UNIVERSITY OF CALIFORNIA
SANTA CRUZ
FISHERY MANAGEMENT IN DATA-LIMITED SITUATIONS:
APPLICATIONS TO STOCK ASSESSMENT, MARINE RESERVE DESIGN
AND FISH BYCATCH POLICY
A dissertation submitted in partial satisfaction
of the requirements for the degree of
DOCTOR OF PHILOSOPHY
in
ENVIRONMENTAL STUDIES
by
Kate I. Siegfried
June 2006
The Dissertation of Kate I. Siegfried is approved
______Professor Marc Mangel, Chair
______Professor Brent Haddad
______Professor Bruno Sansó
______Lisa C. Sloan Vice Provost and Dean of Graduate Studies
Copyright © by
Kate I. Siegfried
2006
Table of Contents
Chapter One: Introduction………………………………………………………….1
Qualitative Uncertainty……………………………………………………...2
Marine Reserves………………………………………………………3
Bycatch Policy………………………………………………………...3
Quantitative Uncertainty……………………………………………………6
Chapter Two: Regulations, Devices, and Quotas: An Analysis of Bycatch
Policy………………………………………………………………....9
Introduction…………………………………………………………………10
Background…………………………………………………………………11
Bycatch Policymaking……………………………………………………...12
Modified Gear………………………………………………………..13
Fishery Regulations in Space and Time……………………………...14
Fish Behavior………………………………………………………...15
Economic Incentives…………………………………………………18
Analysis of Policy Success………………………………………………….19
Chain of Accountability……………………………………………...19
Policy Feedback Loop……………………………………………….20
Bycatch Policy……………………………………………………….21
Policy Analysis……………………………………………………….23
An ITQ Approach to Bycatch……………………………………….……..26
Conclusion...………………………………………………………………...27
Chapter Three: Designing Marine Protected Areas for Fishery Benefits:
Expectations, Evidence, and Rules of Thumb………………….32
Abstract……………………………………………………………………...33
Introduction…………………………………………………………………34
Life History Considerations………………………………………………..37
Larval Dispersal……………………………………………………..37
Adult and Juvenile Movement……………………………………...... 41
Density Dependent Effects in Life History Parameters……………...44
Reproduction………………………………………………………....47
Reserve Design Characteristics…………………………………………....49
Size…………………………………………………………………...49
Spacing……………………………………………………………....52
Shape………………………………………………………………...52
Habitat Representation……………………………………………...53
Species Composition………………………………………………...54
Other Considerations……………………………………………………...55
Discussion…………………………………………………………………..56
Conclusion………………………………………………………………….58
Chapter Four: Bayesian Methods for Estimating Parameters of the von
Bertalanffy Growth Equation…………………………………...63
Abstract………………………………………………………………….…64
Introduction………………………………………… ………………….…..65
Methods……………………………………………… ………………….….66
Least Squares Regression…………………………….…....…...... 67
Full Bayesian Model………………………………… ……..…….…67
Length-Based Bayesian Model...... 70
Results…………………………………………………………. ……..…….72
Least Squares Method…………………………………..…………....72
Full Bayesian Model………………………………………….…...... 72
Length-Based Bayesian Model……………………………….……...72
Convergence………………………………………………….……...72
Discussion…………………………………………………………….….….72
Conclusion…………………………………………………………….….…73
Chapter Five: Estimating Natural Mortality in Fish Populations………….…...84
Introduction…………………………………………………………….…...85
Review of Methods to Estimate M……………………………………..…..87
Life History Methods……………………………………………..…..87
Growth Coefficient……………………………………………..….…91
Predation Methods……………………………………………..….…92
Simulation Study……………………………………………………..……..93
When is Constant Mortality Appropriate? An Application to California
Sheephead………………………………………………………………..….96
Future Work……………………………………………………………..….99
Appendix……………………………………………………………………..…….110
Works Cited………………………………………………………………..……....111
List of Figures
Chapter Two
Table 1: Bycatch weight (in metric tons) in the global oceans by region.…..28
Table 2: Levels of observer coverage from different regions of the United
States………………………………………………………………....29
Figure 1: Policy feedback loop for bycatch policy in the United States….…30
Figure 2: Proposed ITQ system for bycatch in all participating fisheries…..31
Chapter Three
Figure 1: A reserve designed for multispecies management…………….….60
Table 1: Rules of thumb: the relative importance of biological characteristics
on design parameters for a fishery reserve…...... ….61
Table 2: A synopsis of the literature knowledge on the reserve effects in
fishery reserves……………………………………………….……...62
Chapter Four
Table 1: A summary of the results from the three different models………...76
Figure 1: The frequency of values for k given the prior probability density..77
Figure 2: The frequency of values for t0 given the prior probability density.78
Figure 3: A histogram of the transformed data……………………………...79
Figure 4: Comparing the three models……………………………………...80
Figure 5: The posterior of L! for the full Bayesian model……………….....81
Figure 6: A pairwise plot showing the correlations between paramters…….82
Figure 7: The posterior of k for the full Bayesian model plotted against its prior………………………………………………………………….83 Chapter Five
Figure 1: The difference mortality can make on setting yield……………..100
Figure 2: The age distribution of blue shark in the simulated population....101
Figure 3: The distribution of biomass at age in the simulated population ...102
Figure 4: The length at age, mass at age, fecundity at mass, and proportion
mature at age relationships in the simulated population ………..….103
Figure 5: The true mean mortality in the simulated population…..…….....104
Figure 6: Population size through time both mortality models……..……..105
Figure 7: Comparing average mortality estimates ………………….....….106
Table 1: Life history traits related to natural mortality rate as published in the
literature………………………………………………………...….107
Table 2: The results of applying eight mortality models to simulated
data…………………………………………………………..……..108
Table 3: A summary of the estimates of natural mortality for California
sheephead…………………………………………………..………109
Abstract
Fishery Management in Data-Limited Situations: Applications to Stock Assessment,
Marine Reserve Design, and Fish Bycatch Policy
by
Kate I. Siegfried
In 1996, the United States Congress updated the Magnuson-Stevens Fishery
Conservation and Management Act with the Sustainable Fisheries Act (SFA), which
calls for the minimization of bycatch, an attention to efficiency, and the use of the
best available science. My work addresses those demands in three distinct ways.
First, life history parameters of stock assessment models must be estimated
using either statistical tools or functional forms based on physiological or ecological
theory. I use Bayesian methods to fit the parameters of the von Bertalanffy growth equation (VBGE), a function used to model individual growth, and the instantaneous natural mortality rate, M. I also develop a Bayesian model to find asymptotic size from the VBGE without age data. Life history theory provides a number of ways to calculate natural mortality. I test these methods on both simulated and real data. In
general, weight- and age-based methods provide very different estimates for the same data than the methods based on individual growth rate and age at maturity.
Second, the effectiveness of fishery management is judged both by the
abundance of stocks and the continuing yield for fishers. Marine reserves are in the limelight of fishery management as a potential panacea, but analyses of the fishery effects of marine reserves are sparse. I review the literature for specific fishery
benefits of reserves designed for a single or multispecies effect. I find little
consensus on larval export, spillover, or density dependent mechanisms and their
effect on fisheries outside the reserve.
Third, the SFA calls for the immediate minimization of bycatch, and when
practicable, that the mortality of that bycatch be minimized. I address this question
by conducting an analysis of bycatch policy. I focus on the fish component of
bycatch and I review the implementation and the effectiveness of various bycatch
policies in the United States. Such policies require the use of bycatch reduction devices (BRDs), time/area closures, and gear modifications.
Acknowledgements
I have many people to thank, and I have decided to thank them chronologically. I thank my mother and father for spawning me (not a technical term). My mother raised me alone, and gave me every chance to succeed. She has been my mentor and my hero since I was young enough to remember. She has been a shining example of kindness, ambition, and compassion in my life. Thank you mom!
My brother is a sweet-hearted man (oh gosh, he is a man now!) who wishes me success at every turn.
I had wonderful teachers along the way. Most notably were Mr Bittle, who never let me get away with anything; Ms. Douglas, who would still be appalled at my grammar; and Mrs Frias, who gave me my first taste of science. My most pivotal academic moment was when a Professor named Maggie Werner-Washburne at the
University of New Mexico dragged me to the ichthyologist in the department after I told her I wanted to study fish. She was my bravery that day, and my life has been
better ever since. The ichthyologist was Tom Turner, who gave me a spot in his lab and sponsored my senior honors thesis. Megan McPhee, a graduate student in Tom’s
lab, was a true friend through college, and she was the one who encouraged me to
take a Graduate Ecology course. That course was co-taught by Jim Brown and Eric
Charnov, both of whom led me in my search for a graduate program. Both Jim and
Ric constantly encouraged me and pushed me to excel. I would not have been
accepted to the program I really wanted if it was not for them. I went to graduate
1
school with Marc Mangel as my major advisor, in the Environmental Studies
Department at UC Santa Cruz. He is without a doubt the best advisor anyone could ever ask for. He is supportive in many ways, emotionally, intellectually, and financially. He taught me to grow as a person, not just an academic, and I will always be grateful. My committee members, Bruno Sansó, Brent Haddad, and Greg Gilbert were some of my biggest fans. Their guidance helped me to focus my research and finish my dissertation in four years. Thank you all for you help and support through the years. My collaborators deserve a lot of credit for my Ph.D. research; thank you
Bruno Sansó, Enric Cortés, and Mike Beck. I give thanks with all my heart to the members of the Mangel Lab past and present (Nick Wolf, Steve Munch, Teresa Ish,
Yasmin Lucero, EJ Dick, Anand Patil, Kate Cresswell, Dan Merl, Chris Simon, John
W., Andi Stephens, and Leah Johnson) my Environmental Studies cohort (Marisa,
Amy, Alden, John, Pete, and Martha), the Applied Math and Statistics Department
(especially Herbie Lee, Raquel Prado, Bobby Gramacy, and David Draper) and the
scientists I worked with at the National Marine Fisheries lab in Santa Cruz. Finally, I would like to thank my boyfriend Steve. He loves me and supports me and has always shown enthusiasm for my work and my goals. Thank you Steve!
I would also like to thank my funding sources and my collaborators for work on specific chapter components: My work on California sheephead was partially supported by Award P0370009 from California Department of Fish and Game and by the Center for Stock Assessment Research, a partnership between UCSC and NMFS
Santa Cruz Laboratory. For the von Bertalanffy growth equation chapter, my work 2
was partially supported by The Center for Stock Assessment Research (CSTAR). We
appreciate the comments of the anonymous reviewers, and we are especially thankful to John Carlson and Ken Goldman for organizing the symposium in which I presented the Bayesian models for von Bertalanffy growth parameters.
3
Chapter One
Introduction
4
This dissertation is the result of four years of chasing uncertainty in biological
and social problems. For example, I tackled problems with missing data, a lack of
experimentation, and a large amount of biological uncertainty. In some instances the level of uncertainty can be quantified, as is the case in stock assessment and life history theory. However, in fishery management and policy, the uncertainty is often
qualitative, making a quantitative approach infeasible. Therefore, there are two sides
to my research: characterizing qualitative and quantitative uncertainties.
Qualitative Uncertainty
The Magnuson Stevens Fishery Conservation and Management Act (MSA) is
the single most important piece of legislation regarding fisheries management in the
United States. It was designed to create federal jurisdiction over the oceans within
200 miles of the U.S. coast, called the Exclusive Economic Zone (EEZ). The MSA
excluded foreign fishing pressures and drew attention to the status of fish stocks in
the EEZ. The MSA established ten “National Standards” for fishery management.
The four that apply most to my work are:
1) “Conservation and management measures shall prevent overfishing while
achieving the optimum yield from each fishery”
2) “Conservation and management measures shall be based upon the best
scientific information available”
6) “Conservation and management measures shall take into account and allow
for variations in fishery resources and catches”
5
9) “Conservation and management measures shall, to the extent practicable,
minimize bycatch or the mortality of such bycatch”
In light of these National Standards, I focused on two qualitative topics: marine
reserves and bycatch policy.
Marine Reserves
Since traditional fishery management is not performing well in many
fisheries, there is a need for alternative management strategies. Marine reserves are
often advocated as the best alternative strategy for improving fisheries (Fogarty 1999,
Murray et al. 1999, Dayton et al. 2000, Murawski et al. 2000, Lubchenco et al. 2003,
Shipp 2003). There is evidence that marine reserves conserve biodiversity (Halpern
2003), but it is less clear that reserves are an effective tool for fishery management.
As a graduate fellow of The Nature Conservancy (TNC), I studied whether there was sufficient evidence to claim that marine reserves would enhance fishery yields. I conducted a literature review and synthesized the results into concrete advice for fishery managers, or anyone interested in establishing a marine reserve for fishery benefits. My collaborator and co-author, Dr. Michael W. Beck, is my TNC
mentor. I composed Chapter Two alone, and Dr. Beck made suggestions and read drafts as it was necessary.
Bycatch Policy
Bycatch is the incidental catch of living organisms that are not targeted in the fishery. Currently, the Total Allowable Catch (TAC) for a fishery is determined without considering the bycatch of that species in other fisheries. Each fisherman is 6
permitted to catch a portion of that TAC, and that portion is determined by the current
property rights regime for that fishery.
A property right is the privilege of ownership that allows one party to legally exclude all others from access (Conrad 1999). A complete set of property rights designates the ownership of all resources in question with an unambiguous agreement among all parties that is easily enforced (Edwards 2003). Changing ownership may be difficult if there are many parties affected by the decision of who gets the rights, since it is unlikely that all parties will agree. In the case of fisheries, it is debatable not only whether the government is entitled to allocate rights to specific parties but also to which parties the rights should be given (Newkirk 2002). There is a compromise between those resources the government should maintain as a public
trust, and those that should be handed over to private parties (Iudicello et al. 1999,
Eagle et al. 2003). In most cases where the property rights are defined for fisheries,
the distribution of the rights to fishermen is such that they are allotted portions—or
individual quotas—of the TAC for the target species.
There are objections to strengthening private property rights as a method for
solving environmental problems because of the transactions costs. The ‘Coase
Theorem’ states that an efficient economic outcome is likely with bargaining and
social negotiations (Coase 1960). Therefore, it is unnecessary for the government to
regulate externalities, or strengthen property rights, because the market will right itself (Turner et al. 1993). Using this argument, further regulations in the form of
7
stronger property rights will cause an inefficient outcome, compromising both the
economy and the social interactions of bargaining and negotiation.
ITQs, or Individual Transferable Quotas, are one version of property rights that have proven successful in many fisheries (Runolfsson and Arnason 1997, OECD
2001, Witherell 2003). An ITQ is a portion of the TAC that a fisherman may exploit.
He or she, and the other quota owners in a fishery, can fish until they reach the TAC each season. The owners have exclusive rights to harvest the species for which the fishery exists, and they can trade or buy quotas if necessary. Some ITQ regimes include bycatch by requiring all of the catch be retained (NPFMC 2004c). If the bycatch is a large proportion of the catch, the fisherman is penalized for dirty fishing by earning lower profits. However, when bycatch is not included in the ITQ, the
TAC set for each fishery may be too high. Each fishery has a TAC for harvest, but after the bycatch of that species is accounted for in all other fisheries, the TAC is surely exceeded.
Although there are laws requiring a minimization of bycatch, the extent to
which policies have been crafted to avoid bycatch is unclear. In Chapter Three I address this problem. I focus on the U.S. and its policies pertaining to the bycatch of fish and invertebrates. I describe practical problems in the management of bycatch by reviewing current policies to find if there is an improvement in the status of bycatch stocks after policy implementation. I define the way policies categorize bycatch and I show how miscategorizations may be the root of management error. Finally I propose a new category system based on the policy analysis I conducted. 8
Quantitative Uncertainty
Stock assessment science—the science of assessing the status of fished populations—is thriving. Much research is focused on improving stock assessment methods, sampling methods, and the biological knowledge about the species of interest (Schnute and Hilborn 1993, Punt and Hilborn 1997, Methods et al. 1998,
Hammond 2004).
My interest in stock assessment science began when I studied life history theory. Life history theory describes how, in the context of ecological problems,
organisms are naturally selected to maximize their reproductive success (Stearns
1992, Roff 2001). R.A. Fisher described life history theory by asking how the
allocation to reproduction is affected by the environment and the age of the organism.
For instance, we can describe life history theory through a set of unified questions:
What is the intrinsic rate of increase of a population under one set of strategies? How does one calculate the current reproductive value of an organism? How is reproductive value divided into current and future reproductive success? How much energy should an organism invest into current reproduction at the expense of future reproduction? and What is the effect of individual behavior on population growth rates? Life history parameters such as growth rate, mortality rate, and asymptotic size
can be quantified and used in stock assessments to project the future abundance of the
population. However, process variability and observation error are large sources of
uncertainty when quantifying life history parameters (Hilborn and Mangel 1997).
9
Chapters Four and Five focus on statistical methods for estimating natural mortality
and the parameters of the von Bertalanffy growth equation.
The von Bertalanffy growth equation was derived from the idea of balancing
catabolism and anabolism (von Bertalanffy 1938, 1957). Over the years, it has been
transformed into the following equation
#k"t#t0 ! L"t! % L$ "1# e ! (1)
where L is length at age t, k is the growth coefficient, and t0 is the parameter used to
find length at birth (von Bertalanffy 1957, Beverton and Holt 1959). There are
inherent problems applying this equation to data; often, the data are limited to the
younger age classes or there are insufficient age data to regress size and age. When the data are available, a nonlinear regression is typically used to regress size and age using Equation (1). In Chapter Four I discuss two novel methods for finding the parameters of the von Bertalanffy growth equation. Both methods were developed in a Bayesian framework. Bayesian statistics is becoming more prevalent in ecology and fisheries management (Punt and Hilborn 1997, Ellison 2004), because it allows us to quantify uncertainty about the estimation of each parameter in a model.
My final chapter is devoted to M, the natural mortality rate. Typically, M is fixed in stock assessments because there are no empirical estimates (Jennings et al.
2001). However, there are numerous methods available in the literature for
estimating natural mortality. I carried out a literature review of the methods and conducted a simulation study to determine the performance of the available models.
10
Chapters four and five are the results of my collaboration with Dr. Bruno
Sansó for the past three years. I composed all the text in the chapters and wrote all
the programming code. Dr. Sansó contributed with helpful discussions, suggestions
and coding.
The quantitative and qualitative aspects of my research are tied together by a common theme: making decisions in the face of uncertainty. By using Bayesian
statistics I am using the best scientific knowledge available to estimate life history parameters for stock assessment. By synthesizing the information available about the fishery effects of marine reserves, I am providing managers with an up-to-date guide to the best available science. Finally, by illustrating and interpreting the effectiveness of policies that are meant to reduce bycatch, I am contributing to the pool of knowledge that will help us adhere to the National Standards in the MSA.
