Plates CI through C25 were painted on both sides
with one coat of Navy Standard Formula 170 Antifouling

paint.

4. Plates Dl through D25 were painted on both sides
with one coat of Zynolyte Epoxy Rust Mate.

The paint on all plates was then allowed to cure

for 96 hours prior to deployment. The plates were labelled

sequentially in each group (Al,A2,etc) by affixing, through

the identification groove, an embossed DYMO tape label to

each plate using monofilament nylon fishing line. This

method of labelling was chosen to prevent the catalytic

corrosion problems attendant with standard bronze or copper

tags in contact with the steel plates.

C. DEPLOYMENT PROCEDURE

The plates were randomly divided into twelve groups of
eight plates consisting of two plates from each of the four
paint groups. To each plate a one meter length of .32 cm
diameter stainless steel cable was then affixed by passing
the cable through the drilled hole and forming a loop which
was closed using Nico-Press crimp fittings (Figure 3). A
similar loop was formed at the distal end of the cable to
facilitate attachment at the deployment site.

On 22 and 23 May 1982, the plates were suspended (by
groups) beneath the service access covers that extend the
length of the floating dock at the Coast Guard Station
Monterey. Each plate was individually deployed by attaching
the distal loop of the cable to lOd nails driven into the
dock and allowing the plate to hang vertically in the water
(Figure 4). The plates were separated by a minimum
horizontal distance of 40cm with the tops of the plates
approximately one-half meter beneath the surface of the
water. Since the dock rose and fell with the tide, the
depth of immersion remained constant. Water depths below
the plates (at MLLW) ranged from approximately three meters
depth at the shallower end of the dock to more than ten
meters depth at the seaward end. After being submerged for
one month, inspection of the plates revealed that
significant galvanic corrosion had occured at the junction

Monofilament Nylon line
with Identification Tog

Stainless steel cable
with Nico- Press
Crimp fitting

Figure 3. A Drawing Showing the Method of Attachment of
the Suspending Cable and Identification Tag.

SERVICE ACCESS COVER

Figure 4. A Perspective View in Cross Section Showing the
Deployment of the Plates at the Coast Guard Dock.

between the mild steel plates and the stainless steel
cable. As a result, on 23 June 1982, all stainless steel
cables were removed and replaced with .95 cm diameter nylon
line. This necessitated the exposure of each plate to the
atmosphere for approximately thirty seconds during the
replacement operation but , since the plates remained
moist, it was felt no harm was done to the fouling
organisms that had settled.

D. FOULING COMMUNITY CENSUS AND IDENTIFICATION

Each month following the initial deployment, one of the
groups of eight plates was randomly selected for retrieval
and study.

1. Sampling Procedure

For each group of plates, a sampling grid of one-
hundred (100) uniformly distributed random points was
generated and graphically plotted by computer on a 25.4 cm
x 30.5 cm output sheet. These points were then transferred
manually to a clear plexiglass cover. The fouling
communities on the plates were then systematically analyzed
by setting the plates horizontally in a shallow container
filled with seawater and positioning the plexiglass cover
over the top coincident with the edges of the plate.
Animals beneath plotted points were then censused and
identified through the use of a stereo microscope. Since
the plates had been suspended vertically in the water, none

of the sedimentation problems associated with horizontal
deployment strategies developed. Therefore both sides of
the plates were analyzed and counted as separate
substrates.

2. Identification

To eliminate the necessity for compound microscope
identification of settled organisms and to negate the ef-
fects of neuston contamination of census results, only
sessile, attached organisms greater than .5mm in size were
counted and identified. Identification was accomplished
through the use of available keys and literature;
(Osburn,1952; Knight Jones, 1979; Hader lie, 1974 ; Morris
et al,1980; Frazier,1937; Smith and Carlton, 1975) . In all,
some thirty-two taxa were identified as major space occu-
piers during the study (see Appendix H for species list).

III. STATISTICS

A. EXPERIMENTAL DATA

The data obtained from the census and identification of
the organisms on the plates retrieved each month was used
to generate the statistics that described the fouling
populations. The two main descriptive quantities used to
assess the variability of the fouling community were the
total percent fouling cover on each plate and the
similarity of the fouling organizations between plates.

1. Percent Cover

The initial estimate of the total percent fouling
cover on each plate was calculated by dividing the number
of points from the census that had organisms beneath them
(this value was termed St) by the total number of points
censused per plate (N = 100 for all plates). Since this
method was obviously subject to some unknown degree of
uncertainty, revised estimates for the total percent
fouling cover were made using statistical techniques
described below.

2. Similarity

The similarity between the fouling communities on
the plates retreived each month was determined by the
calculation of the Bray-Curtis similarity index, Ia
(Whitaker,1952) . This index is defined as:

Ia = ]jPmin(a,b)
where a and b are the fractional species proportions
present on plates A and B. These fractional species
proportions were determined from the initial census data by
dividing the total number of instances a particular species
was counted during the plate census by 100. In this study,
empty points not occupied by any organism were treated as a
separate species. As an example, suppose the following data
were collected:

Species

Proportion
Plate A ( =

on
=a)

Proportion
Plate B {■■

on
=b)

min (a,b)

Empty
Species #1
Species #2
Species #3

.30

0
.46
.24

.24
.11
.42
.23

.24

0
.42
.23

then the Similarity Index = Ia = T"*min(a,b) = .89
The similarity index is thus a measure of the degree of
variability between the fouling communities on the two
plates in terms of both the total percent cover and the
species composition.

The main purpose of calculating the similarity
index between plates was to examine whether any of the
antifouling coated plates displayed more variability than
did the non-toxic control surfaces. This was of particular
interest since a previous thesis (Kelley,1981) which dealt
with marine microfoulers in Monterey Bay had shown that
surfaces coated with an organo-metallic antifouling paint

served as attractants to the organisms and, hence, were
more heavily fouled, showed greater species diversity , and
were more variable in terms of their fouling communities
than were the control surfaces. Provided that the
macrofouling community investigated in this thesis did not
behave similarly, that is if the fouling communities on the
non-toxic control surfaces were consistently more variable
than were those on the antifouling coated surfaces, then
any sampling strategy which could discern to an acceptable
degree of error the amount of variability of the
communities on the control surfaces would be able to do at
least as well concerning the antifouling coated surfaces.
The thrust of this thesis was to first investigate whether
or not the control surfaces for each month exhibited more
variability than did the antifouling coated surfaces.
Provided this criteria was met, the next step was to devise
an appropriate sampling strategy for the control surfaces
using sophisticated statistical modelling to extrapolate
the data obtained from the four control surfaces retrieved
each month to any desired number of simulated samples.

B. STATISTICAL MODELLING

Once the initial percent fouling coverage estimates for
the four non-toxic control surfaces retreived each month
were determined, the data had to be manipulated to obtain
better estimates of the variability of the superpopulation

of marine fouling organisms the plates were assumed to
be sampling. Since there were only four substrates examined
per month, a model capable of extending the experimental
data to simulated samples of any size was required. The
model also had to be capable of allowing and quantifying
inter-plate variability within the simulated sample set.
The techniques used to successfully meet these requirements
have only recently been developed and this thesis is
apparently the first incorporation of these techniques into
fouling research.

