Sladek Nowlis and Roberts; Fisheries benefits and optimal design of marine reserves 



605 



species richness had increased by over 400'^^ in both 

 the reserve and the fishing grounds after 1 1 years of 

 reserve protection (Russ and Alcala, 1996). Large fish 

 were particularly abundant in the fishing grounds near 

 the border of the reserve, possible evidence of adult 

 spillover. These same authors showed previously that 

 overall catches dropped more than 509^ two years af- 

 ter the re-opening of a closed area on Sumilon Island, 

 Philippines, despite the increased fishing area (Alcala 

 and Russ, 1990), suggesting that the reserve had pro- 

 vided enhancements to surrounding fishing grounds. 



These field studies show that under certain cir- 

 cumstances, reserves are likely to produce fisheries 

 enhancements. However, models are also necessary 

 because they allow more general analyses of the con- 

 ditions under which reserves are likely to produce 

 benefits and of the design attributes that will maxi- 

 mize these benefits. By making use of controlled rep- 

 licates and large-scale manipulations, models can 

 provide a theoretical background on which to inter- 

 pret field results. 



Several authors have built and analyzed models 

 of marine fishery reserves. These models can be clas- 

 sified as those examining adult spillover (Beverton 

 and Holt, 1957; Polacheck, 1990; DeMartini, 1993) 

 and those examining larval transport (Quinn et al., 

 1993; Man et al., 1995; Holland and Brazee, 1996; 

 Sladek Nowlis and Roberts, 1997; Holland et al.'). 

 All of these models predict fisheries enhancements 

 from reserves in at least some situations, particu- 

 larly under heavy exploitation. However, the pre- 

 dicted enhancements were small and uncommon for 

 the adult spillover models. Previous models have ex- 

 amined a variety of factors that influence potential 

 reserve benefits, including adult movement tendencies 

 (Polacheck, 1990; DeMartini, 1993), individual growth 

 rate ( DeMartini, 1993 ), Allee effects ( Quinn et al. , 1993 ), 

 metapopulation patch dynamics (Man et al., 1995 ), and 

 socioeconomic factors (Holland and Brazee, 1996; Hol- 

 land et a\}). None of these examined the effect of popu- 

 lation growth potential on reserve benefits. 



In order to fill this gap, we built a set of models 

 looking at reproductive enhancement and larval 

 transport as mechanisms for providing reserve ben- 

 efits. We analyzed these models with particular em- 

 phasis on how reserve size, fishing mortality, and life 

 history traits, particularly population growth poten- 

 tial, affect long-term fishery yields. We also analyzed 

 the short-term consequences of reserve establish- 



1 Holland, D. S., J. B. Braden, and R. J. Brazee 199.5 

 Managing artisanal fisheries with marine fishery reserves: an 

 alternative to managing catch or effort. Environmental and 

 Natural Resources Policy and Training/Midwest Universities 

 Consortium for International Activities Supplementary Paper 

 3, 36 p. 



ment and these results are presented elsewhere 

 (Sladek Nowlis and Roberts, 1997). 



We used our models to achieve several goals. First, 

 we wanted to identify conditions that favored the 

 success of reserves at enhancing fisheries. Second, 

 we wanted to establish design criteria to help maxi- 

 mize the benefits that could accrue from a closed fish- 

 ing area. Third, we wanted to assess whether re- 

 serves can decrease year-to-year variation in catches. 

 Finally, we wanted to provide guidelines for future 

 field research through the identification of important 

 but poorly understood biological processes and 

 through the generation of testable predictions about 

 the design and function of marine fishery reserves. 



Methods 



Our basic model followed yearly changes in a popu- 

 lation separated into size categories. Although cat- 

 egorization by age is more common than by size, we 

 felt size better represented size-dependent processes 

 such as reproduction and fishing mortality (Polunin 

 and Roberts, 1996). Each size category contributed to 

 future populations through some simple rules (Fig. 1). 



We used the best-available estimates of size-based 

 fecundity and larval survivorship for various species 

 (see Table 1). Little is known about larval survivor- 

 ship in fish, especially for coral reef species (Boehlert, 

 1996). The best estimates we could find came from 

 an analysis of larval performance across a global 

 array of ambient temperatures (Houde, 1989). Houde 

 used linear regression on data from various studies 

 to relate ambient temperature to fish larval dura- 

 tion and daily survivorship. This process produced 

 statistically significant and predictive, but crude, 

 relationships that could then be combined to esti- 

 mate total lar\'al survivorship. At a temperature of 

 26°C, Houde's estimate of survivorship for larvae 

 through the entire larval stage was 5 x 10"'' ( see Ap- 

 pendix for equations). Whenever we had additional 

 information about larval stage duration, we used it 

 along with Houde's temperature-based estimate for 

 daily survivorship to produce our estimate of total 

 larval survivorship. 



Natural mortality estimates were also taken from 

 the literature (see Table 1). Those adults that sur- 

 vived had the additional possibilities of either grow- 

 ing to the next size class or staying in the same one. 

 We used von Bertalanffy growth parameters (Ricker, 

 1975) to determine the chance that a fish of one size 

 class grew to the next in a given year (Fig. 2). Von 

 Bertalanffy parameters describe the growth of indi- 

 vidual fish and are widely estimated in the litera- 

 ture (see Table 1 for the estimates that we used and 