11
Chapter Two
Regulations, Devices, and Quotas: An Analysis of Bycatch
Policy
12
Introduction
The Sustainable Fisheries Act (SFA) defines bycatch as “fish [or invertebrates] which are harvested in a fishery, but which are not sold or kept for personal use” (Kantor et al. 1996). In a landmark review of global bycatch, Alverson et al. (1994) estimated an average of 27 million metric tons per year. The major contributing region, with approximately 9.1 million metric tons, is the Northwest
Pacific (Table 1). Bycatch is a wasteful byproduct of fishing and is of great concern to many biologists, fishermen, and the governments of fishing countries (Alverson et al. 1994, Castro et al. 1996, Sea Grant 1996, NOAA 1998, Davis 2002, Babcock et al.
2003, Chuenpagdee et al. 2003, Coelho et al. 2003, NOAA 2003b, Cochrane et al.
2004, Croxall and Nicol 2004, NMFS 2004, NPFMC 2004b, Pascoe and Revill 2004,
Price and Rulifson 2004, Read et al. 2006).
Here, I focus on the U.S. and examine its policies pertaining to bycatch. I describe practical problems in the management of the fish and invertebrate component of bycatch by reviewing the effectiveness of active policies. I define policy categorizations (e.g. discards, total allowable catch, quotas) and show how miscategorizations may be the root of management error. Then I propose a new set of categories and explain how management would change as a result. Finally I illustrate how alternative systems work in other countries and are therefore practicable.
13
Background
The Magnuson Fishery Conservation and Management Act (1976) is the single most important piece of legislation in fishery management. There are three important products of the act (Kantor et al. 1996, Eagle et al. 2003):
(1) The implementation of a 200-mile Exclusive Economic Zone (EEZ);
(2) The establishment of the eight fishery management councils (Mid-Atlantic,
South Atlantic, New England, Pacific, Gulf of Mexico, North Pacific, Western
Pacific, and Caribbean); and
(3) The creation of seven National Standards for fishery management.
The Sustainable Fisheries Act (SFA 1996), which was spearheaded by Senator Ted
Stevens, updated the Magnuson Act and the Magnuson Act was subsequently referred
to as the Magnuson-Stevens Fishery Conservation and Management Act (MSA).
The significant changes made by the SFA were:
(1) The promotion of a precautionary approach that was meant to prevent stocks
from collapsing;
(2) The requirement to identify Essential Fish Habitat (EFH); and
(3) The addition of three National Standards.
The definition of fish includes all animals and plants except marine mammals and seabirds, which are protected under separate laws. Whales, porpoises, seals and sea lions are protected by the Marine Mammal Protection Act (MMPA, 1972) and
endangered seabirds are protected by the Endangered Species Act (ESA, 1973). The new National Standard 9 to the MSA was created in a political climate of growing 14
concern for the environmental consequences of fishing: “Conservation and management measures shall, to the extent practicable, (A) minimize bycatch and (B), to the extent bycatch cannot be avoided, minimize the mortality of such bycatch.”
§303(a)(11) of the MSA mandates each Fishery Management Plan (FMP) “establish a standardized reporting methodology to assess the amount and type of bycatch occurring in the fishery.” (Kantor et al. 1996). In other words, bycatch should be prevented, reported with a standardized method, and if it must be caught, the mortality as a result of being caught must be minimized. These are clear objectives for which policies can be designed.
Bycatch Policymaking
Bycatch policy has been created to follow the three A’s—Account, Avoid,
and Apply (Witherell 2003). In order for bycatch policies to be effective, accurate and abundant data are required—thus, the first A, “Account”. Justified by the MSA, the National Oceanic and Atmospheric Administration’s National Marine Fisheries
Service (NOAA-NMFS) requires various levels of observer coverage on active vessels. Fishery observers monitor and record fishing practices and compliance with regulations. NOAA Fisheries contracts fishery observers to take data on the species
composition and weight of the bycatch. The observer program has been active since
1972, and almost 42 different commercial fisheries are monitored by the program
each year (NOAA 2006). The 42 fisheries require different percent coverage—the
time an observer must be on board with respect to the cumulative catch of the vessel.
Observer coverage varies by region, between 0 and 100 percent (Table 2 and NOAA 15
2003a). Babcock et al. (2003) show that different levels of observer coverage,
depending on the rarity of the bycatch species, can provide sufficient data for
management to determine total bycatch. They show that 50% coverage for rare species and 20% coverage for common species is adequate.
Until recently, observer data were rarely used or analyzed. Working
conditions on boats impair the ability of observers to take completely random data,
and at times, observers are required to stop taking data altogether for safety reasons
(Campbell 2004). Incomplete coverage of most fisheries and the presence of an
“observer effect” make the analysis of the data very difficult. An “observer effect” is
an anticipated change in the fisherman’s behavior when an observer is on board, and
it can be difficult to quantify the bias in the data. Biased sampling of corrupt
observers—those who underreport catch or omit illegal activities—is also very
difficult to quantify.
The second A of bycatch mitigation is “Avoid”. The majority of bycatch
reduction efforts have been to avoid bycatch in the first place. Technological advances improve a skipper’s ability to find target species. Specific time/area
closures are used in areas where the proportion of bycatch would likely be high.
Studying fish behavioral responses to fishing gives managers and fishermen ways to
avoid bycatch (NOAA 1998).
Modified Gear
An example of a gear modification is the use of Bycatch Reduction Devices
(BRDs) in the Gulf of Mexico shrimp trawl fishery (Broadhurst 2000, Broadhurst et 16
al. 2004, Warner et al. 2004). A BRD provides an opening finfish can use to escape
from the trawl net. The design is similar to and incorporable with the Turtle Excluder
Devices (TEDs) already mandatory in shrimp trawl nets. Declining Red Snapper populations in the Gulf were the impetus for this policy (Atran 1998). The Gulf of
Mexico Fishery Management Council (Gulf Council) has been proactive in testing implementation and monitoring of BRDs. In 1998, the Gulf Council voted to make the testing and analysis of the effect of BRDs more precautionary towards
conservation (Hood 1999). To ensure BRDs were effective in lowering the level of
finfish bycatch, NMFS is conducting a fishery-dependent study to test the
effectiveness of BRDs under actual operating conditions. The study will determine if
BRDs reduce the Red snapper bycatch mortality in shrimp trawls by at least 60%
relative to normal fishing conditions, a level decided by the Gulf Council. The results
of the study had not been released as of April, 2006. In the North Pacific, similar
excluder devices are being tested to exclude Pacific halibut and various salmon and
skate species from walleye pollock, Theragra chalcogramma, nets. These devices are
being tested, and they are meant to complement the Improved Retention/Improved
Utilization project used in the Alaskan pollock fishery.
Fishery Regulations in Space and Time
Changing gear and fishing patterns—where, when, and for what duration—are ways to avoid excessive bycatch. The selectivity, or the types and sizes of species caught by certain gear varies; therefore the ratio of bycatch to catch also varies with
gear type (Alverson et al. 1994). 17
In New England, minimum mesh size requirements are the only effort of
bycatch reduction that is translated into gear regulations. The New England Fishery
Management Council used spatiotemporal regulations—regulations that exist in area, time, or both—in the Loligo squid fishery to reduce the bycatch of scup Stenotomus chrysops (Powell et al. 2004). However, no benefits were realized in the North
Atlantic due to area closures (NEFMC 2004).
The Pacific Fishery Management Council (PFMC) also mainly uses time/area closures to minimize incidental rockfish catch and bycatch (Lohn and McIsaac 2004).
The PFMC uses spectrum bathymetry to define likely and unlikely areas for intense
rockfish congregations. The PFMC also uses strict bycatch limits for prohibited
species such as Salmon. The limits are set at approximately 1% of the total stock size
of the prohibited species. If a fisherman exceeds that limit, s/he is not allowed to
continue fishing. The PFMC’s actions may confer a substantial conservation benefit,
given there is strict enforcement of the bycatch limits.
Fish Behavior
Studying the behavior of fish around fishing gear can shed light on ways to
avoid bycatch. For example, Cartamil and Lowe (2004) studied the diel movements
of the ocean sunfish, Mola mola, a common bycatch species in the Pacific pelagic
longline fishery. Cartamil and Lowe found that lowering the longline in the water
column significantly reduced bycatch. Similarly, King et al. (2004) studied the
behavior of flatfish and rockfish to oncoming traditional and altered trawl nets. The
trawl net was altered to raise less than traditional nets. It was designed with a 18
“cutback” headrope that allows flatfish to rise up and out of the trawl path. The experimental nets reduced bycatch and increased target catch by 25 to 59%.
However, there was a small increase in the catch of skates and sablefish.
The third A of bycatch mitigation, “Apply”, is to create policies that allow for the collection of data and the development of technologies and studies to help avoid
bycatch. In other words, once a methodology is in place to account for bycatch, and
there are data about the effectiveness of different avoidance techniques, we can Apply
the information to create new policies. One way to operationalize the notion “Apply”
is through fishery rationalization. Rationalization comes from the assumption in
economics that agents will act rationally (e.g. a goal of maximizing utility) (Turner
1974, Turner et al. 1993). To rationalize a fishery is to create policies that enable
public goals to be achieved in the context of economically rational behavior by
fishermen. It requires policymakers to anticipate industry’s reactions and behaviors
to proposed regulations, and implement those regulations most likely to be successful
over time. This may include limiting entry to a fishery, or equally distributing
economic rent to all fishermen. If all fishermen were required to pay more for their
access to the fishery, it may be cost prohibitive for some to continue fishing. Only
the most profitable fishermen would remain. Likewise, if all fishermen within a
fishery received equal profits, their fishing effort would likely decline to the
minimum level required to participate in the fishery (Petruny-Parker et al. 2004). The
decline is effort would improve fishery condition.
19
Rationalization may also lead to the elimination of subsidies and safety
concerns that dominate derby-style fisheries. An example is the IFQ, Individual
Fishing Quota, system for walleye pollock in the Bering Sea (NPFMC 2006b). The
North Pacific Fishery Management Council (NPFMC) created a cooperative of fishermen that govern themselves. The cooperative is given a Total Allowable Catch
(TAC) that they may not exceed, and all communication about fishing areas, total catch, and bycatch rates are the responsibilities of the fishermen. Bycatch is counted towards the TAC, and all catch, except prohibited species, is saleable. An observer is placed on each vessel 60 feet or larger, and depending on the size of vessel, the
coverage is 30% to 100%. Based on the daily data provided by the observers, the fishery is closed when the fleet reaches their TAC.
The pollock fishery is the world’s largest fishery, and it has been argued that
the success of the pollock cooperative is due to the abundance of fish (NPFMC
2004b, 2006a). Although the abundance of the stock may be a factor, translating
actions into monetary benefits through regulation is a powerful tool for sustaining a
fishery (Conrad 1999, Iudicello et al. 1999, Russell 2001, Pearce 2002, Edwards
2003, Pascoe and Revill 2004). Fishermen see a reduction in revenue and an increase
in their opportunity costs any time they catch bycatch. Each Skipper spends labor
hours sorting through the catch, removing unwanted individuals. Fishermen lose
money when they catch a non-legal size or sex of their target species, a species of no
market value, or a prohibited species. The time spent sorting and discarding has an
opportunity and labor cost associated with it, and each vessel owner absorbs these 20
costs. The opportunity cost is the possible value of the fish that would have occupied the same hook or place in the net as the bycatch (Conrad 1999, Pearce 2002). The non-legal individuals of the fisherman’s target species are usually too small or of the wrong sex to be within the law. Such regulations about minimum sizes vary greatly between species (Lohn et al. 2004). The prohibited species are usually ones that require special permits, or for which the season is limited by time or to particular fishing grounds.
Indirect economic consequences include the costs of monitoring, enforcement,
and the participation in the regional management councils. Fishermen pay for a
portion of the monitoring in the form of observer wages, room, and board and permit
costs. Enforcement is required when bycatch levels are passed, a vessel retains a
prohibited species, or the improper gear is used. The result is usually a fine for such
offenses, however, in certain circumstances, removal from the fishery may occur.
Given such constraints and economic consequences of bycatch, it is rational for a
fisherman to want to minimize bycatch. Fishery managers can use that fact to Apply economic incentives in order to change fishermen behavior.
Economic Incentives
In 1998, all of the Groundfish FMP Amendments were implemented in the
North Pacific (NPFMC 2004b). These amendments require total retention of all walleye pollock and Pacific cod in the Bering Sea and Gulf of Alaska regardless of gear type or fishery. By requiring total retention, the policy provides an incentive for
fishermen to avoid catching these cod or pollock they are not targeting. This policy 21
also requires landing all retained species. Retention measures for other groundfish
species in the Bering Sea have recently been adopted by the NPFMC. NMFS
approval is required before implementation in 2006. Finally, the NPFMC began an incentive program to reward vessels with low levels of bycatch and penalize the vessels with high bycatch. It had variable success and eventually failed because enforcement issues were overwhelming any possibilities of long term success
(Witherell 2003). Managers were unable to completely monitor the bycatch levels of all vessels due to uneven observer coverage (Table 2).
Analysis of policy success
Chain of Accountability
In order to analyze the success of various policies, we must first understand
the chain of accountability for bycatch policy. Chains of accountability define the
party accountable for following or improving the policy at each step in the policy
process. For instance, in Figure 1, I present a policy feedback loop. The black
arrows signify each link in the chain of accountability, and the rounded blue arrows
signify the impact of each group on the next. The chain of accountability is contained
within the loop, and it starts with the fishermen. Their actions must comply with
regulations, such as fishing in designated areas and accurately reporting their catch.
The second link in the chain is the fishery observer. When an observer is onboard, he
or she is responsible for sampling the catch in order to gather more detailed data that
contribute to the assessment process. The third link is the National Marine Fisheries
Service. The NMFS fishery scientists use the observer and logbook data to assess the 22
status of the stock and estimate total levels of bycatch. Based on fishery scientists’
recommendations, the fourth link in the chain, the regional fishery management
council, sets TACs for the next fishing season. The Council also proposes policies to prevent bycatch or bycatch mortality.
Policy Feedback Loop
The policy feedback loop shown in Figure 1 is constructed as follows.
Starting at the top of Figure 1, a policy or regulatory action, such as gear modifications, spatiotemporal closures, or prohibited species is meant to improve stock status by decreasing bycatch levels. Second, the regulatory action affects the fishermen by reducing the levels of bycatch each vessel can take, whether explicitly or implicitly. For instance, if the policy is a bycatch cap, then the skipper will have an incentive to avoid bycatch in order to continue fishing for his or her target species.
Third, the observer collects data on the catch. An “observer effect” is a source of variability in the catch data between observed and unobserved trips (NOAA 2003a).
Observers may also take biased data if they are influenced by the crew or are not using a consistent sampling style. The next step is one I propose as a result of the policy analysis in the following section: NMFS scientists can compare the pre-policy data to current data in order to determine if there is an effect of the policy on the status of the stock. Finally, the Council can decide to maintain or change policy
based on total bycatch levels and stock assessments performed by the NMFS
scientists, and the cycle continues. Currently, there is very little effort to address the
question, “have the policies improved the stock?”. I now turn to this question. 23
Bycatch Policy
The policies managing bycatch reflect the sparse and variable nature of the available bycatch data. It is important to examine the effects of existing policy and
learn from the implementation of bycatch policy. Here, I argue that the information and policy gaps must be filled in order to follow the MSA and protect bycatch species.
The first problem to address is the omission of important components of
bycatch from policy language. The MSA allows the standards for bycatch reporting
to be determined by each of the eight regional management councils, but it fails to
fully address integral components of bycatch including incidental catch and discards.
Incidental catch is the catch and eventual sale of non-target, non-prohibited species, and discards are catch of the target species that are not landed for various reasons
(e.g. wrong size or sex). However, the regional councils interpret the law in different
ways; for example, some interpretations include incidental catch (PFMC 1990, 2000,
2002a, b). There is a need to develop a national consensus incorporating all aspects
of bycatch into federal policy. The differences between incidental catch, bycatch, and
discards must be described explicitly.
The mission statement for NMFS states, “NOAA Fisheries Service is
dedicated to the stewardship of living marine resources through science-based conservation and management, and the promotion of healthy ecosystems” (NOAA
2003b). However, any bycatch policy is considered unsuccessful if it prevents the fishermen from reaching their TAC (NOAA 1998, Andrews 1999, Witherell 2003, 24
Hall and Mainprize 2005). The paradox between environmental stewardship and maximizing yield has stymied the advent of new bycatch policy: “With regard to practicability, in fishery management you really cannot get to zero on bycatch” (Lohn and McIsaac 2004). There is a trade-off inherent in the system that with less bycatch, and similar fishing levels, yield will likely decrease. The potential of maintaining
yields in practice and decreasing bycatch levels must be understood for the trade-off to be legal and sustainable, following National Standards 1 and 9.
The long term goal of bycatch policy should be that Council decisions on
policies and TACs have a positive affect by reducing bycatch. Evaluating such a goal
is problematic. How and when is it measured? Most bycatch species are not assessed
which poses a serious problem. Monitoring the stock will require more time and
money than is currently spent. Also, environmental variability and demographic
stochasticity within populations affect population numbers (Morris and Doak 2002),
which may make it very difficult to attribute stock trends to bycatch mortality alone.
More data—species composition, age, fecundity, size, and weight, for example—
must be acquired in order to make population trends more apparent. Many fisheries
require only partial observer coverage, and observers are not currently required to
take all the data described above (Campbell 2004). Increases in observer coverage
for many stocks will help managers evaluate whether the bycatch levels are
increasing or decreasing (Babcock et al. 2003, Witherell 2003). Although the
national observer program has been in effect for over thirty years, there are no studies
25
I am aware of that show a marked reduction of fish bycatch due to successful regulation as a result of data gathered by observers.
Policy Analysis
Evaluative criteria for the success of bycatch policy are non-existent; in fact,
how to pick evaluative criteria has been the subject of recent motions and
amendments within council proceedings (NPFMC 2004c, a). I propose the following
evaluative criteria to distinguish an effective policy from an ineffective one:
(1) Is the level of bycatch reduced as a result of the policy?
(2) Is the policy enforceable?
(3) Is the policy economically efficient?
(4) Are yields maintained or improved through the implementation of the
policy?
The first criterion can only be measured through observers. Success can be
marked by a significant decrease in the take of bycatch species. How large the
decrease should be is a political and social decision to be made by the Regional
Council. Evaluating policies that are meant to improve the status of bycatch stocks
can be separated into two parts: biological efficiency and economic efficiency.
Biological efficiency measures the decrease of bycatch as a result of the policy;
economic efficiency is concerned with changes in fisherman profitability due to the
policy. The following example focused on the immediate decrease in bycatch due to
policy.
26
Broadhurst (2000) reviews various bycatch reduction methods, either
mechanical exclusion of bycatch species, or ones that separate species by behavior.
His quantitative tests of success do not test the devices individually, but rather
compare the efficiency between devices. His qualitative conclusion is that BRDs will
both decrease total bycatch and decrease bycatch mortality. A study on the impacts of BRDs (Samonte-Tan and Griffin 2001) casts doubt on their long term economic success. They refer to a marked decrease in bycatch levels, but at the same time, a marked decline in shrimp fishermen’s profits. Thus, the most likely impact of BRDs in the Gulf of Mexico shrimp fishery in terms of total monetary losses ranges from
$44.9 million to $65.7 million. On average, 176 million tons of shrimp are caught in the Gulf of Mexico worth $492 million annually. Regardless of the economic impact, their work is evidence that BRDs reduce bycatch.