1. Model Alternatives

One of the methods that has been used in the past
(Schoener and Greene, 1980) to examine the degree of
variability of biofouling coverage values has been to
assume that the fractional coverage estimates have a normal
distribution. Using this simple model, the upper and lower
95% confidence limits are calculated about the experimental
mean percent fouling cover by use of the formula:

the 95% Confidence Limits = x [+/-] 1.96* d / ^N~
where x is the mean percent fouling cover, d is the
experimental standard deviation, N is the number of samples
examined , and the formula is derived from the standard
normal distribution. By assuming that the mean ( x ) and
standard deviation ( a ) do not vary with the number of
plates examined, one varies N in the formula to determine

the effect that the number of plates has on the approach of
the upper and lower confidence limits to the experimental
mean. It must be pointed out however that this model has
serious drawbacks. The first problem with this approach is
the assumption that fractional fouling coverage values
which will always lie between zero and one can be described
by a normal distribution that is unbounded in range. While
this assumption permits the calculation of various statis-
tical parameters using well known analytical formulas, it
is obviously weak theoretically. Secondly, this model
requires that the mean and standard deviation are stable
with increasing sample size. This requirement has the
effect of forbidding inter-plate variability. Not only is
such a restriction biologically untenable, it reduces the
formula for the calculation of the confidence limits to :

the 95% Confidence Limits =[+/-] constant/ -yN
Note that the above equation will result in a curve similar
to [+/-] 1/JN when plotted. Since the value of 1/ J"n"~
decreases by nearly 70% as N goes from one to ten, use of
this method will always show that approximately ten plates
are sufficient to resolve the var iability of the mean
percent cover. This result however is merely an artifact of
the simplistic model used in its calculation.

Another possible method that could be used to
estimate the degree of variability of the biofouling

community would be to invent a predictive model for fouling
populations. Unfortunately, such a model is considerably
beyond our abilities at the present time. Such a model
would require advective/dif fusive models accurate spatially
to microscale resolution . It would also require the
ability to parameterize the entire range of biological
forcing functions which include predation, nutrient supply,
susceptibility to environmental fluctuations, behaviorism
of the organisms involved and planktonic larva survival
rates to name just a few. Obviously, such sophistication in
a model is not likely in the forseeable future.

Since a stochastic model which assumed the fouling
coverage values had a normal distribution was insufficient
due to its' inherent restrictions which forbid interplate
variability, and since a predictive model was unattainable,
this study used a probabilistic model to explore the
variability of the fouling community. In such a model, the
variability of the initial experimental data is determined
and the statistical descriptors of that varibility are used
as inputs for computer simulations of the experiment.
2. Procedure

Each plate (t) was assumed to have a

random, independent proportion of fouling, P . P. was assumed

to be of the form: e

P = e

(1 + e r)

where ^was assumed to be normally distributed with unknown
mean {/j) and variance (a ) which were independent of the
other plates censused at the same time. Note that the above
equation could be written as:
€t= in(Pt /(l - Pt ))
Each month, the € value for each of the four untreated
plates was determined as were the mean and variance of the
four 6t values. Revised estimates for these parameters were
then determined using the Method of Maximum Likelihood (see
Appendix E for mathematical development) .

Using as inputs the maximum likelihood values for
the mean ( /i ) and variance ( a ) of the monthly epsilon
values, bootstrap computer simulations (Efron,1979) of the
experiment were conducted. The bootstrap method was used to
simulate 200 groups of various fixed numbers of plates (see
Appendix F for a complete discussion) .

Using the results from the bootstrap computer
simulations, the following statistics were calculated:

1. The expected value of the mean percent fouling
coverage. This was determined by calculating the mean of
the 200 simulated group means for each of the various
numbers of plates per group simulated.

2. The upper 95% confidence limit about the expected
value of the mean percent fouling cover for each of the
various numbers of plates per group simulated. This was
estimated by ordering the mean percent foulng coverage
values for each of the 200 simulated groups of plates in
ascending order and then finding the 95% quantile of the
expected mean percent fouling coverage values.

3. The percent fouling cover that one can say 90% of
the simulated plates will have fouling coverage less than
or equal to (with 95% confidence). This was done by
finding the 95% quantile (as described above) of the
parameter NEWCVR(I) where:

0 P

NEWCVR(I) = e /(l + e )

A A

and & - /!{!)+ 1.285* a (I)

Note that /i(I) and <j{I) are the bootstrap simulations
of the mean and standard deviation of for each of the

200 group simulations. The value 1.285 is the 90%
quantile for the standard normal distribution.

The purpose of calculating the parameter NEWCVR was
to estimate how many plates it would take to be 95%
confident of capturing 90% of the variance of the
biofouling population. The confidence and variance values
chosen were arbitrary, and the model can be readily
modified to estimate the number of plates required to
ascertain any degree of variance to any desired
confidence.

4. The standard deviation about the mean percent
fouling coverage that 90% of the simulated plates would
have was also estimated . This was done by finding the
mean and standard deviation of the 200 NEWCVR(I) values
for each of the various numbers of plates per group
simulated each month.

IV. RESULTS

A. GENERAL

Experimental data were collected monthly and the
initial percent cover and similarity values computed (and
the coverage estimates tabulated) for the second through
the eleventh months of the experiment (Appendix G) .
Following the procedure discussed in the statistics
chapter, these initial estimates were used as starting
values for Bootstrap/Maximum Likelihood computer
simulations of the experiment. The computer simulation
results from month 2 are described in some detail. The
simulation using the data from months 3 through 11 followed
the same procedure and are each presented in a brief
synopsis.

1. Method Verification

The procedure described in this thesis to develop
an appropriate sampling strategy for antifouling paint test
purposes was based on the assumption that any strategy
which could ascertain the variance of the biofouling
community on non-toxic control surfaces would be able to do
at least as well regarding antifouling coated surfaces.
This assumption would be correct provided the fouling com-
munities on non-toxic control surfaces were more variable
than were those on the antifouling coated surfaces. By

analyzing the monthly mean similarity values for the
fouling communities on these two types of surfaces (Figure
5), it is clear that the antifouling coated surfaces dis-
played consistently less variability in their fouling
structure than did the control surfaces. Therefore, this
assumption is considered to be quite strong.

A second major assumption used in the development
of this procedure was that the monthly epsilon (6 ) values
used in the calculation of the proportion of fouling (P ),
were independent random values from a normal distribution
with mean (^ ) and variance ( a2 ) .

If the epsilon values were in fact distributed
normally, then dividing the individual epsilon values for
each month by the monthly standard deviation of the epsilon
values and subtracting the mean monthly value of epsilon
from this result, would transform the epsilon distribution
into the standard normal distribution. By plotting the (N)
transformed epsilon values ranked in ascending order
against the theoretical order statistic obtained by finding
the inverse function of the standard normal distribution
for (j/N+1) as j goes from 1 to N, a diagnostic plot of the
model was obtained. If the model was perfect, there would
be a one-to-one correspondence between the transformed
epsilon values and the order statistic. Plotting the forty
transformed epsilon values obtained in this study against

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Figure 5. Chart Showing the Monthly Mean Similarity Values

for the Control Surfaces (Solid) and the Antifouling Coated
Surfaces (Dashed) .

the order statistic (Figure 6) shows that the assumption of
a normal distribution for the variable epsilon is quite
good. The least squares best fit line for the data had a
slope of 1.07 (vice 1.00 for the theoretical perfect
correspondence) and the correlation coefficient between the
transformed epsilon values and the order statistic was
0.98.

Since the initial experimental data for percent
fouling cover and the Bootstrap/Maximum Likelihood model
were not independent but rather were coupled by the esti-
mates of the mean and variance of the monthly epsilon
values, one would reasonably expect the final mean percent
fouling cover predicted by the Bootstrap simulations to
approximate the actual data value if the model behaved
reasonably. A chart comparing the arithmetic mean of the
monthly values for percent cover obtained experimentally to
the expected value of the mean percent cover predicted by
the bootstrap simulations (Figure 7) , shows that the model
agrees quite well with the experimental data. In those
instances where there was a significant difference between
the mean percent cover obtained from the data and that
predicted by the bootstrap model, analysis of the actual
data suggested that simply finding the arithmetic mean of
the four monthly data percent coverage estimates was per-
haps too sensitive to unusually high or low values.

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Figure 6. A Diagnostic Plot of the Model With the Ranked,
Normalized Values for the Individual Epsilon Values Plotted
on the Ordinate (Abbreviated as Z) and the Theoretical
Order Statistic Plotted of the Abscissa. The Dashed Line
Indicates Perfect Correspondence and the Dotted Line is the
Least Squares Best Fit for the Data.

