c catchability parameter for R = cESK model tperson year
intrinsic growth rate of fish biomass per year r
w unit cost of effort person year
S stock on total management area t
stock on fishing ground t S
F
stock on reserve t S
R
open access equilibrium
O O
open access equilibrium with maximal size of reserve
1. Introduction
Following sustained interest from policymak- ers, recent years have seen a number of biological
or bioeconomic models examining effects of ‘no- take’ marine reserves, where fishers are perma-
nently banned from designated parts of a total fishing
management area
Polacheck, 1990;
Holland and Brazee, 1996; Sanchirico and Wilen, 1996, 2000; Brown and Roughgarden, 1997;
Hannesson, 1998; Lauck et al., 1998; Conrad, 1999. Here we develop another model whose
main features are its minimal data requirements, its analytical simplicity, and its relevance to wide-
spread problems of coral reef fisheries. Such fisheries provide about 6 – 7 or 6 Mtyear of
world catches Munro, 1996, worth about 18 billion US dollars per year, and are an important
source of food for the typically poor, developing nations that most reefs surround Birkeland,
1997. Many reef fisheries now suffer from a ‘tragedy of open access’, with widespread and
severe stock depletion as human populations have expanded and unmanaged fishing pressure has
grown McManus, 1996. Overfishing has not only reduced overall fish stocks, but also trans-
formed fish stocks from diverse communities dominated by large, high value carnivorous spe-
cies, to impoverished communities of small, low value fish Roberts, 1995a; Jennings and Lock,
1996.
Efforts to reverse this trend using conventional fishery management approaches have usually
failed Polunin and Roberts, 1996. Coral reefs support the most diverse fish assemblages on the
planet, and catches are obtained using gears with low selectivity. For example, at least 60 species
are caught in trap fisheries of Caribbean reefs Rakitin and Kramer, 1996. The sophisticated
fishery management
schemes usually
recom- mended by resource economics, such as taxes,
catch quotas, effort or gear restrictions, have proved difficult to implement in reef fisheries be-
cause of this diversity Munro, 1996. Related problems are the pervasive lack of data on types
and costs of effort, and on catches and their composition by species, which is typical of small
developing countries Russ, 1991, and the few resources there available for enforcement. No-
take reserves are promising in this respect, since checking that no one is fishing on a reserve is
about the simplest possible scheme to enforce, and data requirements for effective management
are low. So it should be an acceptable approxima- tion to ignore reserve enforcement and informa-
tion costs, as we do here. In practice marine reserves are often combined with community-
based management methods to redirect fishing effort to other locations or occupations see Feeny
et al., 1996 for further discussion. We will see later that dynamic adjustment problems indeed
make these approaches desirable, but for simplic- ity our model leaves them out.
We will compare our model to existing ones in detail as we develop it, but some further features
are worth highlighting here. Firstly, whether or not a reserve is created, fishers are assumed to
have pure open access
1
to any fishing ground the
1
The ‘pure’ is a necessary qualification because of the observation of Homans and Wilen 1997 that open access to
major fisheries is often regulated in practice.
area not in the reserve, and thus to dissipate all rent profit in equilibrium.
Secondly, our model is based on an ad hoc growth function which implicitly reflects two age
classes with completely different movements, as in Brown and Roughgarden 1997: eggs and larvae,
which are dispersed evenly throughout the reserve and fishing ground, and adults, which do not
migrate at all. These are appropriate assumptions for coral reef fish, and also most shellfish such as
abalone, scallops and clams, and some demersal fish. They might also be empirically acceptable
approximations for the whole systems of marine reserves now being suggested McGlade et al.,
1997; Halfpenny and Roberts, 1998 to protect overfished migratory species in temperate areas
such as the North Sea. This is why we call our model one of a ‘marine’ reserve, not just a ‘reef’
reserve; though clearly there are many existing or proposed marine reserves, particularly in temper-
ate waters, to which it would not apply. Finally, for simplicity, the model is spatially homoge-
neous, and so ignores biological variation within a management area.
It is the combination of open access fishing economics, implicitly age-dependent dispersal,
and analytical simplicity which distinguishes our model from other models of marine reserves. We
derive a simple analytic formula, requiring only two data points for any management area, for the
proportional size of a reserve which maximises sustainable catch. In Section 2, we develop the
model, compare its assumptions to those of other models, derive its equilibrium theoretical proper-
ties, and consider their empirical plausibility in three Caribbean locations; data are not yet avail-
able to test them completely. In Section 3, we simulate the dynamic effects of reserve creation
and Section 4 concludes.
2. A modified Schaefer – Gordon model of the equilibrium of a marine fishery reserve