Steele et al. (2002) test the efficiencies of two types of BRDs, the extended
mesh funnel (EMF) and Florida fisheye (FFE), using data on the yield and bycatch of
shrimp nets before and after BRD fitting. Their analysis shows that BRDs reduce
finfish biomass in almost every case, but that the BRDs did not significantly reduce
shrimp biomass in any case. Since the authors cannot replicate their experiments, it
must be assumed that using the same net in the same region is sufficient for
replication.
Overall, there are data to support that BRDs reduce bycatch, but that reduction comes at a high price to fishermen. These few studies are hardly enough on which to base a conclusion, and it is unfeasible to analyze them objectively. 27
Stein et al. (2004) examined the different bycatch levels of three common gear
types: otter trawls, sink gill nets, and drift gill nets. They found that sink gill nets had
the highest bycatch, and they recommended the cessation of sink gill net use, and
Price and Rulifson (2004) argue that using fisherman knowledge can significantly
decrease bycatch. They showed that nets placed with fisherman knowledge caught
lower levels of bycatch while maintaining an adequate yield. Policies that
incorporate the information in these two studies will most likely decrease bycatch
directly. Although partnerships with fishermen make the enforcement simpler and
less costly, there is an inherent lack of trust between fishermen and NMFS (MacCall
2004, Campbell 2005). Enforceability is therefore limited to the reporting of an
observer onboard or an official at the dock until workable resolutions to the distrust between fishermen and the government can be reached.
I have described two cases, prohibited species caps and BRD implementation,
that show the NPFMC and the Gulf Council respectively take a precautionary
approach, following the MSA. These advances, along with the changing technology,
are good for bycatch reduction. Even though it is only a first step, reducing levels of bycatch is a necessary step towards minimizing bycatch according to National
Standard 9. As fisherman behavior changes due to policies, the bycatch reduces and
there will be less need for enforcement and new policy to correct errors in
implementation. As less bycatch is encountered, successful policy will be
perpetuated, leading to a positive feedback loop. Finally, an abundant stock seen by
observers and fishermen year after year will mark the utter success of the policy. 28
An ITQ Approach to Bycatch
The Individual Transferable Quota (ITQ) system seems an ideal combination of incentives to retain profitability alongside a reduction in effort. ITQs are used to assign exclusive individual rights to harvest specific portions of the overall TAC of living marine resources. New Zealand and Iceland have ITQ systems that are generally agreed to be successful (Runolfsson and Arnason 1997, OECD 2001), and more research is needed to translate these systems into action in the U.S. For instance, how could an ITQ system be established and operated; what are the costs and benefits of an ITQ system and how they are distributed; and the potential political opposition or support of the conversion to ITQs?
However, there is a categorical problem with bycatch policy. The problem is
the way TACs are assigned without taking bycatch levels into consideration. Figure 2
illustrates the point. The current TAC for Fishery One is set; however a considerable
number of fish are taken in addition to the TAC as bycatch. Therefore, under a
system without ITQs, the total catch is larger than the TAC after the bycatch taken in
Fisheries Two, Three, and Four. The new categorization would assign an ITQ to the
bycatch, and take into account the proportion of the catch that will be taken as bycatch in other fisheries. The TAC for Fishery One will decrease, and the rest will be allocated to the bycatch ITQs for that species. Fisheries Two, Three, and Four
would have similar systems. The Regional Council will decide how much to set aside based on an assessment by NMFS scientists, and the assessments will be based on bycatch time series from each fishery. This system will provide incentives to 29
fishermen to participate in data collection programs because most fishermen will
want to have accurate estimates of the proportion of the TAC that should go to
bycatch. The proposed system also allows for bycatch to occur, but to categorize it as
catch in a fishery rather than a separate source of mortality. Therefore, the TAC set will be for catch in a fishery (category 1) and the TAC allocated to bycatch will be caught in other fisheries proportional to their take of that species in previous years.
Conclusion
Since the species that compose bycatch are covered under the MSA, it is apposite to use the precautionary approach when managing these species. As argued in an earlier section, there is very little effort to compare bycatch levels before and
after policy implementation. The examples I discuss in previous sections are field
experiments, however a thorough policy analysis should be required of each new bycatch policy for years following its implementation. Such an analysis will provide the best data for creating new policies.
Bycatch reduction is a process. Advancements are possible in several areas of bycatch research, especially in the biologically and economically rationalized fishery
systems, a currently overarching theme in the fishery policy world. The policies
needed to rationalize many fisheries are still being determined, and there will likely
be no universal rationalization system. Each fishery will have its own needs, and
those needs can be uncovered through future research. Placing an ITQ system on
bycatch is one approach worthy of further consideration.
30
Table 1. Bycatch weight (in metric tons) in the global oceans by region (source: Alverson et al. 1994) Area Weight (mt) Northwest Pacific 9,131,752 Northeast Atlantic 3,671,346 West Central Pacific 2,776,726 Southeast Pacific 2,601,640 West Central Atlantic 1,600,897 West Indian Ocean 1,471,274 Northeast Pacific 924,783 Southwest Atlantic 802,884 East Indian Ocean 802,189 East Central Pacific 767,444 Northwest Atlantic 685,949 East Central Atlantic 594,232 Mediterranean and Black Sea 564,613 Southwest Pacific 293,394 Southeast Atlantic 277,730 Atlantic Antarctic 35,119 Indian Ocean Antarctic 10,018 Pacific Antarctic 109
Total 27,012,099
31
Table 2. Levels of observer coverage from different regions of the United States (source: National Marine Fisheries Service 2006). Observer Program Level of coverage
Alaska Marine Mammal Observer Program <5%
Offshore Pacific Whiting Fishery 100% Vessels > 125ft = 100%, 60-124ft North Pacific and Bering Sea Groundfish Trawl and Fixed = 30%, Gear Fishery Observer Program Vessels < 60ft = 0% West Coast Groundfish Observer Program Target 10%
California/Oregon Drift Gillnet Observer Program Approximately 23% Southeast Fishery Science Center (SEFSC) Shark Drift 100% Gillnet Observer Program SEFSC Pelagic Longline Observer Program Target 5%
Southeastern Shark Bottom Longline Observer Program 2-4%
Southeastern Shrimp Otter Trawl Fishery <<1%
Northwest Atlantic Sustainable Fisheries Support <1% in trawl fishery
New England and Mid-Atlantic Gillnet Fisheries 2-5%
Atlantic Sea Scallop Dredge Fishery - Georges Bank 25%
32
Set Total Allowable Catch and propose policies to improve the status of the stock
“Observer effect”
Status of Fishermen Fishery NMFS Regional the stock Observers Council
Approval required for Fishing Biased data management actions pressure
Figure 1. Policy feedback loop for bycatch policy in the United States. The black arrows signify each link in the chain of accountability, and the rounded blue arrows signify the impact of each group on the next.
33
Fishery 3 Fishery 2 Fishery 4
Current TAC for Fishery 1 Species 1
Institute policy
New TAC for Fishery 1 Bycatch TAC for Species 1
Figure 2. Proposed ITQ system for bycatch in all participating fisheries. Each fishery catches some portion of species 1 before the policy implementation. After the bycatch TAC is implemented, the fisheries that encounter species 1 will be closed once either the TAC or the bycatch TAC is caught.
34
Chapter Three
Designing Marine Protected Areas for Fishery Benefits:
Expectations, Evidence, and Rules of Thumb*
*A version of this was submitted with co-author Michael W. Beck to Environmental Conservation
35
Abstract
Marine reserve networks are designed and used globally to help manage fisheries and conserve biodiversity. Managers and stakeholders, from local communities to
fishers to conservationists, are struggling for basic principles that can inform the
design of individual and multiple reserves. While there are thousands of references
addressing marine protected areas (MPAs), few if any synthesize information on
some of the biological characteristics of the target species that are likely to affect
decisions about reserve design parameters. We address this shortcoming.
We focus most on reserve designs with potential fishery benefits in mind;
however, a great deal of the basic advice is relevant for the conservation of non- fished species as well. When considering the size of individual reserves, we
recommend placing more emphasis on the movement abilities and patterns of
juveniles and adults of target species and less on larval dispersal. When considering the distance between reserves (spacing), we recommend placing more emphasis on larval dispersal patterns. When considering how much total area to reserve and what habitats to represent, we recommend placing more emphasis on the broader consideration of the needs of multiple species rather than a few target species.
For all of these factors, we have also considered whether specific advice on exact levels to set the reserve parameters (i.e., how large, how many, how far apart) is
useful. At present it is not possible to provide specific advice on all the parameters, but we do find some general advice for several parameters. We recognize that local or regional ecological, political, and sociological characteristics will drive many 36
decisions, but we also know from experience that managers struggle with determining what biological factors to weigh most heavily in various phases of reserve design. We hope that our advice will help managers prioritize some of the information that must be considered for each phase in reserve design decisions and thus streamline some of the decision process.
Introduction
A significant amount of the world’s marine biodiversity is highly threatened
(Palumbi 2002, Beck 2003). Three main factors underlie most of the threats to marine diversity. First, burgeoning human populations along coasts and their requirements for housing, food, and income are causing harmful effects on nearshore, estuarine, and marine species and ecosystems. Second, even more distant human activities on land and around watersheds have significant and often overlooked effects on coastal and marine ecosystems. Third, we are becoming increasingly adept at exploiting and
destroying the resources of the seas, and it is abundantly clear that the resources of the seas are not limitless.
One of the most obvious direct exploitations is fishing. Fishing impacts include the direct harvest of targeted species, the incidental harvest of other species as
bycatch, and the disruption of habitats. Evidence suggests that recent and historical
overfishing have drastically altered ecosystems (Jackson 2001, Jackson et al. 2001).
Some of the most devastating impacts on marine habitat are the result of practices
such as bottom trawling and blast and cyanide fishing (e.g., Watling and Norse 1998).
37
Overfishing also significantly affects marine trophic structure. As fishermen target and deplete fish populations, it is increasingly common for fishermen to add or shift to new stocks (Pauly et al. 1998, Essington et al. 2006). Also, common practices in fishing such as size selectivity—targeting the largest individuals in a population— change the population size structure (Conover and Munch 2002). Initially the yield is high with all large individuals harvested, but as the fishery matures, the fish are smaller and less abundant. As a consequence the yields decline as well. Smaller individuals and therefore slower growth rates are selected for in populations subject to this kind of fishing.
Many of the worlds’ fisheries, particularly in developed nations, are highly
regulated. Nevertheless, production in most fisheries is in decline, both ecologically
and economically, and the prevalent perception is that the current regulations are not
working or are insufficient (Iudicello et al. 1999). Along with traditional fishery
management, such as identifying target fishing mortality, bycatch limits, gear regulations, and time/area closures, there is now a widespread demand to examine the use of marine protected areas (MPAs) as fishery management tools (NRC 2000,
Lubchenco et al. 2003). Substantial evidence suggests that reserves conserve biodiversity (Gerber et al. 2002, Halpern 2003). However, it is less clear that they are useful tools for fishery management (Mangel 2000c, Gardmark et al. 2006).
An MPA is generally defined as any area of the intertidal or subtidal terrain, together with its overlying water and associated flora, fauna, historical and cultural
features, that has been reserved by law or other effective means to protect part of or 38
the entire enclosed environment. A marine reserve is usually assumed to be a more
restrictive category of marine protected area and excludes some uses, often fishing
(Beck 2003). For the purposes of this paper, we focus our review on marine reserves
in which most or all harvest is prohibited.
Marine reserves have been an intense area of research for biodiversity
conservation as well as fisheries sustainability. However, there is an apparent dichotomy in the scientific literature that reserves are established for either biological
conservation or fishery sustainability (Gerber et al. 2002, Hastings and Botsford
2003, Lubchenco et al. 2003). In practice it is commonly hoped that reserves will
deliver both biodiversity and fishery benefits.
An anticipated benefit of reserves is increased fish production. Examples of different production goals are fishery recovery, rebuilding, sustainability, and enhancement. Although numerous papers have attempted to model the design of a reserve that will deliver fishery benefits(Guenette et al. 1998, Mangel 1998, 2000b,
Mangel 2000c, Botsford et al. 2003, Gerber et al. 2003), a synthesis of the results is lacking.
Managers and stakeholders are confronted with a variety of factors that seem
equally important to effective reserve design. Our goal is to provide synthetic advice
to fishery managers and conservationists on which factors to consider when designing
reserves with fishery benefits in mind. We review the evidence in the literature on the design and efficacy of reserves, and we examine which life history characteristics are most important at various points in the design process. We pay particular 39
attention to the following life history traits: larval dispersal, adult and juvenile movement, reproduction and density-dependent growth, movement, and mortality.
Population dynamics and habitat use of the fished species are also integral to the reserve design. We then weigh the evidence available in the literature for reserve effects given the design of the reserve. We examine several of the most critical factors of reserve design: size, spacing (for a network), shape (edge/area ratio), habitat, and species composition. We also assume that the goal of a fishery reserve is to maintain or increase the population of the fished species outside the reserve. Our synthesis provides advice on the design of reserves by considering which life history factors most strongly affect the individual reserve design parameters.
Life History Considerations
Larval Dispersal
One way marine reserves contribute to yield is through larval export, the net
transport of larvae from a reserve, contributing to the recruitment of outside stock.
Information on the abundance and movement of the larvae of the fished species is
integral to the design of a reserve. Beverton and Holt (1957) first mentioned the
problem of estimating fish dispersal in a marine reserve context. Since that time, good
estimates of dispersal have been elusive (Gaines et al. 2003, Gerber et al. 2003).
Gerber et al. (2003) review reserve modeling efforts, showing that: (1) 4 out of 34
studies include no dispersal information; (2) 23 studies model dispersal as a simple
diffusion process; and (3) only 7 studies contain explicit models of dispersal, rather
than using a diffusion model. They conclude that modeling dispersal explicitly 40
requires more data or expert knowledge of the way larvae move. Since there is so
much uncertainty around larval dispersal, modeling the movement as diffusion may
be a first step, but the assumptions of a diffusion model are rarely representative of
natural systems.
There are two main considerations about explicitly modeling dispersal discussed in the literature: how do larvae disperse, and how far do they disperse? To translate larval dispersal into larval export we must know whether movement is active or passive, whether the movement is diffusive or advective, and whether abiotic factors such as currents play a role in determining both method and distance of dispersal.
Gaines et al. (2003) simulate the population dynamics of a species with benthic
adults and larvae that are transported in the water column. They show that currents
cannot be ignored in reserve design. They contradict the majority of reserve design
models that consider larval dispersal as pure diffusion, arguing that currents can
create spatial structure in an otherwise homogeneous marine habitat. They compared
two approaches to effort control, optimizing allowable catch and reserving a fraction
of the species habitat. They show that uncertainty around optimal reserve fraction has
less impact on fishing yield than uncertainty about setting optimal catch limits.
Therefore, as current strength increases, multiple reserves will better accommodate
the dispersal of the species.
In their review of larval retention and accumulation, Warner et al. (2000) found
that many marine fishes have notably larger amounts of larval retention and
accumulation than is usually assumed in marine reserve models. If larvae are modeled 41
with diffusive dispersion, the movement would be random rather than clumped, and retention would be solely based on the rate of diffusion. Rather, with high local retention and larval accumulation, depending on the size of the reserve, larval export may be very low. Warner et al. (2000) suggest that when local retention and accumulation are high, designing marine reserves for fishery effects must be a spatially explicit process.
Botsford et al. (2001) explicitly model dispersal. They use the fraction of natural larval settlement (FNLS) as a threshold for the size of a reserve. FNLS is measured as
the effect of fragmenting larval habitat on the probability of completing the larval
stage. It is determined after the implementation of a reserve and depends on both
larval dispersal capabilities and the siting of the reserve. Botsford et al. (2001)
determine a minimum FNLS required for a sustainable population. The minimum is
determined per species, based on dispersal capabilities, and can be very large when
considering multiple species. They estimate that greater than 35% of the coastline
must be within the protected area to ensure sustainable populations for multiple
species. They also suggested that smaller reserves may select for species that have
smaller dispersal distances.
Acosta (2002) illustrates the importance of knowing larval dispersal distances. He models of the abundance of target species—Caribbean spiny lobsters and the queen conch—within a marine reserve. He used dispersal parameters estimated from the data to determine the population size. His models predict an increase in the abundance of the two target species; however, the results are based on the ability to 42
accurately estimate the dispersal parameter, which is quite difficult in practice.
Acosta also shows that there are drastic changes in population size when the reserve
is designed without the proper boundary conditions in mind. The boundary condition is the permeability of the perimeter of the reserve. If the boundary conditions are absorbing rather than reflecting, the larvae will likely leave the reserve if they reach the perimeter, resulting in a net loss within the reserve. The remaining individuals in the reserve may have to compensate for the loss of reproduction, depending on the size of the reserve. An example of an absorbing boundary is when the currents
outside of the reserve, or between the reserves for a network, facilitate larval
movement out of the reserve. A reflecting boundary condition would force larvae to
stay inside of the reserve, leading to local retention.
Lockwood et al. (2002) investigate the robustness of reserve design models to
variations in dispersal patterns. They model various dispersal patterns and distances
while monitoring the persistence of species in each reserve. For an isolated reserve,
irrespective of dispersal pattern, they show persistence occurs in reserves that are
about twice the average size of the dispersal distance.
From the previous modeling studies, we have tools to examine the type, distance and patterns of larval dispersal. An empirical study by Shanks et al. (2003) examined the dispersal potential of propagules of benthic invertebrates. They correlated the time spent in the plankton and the dispersal distance to reveal two common dispersal strategies: propagules either disperse <1km or >20km. Their conclusions provide some of the most concrete recommendations for reserve design with special 43
consideration to dispersal—along a coastline, a reserve should be 4-6 km in size
spaced 10-20 km apart.
However, Kinlan and Gaines (2003) consider the effects of extreme dispersal potential of marine organisms on reserve design. Through a comparison of the dispersal strategies of terrestrial and marine organisms, and analysis of genetic isolation-by-distance slopes, they highlight the variations found in the marine organisms. They argue that due to the extreme variation they observed among and between species, no single strategy for marine reserve design would likely be effective for multiple species.
Larval dispersal is an important factor in reserve design. Some of the most concrete evidence shows that larval dispersal leading to net export of larvae from a
reserve is the most important biological consideration when determining reserve
spacing and reserve size (Table 1). We will discuss the impact of larval dispersal on
reserve shape and location in later sections.
Adult and Juvenile Movement
Another way to affect the fishery for stocks outside a reserve is via spillover, the net movement of adults and/or juveniles out of the reserve. High levels of spillover are predicted to provide a boost in stock abundance and more potential reproduction for the stock outside the reserve. However, extremely high spillover will likely detract
from fishery benefits, as fish need to be protected for a long enough period of time to experience some growth and reproduction. In order to account for this in the design of a reserve, aspects of adult movement must be known. 44
If the stock is highly mobile, reserves, and even reserve networks, may fail because they will not be large enough to cover the species’ potential habitat (Gell and
Roberts 2003). A highly mobile species will not be in a reserve area long enough to be protected from fishing. However, there is empirical evidence of a positive reserve effect in sharks when their nursery areas are protected by a reserve (Heupel et al.