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Figure 7. Chart Showing the Arithmetic Mean of the Percent
Fouling Cover From the Experimental Data (Solid) and the
Bootstrap Simulated Mean Percent Cover (Dashed) .

In summary, it is felt that the assumptions made in
the formulation of this model are quite good and that the
model gives very reasonable estimates of the most likely
value for the percent fouling cover.
2. Explanation of Figures

The similarity indices between the plates retrieved
each month were plotted on two separate graphs for the
control surfaces and the antifouling coated surfaces. The
range of the similarity values from zero to one was plot-
ted on the ordinate and the plate designations were listed
on the abscissa. The 'F' and 'B' that follow the plate
group number refer respectively to the front and back of
the plate. To obtain the similarity value between any two
plates, find the horizontal line above the abscissa with
arrowheads which terminate at points above the desired
plate designations, then proceed horizontally to the
ordinate to find the similarity index value.

The expected value of the computer simulated mean
percent fouling cover and the upper 95% confidence limit
about the mean as functions of increasing sample size were
plotted for each month. The expected value of the mean
percent cover was dispayed as a solid line and the upper
95% confidence limit was dashed.

Graphs were also prepared showing the results of
the monthly computer simulations used to determine the 95%

confidence limit of the percent fouling coverage that 90%
of the simulated plates will have fouling coverage less
than or equal to. The ordinate of these figures was gra-
duated in percent cover from zero to one hundred percent.
The abscissa was labelled with the number of plates per
group used in the simulations. The 95% confidence limit for
the percent cover of 90% of the plates was then plotted as
a function of increasing sample size.

The same units for the ordinate and abscissa were
used in the figures showing the standard deviation about
the mean percent cover that 90% of the plates would have as
functions of increasing sample size. For these figures,
however, the percent cover label on the ordinate refers to
the deviation about the mean percent cover and not the
total percent fouling cover these plates will have.

B. RESULTS FROM MONTH 2
1. Experimental Data

The fouling community on the control surfaces after
two monhs immersion was dominated by the hydroid Obelia
spp. Ectoproct colonies each consisting of several dozen
zooids had also settled by this time. These initial
bryozoans were primarily Hippothoa hyalina and Celloporaria
b r_ u n n e a although the ancestrula stage of a recently
introduced species, ^a_ter_s__i£or_a cucullata was also
present.Watersipora is indigenous to the Galapagos Islands

and has not been reported in the literature farther north
than the Gulf of California (Osburn, 1952) . It has not been
noted in fouling studies conducted in Monterey Bay over the
last twenty years and its appearance on the plates in this
study is probably due to the abnormally warm coastal waters
caused by the recent El Nino event.

The similarity values for the control surfaces
ranged from .74 to .92 with a mean of .83 (Figure 8A). The
lack of any settlement on the antifouling coated surfaces
resulted in similarity values of 1.0 for all of those
plates (Figure 8B) .

2. Computer Simulations

The bootstrap computer simulation of the expected
mean percent fouling cover (Figure 9) resulted in a final
iterated estimate of 44.4% for the simulated mean percent
cover (vice 44.5% for the data arithmetic mean). Note that
the dashed line indicating the upper 95% confidence limit
of the mean percent cover does show some inverse
relationship to N (the number of samples) but does not show
the precipitous approach to the mean as N goes from one to
ten that was predicted by the model which assumed a normal
distribution for the fractional coverage values.

Perhaps the most striking result of the computer
simulations was that of the effect of increasing the
number of simulated plates sampled on the 95% confidence

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Figure 8. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces for Month 2.
Dashed Lines Indicate Mean Similarity Values.

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Figure 9. Computer Simulations Using Data From Month 2
Showing the Expected Value of the Mean Percent Fouling
Cover (the Mean of the 200 Individual Group Simulation
Percent Fouling Covers) as a Solid Line and the 95%
Quantile (Dashed) of the Expected Mean Percent Fouling
Cover as a Function of Increasing Sample Size.

limit of the percent fouling cover that 90% of the plates
would have (Figure 10A). Note that there is very little
dependence on N on the percent cover that one can say 90%
of the plates will have fouling cover less than or equal
to. This is in spite of the fact that the standard
deviation that these 90% of the plates will have about the
mean percent cover does display a strong inverse dependence
on N (Figure 10B). While these two results might seem
dichotomous, they are not. The standard deviation about the
mean does decrease with increasing sample size just as one
would expect from the Central Limit Theorem. The fact that
the 95% confidence limit of the fouling cover of 90% of the
plates does not behave similarly is simply a result of the
fact that by allowing interplate variability, one no longer
constrains the parameter to have a 1/ N dependence.

C. RESULTS FROM MONTH 3
1. Experimental Data

The fouling community structure on the control
surfaces after three months immersion remained dominated by
the hydroid Obelia spp. The four species of spirorbid
worms that live in Monterey Bay particularly Circeis
armor icana, were also present. The protozoan Folliculina
sp. was present in large numbers on three of the plates. The
bryozoans were represented by four species with
Celloporaria brunnea dominating this group.

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Figure 10. Computer Simulations Using Data From Month 2
Showing : (A) the Percent Fouling Coverage That One Can Say
90% of the Samples Will Have Fouling Coverage Less Than or
Equal to ( With 95% Confidence); and (B) the Standard
Deviation of Percent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing Sample Size.

The similarity values ranged from .57 to .86 with a
mean of .74 for the control surfaces (Figure 11A). The
mean similarity for the antifouling coated surfaces
remained at 1.0 (Figure 11B) since no settlement of
organisms had occured.

2. Computer Simulations

The computer simulations of the expected value of
the mean percent fouling cover (Figure 12) resulted in a
final iterated value of 49.5% vice a 49.3% arithmetic mean
of the initial data. The upper 95% confidence limit about
the mean decreased by nearly 8% as the number of simulated
plates per group increased from 2 to 15 and then only
decreased an additional 3% as the number of plates per
group was increased to 80.

The computer simulations of the 95% confidence
limit of the fouling cover that 90% of the plates would be
fouled to an equal or lesser extent showed the value
remained nearly constant at approximately 70% (Figure
13A).The standard deviation of the percent cover on these
plates about the mean percent cover showed little relative
decrease past the simulated analysis of 20 plates per group
(Figure 13B) .

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Figure 11. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces for Month 3.
Dashed Lines Indicate Mean Similarity Values.

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Figure 12. Computer Simulations Using Data From Month 3
Showing the Expected Value of the Mean Percent Fouling
Cover (the Mean of the 200 Individual Group Simulation
Percent Fouling Covers) as a Solid Line and the 95%
Quantile (Dashed) of the Expected Mean Percent Fouling
Cover as a Function of Increasing Sample Size.

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Figure 13. Computer Simulations Using Data From Month 3
Showing : (A) the Percent Fouling Coverage That One Can Say
90% of the Samples Will Have Fouling Coverage Less Than or
Equal to ( With 95% Confidence); and (B) the Standard
Deviation of Percent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing Sample Size.

D. RESULTS FROM MONTH 4
1. Experimental Data

The fouling community on the control surfaces after
four months immersion was dominated by the bryozoan
Watersipora cuculatta. Thehydroid Obelia spp. had been
overgrown to a large extent by W^_ cuculatta and as a result
its relative contribution to the percent cover was
diminished considerably. In addition to W^_ cuculatta, there
were six other species of either upright or encrusting
bryozoans present. Various spirorbid and serpulid worms
were present in limited numbers.

The percent coverage estimates varied greatly from
plate to plate with a maximum of 84% and a minimum estimate
on one plate of 2% cover. The wide variability was perhaps
partially caused by the ascendency of the bryozoans as the
dominant organism but the reason for the nearly total lack
of fouling on two of the surfaces is unknown.