2005). Marine reserve design is often based on species’ territories, and with highly migratory species such as tuna and some elasmobranchs, their ranges may be very large fractions of the Pacific or Atlantic Ocean. Since fishery reserves are designed to
mitigate the effects of fishing mortality, protecting a very small portion of a species’
range is unlikely to compensate for the losses seen in the rest of their range (Mangel
1998, 2000b). If a breeding ground, spawning aggregation, or over-wintering area can
be identified, a reserve in that place may protect the species for a small portion of
their life. However, given their longevity, this time may not be adequate.
Consequently, reserve benefits for highly mobile species are unlikely, since an
extraordinarily large reserve is politically and economically unlikely. Conversely, an immobile or slightly mobile species benefits from a reserve; although density dependent effects may be seen for these species (see the following section).
For less mobile species such as reef fishes, there is evidence of reserve effects.
Rakitin and Kramer (1996) hypothesized that there would be a significant difference in abundance and size of fish inside and outside reserves between sedentary and
mobile species. They tested their hypothesis in the Barbados Marine Reserve (BMR) with a control in a non-reserve (NR) area. They found that the average size of fish 45
was larger in the reserve and that this effect decayed as they moved away from the
reserve. The relative abundance of the smaller fish of both motilities was not significantly different between reserve and non-reserve. However, the evidence for emigration from a reserve was inconclusive, and they concluded there was not a significant difference in spillover rates between sedentary and mobile species.
Chapman and Kramer (2000), in another study in Barbados, investigated the site
specificity of reef fishes. Through tagging and visual surveys they concluded that there is strong site specificity in reef fishes. Therefore the greatest spillover effect is expected in species with intermediate mobility that also exhibit density dependent competition for space. For instance, the jacks (a more mobile genus (Caranx spp.), were rarely observed again, while the species of intermediate mobility were recaptured at an intermediate rate. However, all movements observed were generally small and rarely crossed the natural home range created by sandy sections >20 m between sections of reef. In this instance, the habitat or predation risk between reefs was extremely important for spillover.
A number of other studies explore adult movement in relation to a marine reserve.
A study in the Mombasa Marine Park in Kenya (McClanahan and Mangi 2000)
shows significant adult movement in moderately vagile species in small reserves.
Roberts et al. (2001) describe an overall positive effect of marine reserves on adjacent
fisheries. From two separate reserves, one in St. Lucia, and one in Cape Canaveral,
FL, they find more large fish outside the reserves than before the reserves were
implemented. They contribute a large portion of the success of each reserve to the 46
strict enforcement of reserve boundaries and non-exploitative use. However, doubt has been cast on the their study because of non-replication in experimental design and
the lack of other management measures with which to compare their results (Hilborn
2002, Tupper 2002, Wickstrom 2002). Hilborn (2002) also doubts that the reserve
effect noted in Roberts et al. (2001) is due to the reproductive stock inside the
reserve.
Finally, some of the most compelling evidence for spillover potential is the
analysis of a long-standing reserve in the Philippines (Russ and Alcala 1996, Russ et
al. 2003, Abesamis and Russ 2005). These studies show a 40-fold increase in the
abundance of the target species within 200 m of the reserve boundary, with little increase farther away. Russ and colleagues argue that the catch per unit effort (CPUE) within 200 m of the reserve boundary is higher than all the other local fishing grounds, which is likely the reason they see only a very local increase in abundance of fish.
Adult and juvenile movement is one of the most important considerations of reserve design (Table 1). Reserve size is the most important reserve characteristic in determining how much spillover a reserve will provide, given the biology of the protected species. We will discuss the effect of adult and juvenile movement on spacing, shape and location in later sections.
Density Dependent Effects in Life History Parameters
It is important to consider whether strong density dependent effects will be seen
in target species, as they will likely affect movement, reproduction, growth, and 47
mortality in space and through time. A reserve may be most effective when the
density dependence is such that it aids spillover and export but does not impede
growth or minimal retention. Part of the concern over reserve design—sizing, spacing
and siting—comes from the risk of negative density dependence (too little retention
of adults or larvae) or an expectation of positive density dependence (rebuilding a
decimated stock) (Gardmark et al. 2006).
Siting may situate a reserve such that there are natural barriers to movement.
Ricketts (2001) showed that the matrix, or the landscape between fragments of
habitat, matters in a terrestrial environment. An example in the previous section
(Chapman and Kramer 2000) corroborates this idea in the marine setting. Chapman and Kramer (2000) showed that reef species rarely travel between reef habitats if the
intervening habitat is unsuitable. Bene and Tewfik (2003) also studied this problem with the Queen Conch in a fishery reserve near the Turks and Caicos islands. They documented a crowding effect, or a reduction in growth rate attributed to density of individuals to two factors: reduced fishing mortality and barriers to emigration.
Within the reserve, the adult abundance increased while the average adult size decreased. Natural barriers to emigration prevented spillover which might have alleviated the crowding affect. A marine reserve should be suited to the movement capabilities of the target species if spillover effects are desired.
Sanchez-Lizaso et al. (2000) reviewed density dependence in protected marine
populations. They synthesized the available information on resource limitation in
marine ecosystems, the corresponding density dependent or independent changes in 48
size, and evidence of emigration from reserves. They suggest that if reserves themselves are resource-limited, mobile species would leave the reserve in search of resources, leading to a spillover effect. There may also be density-independent effects in a depleted population if no evidence exists for crowding. Resource limitation may be a function of, or can be affected by, reserve size or siting, depending on the
resource. If a portion of a reserve network is resource-limited, enhancing spillover
effects, then the spacing of the individual reserves is a function of how far the adults can travel for resources.
Predation may be enhanced in a reserve if the reserve is designed to preserve larger fished species. In theory, too many predators will eventually decline when their prey disappear, after which the prey will become more abundant due to the
corresponding predator decline. The predators will then rebound and the cycle will
continue(Volterra 1928). Mangel and Levin (2005) studied the effects of marine reserves using a community ecology perspective. They followed the dynamics of a
simulated population of predator (lingcod, Ophiodon elongates) and prey (bocaccio,
Sebastes paucispinis) in three scenarios: offshore reserve, nearshore reserve, and the
cessation of all directed take of the predator. In the first five years, there was no
discernable difference between scenarios. However, after five years, the nearshore
reserve contained the smallest prey populations due to the recovery of predator
populations.
Graham et al. (2003) investigated predator-prey interactions in a reserve in the
Great Barrier Reef. Nine of the prey species of the predator were surveyed inside and 49
outside the reserve for abundance. Six of the nine prey species were significantly
more abundant outside the reserve, despite the similar habitat quality in both areas.
Their study shows that a fishery reserve can cause a decrease in prey biodiversity, which may lead to eventual predator decline.
Density dependence factors into many aspects of a species’ biology, hence density
dependent factors impact characteristics of marine reserve design. For instance, crowding effects in undersized reserves can cause a decreased growth rate in organisms it contains. If a reserve is designed to facilitate spillover, the area outside
the reserve must contain habitat that is conducive to movement. Placing a reserve in
a location with limited resources may cause spillover, but protecting sources with no
sinks may be a futile effort. Finally, protecting predators within a reserve may
exacerbate the predator-prey dynamics leading to a paucity of prey within the reserve
for periods followed by a severe decline of the predators.
Reproduction
Promoting the reproductive success of a species requires detailed knowledge
of their reproductive strategies and behaviors. Size at maturity and other adult
attributes also affect reproduction and recruitment (Trippel et al. 1997), but in this
section we cover the logistics and the act of reproduction. For instance, species with
internal fertilization may have density-dependent recruitment, depending on how
often they reproduce. Their reproductive success depends on the number of potential
mates in the reserve and how often they are encountered. Hilborn et al. (2004)
suggest that spatial management, such as that of marine reserves, protects broadcast 50
spawners more effectively than traditional management methods. Broadcast spawners need high local densities to breed successfully, and these congregations are usually
targeted by fishers (e.g., abalone species).
Other external fertilizers (e.g., groupers) form large spawning aggregations. A main goal of many reserves is to protect these spawning aggregations from intense
fishing pressure. If all or most a spawning group is fished, there will be essentially no
reproduction from that group, which may severely deplete local populations. Koenig
and others (2000) studied the spawning habitat of some commercially important
grouper species off the southeastern United States, and determined historical
population sizes were much larger than current population sizes. They recommend
marine fishery reserves in the area to increase and protect the rare spawning
aggregation sites.
Sex ratios within a reserve particularly affect recruitment. Many fish change sex
based on the population sex ratio or the number of large individuals present (Ross
1990). Fishing may cause highly disproportionate sex ratios in some populations, but marine reserves may function to protect and maintain sex ratios (Ward et al. 2001).
Maintaining gene flow and a diverse gene pool are also concerns for long term
marine reserves. Trexler and Travis (2000) show through quantitative genetic models that for species with planktonic larvae, which encompasses most commercially important fishes, there is sufficient genetic variation to potentially increase the age at
maturity. This means population changes that occur within the reserve will radiate through the non-reserve population as well, as long as the recruitment into the reserve 51
is not limited by density dependent mortality. Reserving areas where reproduction is
likely successful (i.e. a source population) will then confer positive genetic
consequences to the stock outside the reserve.
The evidence we review points toward one potential use of marine reserves to protect the reproductive success of a species: spawning aggregations. The location of a marine reserve can have a dramatic effect on the reproductive success of site- specific spawners (Table 1 and 2)
Reserve Design Characteristics
Important characteristics of a reserve are size, spacing (for a network), shape,
habitat representation, and species composition. In the following sections we identify
key life history characteristics as they relate to each design characteristic. We offer
predictions and suggestions on the design of marine reserves with fishery benefits in
mind followed by a review of any general agreements for each design characteristic.
In Table 1, we list the relative weights of each life history characteristic on each
design characteristic.
Size
How large, or small, should a reserve be? There is no general consensus to answer
this question. The National Resource Council (NRC 2000) suggests that anywhere from 8-80% of the species home range must be covered by a reserve in order to observe positive reserve effects based on studies from fisheries for temperate species.
They identify two goals relating to fisheries: risk management and yield maximization. For risk management, the examples they gathered come from 52
uncertainty in stock assessments, recruitment overfishing, cost-benefit analysis, and spatial models of abundance. For instance, Mangel (2000a) put forth a modeling framework that acknowledges irreducible uncertainties while estimating the fraction of habitat that must be reserved to maintain a fraction of the population. He argues that the decision to conserve a proportion of a population (e.g. 20% versus 40%) is a social one. However, once the decision is made, his modeling framework can be used
to calculate the size of a reserve in the face of uncertainties.
Mangel (1998) addressed the same question and derived an invariant for the
fraction of habitat to be allocated to a no-take marine reserve. The invariant is a function of the maximum per capita growth rate of the species, the maximum harvest fraction, the reserve fraction, and fishing mortality. Overall, the optimal size of reserve depends strongly on the adult and larval mobility of the species and the population growth rate.
There is a debate in the terrestrial literature about whether a single large reserve or several small reserves is the better plan for conservation (SLOSS). For fishery effects, it is unlikely we will need to protect several small endemic populations, which is one benefit of several small reserves on land. However, a single large marine reserve similarly carries the risk of catastrophe. Catastrophes are likely to occur in time and/or space (Mangel and Tier 1994), therefore the risks of a single large reserve must be considered. Moreover, invasive species and disease may degenerate reserve effects, such as increased biomass and improved recruitment, through time
(Simberloff 2000). Reserves can fail for many other reasons; everything from poor 53
design to spatial and temporal variability can contribute to a lack of reserve effects.
These reasons are of particular concern when managers consider permanent reserves,
since there is no possibility to modify a failing reserve. Serious doubt has been cast
on the feasibility and resilience of permanent reserves for such reasons (NFCC 2004).
Once a reserve is in place, fishing effort is displaced to outside the reserve.
Spillover is greatest at the borders of a reserve, therefore fishing is likely intense at the reserve border. A buffer zone may be needed for the sizing of marine reserves to mitigate the intense fishing pressure likely at the periphery of the reserve (Walters
2000). Fogarty (1999) argues that a reserve must be instituted with an equivalent reduction in fishing capacity in order to be effective. The fishing pressure will otherwise transfer to the remaining stock outside the reserve, increasing fishing mortality.
Designing a multispecies reserve is an issue of sizing, spacing, and species
composition. If a reserve manager considers the home ranges and habitat
requirements of many species the design becomes exponentially more difficult.
Figure 1 illustrates a situation in which the species of interest have a variety of home
ranges, and to cover a percentage of all would be to place a reserve on nearly half of
the total space. Such a large reserve may be both economically and politically
infeasible.
Overall, adult and juvenile movement is the most important factor to consider for the size of a reserve. Larval dispersal is the second most important characteristic.
Species range and larval dispersal patterns significantly affect the retention and 54
transport of animals across reserve boundaries (Rakitin and Kramer 1996, Russ and
Alcala 1996, Chapman and Kramer 2000, McClanahan and Mangi 2000, Botsford et al. 2001, Acosta 2002, Russ et al. 2003, Shanks et al. 2003, Abesamis and Russ
2005).
Spacing
Roberts et al. (2001) describe a small network of reserves created for artisanal fisheries in St. Lucia which produced results for adjacent fisheries in 5 years.
Successful recovery of some groundfish species on Georges Bank and Spiny lobster in New Zealand are other examples of reserve network success (Kelly et al. 2000,
Murawski et al. 2000, Ward et al. 2001). Kinlan and Gaines argue that multiple reserves are best suited to create sustainable populations of multiple species (2003).
Shanks et al.(2003) offer very specific conclusions: larvae disperse >20km or less
than 1 km (2003).
The distance between reserves in a network should be determined mainly by the
larval dispersal of the target species (Table 1) (Rakitin and Kramer 1996, Botsford et
al. 2001, Acosta 2002, Shanks et al. 2003). This reserve characteristic is also
influenced by adult and juvenile movement and multiple species considerations,
although to a lesser degree.
Shape
The shape of a reserve will affect adult and juvenile movement and larval
dispersal. For example, a small area/edge ratio may have higher spillover and larval
dispersal when all else is equal. However, the larger reserve edges require more 55
enforcement time. A design that creates the smallest perimeter to volume ratio
possible will have the maximum net effect on the fishery per unit area. Creating the largest perimeter possible maximizes the spillover and larval export per unit of area inside the reserve while minimizing the periphery where fishermen aggregate (Wilcox and Pomeroy 2003). In countries where enforcement is not technology-based (GPS, satellite, etc.) a large reserve is much easier to enforce than several small widely spaced areas. We discuss enforcement issues briefly later.
Habitat Representation
Protecting the habitat of a species is as important to persistence as lessening
fishing mortality rates. Mangel (2000c) argues that fishing mortality and loss of
spawning habitat may affect the fish population in similar ways. In both cases there is
a decline in the steady state population. However, there is a lag from the time habitat
is lost to the time when the decline in the steady state is apparent. He argues that
monitoring the habitats directly is necessary in order to gain more immediate
information about the effect on the stock. Monitoring will uncover trends in stock
response to habitat loss, which can then be compared to the stock response to fishing
mortality. He also suggests there may be an optimal combination of reserves on
spawning habitat and fishing grounds that creates the highest probability of sustaining
the population. A number of other scientists specifically endorse marine reserves as
effective tools for habitat protection (Fogarty 1999, Koenig et al. 2000, Lubchenco et
al. 2003).
56
A reserve containing a range of habitats is more likely to protect multiple species.
Also, adult and juvenile movement between reserves in a network is based on accommodating habitat between reserves (Chapman and Kramer 2000, Ricketts
2001).
Species Composition
Gerber et al. (2002) compared conservation goals (number of adults present now
vs. before reserve) and fishery goals (current yield outside reserve, given new area) in
a single species reserve design. The reserve effects were limited to adult density; a
significant increase in yield was not observed in their study. Furthermore, since the
reserve protected a large predatory species, the diversity of prey species declined
within the reserve.
Mangel (2000b) used deterministic and stochastic models to show changes in
population abundance as a result of a single reserve. For the single species version,
there are benefits, depending on conditions, but when multiple species—even just
two—are considered, the story changes. If rockfish nursery habitat is reserved, it also
creates a positive effect on their inshore predators (e.g. lingcod). When considering
multiple species, predator-prey interactions must be considered; it is difficult to do so
with multiple stages and predators, let alone multiple target species. Mangel and
Levin (2005) also found negative effects through time on prey populations when predators are also protected in a reserve. However, Horwood et al. (1998) analyzed a reserve for fishery effects and noted that benefits will likely extend to many non- target species. Relocated fishing effort on the same population, a portion of which is 57
protected by the reserve, will have no positive effect on the stock. However, is it
possible to account for all trophic interactions? Clearly, trophic interactions are
important and will have substantial effects on the efficacy of a reserve. These must be
accounted for as well as possible, but it will simply not be possible to account for
them all.
Other Considerations
Designing a successful marine reserve requires not only the best available science,
but also a solid awareness of the social climate in which the reserve will operate.
Creating a reserve takes political will and public support. Therefore, an erroneous claim of the benefits of the reserve will be detrimental to the social structure (politics and/or economy) that allowed the reserve placement in the first place (Hilborn et al.
2004). Coleman et al. (2004) argue that marine reserves do not reduce fishing effort and fishing effort is displaced in space or time. Compliance is crucial to an effective reserve, no matter what the design. Thus, enforcement feasibility is an integral component of effective reserve design. Fishing interests are able to adapt to management faster than regulators can react. Therefore, management is inherently flawed, and there may be reactions by fishing interests which may not have been predicted. However, gathering data on the industry’s reaction to past and present regulations may also be a valuable tool when designing a marine reserve.
Clear and measurable goals for the populations and habitat must be established and monitored, and adaptive management may be appropriate (e.g. Shea 1998,
Hilborn et al. 2004). Implementing permanent reserves may be a mistake because 58
adaptive management may be necessary to account for variability in ecology and socioeconomics. Fishermen and policymakers find permanent reserves very unappealing because of the loss of the opportunity, now or in the future, to change fishing practices (NFCC 2004).
Discussion
To design a marine reserve anticipating fishery benefits, we must carefully consider many factors, since an improperly designed reserve may cause more harm
than good (Crowder et al. 2000). Modeling can help to estimate how larvae disperse, adults move, and at what rate both will change due to density dependence when
empirical studies are rare. Since reserve effects are functions of both effective reserve
design and adequate enforcement, there is no substitute for empirical studies and
long-term reserve monitoring. It is imperative that empirical and theoretical considerations based on scientific analysis are taken into account before establishing a marine reserve.
In Table 1 we weigh the consideration of each life history characteristic on each
aspect of reserve design. For instance, when managers are concerned with the size of
individual reserves, we recommend placing most emphasis on the movement abilities
and patterns of juveniles and adults of target species and less on larval dispersal.
When considering the distance between reserves (spacing), we recommend placing
most emphasis on larval dispersal patterns and placing less emphasis on reproduction.