The wide range in the percent coverage estimates
was mirrored in the variability of the similarity indices
between the control surfaces. The values ranged from .16 to
.98 (Figure 14A). The antifouling coated plates still had
no fouling so again the mean similarity was 1.0 for those
plates.

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Figure 14. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces for Month 4.
Dashed Lines Indicate Mean Similarity Values.

2. Computer Simulations

The final iterated value for the simulated mean
percent fouling cover was 31% (Figure 15). The upper 95%
confidence limit about this mean was quite large and
decreased by nearly 40% as the number of simulated plates
per group went from two to twenty (Figure 15) .

The wide variability of the percent coverage
estimates caused the 95% confidence about the fouling
coverage estimate of 90% of the plates to be quite high
(Figure 16A). As can be seen, the only statement that can
be made about the fouling coverage that 90% of the plates
willhave is that the coverage will be something less than
93% (Figure 16A) even though the estimated mean percent
coverage was 31%.

The standard deviation that these 90% of the plates
will have about the mean was also quite large (Figure 16B)
and showed significant decline out to approximately the
thirty plates per group simulation point.

E. RESULTS FROM MONTH 5
1. Experimental Data

The bryozoan dominance of the fouling community was
firmly established by the fifth month of immersion.
Watersipora cuculatta was the primary fouler on three of
the four control surfaces and there were an additional

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Figure 15. Computer Simulations Using Data From Month 4
Showing the Expected Value of the Mean Percent Fouling
Cover (the Mean of the 200 Individual Group Simulation
Percent Fouling Covers) as a Solid Line and the 95%
Quantile (Dashed) of the Expected Mean Percent Fouling
Cover as a Function of Increasing Sample Size.

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Figure 16. Computer Simulations Using Data From Month 4
Showing : (A) the Percent Fouling Coverage That One Can Say
90% of the Samples Will Have Fouling Coverage Less Than or
Equal to ( With 95% Confidence); and (B) the Standard
Deviation of Percent Coverage (About the Mean) That These
oamples Will Have As a Function of Increasing Sample Size.

eight other species of bryozoans identified during the
census.

There was a fairly large range of initial percent
cover estimates for the control surfaces with a minimum of
13% and a maximum of 96%. The mean percent coverage
estimate for these plates was 63% and the standard
deviation was 31%.

The similarity indices for the control surface
plates ranged from .17 to .67 with a mean value of .45
(Figure 17A). The s i m i 1 a r i t y v a 1 u e s for the
antifouling coated surfaces ranged from .85 to 1.0 (Figure
17B). This variability was caused by the settlement of
Obelia spp. and the spirorbid worm Circeis armor icana on
several of the antifouling coated plates.
2. Computer Simulations

The final iterated estimate for the mean percent
cover was 69% (Figure 18) vice the arithemetic mean of 63%
for the initial data. The 95% coinfidence limit about this
mean showed an appreciable decrease out to approximately
twenty plates per group simulated.

The population variability again resulted in the
95% confidence limit of the fouling cover of 90% of the
plates having virtually no dependence of the number of
samples analyzed (Figure 19A). The standard deviation about
the mean that these 90% of the plates would have showed

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PLRTE DESIGNATION

Figure 17. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces for Month 5.
Dashed Lines Indicate Mean Similarity Values.

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NO. OP PLATES

Figure 18. Computer Simulations Using Data From Month 5
Showing the Expected Value of the Mean Percent Fouling
Cover (the Mean of the 200 Individual Group Simulation
Percent Fouling Covers) as a Solid Line and the 95%
Quantile (Dashed) of the Expected Mean Percent Fouling
Cover as a Function of Increasing Sample Size.

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NO. OF PLATES

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Figure 19. Computer Simulations Using Data From Month 5
Showing : (A) the Percent Fouling Coverage That One Can Say
90% of the Samples Will Have Fouling Coverage Less Than or
Equal to ( With 95% Confidence); and (B) the Standard
Deviation of Percent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing Sample Size.

little decrease past approximately 20 plates per group
simulated (Figure 19B) .

F. RESULTS FROM MONTH 6

1. Experimental Data

The fouling community structure on the control
surfaces after six months immersion was dominated either by
bryozoans or the hydroid Obelia spp. depending on the plate
examined. Two species of solitary tunicates, Ascidia
ceretodes and Styela truncata were also censused for the
first time during the experiment.

The initial percent cover estimates for the control
surfaces ranged from 16% to 54%. The mean percent cover for
the control surfaces was 37% with a standard deviation of
18%.

The antifouling coated surfaces showed fouling on
several of the plates with the barnacles Megabalanus
californicus and Balanus crenatus appearing for the first
time on these surfaces. Obelia spp. remained the dominant
fouler on the antifouling coated surfaces.

The similarity values for the control surfaces
ranged from .48 to .88 with a mean of .70 (Figure 20A). The
mean similarity of the antifouling coated surfaces was .99
(Figure 20B) .

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PLATE DESIGNATION

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Figure 20. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces for Month 6.
Dashed Lines Indicate Mean Similarity Values.

2. Computer Simulations

The computer simulated value of the mean percent
cover was 33%. The upper 95% confidence limit about the
mean showed significant decrease out to approximately 20
plates per group simulated (Figure 21). Note again that
there was a significant decrease in the width of the 95%
confidence limit about the mean as the number of plates per
group simulated went from ten to twenty.

The rather high mean similarity value for the sixth
month control plates and by inferrence the lessened
interplate variability permitted the 95% confidence limit
of the fouling cover of 90% of the plates (Figure 22A) to
be less than that of the fourth month simulations even
though the mean percent coverage value for the sixth month
group was higher. The 95% confidence limit of the fouling
cover of 90% of the plates value decreased until
approximately the twenty plates per group simulation point
and then remained fairly constant.

The standard deviation about the mean percent cover
that these simulated plates displayed decreased only
slightly past the 20 plates per group simulated point
(Figure 22B). Note however that there was a 5% decrease in
this value between the 10 plates per group simulated point
and the 20 plates per group simulated.

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NO. OF PLATES

Figure 21. Computer Simulations Using Data From Month 6
Showing the Expected Value of the Mean Percent Fouling
Cover (the Mean of the 200 Individual Group Simulation
Percent Fouling Covers) as a Solid Line and the 95%
Quantile (Dashed) of the Expected Mean Percent Fouling
Cover as a Function of Increasing Sample Size.

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NO. OF PLATES

Figure 22. Computer Simulations Using Data From Month 6
Showing : (A) the Percent Fouling Coverage That One Can Say
90% of the Samples Will Have Fouling Coverage Less Than or
Equal to ( With 95% Confidence); and (B) the Standard
Deviation of Percent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing Sample Size.

G. RESULTS FROM MONTH 7

1. Experimental Data

The fouling community structure of the seventh
month conrol plates remained dominated by bryozoans with
the hydroid Obelia spp. still in an important but secondary
role. The spirorbid worm Circeis armoricana was dominant on
one of the plates and was common on all the control
surfaces.

The primary fouling organisms on the antifouling
coated surfaces were the barnacle Balanus crenatus , the
bryozoan Celloporaria brunnea ,and the hydroid Obelia spp.
Several of these plates were also fouled by an unknown tube
dwelling amphipod, possibly of the genus Ampithoe.

The percent coverage estimates for the control
surfaces ranged from 31% to 62% with a mean of 49%. The
standard deviation of these values was 11.5%.

The similarity indices between the control surfaces
ranged from .22 to .88. The mean similarity value for the
control plates was .55 (Figure 23A).

For the antifouling coated surfaces, the range of
similarity values was from .81 to 1.0. The mean value was
.92 (Figure 23B).

2. Computer Simulations

The final iterated value for the simulated mean
percent fouling coverage was 49%. The upper 95% confidence

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PLATE DESIGNATION

Figure 23. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces for Month 7.
Dashed Lines Indicate Mean Similarity Values.

limit about this mean remained fairly constant past the 20
plates per group simulated point (Figure 24) .

The simulated percent cover that one could say 90%
of the plates would have fouling coverage less than or
equal to (Figure 25A), decreased slightly until
approximately the 20 plates per group simulation point and
then remained fairly constant at approximately 65%
coverage. The standard deviation that these simulated
plates had about the mean percent fouling cover showed
little decrease past the 30 plates per group simulation
point (Figure 25B) .

H. RESULTS FROM MONTH 8
1. Experimental Data

The fouling community structure on the control
surfaces after eight months immersion was dominated nearly
exclusively by bryozoans. The contribution of hydroids to
the percentage of cover had been reduced on three of the
surfaces to less than 5%. Serpulid worms, solitary
tunicates, and barnacles were beginning to emerge as
important foulers as their increasingly large size
prohibited their overgrowth by encrusting species.

The fouling organisms present on the antifouling
coated surfaces were primarily the hydroid Obelia spp. and
barnacles. The spirorbid worm Circeis armor icana was also
present on several of the plates.

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NO. OP PLATES

Figure 24. Computer Simulations Using Data From Month
Showing the Expected Value of the Mean Percent Fouling
Cover (the Mean of the 200 Individual Group Simulation
Percent Fouling Covers) as a Solid Line and the 95%
Quantile (Dashed) of the Expected Mean Percent Fouling
Cover as a Function of Increasing Sample Size.

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NO. OF PLATES

Figure 25. Computer Simulations Using Data From Month 7
Showing : (A) the Percent Fouling Coverage That One Can Say
90% of the Samples Will Have Fouling Coverage Less Than or
Equal to ( With 95% Confidence); and (B) the Standard
Deviation of Percent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing Sample Size.

The estimates for the percentage of fouling cover
ranged from 48% to 97% for the control surfaces. The mean
of these values was 76% and the standard deviation was 19%.

For the control surfaces, the range of similarity
values was from .22 to .67. The mean value was .44 (Figure
26A) .

The similarity values for the antifouling coated

surfaces ranged from .75 to 1.0. The mean value was .94
(Figure 263) .

2. Computer Simulations

The computer iterated estimate for the mean percent
fouling coverage for the control surfaces was 81%. Note
that the 95% confidence limit about this value remained
fairly constant past approximately the 25 plates per group
simulation point (Figure 27) .

The high estimate for the simulated mean percent
cover and the variability permitted by the model forced
the upper 95% confidence limit about the percent cover that
90% of the plates would have to remain greater than 96% for
the entire range of the simulations (Figure 28A). The
standard deviation about the mean percent cover that these
plates would have showed a precipitous decrease out to the
20 plates per group simulated point and then decreased only
2% out to the 80 plates per group simulation point (Figure
28B) .

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PLHTE DESIGNATION

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Figure 26. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces for Month 8.
Dashed Lines Indicate Mean Similarity Values.

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NO. Of PLATES

Figure 27. Computer Simulations Using Data From Month 8
Showing the Expected Value of the Mean Percent Fouling
Cover (the Mean of the 200 Individual Group Simulation
Percent Fouling Covers) as a Solid Line and the 95%
Quantile (Dashed) of the Expected Mean Percent Fouling
Cover as a Function of Increasing Sample Size.

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NO. OF PLATES

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Figure 28. Computer Simulations Using Data From Month 8
Showing : (A) the Percent Fouling Coverage That One Can Say
90% of the Samples Will Have Fouling Coverage Less Than or
Equal to ( With 95% Confidence); and (B) the Standard
Deviation of Percent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing Sample Size.

I. RESULTS FROM MONTH 9

1. Experimental Data

The bryozoan Watersipora cuculatta dominated the
fouling assemblages on three of the four control surfaces
while the hydroid Obelia spp. dominated on the fourth. The
total number of species represented in the census began to
stabilize as the more successful species excluded others in
the competition for the rapidly diminishing space.

The dominant fouling organism on the antifouling
coated surfaces was the bryozoan, Membranipora membranacea.
This organism is usually found nearly exclusively on the
fronds of the giant kelp Macrocystis and it is not known
what chemical or other stimulus attracted it to the
antifouling coated surfaces.

The percent coverage estimates for the control
surfaces ranged from 35% to 92%. The mean percent cover was
67% and the standard deviation was 25%.

The similarity values for the plates ranged from
.18 to .74 for the control surfaces and from .60 to 1.0 for
the antifouling coated surfaces. The mean similarity value
for the control surfaces was .41 (Figure 29A) and was .89
for the antifouling coated surfaces (Figure 29B) .

2. Computer Simulations

The final estimate for the mean percent fouling
cover for the computer simulated plates was 73%. The upper

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PLATE DESIGNATION

Figure 29. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces for Month 9.
Dashed Lines Indicate Mean Similarity Values.

95% confidence limit about this mean showed little decrease
past the 20 plates per group simulation point (Figure 30) .

The 95% confidence limit on what one can say 90% of
the simulated plates will have fouling coverage less than
or equal to remained above 95% coverage for the entire
range of the simulations (Figure 31A). The standard
deviation that these plates had showed little change past
the 20 plates per group simulation point (Figure 31B) .

J. RESULTS FROM MONTH 10

1. Experimental Data

Bryozoans dominated the fouling assemblages on all
of the control plates with Watersipora cuculatta occupying
60% of the space on one of the surfaces. Eleven species of
bryozoans were identified during the census.

The similarity values for the plates ranged from
.20 to .79 for the control surfaces and from .67 to 1.0 for
the antifouling coated surfaces. The mean similarity value
for the control surfaces was .47 (Figure 32A) and for the
antifouling surfaces was .90 (Figure 32B).

2. Computer Simulations

The final iterated value for the computer
simulation of the mean percent cover was 70%. The upper 95%
confidence limit about this mean showed little decrease
past the 20 plates per group simulation point (Figure 33).

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Figure 30. Computer Simulations Using Data From Month 9
Showing the Expected Value of the Mean Percent Fouling
Cover (the Mean of the 200 Individual Group Simulation
Percent Fouling Covers) as a Solid Line and the 95%
Quantile (Dashed) of the Expected Mean Percent Fouling
Cover as a Function of Increasing Sample Size.

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NO. OF PLATES

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NO. OP PLATES

Figure 31. Computer Simulations Using Data From Month 9
Showing : (A) the Percent Fouling Coverage That One Can Say
90% of the Samples Will Have Fouling Coverage Less Than or
Equal to ( With 95% Confidence); and (B) the Standard
Deviation of Percent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing Sample Size.

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PLATE DESIGNATION

Figure 32. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces for Month 10.
Dashed Lines Indicate Mean Similarity Values.

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NO. OF PLATES

Figure 33. Computer Simulatioms Using Data From iMonth 10
Showing the Expected Value of the Mean Percent Fouling
Cover (the Mean of the 200 Individual Group Simulation
Percent Fouling Covers) as a Solid Line and the 95%
Quantile (Dashed) of the Expected Mean Percent Fouling
Cover as a Function of Increasing Sample Size.

The percent cover that one can say 90% of the
plates would have coverage less than or equal to (with 95%
confidence) remained above 90% cover for the entire range
of the simulations (Figure 34A). The standard deviation
these plates would have showed little decrease past the 20
plates per group simulation point (Figure 34B) .

K. RESULTS FROM MONTH 11
1. Experimental Data

The fouling communities on the control surfaces
remained dominated by bryozoans with Watersipora cuculatta
dominating on three of the plates and the upright bryozoan
Bugula californica dominating on the fourth. Of the seven-
teen species identified on these control surfaces, thirteen
were bryozoans.

The predominant fouling organism on those
antifouling surfaces that showed fouling was the bryozoan
Membranipora membranacea. The hydroid Obelia spp. and the
spirorbid worm Circeis armor icana were also in evidence.

The initial percent coverage estimates for the
control surfaces ranged from 64% to 98%. The mean value was
85% and the standard deviation was 15%.