When considering how much total area to reserve and what habitats to represent, we
59
recommend placing most emphasis on the broader consideration of the needs of
multiple species rather than a few target species.
In Table 2 we list expected reserve effects in each life history category based on
our review of the literature. We find that most scientists model larval dispersal as a
diffusion through the water column in two dimensions. These models do not account
for currents or generally high levels of larval retention and accumulation. There may
be sufficient larval transport to compensate for a reserve, but as currents increase in
strength, multiple reserves will better accommodate the dispersal of the species. The
reserve boundary type, whether reflecting or absorbing, is important for both larval
export and spillover.
How and why juveniles and adults move across reserve boundaries is integral to
reserve design. The size of a fishery reserve should most depend on the expected
spillover level, although all aspects of reserve design are quite dependent on this factor. For instance, predation can act as a barrier to movement, whether it affects mortality or movement rates. Also, unsuitable habitat between reserve fragments of a network will greatly affect the movement rates. Fishery benefits of marine reserves are unlikely for highly mobile species, but there may be an affect on such species if their nursery grounds and potentially other essential habitat are protected. The greatest spillover effect is expected in species with intermediate mobility that occupy density dependent space, but significant movement in moderately vagile species was
found in relatively small reserves.
60
There is overwhelming evidence that reserves can facilitate the increases of size and density for organisms. These increases should then affect the growth, reproduction, and mortality of individuals within the reserve. Average adult size can be smaller in reserves with barriers to natural emigration, but the overwhelming evidence is for larger individuals and higher densities leading to export and higher reproductive potential. If a reserve is resource-limited, spillover may occur when adults leave in search of food. There may be a low level of trans-boundary movement if the population is small (usually a rebuilding stock), and it may take time to see net movement out of the reserve without density dependence.
Protecting spawning aggregations and habitat may be the most effective uses of
marine reserves. If spawning locations are known, marine reserves can protect the
stock while it replenishes and grows during certain times of the year. Likewise,
habitat that is protected from trawling or other destructive activities will be available to accommodate larger portions of the local ecosystem.
Conclusion
At present it is not possible to provide advice on exactly how to design a reserve,
but we have presented some general advice for several design characteristics. We recognize that local or regional ecological and sociological characteristics will drive many decisions, but we also know from experience that managers struggle with determining what biological factors to weigh most heavily in various phases of
reserve design. Our advice will help managers prioritize some of the information that
61
must be considered for each phase in reserve design decisions and thus streamline
some of the decision process.
Empirical studies of marine reserves are both costly and time-consuming.
However, in order to test the models used for larval dispersal, adult movement, and
density-dependent mechanisms, more data must be gathered. Large-scale marine
reserves have been proposed to supplement traditional fishery management (Lauck et al. 1998), but more empirical data must be collected in order to determine if there are consistent benefits of marine reserves to fisheries. Based on our synopsis, we think marine reserves have the potential to become a strategic tool for supplementing
fishery regulations.
62
Figure 1. A reserve designed for multispecies management requires a much larger area than a reserve for single species management. Each color represents a different habitat type in the Southern California Bight (Greene and Bizarro 2003, TerraLogic 2003). These habitat types are closely correlated with the habitats for different suites of rockfish species. It would be difficult to design a reserve that protected some of all of these habitats and associated species. An example of such an effort is the 100nm X 30nm rectangle.
63
Table 1. Rules of thumb: the relative importance of biological characteristics on design parameters for a fishery reserve. Species Characteristics Reserve Larval Adult Multiple Characteristics Reproduction dispersal movement Species
Reserve size Medium High Low Low
Spacing High Medium Medium Low
Shape Medium Medium Low Low
Total area Low Medium High Low
Habitat Low Med High Low representation Location1 Med Low Low High
1 Location is a site specific parameter meant to encompass considerations such as spawning grounds or nursery grounds specific to a species’ life history. 64
Table 2. A synopsis of the literature knowledge on the reserve effects in fishery reserves. Life History Expected Reserve Effects; what we know Characteristic Larval Dispersal & The uncertainty around what fraction of habitat to reserve has less negative effects on populations than the uncertainty around levels of fishing effort. & The habitat and abiotic conditions outside reserves cause changes in the productivity of a reserve. “Absorbing” reserve perimeters facilitate larval export, while “reflecting” perimeters prevent larval export. & There may be sufficient larval production to compensate for reserves up to 50% the size of the species’ range & There are two stable dispersal strategies: <1km or >20km. & An isolated reserve is recommended to be about twice the size of average dispersal distance of the species. & The stronger the currents, the better multiple reserves will perform. Adult and Juvenile & There is limited evidence that reserves will benefit highly Movement migratory adults. & Spillover in reef fishes depends on the habitat quality/type outside the reserve (or between reserves for a network). & The greatest reserve effect is expected in intermediately mobile species with depleted populations. & Spillover will likely be harvested by extreme fishing effort at the reserve periphery. & High levels of spillover are facilitated by strict enforcement of reserve boundaries. & “Absorbing” reserve perimeters can facilitate spillover, while “reflecting” perimeters are barriers to emigration. Density Dependence & The type of reserve perimeter (absorbing or reflecting) may lead to density dependence in growth and/or reproduction. & Resource limitation in a reserve may enhance spillover. Reproduction & Reserves are capable of protect spawning aggregations effectively. & Reserving known source populations will have a positive effect on the population(s) outside the reserve
65
Chapter Four
Bayesian Methods for Estimating Parameters of the von
Bertalanffy Growth Equation*
*A version of this paper was published in Environmental Biology of Fishes within a special edition on age and growth methods. My co-author is Bruno Sansó. 66
Abstract
The von Bertalanffy growth equation is commonly used in ecology and
fisheries management to model individual growth of an organism. Generally, a
nonlinear regression is used with length-at-age data to recover key life history
parameters: L! (asymptotic size), k (the growth coefficient), and t0 (a time used to
calculate size at age 0). However, age data are often unavailable for many species of
interest, which makes the regression impossible. To confront this problem, we
develop a Bayesian model to find L! using only length data. We use length-at-age data for female blue shark, Prionace glauca, to test our hypothesis. Preliminary comparisons of the model output and the results of a nonlinear regression using the von Bertalanffy growth equation show similar estimates of L!.
We also develop a full Bayesian model that fits the von Bertalanffy growth
equation to the same data used in the classical regression and the length-based
Bayesian model. Classical regression methods are highly sensitive to missing data points, and our analysis shows that fitting the von Bertalanffy growth equation in a
Bayesian framework is more robust. We investigate the assumptions made with the traditional curve fitting methods, and argue that either the full Bayesian or the length- based Bayesian models are preferable to classical nonlinear regressions. These methods clarify and address assumptions made in classical regressions using von
Bertalanffy growth and facilitate more detailed stock assessments of species for
which data are sparse.
67
Introduction
The von Bertalanffy growth equation (VBGE) can be used to describe the way
individual organisms grow (von Bertalanffy 1938, 1957). The form used by Beverton
and Holt (1959) is the following
#k"a#t0 ! L"a! % L$ "1# e ! (1)
where a is age, k is the growth coefficient, L$ is asymptotic size, and t0 is the theoretical time when size was zero. Generally, to obtain estimates of the parameters, the VBGE is fit to length-at-age data using classical nonlinear regression techniques
(Grafen and Hails 2002). This curve-fitting technique somewhat changes the assumptions of the VBGE: using a least squares estimate assumes an average maximum size for the population rather than a truly asymptotic size—often termed
Lmax in the literature rather than L$ . However, there is a physiological maximum size
a fish can attain. Bayesian methods presented in this paper allow for the use of the
VBGE while maintaining its biological assumptions.
Individual growth is the basis of many stock assessment models (Jennings et al. 2001). However, length-at-age data—required for parameter estimation—are not available or abundant for many populations, particularly for long-lived species.
Length data are easier to gather, and more available for fished species. We develop a
Bayesian model to estimate the maximum size using only length data.
68
We also present a full Bayesian model designed to fit the length-at-age data to
the VBGE. We include literature-derived priors in our analysis and compare our results from both Bayesian models to the results from a classical nonlinear regression.
Methods
In some cases, we have length-at-age data with a = 0,…, i indexing age and r indexing the number of length data per age. The number of data varies per age, and the following is a visualization of our data:
a %1 L ! L 1,1 1,r1 " " " (2) a % i L ! L i,1 i,ri
There are likely two sources of error in our data: process error and observation error
(Hilborn and Mangel 1997). We expect the process uncertainty to be the variability of vital rates such as growth and mortality within each age class. Observation error will manifest in the way each population is sampled; we expect to see variation in the selectivity of the gear (i.e. the distribution of sizes caught by the gear type).
However, for this paper, we include one multiplicative error term to represent all error.
For each of the following models, we used the same data set from the
literature to test the ideas (Acuña et al. 2001)2. The length-at-age data are for female blue shark, Prionace glauca, from the Eastern Tropical Pacific, representing ages 0-
14. We used only female shark data, since many shark species have different growth
2 See the reference for sampling and aging methods. 69
trajectories for each sex (Cortés 2000). We use the age data for the least squares
regression and the full Bayesian model, but not for the ageless model.
Least Squares Regression
Least squares regression is a common technique used to fit curves to data
(Grafen and Hails 2002). We used the VBGE (Eqn. 1) to calculate predicted length- at-age and then compared those values with the observed length data. The best fit parameters minimize the sum of the squared differences between predicted and observed lengths. For this analysis, we used the solver in Microsoft Excel to find the
best combination of parameters to minimize the sum of all squared error.
Full Bayesian Model
Our full Bayesian model fits the VBGE to the length-at-age data using
Markov Chain Monte Carlo (MCMC) methods (Hastings 1970, Gelman et al. 2004).
These methods require the following four steps:
1) Find the likelihood of the data,
2) Establish priors for all parameters,
3) Find the full conditional probabilities for parameters, when possible, and
4) Sample the posterior distribution for each parameter (Gelman et al. 2004).
We start with the VBGE, including multiplicative error
#k"a#t0 ! 'a L"a! % L$ "1# e !e (3)
and then find the log transform
70
#k"a#t0 ! la % l$ ( log"1# e ! ( 'a (4)
2 ' a ~ N "0,) ! (5) where the lower case l indicates the log of the value. Thus, our likelihood is the following:
2 L"lar l$ ,k,t0 ,) ! - 15 Ra 1 . 1 2 / (6) exp 0# lar # l$ ( log 1# exp #k "a # t0 ! 1 44 2 2 " " " * +!!! a%0 r%1 2,) 2 2) 3 where Ra is the number of length data for each age.
We construct informative priors for k and t0 based on published estimates of the same parameters in the literature for blue shark (Holden 1973, Cailliet et al. 1983,
Hoenig and Gruber 1990, Cortés 2000) :
p"k ! % Gamma"15,100! 3 (7)
p"#t0 ! % Gamma"14,4! (8)
We show the probability density functions (pdfs) of the priors for k and t0 in figures
2 one and two respectively. We used diffuse priors for l! and " , giving the full power of estimation to the data:
p"l$ ! -1 (9)
3 We used the following form of the gamma distribution: 6 5 Gamma"5, 6 ! # x5 #1e#x6 for x 7 0 8"5 ! 71
2 1 p") ! - 2 (10) )
Our prior for ) 2 is a Jeffreys prior (a form of non-informative prior, see Gelman et al. 2004). Marginalizing the joint posterior—the likelihood multiplied by the four priors—for each parameter gave two full conditionals4:
9 14 Ra : log 1# exp #k "a # t ! ; ?? " * 0 +! ) 2 < L ~ log normal ; l # a%0 r%1 , < (11) $ ; n n < ; < = >
9 n 14 Ra 9 2 :: ) 2 ~ Inverse # gamma ,2 l # l ( log 1# exp #k a # t (12) ; ??;" ar " $ " * " 0 !+!!! << = 2 a%0 r%1 = >> where l is the mean log length and Ra is the number of lengths for each age
(Appendix).
2 Since the conditional probabilities for l! and ) are known pdfs (Eqns. 9 and
10), we used a Gibbs sampler for these parameters in the MCMC. However, we had
to use a Metropolis step for k and t0 because we could not find their full conditional distributions. We used a random walk jumping distribution5 for both Metropolis steps.
4 For the functional forms of the lognormal or inverse-gamma distributions, see Gelman, A., J.B. Carlin, H.S. Stern & D.B. Rubin. 2004. Bayesian Data Analysis. Chapman and Hall, Boca Raton. 668 pp. 5 A random walk jumping distribution samples the probability space around the initial point following a normal distribution, with the initial point as the mean of the normal. The variance is subjectively changed at the start of each MCMC run to achieve a desirable acceptance rate, between 0.3 and 0.5. See (Hastings 1970) 72
Length-Based Bayesian Model
The full Bayesian model is not only computationally intensive but also requires length-at-age data. For cases where only length data are available—which is frequently the case in developing fisheries—we develop a method to estimate the maximum size for the stock using the available data. The new method employs the following Bayesian model.
Let *x1,!, xn + be individual lengths and
9 xi : ; < Y % log @ for x A @ (13) i ; x < i ;1# i < = @ >
2 where @ is our proxy for Lmax and we assume Yi ~N(#, " ). A plot of the transformed data was used to determine if the Yis were distributed normally (Figure 3). We used the logit transformation of the individual lengths divided by the maximum datum.
The parameter @ is our proxy to the maximum attainable size a fish in the population can achieve. Our key condition is that all data be less than@ .
Our likelihood is the following, based on the normal distribution of the Yis and the derivative of the transformation of the data:
. 2 / 9 : 9 9 xi : : n C n C ; n < 1 ; ; < < 1 2 1 2 C @ C9 : ; < L"B,) ,@ ! % exp 0 2 ;log; < # B < 1; 2 < (14) 2) ? x ) 4 x C i%1 ; ;1# i < < C= > ; i%1 9 i : < ; < ; xi ;1# < < 2C = = @ > > 3C = = @ > >
73
We include no information from the literature for the mean and variance parameters of the normal distribution in Equation 14 by assuming Jeffreys priors for both parameters
2 1 p "B,) ! - 2 (15) )
However, we used information from the literature for our prior for Lmax (!)
p"@ ! # Normal "310,80! (16) where 310 cm TL is the mean and 80 is the variance of the normal prior. From the full joint posterior, we found two full conditionals
9 9 xi : : ; ; < 2 < 2 1 @ ) p"B ) ,@,data! - Normal ; ; <, < (17) n ? x n ; i ;1# i < < = = @ > >
9 : ; < ; < ; < ; n 2 < p ) 2 B,@,data - Inverse # gamma; , < (18) " ! 2 2 ; 9 9 xi : : < ; n ; ; < < < ;log @ # B < ; ? ; x < < i%1 ; i < ; ; ;1# < < < = = = @ > > >
Again, since we have recognizable pdfs for # and "2, we used a Gibbs sampler for these parameters. We used the Metropolis Hastings algorithm with a random walk jumping distribution3 to find $ (Hastings 1970).
74
Results
Least Squares Method
The combination of parameters that minimized the sum of the squared error
was 252 cm, 0.13, and -3.09 for L$ , k , and t0 respectively (Table 1).
Full Bayesian Model
We used a burn-in period of 1000 samples and generated posteriors for the three parameters of the VBGE with the remaining samples. Our mean results are as
follows: 419 cm TL, 0.06, and -3.25 for L$ , k , and t0 respectively. We include 95% probability intervals for each estimate in Table 1.
Length-Based Bayesian Model
We initialized the model with a number slightly larger than the maximum data point. The chain converged quickly to an estimate of 308cm (Table 1). Using our
estimate for L$ in the least squares regression, we generated a value for k and t0 to use for comparison (0.08 and -4.13 respectively).
Convergence
We tested the convergence of our Bayesian models using both the Z-scores of the Geweke test, and by starting the runs at various initial values to see if the sample chains converge on the same number. Both tests were successful, showing convergence in the models6.
6 See (Gelman et al. 2004) For information on convergence diagnostics. 75
Discussion
First, we compare the least squares regression and the full Bayesian model
(Figure 4, 5, & Table 1). The estimates of t0 are very similar; however, the difference in assumptions is very obvious when comparing the estimates of L! and k.
The full Bayesian model estimates a much larger asymptote which leads to a smaller estimate for k7. To ensure the difference between the model estimates was not only due to that correlation, we checked the correlation between parameters and the influence of the priors on the estimates (Figure 6). The scatter plots have no structure in any of the other parameters, therefore we ruled out other correlations. We then examined the sensitivity of the full Bayesian model to the informative prior for k.
Recall the mean of the gamma prior for k was 0.15. Our full Bayesian model estimate is 0.06, which means that there was enough information in the data to overwhelm any influence of the prior on the estimate (Figure 7). In fact, when we used a non- informative prior for k, the posterior estimate was not significantly different. We also removed the ten largest data points and ran the full Bayesian model and classical regression again. The Bayesian model output did not change significantly, but the regression results changed drastically. Therefore, we are confident with our model estimates for the full Bayesian model.
dL 7 The VBGE comes from the following differential equation: % k "L # L! . When most of the dt $ dL data are small lengths, it becomes D kL if L $ L , exacerbating the correlation problem. dt $ $ 76
Next, we compare the least squares regression with the length-based Bayesian model. The estimates of these two models overlap significantly (Table 1). In fact, the mean of the length-based model is well within the confidence interval of the regression.
Finally, we compare the two Bayesian models (Table 1). The length-based model is essentially a compromise between the physiological basis of the VBGE and the availability of length-at-age data. It performs similarly to the least squares regression while maintaining the maximum size assumption (recall that the logit treats all data as a proportion relative to the maximum datum). However, we argue that the full Bayesian model is the most desirable model, if the data are available.
The maximum reported size of blue shark is 396 cm TL8 and our full Bayesian estimate is closer than the length-based model estimate. However, when length-at- age data are unavailable, this new method provides a sound estimate of asymptotic size. As data availability and sampling coverage improve, we expect the length-based model estimate to converge on the full Bayesian estimate.
Conclusion
Our full and length-based models are designed to solve two problems: estimate asymptotic size in the absence of length-at-age data, and maintain the biological assumptions of the VBGE when fitting the model to data.
8 Smith, S., D. Holts, D. Ramon, R. Rassmussen & C. Show. 2006. Shark Research-Blue shark (Prionace glauca), Southwest Fisheries Science Center, La Jolla, California, http://swfsc.nmfs.noaa.gov/frd/HMS/Large%20Pelagics/Sharks/species/blue.htm 77
The length-based method uses the distribution of the data to determine what the maximum size is for the population. In contrast, the least squares regression calculates an average maximum size across individuals in the population. The distinction is a subtle, but important one. That is, how should one think about asymptotic size? Is it an individual or population-level parameter? Data are gathered to assess population dynamics, and we offer our length-based and full Bayesian models to assess parameters on the population scale. Our methods are generally applicable to species for which we expect asymptotic growth, and they may be particularly useful for assessments of developing fisheries or of long-lived fishes.