The similarity values for the plates ranged from
.28 to .79 for the control surfaces and from .64 to 1.0 for
the antifouling coated surfaces. The mean similarity value

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Figure 34. Computer Simulations Using Data From Month 10
Showing : (A) the Percent Fouling Coverage That One Can Say
90% of the Samples Will Have Fouling Coverage Less Than or
Equal to ( With 95% Confidence); and (B) the Standard
Deviation of Percent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing Sample Size.

for the control surfaces was .52 (Figure 35A) and for the
antifouling coated surfaces was .87 (Figure 35B) .
2. Computer Simulations

The final iterated value for the computer
simulations of the mean percent cover was 89%. The upper
95% confidence limit about this mean decreased by only 7%
over the entire range of the simulations (Figure 36) .

Quite obviously, with such a large valuefor the
mean percent cover, the percent cover that 90% of the
plates will have will be equally large. As can be seen
(Figure 37A) , this value never became less that 97% cover
over the entire range of the simulations. The standard
deviation about the mean percent cover that these plates
would have again showed little decrease past the 20 plates
per group simulation point (Figure 37B) .

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PLATE DESIGNATION

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PLATE DESIGNATION

Figure 35. Similarity Graphs for (A) Non-treated Control
Surfaces and (B) Anti-fouling Coated Surfaces for Month 11.
Dashed Lines Indicate Mean Similarity Values.

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NO. OP PLATES

Figure 36. Computer Simulatioms Using Data From Month 11
Showing the Expected Value of the Mean Percent Fouling
Cover (the Mean of the 200 Individual Group Simulation
Percent Fouling Covers) as a Solid Line and the 95%
Quantile (Dashed) of the Expected Mean Percent Fouling
Cover as a Function of Increasing Sample Size.

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NO. OF PLATES

Figure 37. Computer Simulations Using Data From Month 11
Showing : (A) the Percent Fouling Coverage That One Can Say
90% of the Samples Will Have Fouling Coverage Less Than or
Equal to ( With 95% Confidence); and (B) the Standard
Deviation of Percent Coverage (About the Mean) That These
Samples Will Have As a Function of Increasing Sample Size.

V. CONCLUSIONS AND RECOMMENDATIONS

A. DISCUSSION

The choice of an appropriate sampling strategy for the
study of fouling organisms in Monterey Bay has been shown
to be dependent upon the type of information desired.

By analyzing the width of the upper 95% confidence

limit about the expected value of the mean percent fouling

cover, estimates were made concerning the optimum number of

plates to be deployed. This optimum number was found by

determining that point where the addition of additional

plates had a negligible effect upon the width of the
confidence interval. In nearly all the cases simulated, the

value for the optimum number of plates to deploy appeared

to be approximately twenty.

A similar procedure was followed to estimate the

optimum number of plates to deploy to minimize the standard

deviation about the mean percent fouling cover that 90% of

the plates would have. The optimum number of plates to

deploy to satisfy this requirement was again estimated to

be approximately twenty for most of the simulations.

However, the results from several cases suggested that

thirty plates would be a more appropriate sample size.

Based on these results, it is concluded that twenty
plates is probably the minimum number of plates that should
be deployed to obtain accurate estimates of the mean
percent fouling cover of a group of plates for this
locality. Thirty plates per group is probably a more
appropriate number of plates to deploy to insure that
accurate results are obtained for groups that display
heightened variability in the individual plate fouling
coverage estimates.

The experimental results showing the negligible effect
of the addition of more plates on what one could say 90% of
the plates would have fouling coverage less than or equal
to (with 95% confidence) lead to the conclusion that the
inherent variability of fouling populations is
significantly greater than previous studies indicated. This
means that while twenty to thirty plates are probably
sufficient to resolve ambiguities concerning the mean per-
cent fouling cover, this number is clearly insufficient to
ascertain with any high degree of confidence the amount of
variability of a large segment of the population. For
example, if it is desired to ascertain with 95% confidence
the variability of 90% of the fouling population, it must
be understood that this will require the committment of
substantial resources to the study.

In addition to the development of an appropriate
fouling community sampling strategy for Monterey Bay, more
far reaching conclusions can be drawn concerning the
applicability of the procedures used in this thesis to
other locations. Since the computer modelling procedure
used in this study dealt with the extension of
the experimentally observed variability and contained no
site-specific parameters, it is believed that the procedure
can be directly applied to the study of fouling community
variability at any desired geographical location. This
means that the computer programs developed for this study
can be coupled with archived fouling coverage data from
any site, depth, season, and so on to provide information
on how best to sample the fouling populations.

The final conclusion drawn from this study is that the
bootstrap method of computer intensive statistical analysis
has profound implications in the study of other biological
problems. It is believed that this method could be applied
to a wide range of other data intensive biological areas
including fisheries management, larval settlement studies,
the pelagic distributions of plankton and nekton, and
growth rate studies to name just a few.

B. RECOMMENDATIONS FOR FURTHER RESEARCH

The model developed in this thesis should be applied to
a number of other geographical locations to determine the

differences in fouling variability in terms of latitude,
longitude, depth, environmental stresses, and a host of
other biological forcing functions. Since the computer
program already exits and the only required inputs are
archived fouling coverage data, this should present no
insurmountable difficulties.

Once such studies have been completed, the development
of empirically derived sampling strategies for any location
could be attempted.

Finally, the use of the bootstrap or other computer
intensive statistical techniques should be vigorously
investigated in other areas of biological interest. It is
believed that the use of these techniques might well
provide answers to a wide range of biological problems that
have so far proved intractable.

APPENDIX A

MICRON 22 ORGANO-METALLIC
POLYMER ANTIFOULING PAINT

INGREDIENTS PERCENT BY WEIGHT

Active:

Bis (tributyltin) Oxide 11.7

Cuprous Thiocyanate 17.2

Inert: 71.1

100

Elemental Tin 4.4%

Elemental Copper 8.9%

Paint contains 1.1 lbs of Bis ( tr ibutyltin) oxide per
gallon and 1.6 lbs of Cuprous Thiocyanate per gallon.

Source: Product infromation breakdown on label

APPENDIX B

NAVY STANDARD FORMULA 121
RED VINYL ANTIFOULING PAINT

INGREDIENTS PERCENT BY WEIGHT

Cuprous Thiocyanate 70.3

Rosin 10.5

Vinyl Resin 2.7

Tricreysl Phosphate 2.4

Methyl Isobutyl Ketone 8.1

Xylene 5.6

Antisettling Agent .4

Source: Department of the Navy Specification MIL-P-15931C,
Painty Antifouling, Vinyl (Formula Numbers 121 and 129)

APPENDIX C

NAVY STANDARD FORMULA 170 BLACK
CAMOFLAGE ANTIFOULING PAINT

INGREDIENTS PERCENT BY WEIGHT

Vinyl Resin 17.5

Bis ( tributyltin) oxide 4.2

Tributyltin Fluoride 18.1

Carbon Black 2.1

Titanium Dioxide .8

Ethylene Glycolmonoethyl 3.0
Ether Acetate

Normal Propanol 11.1

Normal Butyl Acetate 43.2

Source: Department of the Navy Military Specification DOD-
P-245 8 8 , Paint , Ant i foul ing, Vinyl, Camoflage( Formula numbers

170, 171, 172, and 173) , 2 May 1979.

APPENDIX D
ZYNOLYTE EPOXY RUST MATE PAINT

INGREDIENTS PERCENT BY WEIGHT

Non-Volatile (58.4% of total)

Pigments 43.4

Vehicle 56.6

Epoxy and Menhaden
Alkyd Resins

100.

Volatile (41.6% of total)

Exempt Mineral Spirits 98.0

Aromatic Hydrocarbons 2.0

100.

Source: Product ingredient breakdown on label

APPENDIX E

A DISCUSSION OF THE METHOD OF MAXIMUM LINELIHOOD AND ITS
INCORPORATION INTO A MODEL FOR FOULING COVER

A. GENERAL

The following model was used to describe the properties
of the proportion of a plate that was fouled. Each plate
(t) has a random proportion of fouling, P . Given P the
number of the 100 censused sites that are fouled , (S ), on
the tth plate has a binomial distribution:

p{st = k) = c1^) ptk a - pt)100-k (1>

for k = 0,1,2. ,100 independent of the other plates. The
proportion of fouling, Pt/ is assumed to have the form

P - S (2)

(1 + e Z) .
where e has a normal distribution with mean fi and

variance a2 independent of the other plates censused at
the same time. The mean fi and variance <J will in general
be a function of the amount of time the plate is submerged
though the many variables involved in population dynamics
will keep the function from being linear.

Assume N plates are inspected at a time with the result
that S of the censused sites are fouled on the ttn plate.

The likelihood function for the model is:

S. 100-S

L--J\ <Ket; u,c } C1™) Ptt (1- Pt) (3)

t=l

where

^e^a2} = — e 2(~ } for - < et < - <4>

Note that L is the probability of observing S„ ,..,SM

1 N

fouled sites on each of the plates.

The method of maximum likelihood is to find those

values of /i , a , and € , for t = 1,2, ...N which maximize

L; that is, those values which maximize the probability of

observing the outcome. These values also maximize the log

likelihood function, In L, where
N 2

X' Jin L = V1 ( £— j + St2,nPt - £na + (100-StHn(l-Pt)} (5)

t=l [+ constant]

To find the maximum of <X the partial derivatives of J£
with respect to fj. , a and €t are set equal to zero. This

results in the equations:

t=l

3y ~ 2-j '

2
a

- 0

solving for /i results in:

■*E

£t

(6)

t=l

similarly M

3^ .V1 /£t-^" 1

* -E «=*

a3
t=l

solving for a2 results in

-i} = 0

(7)

a =n2j (£t - y)

t=l

and

3y Ce - y) S 3P

If =--V~ + ^^Pt + (100"Vn^y[-^i] = 0 (8)

t a t t t t

where K> 9 £t £t

TSF1 = 4^- C-V-3 = —5- = P^l-P.)

tf£ d£ E. £ „ t t

r r 1+e T (1+e V

Equation (8) simplifies to

2^ o 2 . n (9)

e- + — (100 a ) - \i - S.a = 0

t et t

1+e

B. SOLUTION OF THE LOG LIKELIHOOD EQUATION

A recursive method was used to solve the system of
equations (6) , (7) , and (9). For each month, the 100 sites
were censused on each of the four untreated plates and S.
the number of fouled sites was determined. Initial values

A A «* A 9

for p , €. / ]i , and a were determined as follows

Pt(0) = V100 (=PNOT,

100

£ (0) = HnCPt(0)/(l-Pt(0))] (=EPSNOT)

Jj(0) = i 2_ £t(0) (=MUNOT)

t=l
4-

S(0) = ? H (£t(0) " ^C°))2 (=SIGNOT)
t=l

The values /zfo) and (P(o)were then used in equation (9) and
the equation solved for £.(1), for t = 1,2,3,4. Since
equation (9) is transcental, Newton's method was used to

solve for £(1) . Newton's method is an iterative procedure
in which the (n+l)st member of the iterative sequence (Xn)

is: fCXn)

Xn+1 = Xn + FTXT

where in our case

X
fCX ) = X„ + e y (100 S2(0)) - y(0) - StS2(0)

n n X

1+e
and

x~ Xru2. -~~ "2,

f'CX ) = 1 + [en/(l+en)Z] 100 a (0)
n

Equation (10) was iterated until iv - X I < 1 x 10~

• n+1 n1

The e (1), t = 1,2,3,4 were then used to compute iterated
values of \i , G , and p as follows:

e.(l) £t(D

Pt(l) = e r /(1+e T )

101

^(1) = k Yj £t(1)

t=l

$1) =i ]P (£t(1) - '^(1))2

t=l

and equation (9) was then solved with M = /J. (1) and a
= a (1) for €f(2) , t = 1,2,3,4. The iterative procedure

was continued until the achievement of a tolerance value of

"6 1 ,

(1x10 ) calculated by |u(k) - u(k+l; [ indicated the system of

equations had converged. The final iterated values for

Pt (=PNEW), € (=EPSNEW), a2 (=SIGNEW) , and fl (=MUNEW)

were the values that maximized the likelihood function for

the model. SIGNEW (a) and MUNEW (£) were then used as

initial input values in the bootstrap simulations of the

experiment (Appendix F) .

102

APPENDIX F
BOOTSTRAP COMPUTER SIMULATIONS

A. AN EXPLANATION OF THE BOOTSTRAP METHOD OF COMPUTER
SIMULATIONS OF RANDOM PROCESSES AND ITS INCORPORATION
INTO AN ASSUMED STOCHASTIC MODEL FOR FOULING COVERAGE

1. Discussion

The common statistical tools utilized in the study

of biofouling have as their basis the simplifying

assumption that the data collected from the analysis of

such communities can be described by a normal or Gaussian

distribution. That is to say, it is assumed that

fluctuations in the values of some experimentally observed

parameter are scattered symmetrically about the true value

of the parameter. It is further assumed that the larger the

difference between the the true value and the observed

value of the parameter, the less likely it is that the

value will be observed experimentally (Diaconis and

Efron,1983). Many years of experience using these

assumptions have shown that even if the dataare only

approximately or "pseudo" normal, the Gaussian theory still

works quite well. If however, the data do not satisfy the

requirements for the assumption of normality or, if the

sample size is such that the various tests used to check

for normality can only give ambiguous results, it is clear

103

that the results of statistical techniques based on the
assumption of normality will be unreliable.

Recent developments in the use of computer-
intensive techniques for statistical analysis, particularly
the invention of the bootstrap technique (Ef ron,1977) , have
enabled the computation of various statistical parameters
without the necessity of assuming a Gaussian distribution.
This technique has also enabled the computation of those
statistics which do not have a simple analytical formula.
Prior to the advent of large main frame computers, the
difficulty of finding numerical solutions to non-linear
problems forced statistical methods to concentrate on those
statistical models and procedures for which analytical
results could be obtained. These models and procedures did
give useful large sample size results for the common
statistics such as the mean and variance of a population.
However, they ignored other important statistical questions
that did not have analytical formulas; such as, the degree
of variability in an estimate due to the sample being of
finite size or the confidence limits about estimates from a
finite sample (Diaconis and Efron,1983). In general terms,
the bootstrap method consists of coupling a probabilistic
model with the data gathered experimentally from one sample
of size N to generate a large number of simulated samples
of size N. These simulated samples are then analyzed to

104

determine the variability of estimates of the true values
of the statistics of the population.
2. Procedure

The model described in Appendix E was used in a
simulation study of the variability of the estimate of the
fraction of plate coverage. The model was used to simulate
200 groups of fixed numbers of plates. The inputs into the
simulation were the values for the maximum likelihood
estimates of the mean (MUNEW 11 ) and variance

(SIGNEW a2) for the monthly epsilon ( 6 ) values
determined from the analysis of the fouling cover on the
four untreated plates.

The stochastic model used in this case assumed a
normal distribution for the epsilon ( e.) values ( that is
€. ~ N( n f a ) ) . Using available computer software, the
required number of normally distributed random numbers with
mean equal to zero and variance equal to unity were
generated for 200 groups of the following number of plates:

Number of Simulated Required Number (I)

Plates per Group of Random Numbers

I = 400

I = 800

I = 1000

I = 2000

105

Number of Simulated Required Number (I)
Plates per Group of Random Numbers

I = 3000

I - 4000

I = 6000

I = 8000

I =16000

Eacn of the (I) computer generated random numbers
from the standard normal distribution were then transformed
into random numbers(n^) with a normal distribution with
mean fi and standard deviation o by multiplying each
invariable by a (the square root of a ) and adding // .
The random number n^ was transformed to give PINIT(I)
defined as:

PINIT(I) = eni/(l + eni) , the average proportion of
the ith plate fouled.