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Table 1. A summary of the results from the three different models. All three parameters are estimated using the two models that use age data. Although our length-based model only estimates L!, it is possible to draw a von Bertalanffy growth curve using the inverse relationship between k and L!. Estimate of Model Estimate of k Estimate of t0 L! Least squares 252 cm 0.13 -3.09 [192, 312] estimation (VBGE) Full Bayesian model 419 cm 0.06 -3.25 (VBGE) [378, 457] [0.05, 0.07] [-3.23, -3.29] Length-based 308 cm 0.08 -4.13 [304, 312] Bayesian model
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Figure 1. The frequency of values for k, the Brody growth coefficient, given the prior probability density. Most of the density lies between 0.09 and 0.19.
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Figure 2. The frequency of values for t0 given the prior probabilities. Most of the density lies between -2 and -5.
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y t i s n e D
x i @
Figure 3. A histogram of the transformed data shows an approximate normal distribution.
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Figure 4. The full Bayesian model and the least squares regression are fit to the length-at-age data for the female blue shark. The Bayesian model assumes L! is a true asymptote.
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Figure 5. The posterior of L! for the full Bayesian model.
84
Figure 6. This plot illustrates the correlation between each of the estimated parameters. Each row and column is one parameter; in order from top to bottom we plotted k, L!, t0, and "2. For little or no correlation, we expect a structureless scatterplot. There is an apparent inverse correlation between k and L!.
85
Figure 7. The posterior of k for the full Bayesian model (dashed line) plotted against its prior (solid line).
86
Chapter Five
Estimating Natural Mortality in Fish Populations*
*A version of this paper has been submitted to Fishery Bulletin with co-author Bruno Sansó.
87
Introduction
Natural mortality is a very important, yet illusive life history parameter.
Errors in the estimation of natural mortality affect the outcome of various models used in stock assessments. Mertz and Myers (1997) show that an error in cohort reconstruction (cohort analysis) occurs when an inaccurate estimate of natural mortality is provided. Clark (1999) determined that an erroneous estimate of natural mortality creates bias in the estimates of stock size provided by an age-structured model. Williams and Shertzer (2003) state that policy based on mortality is particularly sensitive to the estimation of model parameters
Natural mortality (M) is a parameter in most fish stock assessment models.
For instance, the yield equation (Quinn and Deriso 1999) depends directly on M
#F #M 9 F : Y (a,t, F, M ) % "1# e ! N(a,t)W (a); < (19) = F ( M >
where a is for age, t is time, F is fishing mortality, and W(a) is mass at age a, and
N(a,t) is the number of individuals of age a at time t. I demonstrate in Figure 1 the difference in yield when fishing mortality is fixed and M is allowed to vary.
Natural mortality can occur through predation or non-predation events such as senescence and disease. The von Bertalanffy growth equation (VBGE) is widely used to give estimates of growth parameters, but methods for estimating M are far less uniform within the discipline. It is also a difficult life history trait to measure in the laboratory or the field. 88
It is generally accepted that natural mortality is very high during the larval stages and decreases as the age of the fish increases, approaching a steady rate
(Lorenzen 1996a, Jennings et al. 2001). The rate then increases exponentially when the fish nears maximum age. A graphical representation looks like a vertical section of a bathtub, and was described by Chen and Watanabe as a “Bathtub Curve” (Chen and Watanabe 1989). Natural mortality may also vary with size, sex, parasite load, density, food availability and predator numbers. However, in most cases, a single value—usually 0.2—for natural mortality is assumed for stock assessments, despite evidence to the contrary (Pope 1979, Quinn and Deriso 1999, Jennings et al. 2001).
Size-specific models of natural mortality are rarely used due to the difficulty of obtaining even a general estimate. It is recognized, however, that mortality is variable with age (Beverton and Holt 1957, Ricker 1975). There is a general consensus that mortality is higher in larval and juvenile stages, lowers at maturity, and increases again when the maximum age is approached (Vetter 1988).
When the same value of a parameter is used in almost all analyses, it may mean that there are no methods for obtaining a better estimate. There are, however, a variety of methods available for estimating natural mortality, and Vetter published a review of those methods (1988). Vetter reviewed catch-analysis methods, life history-based models, and predation models. Since her review, there have been a number of new models and model improvements.
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Here I review the methods available to estimate natural mortality since
Vetter’s review. I describe a simulation study that tests the performance of most of the models I review when the parameters are known. Finally, I illustrate, through a case study on California sheephead, Semicossyphus pulcher, how one determines when it is appropriate to use a constant value for natural mortality in a stock assessment.
Review of Methods to Estimate M
Life History Methods
Life history-based methods for estimating natural mortality describe relationships between M and traits like age, growth rate, and mass. Table 1 illustrates the methods that Vetter (1988) reviewed.
Building on Gunderson (1980), Gunderson and Dygert (1988) relate reproductive effort to mortality rate:
M % 0.03(1.68GSI (20) where GSI is the gonado-somatic-index, a ratio of gonad mass to total body mass. A high value indicates a large investment in reproduction. (still need the paper for a few more details)
Chen and Watanabe (1989) provide the first age-dependent model of natural mortality:
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k M "t! % for t A tm 1# e-k"t-t0 ! " ! (21) k 2 M "t! % ( a1 "t # tm ! ( a2 "t # tm ! for t 7 tm a0
#k"tm #t0 ! a0 %1# e (22)
#k"tm #t0 ! a 1% ke (23)
# k"t #t ! 2e" m 0 ! a2 % #0.5k (24)
9 1 : kt0 tm % #;
where M "t! is natural mortality at age t, tm is the age at maturity, t0 is the theoretical age when size is zero from the von Bertalanffy growth equation, and k is the von
Bertalanffy growth coefficient. This equation may be applied to data for which the von Bertalanffy growth parameters are known. Chen and Watanabe’s results show strong coherence to results obtained using past methods, and they therefore deem their equations as “suitable for fish population dynamics”. However, if the fish lives very long after the age at maturity, Chen and Watanabe’s methods starts declining with very old age classes.
Hoenig’s method is commonly used in fishery biology (Hoenig 1983,
Jennings et al. 2001, Hewitt and Hoenig 2005)
3 M D (26) tmax 91 if approximately 5% of the population is still alive at the maximum age.
Hewitt and Hoenig (2005) expand on the earlier version with a larger data set. The new empirically derived method is the following
4.22 M D (27) tmax if approximately 1.5% of the population is still alive at the maximum age.
Jensen (1996) revisits the Beverton and Holt invariants
M Mt and (28) m k and relates them to constant values calculated by regressions across species of lake trout. His results are the following:
1.65 M % (29) xm
M %1.5 (30) k
He reasons that since the Beverton Holt invariants were derived independently from any growth model, these relations are applicable across fish regardless of their growth function. However, since the parameter k is the von Bertalanffy growth coefficient, there must be sufficient data to estimate k in order for one to use Jensen’s equations.
Therefore Jensen’s models are very specific and require age and growth data.
Richter and Efanov (1977) used data from temperate stocks to relate natural mortality to the age at which 50% of the stock is mature 92
9 : ; 1.52 < M % 0.72 # 0.16 (31) ; < = tmass >
where tmass is the age in years when 50% of the stock is mature.
There is empirical evidence in fish populations that natural mortality is closely related to individual body mass (Post and Evans 1989, Lorenzen 1996a, b, 2000).
McGurk expands on the Peterson-Wroblewski model in his 1986 paper:
M "W ! % 0.00526W #0.25 (32) where M "W ! is natural mortality at dry body mass, W. He believed an issue with previous models was the assumption that predation occurs everywhere randomly. As a result he included a measure of spatial patchiness using Lloyd’s index (1967). He uses data from pelagic eggs and larvae to test his model output against the Peterson-
Wroblewski estimates of M. His results show that the Peterson-Wroblewski model fits data for average-sized to large animals, but constantly underestimates the mortality of the eggs and larvae of the same animals. However, his model represents eggs and larvae with relatively low mortality very well. He attributes the poorer fit to eggs and larvae with higher mortality to real variation in time and space of patchiness and mortality.
Lorenzen (1996a, 1996b) also models natural mortality as a power function of mass:
93
b M "W ! % MuW (33)
where M "W ! is natural mortality at mass W in grams, M u is mortality at unit mass, and b is the scaling factor. Natural mortality is measured as an annual rate. Lorenzen compared results for fish in natural ecosystems and in aquaculture ponds. He found a higher mortality at unit mass for fish in natural ecosystems than for those in aquaculture ponds, even though they were held in the same latitudinal zone.
Growth Coefficient
Since many of the life history models depend on the parameters of the von
Bertalanffy growth equation (VBGE), I review some methods for estimating its parameters. Two commonly used methods for estimating k are ELEFAN and
MULTIFAN. ELEFAN (Pauly and David 1981) is a computer-based method developed to analyze size-frequency distributions. The program “traces” the average of five age classes using the VBGE. ELEFAN is still used by the FAO to assess stocks in developing countries. MULTIFAN is a maximum likelihood method that assumes von Bertalanffy growth and normal distributions for mean lengths at age
(Fournier et al. 1990, 1991). MULTIFAN can be used on multiple size-frequency data sets and is typically used to assess tuna stocks in the Eastern Tropical
Pacific(Hampton 1997, Hampton 2000, Goodyear 2002).
Chapter Four in this thesis describes two Bayesian methods for estimating all parameters of the VBGE.
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Predation Methods
These methods were developed to take into account the species interactions between predator and prey and translate that interaction to a mortality rate for the stock species. Multispecies virtual population analysis (MSVPA) was initiated by both Pope (1979) and Helgason & Gislason (1979). Vetter (1988) provides earlier references and a discussion of the application of MSVPA, and Magnusson (1995) provides a review.
Catch-Analysis Methods
Pine et al. (2003) published a review of tagging methods for estimating components of natural mortality. Here, I review the key papers Pine et al. (2003) omitted.
The Tag-attrition model (Kleiber et al. 1987; Hampton 1997) is a size aggregated capture-recapture model. Hampton (2000) builds upon the Tag-attrition model to estimate mortality in tropical tunas. In Hampton’s model, the tagging data were classified based on the size at release. A VBGE was used to calculate growth while the tagged fish was at liberty. Then, using maximum likelihood, natural and fishing mortality are estimated. Hampton (2000) found that natural mortality increased at the latest age classes.
Brooks et al. (1998) suggest generalizations of tagging models that produce estimates for natural mortality when both recreational and commercial fishing is present. Their method allows for the inclusion of data from fisheries that have been open for any length of time; normally, fishing is considered pulse or continuous. 95
Brooks et al.’s (1998) method had good precision and will likely perform well in contentious situations with multiple user groups.
Beyer et al. (1999) present a size-specific method that assumes an inverse relationship between mortality and body size and a mortality that is approaching a minimum as fish grow to their maximum size. If there is no evidence that the species senesce or avoid fishing gear at older ages, this model will likely perform well.
Simulation Study
The number of models to estimate natural mortality is quite large; however, the data that are available to use for the stock assessment will certainly limit the choice. In order to test the performance of many of the models I reviewed, I simulated a population with known parameters.
I used literature values for life history parameters of the blue shark, Prionace glauca, from the Apostolaki et al. paper (2005). Individuals grow according to the von Bertalanffy growth equation
#k"a#t0 ! L"a! % L$ "1# e ! ( ' a (34)
where L$ is asymptotic size, k is the individual growth rate, a is an index of age, t0 is
used through out to calculate size at birth, and 'a is a random normal error with mean
0 and variance 5. Mass scales with length allometrically:
W "a! % 8.04*10#7 L"a!3.2319 (35)
96 where W "a!is kilograms at age a in kilograms. Since blue sharks are livebearers, fecundity is in calculated in pup units
E(a) % #91.97 ( 0.6052W "a! (36) where E"a! is the number of pups each mother of age a produces. The previous equation does not account for whether the mother is mature, so I included a function that describes the probability that an individual of age a is mature:
1 pm "a! % (37) 1( e#c"a# A50 !
where A50 is the age when 50% of the population is mature (5 years) and c is a shape parameter.
The stock-recruitment relationship follows a Beverton-Holt relationship
5E "t ! R "t ! % (38) 1 ( 6 E "t ! where R"t! is recruits in time t, 5 and 6 are Beverton-Holt parameters, and E"t! is the number of pups in time t. Natural mortality is included in three forms: independent, size dependent, and age dependent. Each age class survives according to the following:
9 m2 : #; #m1 ( (m3U "a!< N "a (1,t (1! % N "a,t!e = L"a! > (39)
where N "a,t! is the number of individuals of age a at time t, m1 is the size and age- 97
independent mortality rate, m2 is the size-based mortality rate, m3 is the age-based component, and U "a! is the function describing the bathtub curve U a % c Ge"#Fd "a#d !! ( e"Fg"a#g !! H (40) " ! I J where c is a scaling factor, d is the approximate age when constant mid-life mortality begins, and g is the approximate age when constant mid-life mortality ends. In our case, d % 3and g %15 .
I simulate through 100 time steps 1000 times, which gives us an array of the stochastic population sizes through time and simulation runs. I allow the population to reach a stable age and size distribution (Figures 2 and 3) and I have 100 matrices for length, mass, and proportion mature at age (one example is given in Figure 4).
Application of the models to our simulated data
For our population simulation I used a combined mortality of 0.2, without considering the age-based mortality (only components m1 and m2 of Equation 21).
Once the age-based component is included, the true mortality at age looks like the bathtub curve described earlier {See Figure 4, \Chen, 1989 #144}. I list the results in
Table 2. The constant methods provide an average fit across the lifespan of our simulated fish. However, a constant mortality estimate may lead to overestimates of yield for some age classes and underestimates for others. McGurk’s method fits very well until the oldest age classes, and the Chen and Watanabe method fits quite well throughout (Table 2). The constant values derived from the life history methods 98 average across periods of very high mortality (early and late life). Thus, the McGurk method and the Chen and Watanabe method are far superior at estimating the true natural mortality. The difference between the two is whether the fish senesce. Also, the Chen and Watanabe method will fail if the fish lives many years past maturity.
When is a Constant Mortality Appropriate? An Application to California sheephead
Calculating key life history parameters for long-lived fishes is often difficult.
There are rarely sufficient length-at-age or catch-at-age data to derive the parameters directly; in these cases one cannot depend on established growth models or methods for estimating natural mortality that require age data.
A prime example of this dilemma is the recent stock assessment of California sheephead, Semicossyphus pulcher (Alonzo et al. 2004). In the following section, I compare estimates of natural mortality for California sheephead using data from the commercial fishery compiled during the sheephead assessment.
I used the following length-mass relationship that was used throughout the sheephead assessment:
W % 2.6935K10#5 "FL2.857 ! (41) where W is mass in kilograms and FL is fork length in centimeters. I used total length data for the estimate of asymptotic size, therefore I needed to convert to fork length to use Equation (41) for our estimates (Alonzo et al. 2004).
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Given W, the Peterson and Wroblewski (1984) equation relating mortality to mass is
M "W ! %1.29year #1W #0.25 (42)
where MW is natural mortality at mass W.
Lorenzen (1996a) models natural mortality as a power function of mass in natural ecosystems
#1 #0.288 MW % 3.00year W . (43)
The coefficient in Equation 43 is a joint estimate of fish in natural ecosystems based on Lorenzen’s empirical work (Lorenzen 1996a). Jensen (1996) derived two models
to estimate M (Equations 29 and 30) I used k = 0.0683 and xm = 4-6 years for our analysis, which is consistent with Alonzo et al. (2004). The estimates of M using each of the models discussed are summarized in Table 3.
Since California sheephead are long-lived fish (tmax = 50 years), calculating an average natural mortality across a population is also appropriate (Beverton and Holt
1959). Assuming individuals follow von Bertalanffy growth I can find mass at age using Equation (41). I can then relate this to the population using the following equations:
N "t! % N "0!e #M "tr !t (44)
100
1 T #1 M "tr ! % ? M "W "t!! (45) T t%tr
where N(t) is the population size at time t, M "tr ! is the estimate of average mortality when fish are recruited to the model at age tr , T is the endpoint (50 in this case), and
M "W "t!! is a mass-dependent mortality model (either Lorenzen’s or Peterson and
Wroblewski’s). Simulating this population through 50 years, I use the population size at T = 50 and compare it to the population size at t = 1 using Equation (42) and
Equation (42). Running the simulations twice, once for Lorenzen’s equation and once for Peterson and Wroblewski’s, I arrive at estimates of average natural mortality. In Figure 6 I show the population size as a function of time for both mortality models. Using Lorenzen’s model for mortality, I calculated an average natural mortality rate of 0.54. Using Peterson and Wroblewski’s mortality model, I calculated 0.60 as the average natural mortality rate.
This example shows that the age at which the fish recruit to the fishery can have a large impact on the estimate of a constant M. Assuming a mass-based mortality in fishes, Figure 6 shows that there is severe mortality in the first few years.
Average natural mortality will change drastically—likely an order of magnitude or more—if those first few years are excluded from the calculation. In Figure 7, I plot
M "tr ! as a function of the age the fish recruit to the model; after age two, the estimates of M become more stable for California sheephead. Alonzo et al. (2004) 101
used an estimate of 0.2. As shown in Figure 6, our analysis supports their findings if the Peterson and Wroblewski mortality model is assumed.
Future Work
From our population simulation, I calculated mean mass at age and mean population sizes at age. For a future area of research, I propose using a distribution- based approach to estimating M. I suggest using Bayesian statistics to find a posterior distribution for M given a model choice and then simulate stochastic population by drawing from the distribution for M. Bayesian Model Averaging is an approach that would allow all or part of the relevant models to be applied. More attention should be paid to estimating M, given it is a foundational parameter in stock assessment.
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The Effect of Natural Mortality on Yield
0.3 120 0.4 0.5 100 0.6 0.7 80 0.8 2 . 0
0.9 =
F 1
t 60 a
1.1 d l
e 1.2 i Y 40 1.3 1.4 20 1.5 1.6 1.7 0 1.8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1.9 Age 2 Figure 1. This graph illustrates the difference mortality can make on setting yield.
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Figure 2. The age distribution of blue shark in the simulated population.
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Figure 3. The distribution of biomass at age in the simulated population.
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Figure 4. The length at age, mass at age, fecundity at mass, and proportion mature at age relationships in the simulated population.
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True Mortality
1.8 1.6
e t
a 1.4
r y t 1.2 i l a
t
r 1 o
m 0.8 l a r 0.6 u t
a n 0.4 0.2 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Age
Figure 5. The true mean mortality at each age in the simulated population.
107
100
95 Peterson and Wroblewski 90 Lorenzen
85 e
z 80 i S n o i 75 t a l u p o 70 P
65
60
55
50 0 5 10 15 20 25 30 35 40 45 50 Time
Figure 6. Population Size as a function of time for both mortality models.
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0.7 Peterson and Wroblewski 0.6 Lorenzen
0.5
0.4
M "t ! r 0.3
0.2
0.1
0 1 2 3 4 5 6 7 8 9 10 Age "recruited" to the model
Figure 7. Comparing average mortality estimates, both with different ages of recruitment to the model, and different mortality models. When fish recruit to the model at age two, I see a dramatic change in the average mortality estimate—approximately 0.2 and 0.1 compared to 0.6 and 0.54 when the fish immediately recruit to the model.
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Table 1. Life history traits related to natural mortality rate as published in the literature. Traits Species Source t , k , L , metabolic rate, max $ various (Beverton and Holt 1959) reproduction Clupeids, t , k , L (Beverton 1963) max $ Engraulids
W$ general (Ursin 1967) (Alverson and Carney t , k general max 1975) growth rate larval fish (Ware 1975) L , gonad size, condition $ Gadoids (Jones and Johnston 1977) factor
tmax general (Blinov 1977)
GSI, ASM, tmax , L$ general (Gunderson 1980) W , k , L , water $ $ 175 stocks (Pauly 1980) temperature energy cost of reproduction general (Myers and Doyle 1983)
tmax various (Hoenig 1983) (Peterson and Wroblewski mass various 1984)
k , L$ various (Roff 1986)
110 Table 2. The results of applying eight mortality models to simulated data. Constant Mass-based Age-based Rickter True Peterson and Chen and Age Mass Hoenig's Jensen and Lorenzen McGurk Mortality Wroblewski Watanabe Efanov
1 1.90 1.68 0.16 0.25 0.41 0.43 M = 0.33 2 4.23 M=0.28 M = 0.32 0.13 0.20 0.31 0.34 0.74 and
3 7.47 0.40 M = 0.195 0.12 0.17 0.25 0.28
4 11.48 0.10 0.15 0.21 0.25 0.27
5 16.04 0.23 0.10 0.13 0.19 0.22
6 20.96 0.21 0.09 0.12 0.17 0.20
7 26.07 0.08 0.12 0.16 0.19 0.20
8 31.22 0.20 0.08 0.11 0.15 0.18
9 36.28 0.20 0.08 0.11 0.14 0.17
10 41.17 0.20 0.08 0.10 0.13 0.17
11 45.83 0.20 0.07 0.10 0.13 0.18
12 50.20 0.20 0.07 0.10 0.12 0.20
13 54.27 0.21 0.07 0.09 0.12 0.22
14 58.03 0.24 0.07 0.09 0.12 0.24
15 61.48 0.40 0.07 0.09 0.11 0.25
16 64.62 1.10 0.07 0.09 0.11 0.26
111
Table 3. A summary of the estimates of natural mortality for California sheephead. The last two rows of the last two columns contain estimates for M with respect to a range of body mass: 5.84 kg to 0.15 kg respectively. Model Parameters Estimates of M M %1.5 k = 0.0683 0.1025 Jensen k (1996) 1.65 M % xm = 4 to 6 years 0.4125 to 0.275 xm
0.22 for 5.84kg Peterson and #1 #0.25 M %1.29year W to Wroblewski 1984 W W 2.6935 10#5 FL2.857 % K " ! 0.55 for 0.15kg
0.24 for 5.84kg Lorenzen (1996a, #1 #0.288 M % 3.00year W to 2000) W W % 2.6935K10#5 FL2.857 " ! 0.71 for 0.15kg
112
Appendix
The Full Bayesian Model:
In our computations, we replaced t0 with q because it is easier to work with a strictly positive distribution. At the end of the model runs, we take the negative
results for q and set them equal to t0 .
Our joint posterior is the combination of the four priors—for k , q , L$ , and ) 2 —and the likelihood:
2 1 13 #85 p"l$ ,k,q,) lar ! - 2 q exp*#4q+k exp*#k "100!+ )
15 R 1 . 1 / K exp 0# lar # l$ ( log 1# exp #k "a ( q! 1 44 2 2 " " " * +!!! a%0 r%1 2,) 2 2) 3
Marginalizing, or multiplying out each of the parameters one at a time, give us
either a formula to use in a Metropolis Hastings algorithm or a full conditional
to use with a Gibbs sampler as detailed in the main text.
113
Works Cited
Abesamis, R. A., and G. R. Russ. 2005. Density-dependent spillover from a marine reserve: long-term evidence. Ecological Applications 15:1798- 1812.
Acosta, C. A. 2002. Spatially explicit dispersal dynamics and equilibrium population sizes in marine harvest refuges. ICES Journal of Marine Science 59:458-468.
Acuña, E., L. Cid, E. Pérez, I. Kong, M. Araya, J. Lamilla, and J. Peñailillo. 2001. Estudio biológico de tiburones (marrajo dentudo, azulejo y tiburón sardinero) en la zona norte y central de chile. FIP Nº 2000-23, Subsecretaría de Pesca.
Alonzo, S., M. Key, T. Ish, and A. MacCall. 2004. Status of California sheephead (Semicossyphus pulcher) stock (2004).
Alverson, D. L., and M. J. Carney. 1975. A graphic review of the growth and decay of population cohorts. J. Cons. int. Explor. Mer 36:133-143.
Alverson, D. L., M. H. Freeberg, S. A. Murawski, and J. G. Pope. 1994. A global assessment of fisheries bycatch and discards, FAO Fisheries Technical Paper 339. Food and Agriculture Organization of the United Nations, Rome.
Andrews, R. N. L. 1999. Managing the Environment, Managing Ourselves. Yale University Press, New Haven.
Apostolaki, P., E. Cortés, E. A. Babcock, E. N. Brooks, and L. Beerkircher. 2005. Use of an age-structured model for the stock assessment of blue shark in the north atlantic. Col. Vol. Sci. Pap. ICCAT 58:1001-1018.
Atran, S. 1998. Reef fish advisory panel and SSC to review Gag and Vermilion Snapper assessments; SSC to also review finfish MSY alternatives and 114
shrimp trawl BRD analysis. in http://www.gulfcouncil.org/prrel/pr1998- 20.htm.
Babcock, E. A., E. K. Pikitch, and C. G. Hudson. 2003. How much observer coverage is enough to adequately estimate bycatch. Oceana, Washington, DC.
Beck, M. W. 2003. The sea around: marine regional planning. in C. R. Groves, editor. Drafting a conservation blueprint:a practitioners' guide to planning for biodiversity. Island Press.
Bene, C., and A. Tewfik. 2003. Biological Evaluation of Marine Protected Area: Evidence of Crowding Effect on a Protected Population of Queen Conch in the Caribbean. Marine Ecology 24:45-58.
Beverton, R. J. H. 1963. Maturation, growth, and mortality of clupeid and engraulid stocks in relation to fishing. Rapports et Proces-Verbaux des Reunions du Conseil International pour l'Exploration de la Mer 154:44- 67.
Beverton, R. J. H., and S. J. Holt. 1957. On the dynamics of exploited fish populations. The Blackburn Press, New Jersey.
Beverton, R. J. H., and S. J. Holt. 1959. A review of the lifespans and mortality rates of fish in nature and the relation to growth and other physiological characteristics. V, Ciba Foundation colloquia in ageing; the lifespan of animals, Churchill, London.
Beyer, J. E., C. H. Kirchner, and J. A. Holtzhausen. 1999. A method to determine size-specific natural mortality applied to westcoast steenbras (Lithognathus aureti) in Namibia. Fisheries Research 41:133-153.
Blinov, V. V. 1977. The connection between natural mortality and reproduction of food fishes and modeling of the processes involved. J. Ichthyol. 16:1033-1036.
115
Botsford, L. W., A. Hastings, and S. D. Gaines. 2001. Dependence of sustainability on the configuration of marine reserves and larval dispersal distance. Ecology Letters 4:144-150.
Botsford, L. W., F. Micheli, and A. Hastings. 2003. Principles for the design of marine reserves. Ecological Applications 13:S25-S31.
Broadhurst, M. K. 2000. Modifications to reduce bycatch in prawn trawls: a review and framework for development. Reviews in Fish Biology and Fisheries 10:27-60.
Broadhurst, M. K., D. J. Young, and R. Damiano. 2004. Effects of Nordmore- grid angles, profiles and other industry-developed modifications on catches in an Australian penaeid-trawl fishery. Ciencias Marinas 30:155- 168.
Brooks, E. N., K. H. Pollock, J. M. Hoenig, and W. S. Hearn. 1998. Estimation of fishing and natural mortality from tagging studies on fisheries with two user groups. Canadian Journal Fish. Aquat. Sci. 55:2001-2010.
Cailliet, G. M., L. K. Martin, J. T. Harvey, D. I. Kusher, and B. A. Welden. 1983. Preliminary studies on the age and growth of blue, Prionace glauca, common thresher, Alopias vulpinus, and shortfin mako, Isurus oxyrinchus, sharks from California waters. Pages 179-188 in E. D. Prince and L. M. Pulos, editors. Proceedings of the international workshop on age determination of oceanic pelagic fishes: Tunas, billfishes, and sharks. NOAA Tech. Rept. NMFS 8.
Campbell, S. 2004. North Pacific Groundfish Fishery Observer. in, Dutch Harbor, AK.
Campbell, S. 2005. email. Pages discussion with author about observer relations with NMFS in.
116
Cartamil, D. P., and C. G. Lowe. 2004. Diel movement patterns of ocean sunfish Mola mola off southern California. Marine Ecology - Progress Series 266:245-253.
Castro, K., T. Corey, J. T. DeAlteris, and C. Gagnon. 1996. Proceedings of the East Coast Bycatch Conference. Pages 159 in. Sea Grant Program, Newport, RI.
Chapman, M. R., and D. L. Kramer. 2000. Movements of fishes within and among fringing coral reefs in Barbados. Environmental Biology of Fishes 57:11-24.
Chen, S., and S. Watanabe. 1989. Age Dependence of Natural Mortality Coefficient in Fish Population Dynamics. Nippon Suisan Gakkaishi 55:205-208.
Chuenpagdee, R., L. Morgan, S. Maxwell, E. Norse, and D. Pauly. 2003. Shifting gears: assessing collateral impacts of fishing methods in US waters. Frontiers in Ecology and the Environment 1:517-524.
Clark, W. J. 1999. Effects of an erroneous natural mortality rate on a simple age-structured stock assessment. Canadian Journal of Fisheries and Aquatic Sciences 56:1721-1731.
Coase, R. 1960. The Problem of Social Cost. J. Law & Econ. 3:1-23.
Cochrane, K., C. Augustyn, A. Cockcroft, J. David, M. Griffiths, J. Groeneveld, M. Lipinski, M. Smale, C. Smith, and R. Tarr. 2004. An ecosystem approach to fisheries in the southern Benguela context. African Journal of Marine Science 26:9-35.
Coelho, R., L. Bentes, J. Goncalves, P. Lino, J. Ribeiro, and K. Erzini. 2003. Reduction of elasmobranch by-catch in the hake semipelagic near- bottom longline fishery in the Algarve (Southern Portugal). Fisheries Science 69:293-299.
117
Coleman, F. C., P. B. Baker, and C. C. Koenig. 2004. A review of Gulf of Mexico Marine Protected Areas: successes, failures, and lessons learned. Fisheries 29:10-21.
Conover, D. O., and S. B. Munch. 2002. Sustaining Fisheries Yields Over Evolutionary Time Scales. Science 297:94-96.
Conrad, J. M. 1999. Resource Economics. Cambridge University Press, New York.
Cortés, E. 2000. Life History Patterns and Correlations in Sharks. Reviews in Fisheries Science 8:299-344.
Crowder, L. B., S. J. Lyman, W. F. Figueira, and J. Priddy. 2000. Source-sink population dynamics and the problem of siting marine reserves. Bulletin of Marine Science 66:799-820.
Croxall, J., and S. Nicol. 2004. Management of Southern Ocean fisheries: global forces and future sustainability. Antarctic Science 16:569-584.
Davis, M. W. 2002. Key principles for understanding fish bycatch discard mortality. Canadian Journal of Fisheries and Aquatic Sciences 59:1834- 1843.
Dayton, P. K., E. Sala, M. J. Tegner, and S. Thrush. 2000. Marine reserves: parks, baselines, and fishery enhancement. Bulletin of Marine Science 66:617-634.
Eagle, J., S. Newkirk, and B. H. Thompson Jr. 2003. Taking stock of the regional fishery management councils. Island Press, Washington D.C.
Edwards, S. 2003. Property rights to multi-attribute fishery resources. Ecological Economics 44:309-323.
118
Ellison, A. M. 2004. Bayesian inference in ecology. Ecology Letters 7:509-520.
Essington, T. E., A. H. Beaudreau, and J. Wiedenmann. 2006. Fishing through marine food webs. PNAS 103:3171-3175.
Fogarty, M. J. 1999. Essential habitat, marine reserves and fishery management. Trends in Ecology and Evolution 14:133-134.
Fournier, D. A., J. R. Sibert, J. Majkowski, and J. Hampton. 1990. MULTIFAN a likelihood-based method for estimating growth parameters and age composition from multiple length frequency data sets illustrated using data for Southern Bluefin Tuna (Thunnus maccoyii). Canadian Journal of Fisheries and Aquatic Sciences 47:301-317.
Fournier, D. A., J. R. Sibert, and M. Terceiro. 1991. Analysis of Length Frequency Samples with Relative Abundance Data for the Gulf of Maine Northern Shrimp (Pandalus borealis) by the MULTIFAN Method. Canadian Journal of Fisheries and Aquatic Sciences 48:591- 598.
Gaines, S. D., B. Gaylord, and J. L. Largier. 2003. Avoiding current oversights in marine reserve design. Ecological Applications 13:S32-S46.
Gardmark, A., N. Jonzen, and M. Mangel. 2006. Density-dependent body growth reduces the potential of marine reserves to enhance yields. Journal of Applied Ecology 43:61-69.
Gell, F., and C. M. Roberts. 2003. Benefits beyond boundaries: the fishery effects of marine reserves. Trends in Ecology and Evolution 18.
Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin. 2004. Bayesian Data Analysis, 2nd edition. Chapman and Hall, Boca Raton.
Gerber, L. R., L. W. Botsford, A. Hastings, H. P. Possingham, S. D. Gaines, S. R. Palumbi, and S. Andelman. 2003. Population models for marine 119
reserve design: a retrospective and prospective synthesis. Ecological Applications 13:S47-S64.
Gerber, L. R., P. M. Kareiva, and J. Bascompte. 2002. The influence of life history attributes and fishing pressure on the efficacy of marine reserves. Biological Conservation 106:11-18.
Goodyear, C. P. 2002. Factors affecting robust estimates of the catch-and- release mortality using pop-off tag technology. American Fisheries Society Symposium 30:172-170.
Grafen, A., and R. Hails. 2002. Modern Statistics for the Life Sciences. Oxford University Press, New York.
Graham, N. A. J., R. D. Evans, and G. R. Russ. 2003. The effects of marine reserve protection on the trophic relationships of reef fishes on the Great Barrier Reef. Environmental Conservation 30:200-208.
Greene, H. G., and J. J. Bizarro. 2003. Essential Fish Habitat Characterization and Mapping of the California Continental Margin. Final Report Center for Habitat Studies, Moss Landing Laboratories, Moss Landing, CA.
Guenette, S., T. Lauck, and C. W. Clark. 1998. Marine reserves: from Beverton and Holt to the present. Reviews in Fish Biology and Fisheries 8:251- 272.
Gunderson, D. R. 1980. Using r-K Selection Theory to Predict Natural Mortality. Canadian Journal of Fisheries and Aquatic Sciences 37:2266- 2271.
Gunderson, D. R., and P. H. Dygert. 1988. Reproductive effort as a predictor of natural mortality rate. J. Cons. int. Explor. Mer 44:200-209.
120
Hall, S. J., and B. M. Mainprize. 2005. Managing by-catch and discards: how much progress are we making and how can we do better? Fish and Fisheries 6:134-155.
Halpern, B. S. 2003. The impact of marine reserves: do reserves work and does reserve size matter? Ecological Applications 13:S117-S137.
Hammond, T. R. 2004. A recipe for Bayesian network driven stock assessment. Canadian Journal Fish. Aquat. Sci. 61:1647-1657.
Hampton, J. 1997. Estimates of tag-reporting and tag-shedding rates in a large- scale tuna tagging experiment in the western tropical Pacific Ocean. Fishery Bulletin 95:68-79.
Hampton, J. 2000. Natural mortality rates in tropical tunas: size really does matter. Canadian Journal of Fisheries and Aquatic Sciences 57:1002- 1010.
Hastings, A., and L. W. Botsford. 2003. Comparing designs of marine reserves for fisheries and for biodiversity. Ecological Applications 13:S65-S70.
Hastings, W. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57:97-109.
Helgason, T., and H. Gislason. 1979. VPA-analysis with species interactions due to predation. in International Council for the Exploration of the Seas Meeting.
Heupel, M. R., D. B. Keeney, C. A. Simpendorfer, G. G. Freitas, T. R. Wiley, and R. E. Hueter. 2005. Using acoustic monitoring to evaluate MPAs for shark nursery areas: the importance of long-term data. Marine Technology Society Journal 39:10-18.
121
Hewitt, D. A., and J. M. Hoenig. 2005. Comparison of two approaches for estimating natural mortality based on longevity. Fishery Bulletin 103:433-437.
Hilborn, R. 2002. Marine reserves and fisheries management. Science 295:1234.
Hilborn, R., and M. Mangel. 1997. The Ecological Detective: Confronting Models with Data. Princeton University Press, Princeton.
Hilborn, R., K. Stokes, J. Maguire, T. Smith, L. W. Botsford, M. Mangel, J. Orensanz, A. Parma, J. Rice, J. Bell, K. L. Cochrane, S. Garcia, S. J. Hall, G. P. Kirkwood, K. Sainsbury, G. Stefansson, and C. J. Walters. 2004. When can marine reserves improve fisheries management? Ocean & Coastal Management 47:197-205.
Hoenig, J. M. 1983. Empirical Use of Longevity Data to Estimate Mortality Rates. Fishery Bulletin 82:898-903.
Hoenig, J. M., and S. H. Gruber. 1990. Life History Patterns in the Elasmobranchs: Implications for Fisheries Management In Elasmobranchs as Living Resources: Advances in the Biology Ecology, and Systematics, and the Status of the Fisheries. NOAA Technical Report NMFS 90, National Oceanic and Atmospheric Administration, Washington D.C.
Holden, M. J. 1973. Are long-term sustainable fisheries for elasmobranchs possible? Rapports et Proces-Verbaux des Reunions du Conseil International pour l'Exploration de la Mer 164:360-367.
Hood, P. 1999. Gulf Fishery News. NOAA.
Horwood, J. W., J. H. Nichols, and S. Milligan. 1998. Evaluation of Closed Areas for Fish Stock Conservation. Journal of Applied Ecology 35:893.
122
Iudicello, S., M. Weber, and R. Wieland. 1999. Fish, Markets, and Fishermen: The Economics of Overfishing. Island Press, Washington D.C.
Jackson, J. B. C. 2001. What was natural in the coastal oceans? Proceedings of the National Academy of Sciences of the United States of America 98:5411-5418.
Jackson, J. B. C., M. X. Kirby, W. H. Berger, K. A. Bjorndal, L. W. Botsford, B. J. Bourque, R. H. Bradbury, R. Cooke, J. Erlandson, J. A. Estes, T. P. Hughes, S. Kidwell, C. B. Lange, H. S. Lenihan, J. M. Pandolfi, C. H. Peterson, R. S. Steneck, M. J. Tegner, and R. R. Warner. 2001. Historical overfishing and the recent collapse of coastal ecosystems. Science 293:629-638.