The initial simulated percent cover for the ifc"
plate was determined by calculating a random number having
the properties of a binomial distribution with probability
(P) equal to PINIT(I) and N equal to 100. The resulting
variable was termed PNOT(I). The variables EPSNOT(I) , MUNOT,
SIGNOT, PNEW(I) ,EPSNEW(I) , MUNEW, and SIGNEW were then
calculated using the method of maximum likelihood described
in Appendix E.

106

APPENDIX G

TABULATED MONTHLY PERCENT FOULING COVERAGE VALUES
FOR THE NON-TOXIC CONTROL SURFACES

MONTH

PLATE #

1
2
3
4

FRACTIONAL COVERAGE

.50
.50
.24
.54

MONTH

PLATE £

1
2
3

FRACTIONAL COVERAGE

.33
.49
.69
.46

MONTH

PLATE #

1
2
3
4

FRACTIONAL COVERAGE

.73
.02
.07
.84

MONTH

PLATE £

1
2
3
4

FRACTIONAL COVERAGE

.13
.96

.61
.81

MONTH

PLATE £

1
2
3
4

FRACTIONAL COVERAGE

.54
.46
.41
.06

MONTH

PLATE #

1
2
3
4

FRACTIONAL COVERAGE

.54
.47
.62
.31

107

MONTH PLATE £ FRACTIONAL COVERAGE

1
8 2

3
4

MONTH PLATE #

9 2

MONTH PLATE £

10 2

3
4

MONTH PLATE £

1
11 2

3
4

.48

.88

.69

.97

FRACTIONAL COVERAGE

.91

.49

.92

.35

FRACTIONAL COVERAGE

.70

.56

.29

.97

FRACTIONAL COVERAGE

.83

.95

.64

.98

108

APPENDIX H

LIST OF THE SESSILE SPECIES IDENTIFIED BY THE RANDOM POINT
CENSUS AND THE MONTHS THEY WERE PRESENT ON THE NON-TOXIC

CONTROL SURFACES

ORGANISMS

MONTH NUMBER
23456789 10 11

Protozoa:

Folliculina spp.
Ephelota gemmipara

Coelentrata:

Obelia spp.
Hydractinia spp.

Anthopleura spp.

Ectoprocta: (Bryozoans)

Bugula neretina
Bugula californica
Watersipora cucullata
Hippothoa hyalina
Celloporaria brunnea
Cryptosula pallianasa
Schizoporella unicornis
Microporella ciliata
Microporella californica
Mernbranipora membranacea
Membranipora serilamella
Unknown bryozoan #1
Unknown bryozoan #2

Annelida:

Circeis armor icana
Janua nipponica
Pileolaria potswaldi
Protolaeospira exima
Serpula vermicular is
Anatides groenlandica

Arthropoda:

Balanus crenatus
Megabalanus californicus
Amphipod (unknown)

Mollusca:

Mytilus edulis

XXX
X

X X

X
X

X
X
X
X

X
X

X
X
X

XXX
X
X

X X

X
X X

X X

109

MONTH NUMBER
ORGANISMS 234567891011

Echinodermata :

Strogylocentrotus spp. X

Chorda ta :

Ascidia ceretodes X XXX

Styela truncata X

Pyura haustor X

110

LIST OF REFERENCES

Boyd, M., 1972. Fouling Community Structure and Development
in Bodega Harbor, California. Doctoral Dissertation. Unive-
rsity of California, Davis.

Diaconis,P., and Efron,B.,1983. Computer-Intensive Methods
in Statistics.Scientif ic Amer ican.,v.248,No.5;116-130.

Ef ron,B.,1979. Computers and the Theory of Statistics:
Thinking the Unthinkable. I_n SIAM Rey_iew, v. 21, No. 4. Octo-
ber ,1979 : 460-480 .

Fisher, E.C., Birbaum,L.S. ,Depalma, J. , Mur acka, J.S. , Dear H. ,
and Wood,F.G. 1975. Survey Report: Navy Biological Fouling
and Biodeterioration. Naval Undersea Center Report NUC-TP-
456.

Fraser ,C.M. , 1 9 3 7 . Hy_dr_oids o_f the Pacific Coast of Canada
and the United States, University of Toronto Press. 297pp.

Haderlie,E.C. 1974. Growth Rates, Depth Preference, and
Ecological Succession of Some Sessile Marine Invertebrates
in Monterey Harbor. Veliger. v.17 (supplement) :l-35.

Kelley,P.R.,1981. Scanning Electron Microscope Observations
of Marine Microorganisms on Surfaces Coated with
Antifouling Paint. Master's thesis, Naval Postgraduate
School. Monterey, California, U.S.A.

Knight-Jones, P. , and Knight-Jones , E. W. 197 9. Spirorbidae
(Polychaeta Sedentaria) from Alaska to Panama. Jj_ Zool.
Lond.v. 189:419-458.

Mook, D. , 1976. Studies of Fouling Invertebrates in the
Indian River. Bulletin of Marine Science. v. 26 : 610-615 .

Morris,R.H.,Abbott,D.P.,and Hader lie, E.C., 1980. Intertidal
Inver teb rates o f California. Stanford University
Press. 690pp.

Osburn,R.C, 1952. Allen Hancock Pacific Expeditions v. 14,
parts 1,2, and 3 , Univ. of Southern California Press. 841pp.

Osman,R.W. ,1977. The Establishment and Development of a
Marine Epifaunal Community. EcoljO£_ica_l Monog_r_aphs_. v.
47:pp 37-63.

Ill

Schoener,A.,Long,E.R. ,Depalma,J.R.,1978. Geographic
GVvariation in Artificial Island Colonization Curves
Ecology. v. 47 , No. 2:367-382.

Schoener,A., and Gr eene , C. H. , 19 8 0 . Variability Among
Identical Fouling Panels in Puget Sound, Washington,
U.S.A.In Proceedings of the Fifth Internationl Congress on
Marine Fouling and Cor rosion. Barcelona , Spain. May 1979.

Smi th,R. I. , and Car 1 ton , J.T. , 19 7 5 . Eds. Light' s Manual,
Intertidal Invertebrates of the Central California Coast,
3rd ed. , University of California Press. 716pp.

Sutherland, J. S., 1974. Multiple Stable Points in Natural
communities. American Naturalist. v. 108:859-873.

Whitaker,R.H.,1952. A Study of Summer Foliage Insect
Communities in the Great Smoky Mountains. Ecological
Monographs. v. 22, No. 1 :pp 1-42.

Woods Hole, 1952. Marine Fouling and its Prevention. U.S.
Naval Institute, Annapolis, Md.

112

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Technical Information Center 2
Cameron Station

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2. Library, Code 0142 2
Naval Postgraduate School

Monterey, California 93940

3. Professor Robert J. Renard, Code 63Rd 1
Department of Meteorology

Naval Postgraduate School
Monterey, California 93940

4. Professor Christopher N. K. Mooers, 1
Code 68Mr

Department of Oceanography
Naval Postgraduate School
Monterey, California 93940

5. Professor Eugene C. Haderlie, Code 68Hc 1
Department of Oceanography

Naval Postgraduate School
Monterey, California 93940

6. Professor Patricia A. Jacobs, Code 55Jc 1
Department of Meteorology

Naval Postgraduate School

7. Professor Donald P. Gaver, Code 55Gv 1
Department of Operations Research

Naval Postgraduate School
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8. LT. David L. Martin 1
Route 3, Box 667

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9. Director 1
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Naval Observatory

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113

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Naval Ocean Research and Development

Activity
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19. Mrs. Anne Harrington
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114

20. Dr. Amy Schoener
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and Development Center
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115

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