Jennings, S., M. J. Kaiser, and J. D. Reynolds. 2001. Marine Fisheries Ecology. Blackwell Science Ltd., London.
Jensen, A. L. 1996. Beverton and Holt life history invariants result from optimal trade-off of reproduction and survival. Canadian Journal of Fisheries and Aquatic Sciences 53:820-822.
Jones, R., and C. Johnston. 1977. Growth, reproduction, and mortality in gadoid fish species. Pages 37-62 in J. H. Steele, editor. Fisheries Mathematics. Acad. Press, New York.
Kantor, M., D. J. Baker, and R. A. Scmitten. 1996. Magnuson-Stevens Fishery Conservation and Management Act; As Amended through October 11, 1996. NOAA Technical Memorandum NMFS-F/SPo-23 NOAA.
Kelly, S., D. Scott, A. B. MacDiarmid, and E. A. Babcock. 2000. Spiny Lobster, Jasus edwardsii, recovery in New Zealand marine reserves. Biological Conservation 92:359-369.
King, S., R. Hannah, S. Parker, K. Matteson, and S. Berkeley. 2004. Protecting rockfish through gear design: development of a selective flatfish trawl 123
for the US west coast bottom trawl fishery. Canadian Journal Fisheries and Aquatic Sciences 61:487-496.
Kinlan, B. P., and S. D. Gaines. 2003. Propagule dispersal in marine and terrestrial environments: a community perspective. Ecology 84:2007- 2020.
Koenig, C. C., F. C. Coleman, C. B. Grimes, G. R. Fitzhugh, K. M. Scanlon, C. T. Gledhill, and M. Grace. 2000. Protection of fish spawning habitat for the conservation of warm-temperate reef-fish fisheries of shelf-edge reefs of Florida. Bulletin of Marine Science 66:593-616.
Lauck, T., C. W. Clark, M. Mangel, and G. R. Munro. 1998. Implementing the precautionary principle in fisheries management through marine reserves. Ecological Applications 8:S72-S78.
Lloyd, M. 1967. Mean crowding. J. Anim. Ecol. 36:1-30.
Lockwood, D. R., A. Hastings, and L. W. Botsford. 2002. The Effects of Dispersal Patterns on Marine Reserves: Does the Tail Wag the Dog. Theoretical Population Biology 61:297-309.
Lohn, D. R., and D. O. McIsaac. 2004. The Pacific Coast Groundfish Fishery Management Plan Bycatch Mitigation Program, DRAFT Programmatic Environmental Impact Statement. NOAA Fisheries (National Marine Fisheries Service), Portland, OR.
Lorenzen, K. 1996a. The relationship between body weight and natural mortality in juvenile and adult fish: a comparison of natural ecosystems and aquaculture. Journal of Fish Biology 49:627-647.
Lorenzen, K. 1996b. A simple vonBertalanffy model for density-dependent growth in extensive aquaculture, with an application to common carp (Cyprinus carpio). Aquaculture 142:191-205.
124
Lorenzen, K. 2000. Allometry of natural mortality as a basis for assessing optimal release size in fish-stocking programmes. Canadian Journal of Fisheries and Aquatic Sciences 57:2374-2381.
Lubchenco, J., S. R. Palumbi, S. D. Gaines, and S. Andelman. 2003. Plugging a hole in the ocean: the emerging science of marine reserves. Ecological Applications 13:S3-S7.
MacCall, A. 2004. NMFS relations with fishermen. Pages email in K. I. Siegfried, editor., Santa Cruz, CA.
Magnusson, K. G. 1995. An overview of multispecies VPA--theory and applications. Reviews in Fish Biology and Fisheries 5:195-212.
Mangel, M. 1998. No-take areas for sustainability of harvested species and a conservation invariant for marine reserves. Ecology Letters 1:87-90.
Mangel, M. 2000a. Irreducible uncertainties, sustainable fisheries and marine reserves. Evolutionary Ecology Research 2:547-557.
Mangel, M. 2000b. On the fraction of habitat allocated to marine reserves. Ecology Letters 3:15-22.
Mangel, M. 2000c. Trade-offs between fish habitat and fishing mortality and the role of reserves. Bulletin of Marine Science 66:663-674.
Mangel, M., and P. S. Levin. 2005. Regime, phase and paradigm shifts: making community ecology the basic science for fisheries. Phil. Trans. R. Soc. B 360:95-105.
Mangel, M., and C. Tier. 1994. Four facts every conservation biologist should know about persistence. Ecology 75:607-614.
125
McClanahan, T. R., and S. Mangi. 2000. Spillover of exploitable fishes from a marine park and its effect on the adjacent fishery. Ecological Applications 10:1792-1805.
Mertz, G., and R. A. Myers. 1997. Influence of errors in natural mortality estimates in cohort analysis. Canadian Journal of Fisheries and Aquatic Sciences 54:1608-1612.
Methods, C. o. F. S. A., E. a. R. C. Commission on Geosciences, O. S. B. (OSB), and N. R. Council. 1998. Improving Fish Stock Assessments. National Academy Press, Washington D.C.
Morris, W. F., and D. F. Doak. 2002. Quantitative Conservation Biology. Sinauer Associates, Inc., Sunderland, Massachusetts.
Murawski, S. A., R. Brown, H. L. Lai, P. J. Rago, and L. Hendrickson. 2000. Large-scale closed areas as a fishery-management tool in temperate marine systems: the Georges Bank experience. Bulletin of Marine Science 66:775-798.
Murray, S. N., R. F. Ambrose, J. A. Bohnsack, L. W. Botsford, M. H. Carr, G. E. Davis, P. K. Dayton, D. Gotshall, D. R. Gunderson, M. A. Hixon, J. Lubchenco, M. Mangel, A. MacCall, D. A. McArdle, J. C. Ogden, J. Roughgarden, R. M. Starr, M. J. Tegner, and M. M. Yoklavich. 1999. No-take reserve networks: Sustaining fishery populations and marine ecosystems. Fisheries 24:11-25.
Myers, R. A., and R. W. Doyle. 1983. Predicting natural mortality rates and reproduction-mortality trade-offs from fish life history data. Canadian Journal Fish. Aquat. Sci. 40:612-629.
National Marine Fisheries Service, F. S. D. 2006. Observer Coverage. in. http://www.st.nmfs.gov/st4/nop/index.html, Silver Spring, MD.
NEFMC. 2004. Website. in http://www.nefmc.org/about/index.html.
126
Newkirk, S. 2002. Examining the Public Trust Doctrine, unpubl. Stanford University.
NFCC. 2004. Integrating Marine Reserve Science and Fisheries Management, NFCC Consensus Statement, June 7-9. Long Beach, CA.
NMFS. 2004. Evaluating bycatch: a national approach to standardized bycatch monitoring programs. US Department of Commerce, NOAA, National Marine Fisheries Service, Silver Spring, MD.
NOAA. 1998. Managing the Nation's Bycatch: priorities, programs, and actions for the National Marine Fisheries Service. NOAA Fisheries, Department of Commerce, Washington D.C.
NOAA. 2003a. Annual Report of the Activities of the International Bycatch Reduction Task Force. NOAA Fisheries, Silver Springs, MD.
NOAA. 2003b. National bycatch strategy announced. Fisheries 28:6-6.
NOAA. 2006. The National Observer Program. in http://www.st.nmfs.gov/st4/nop/.
NPFMC. 2004a. Amendment 80 Component and Options, April 10, 2004. NPFMC.
NPFMC. 2004b. Bycatch Reduction, IR/IU. in http://www.fakr.noaa.gov/npfmc/current_issues/bycatch/bycatch.htm.
NPFMC. 2004c. IR/IU Discussion Paper, June 2004 Meeting. NPFMC.
NPFMC. 2006a. The Bering Sea Pollock Fishery; a case study of successful fisheries management. in ttp://www.scscertified.com/PDFS/fish_pollockdescrip.pdf., Anchorage, AK.
127
NPFMC. 2006b. Fishery Management Plans. in http://www.fakr.noaa.gov/npfmc/fmp/goa/goa.htm, Anchorage, AK.
NRC. 2000. National Research Council. Marine Protected Areas: Tools for Sustaining Ocean Ecosystems. National Academy Press, Washington D.C.
OECD. 2001. New Zealand Case Study: Institutional Effects of the Introduction of Individual Transferable Quotas (ITQs). in http://www.oecd.org/dataoecd/38/27/2349219.pdf. The Organisation for Economic Co-operation and Development.
Palumbi, S. R. 2002. Marine Reserves: A Tool for Ecosystem Management and Conservation. Pew Oceans Commission, Arlington, VA.
Pascoe, S., and A. Revill. 2004. Costs and benefits of bycatch reduction devices in European brown shrimp trawl fisheries. Environmental and Resource Economics 27:43-64.
Pauly, D. 1980. On the interrelationships between natural mortality, growth parameters, and mean environmental temperatures in 175 fish stocks. J. Cons. int. Explor. Mer 39:175-192.
Pauly, D., V. Christensen, J. Dalsgaard, R. Froese, and F. Torres, Jr. 1998. Fishing Down Marine Food Webs. Science 279:860-863.
Pauly, D., and N. David. 1981. ELEFAN I, a BASIC program for the objective extraction of growth parameters from length-frequency data. Meeresforsch. 28:205-211.
Pearce, D. 2002. Economic Values and the Natural World. MIT Press, Cambrdge.
128
Peterson, I., and J. S. Wroblewski. 1984. Mortality Rates of Fishes in the Pelagic Ecosystem. Canadian Journal of Fisheries and Aquatic Sciences 41:1117-1120.
Petruny-Parker, M. E., K. M. Castro, M. L. Schwartz, L. G. Skrobe, and B. Somers. 2004. Who Gets the Fish? Proceedings of the New England Workshops on Rights-Bases Fisheries Management Approached. Rhode Island Sea Grant. in, Narragansett, RI. 28 pp.
PFMC. 1990. Status of the Pacific Coast Groundfish Fishery Through 1990 and Recommended Acceptable Biological Catches for 1991. Pacific Fishery Management Council, Portland, OR.
PFMC. 2000. Research and Data Needs. Pacific Fishery Management Council, Portland, OR.
PFMC. 2002a. DRAFT. Fishery Management Plan and Environmental Impact Statement for U.S. West Coast Fisheries for Highly Migratory Species. DRAFT Pacific Fishery Management Council, Portland, OR.
PFMC. 2002b. Status of the Pacific Coast Groundfish Fishery Through 2001 and Recommended Acceptable Biological Catches for 2002. Pacific Fishery Management Council, Portland, OR.
Pine, W. E., K. H. Pollock, J. E. Hightower, T. J. Kwak, and J. A. Rice. 2003. A review of tagging methods for estimating fish population size and components of mortality. Fisheries 28:10-23.
Pope, J. G. 1979. A modified cohort analysis in which constant natural mortality is replace by estimates of predation levels. in International Council for the Exploration of the Seas Meeting.
Post, J. R., and D. O. Evans. 1989. Size-dependent overwinter mortality of young-of-the-year yellow perch (Perca flavescens):laboratory, in situ enclosure, and field experiments. Canadian Journal of Fisheries and Aquatic Sciences 46:1968-1985. 129
Powell, E., A. Bonner, B. Muller, and E. Bochenek. 2004. Assessment of the effectiveness of scup bycatch-reduction regulations in the Loligo squid fishery. Journal of Environmental Management 71:155-167.
Price, A., and R. Rulifson. 2004. Use of traditional ecological knowledge to reduce striped bass bycatch in the Currituck Sound white perch gill-net fishery. North American Journal of Fisheries Management 24:785-792.
Punt, A. E., and R. Hilborn. 1997. Fisheries stock assessment and decision analysis: the Bayesian approach. Reviews in Fish Biology and Fisheries 7:35-63.
Quinn, T. J., and R. B. Deriso. 1999. Quantitative Fish Dynamics. Oxford University Press, Inc., New York.
Rakitin, A., and D. L. Kramer. 1996. Effect of a marine reserve on the distribution of coral reef fishes in Barbados. Mar. Ecol. Prog. Ser. 131:97-113.
Read, A. J., P. Drinker, and S. Northridge. 2006. Bycatch of Marine Mammals in U.S. and Global Fisheries. Conservation Biology 20:163-169.
Richter, V. A., and V. N. Efanov. 1977. On one of the approaches for estimating natural mortality in fish populations (in Russian). Tr AtlantNIRO, via FAO 73:77-85.
Ricker, W. E. 1975. Computation and interpretation of biological statistics of fish populations.
Ricketts, T. H. 2001. The matrix matters: effective isolation in fragmented landscapes. American Naturalist 158:87-99.
Roberts, C. M., J. A. Bohnsack, F. Gell, J. P. Hawkins, and R. Goodridge. 2001. Effects of Marine Reserves on Adjacent Fisheries. Science 294.
130
Roff, D. A. 1986. Predicting body size with life history model. Bioscience 6:316-323.
Roff, D. A. 2001. Life History Evolution. Sinauer Associates, Sunderland, MA.
Ross, R. M. 1990. The evolution of sex change mechanisms in fishes. Environmental Biology of Fishes 29:81-93.
Runolfsson, B., and R. Arnason. 1997. Individual Transferable Quotas in Iceland. Pages 178 in L. Jones and M. Walker, editors. Fish or Cut Bait! The Case for Individual Transferable Quotas in the Salmon Fishery of British Columbia. Fraser Institute.
Russ, G. R., and A. C. Alcala. 1996. Do marine reserves export adult fish biomass? Evidence from Apo Island, central Philippines. Mar. Ecol. Prog. Ser. 132:1-9.
Russ, G. R., A. C. Alcala, and A. P. Maypa. 2003. Spillover from marine reserves: the case of Naso vlamingii at Apo Island, the Philippines. Mar. Ecol. Prog. Ser. 264:15-20.
Russell, C. 2001. Applying Economics to the Environment. Oxford University Press, New York.
Samonte-Tan, G. P. B., and W. L. Griffin. 2001. Bycatch reduction impacts on the shrimp harvesting and consumer sectors in the Gulf of Mexico. Society and Natural Resources 14:223-237.
Sanchez-Lizaso, J. L., R. Goni, O. Renones, J. A. Garcia Charton, R. Galzin, J. T. Bayle, P. Sanchez Jerez, A. Perez Ruzafa, and A. A. Ramos. 2000. Density dependence in marine protected populations: a review. Environmental Conservation 27:144-158.
131
Schnute, J. T., and R. Hilborn. 1993. Analysis of Contradictory Data Sources in Fish Stock Assessment. Canadian Journal of Fisheries and Aquatic Sciences 50:1916-1923.
Sea Grant, U. o. A. 1996. Solving bycatch: considerations for today and tomorrow. Pages 322 in. Alaska Sea Grant College Program, Seattle, WA.
Shanks, A. L., B. A. Grantham, and M. H. Carr. 2003. Propagule dispersal distance and the size and spacing of marine reserves. Ecological Applications 13:S159-S169.
Shea, K. 1998. Management of populations in conservation, harvesting and control. Trends in Ecology & Evolution 13:371-375.
Shipp, R. L. 2003. A perspective on marine reserves as a fishery management tool. Fisheries 28:10-21.
Simberloff, D. 2000. No reserve is an island: marine reserves and nonindigenous species. Bulletin of Marine Science 66:567-580.
Stearns, S. C. 1992. The Evolution of Life Histories. Oxford University Press.
Steele, P., T. M. Bert, K. H. Johnston, and S. Levett. 2002. Efficiency of bycatch reduction devices in small otter trawls used in the Florida shrimp fishery. Fishery Bulletin 100:338-350.
Stein, A., K. Friedland, and M. Sutherland. 2004. Atlantic sturgeon marine bycatch and mortality on the continental shelf of the northeast United States. North American Journal of Fisheries Management 24:171-183.
TerraLogic, G. 2003. West Coast Benthic Habitat. in Pacific Coast Marine Habitat Program, Trexler, J. C., and J. Travis. 2000. Can marine protected areas restore and conserve stock attributes of reef fishes. Bulletin of Marine Science 66:853-873. Trippel, E. A., O. S. Kjesbu, and P. Solemdal. 1997. Effects of adult age and size structure on reproductive output in marine fishes. in R. C. Chambers and E. A. Trippel, editors. Early Life History and Recruitment in Fish Populations. Chapman & Hall, London. Tupper, M. H. 2002. Marine reserves and fisheries management. Science 295:1233. Turner, J. 1974. The Structure of Sociological Theory. Dorsey Press, Homewood. Turner, R. K., D. Pearce, and I. Bateman. 1993. Environmental Economics: An elementary introduction. Johns Hopkins University Press, Baltimore. Ursin, E. 1967. A mathematical model of some aspects of fish growth , respiration, and mortality. J. Fish Res. Board Can. 24:2355-2452. Vetter, E. F. 1988. Estimation of natural mortality in fish stocks: a review. Fishery Bulletin 86:25-43. Volterra, V. 1928. Variations and fluctuations of the number of individual Animal species living together. J. Cons. int. Explor. Mer 3:117. von Bertalanffy, L. 1938. A quantitative theory of the organic growth (inquires on growth laws. II). Human Biology 10:181-213. von Bertalanffy, L. 1957. Quantitative laws in metabolism and growth. The Quarterly Review of Biology 32:217-231. 133 Walters, C. J. 2000. Impacts of dispersal, ecological interactions, and fishing effort dynamics on efficacy of marine protected areas: how large should protected areas be? Bulletin of Marine Science 66:745-757. Ward, T. J., D. Heineman, and N. Evans. 2001. The Role of Marine Reserves as Fisheries Management Tools: a review of concepts, evidence and international experience. Bureau of Rural Sciences, Canberra, Australia. Ware, D. M. 1975. Relation between egg size, growth and natural mortality of larval fish. J. Fish Res. Board Can. 32:2503-2512. Warner, D. A., A. L. McMillen-Jackson, T. M. Bert, and C. R. Crawford. 2004. The efficiency of a bycatch reduction device used in skimmer trawls in the Florida shrimp fishery. North American Journal of Fisheries Management 24:853-864. Warner, R. R., S. E. Swearer, and J. E. Caselle. 2000. Larval accumulation and retention: implications for the design of marine reserves and essential fish habitat. Bulletin of Marine Science 66:821-830. Watling, L., and E. A. Norse. 1998. Disturbance of hte seabed by mobile fishing gear: a comparison to forest clearcutting. Conservation Biology 12:1180-1197. Wickstrom, K. 2002. Marine reserves and fisheries management. Science 295:1233. Wilcox, C., and C. Pomeroy. 2003. Do commercial fishermen aggregate around marine reserves? North American Journal of Fisheries Management 23:241-250. Williams, E. H., and K. W. Shertzer. 2003. Implications of life-history invariants for biological reference points used in fishery management. Canadian Journal of Fisheries and Aquatic Sciences 60:710-720. 134 Witherell, D., editor. 2003. Managing Our Nation's Fisheries: Past, present and future. Proceedings of a conference on fisheries management in the United States held in Washington D.C., November 2003:256. 135