We applied a deterministic bioeconomic model of a multispecies fishery (Conrad, 1999) that accounts explicitly for the effect of staghorn coral coverage on commercially harvestable reef fish biomass and productivity to quantify changes in the optimal equilibrium commercial reef fish stocks, harvest rate and profit from restocking and protecting staghorn coral populations. The model is spatially implicit, in that the precise relative location of each restoration site is not specified. Because stocks of the most economically important commercially harvested reef fish in Florida are managed, we examine equilibrium conditions characterizing maximum economic yield (MEY), or the stocks and harvest which maximize economic benefits to society, rather than that of an open-access fishery. Key parameters were estimated from existing datasets of regionally collected staghorn and reef fish size and abundance (Miller and Huntington, 2015; SEFSC, 2016). Bioeconomic model parameters requiring estimation included: (1) annual changes in rehabilitated reef area covered by outplanted staghorn colonies at the
simulated restoration site resulting from restocking and protection, (2) baseline
abundance of commercially important reef fish on the FRT inside and outside of areas prohibiting consumptive activities, (3) reef fish carrying capacity in the study area, (4) harvest cost, and; (5) the biophysical relationship between staghorn coral area and reef fish biomass.
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To estimate the change in area of staghorn corals over time resulting from outplanting, we developed a simple linear staghorn growth model. For our baseline bioeconomic model run, the results presented here, we assume, at the time of outplanting, simulated colonies are elliptical in shape, 25 cm in length. Change in outplanted staghorn area was simulated following the equation for the area of an ellipse (Kiel, 2014),
[37]
where and are one-half the length and width of the colony’s major and minor axis, respectively. Simulated colonies are assumed to be outplanted in a grid pattern at a uniform density of 10,000 outplants per hectare (ha) and assumed to maintain an annual major axis growth rate of 5 cm; published staghorn linear growth ranges from 3 to 11.5 cm yr-1 (Shinn 1966, Gladfelter et al. 1978).
We cap colony length at 100 cm (at which point colonies begin to interlock at the simulated treatment area and the marginal ecological value of continued growth declines) and cap coverage to 54.31% of the treatment area, the 95th percentile estimated from the Miller and Huntington (2015) dataset. Simulated outplants in the baseline scenario experience first and second year mortality of 15% and 10%, and none thereafter (Schopmeyer et al, 2017).
To derive baseline reef fish biomass and carrying capacity in the study area, we use an observational dataset of reef fish counts and measures inside and outside of no- take marine reserves in the FKNMS (SEFSC, 2016). We use the median biomass estimates as parameters representing fishery carrying capacity prior to restocking.
With double log-linear regression we quantify the biophysical relationship between staghorn coral coverage and reef fish biomass using a dataset of reef fish and
AB Area=
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staghorn colony measures and abundance collected between 2012-2014 from underwater visual surveys (n=65 transects) in the Dry Tortugas National Park, a relatively rich coral reef ecosystem at the western tip of the Florida Keys (Miller and Huntington, 2015)
Using the ex-ante estimates of outplanted staghorn coverage from the coral growth model, reef fish abundance and carrying capacity estimated from the SEFCS (2016) datasets, harvest costs derived from data queried by provided by professionals within the Fisheries Monitoring Branch (FMB) of the Southeast Fisheries Science Center (SEFSC) in Miami, Florida, market fish prices, and fish stock growth from peer reviewed literature (Froese and Pauly, 2018), and estimated diffusion coefficient, the model
enables characterization of the linkages between coral abundance, commercial reef fish stocks and optimal sustainable harvest. A detailed solution of the bioeconomic model is contained in Chapter One.
3.0 Results and discussion
The monetized value of the subset of ecosystem services affected by restocking and protecting staghorn corals that are examined by this study are shown in Tables 31 and 32. In Table 31, household WTP results are presented for 300,000 25 cm2 colonies outplanted annually for 30 years. The bioeconomic model annual WTP values were discounted at a 4% discount rate to arrive at the discounted NPV in Table 31 and reveal the incremental benefit of management alternatives (restocking and protection) over no staghorn restocking. Table 33 presents mean household WTP results for a one-time planting of 50,000 25cm2 staghorn colonies under each of the two management
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Florida over the past three years. Results confirm that recreational values are dramatically larger than commercial reef fish fishery values.
The adjusted per hectare annual WTP values are presented in Table 34. Because outplanted colonies do not reach their carrying capacity until year 22, adjusted values are less than base values for years 1-22 and reach base values in year 22, at which staghorn coverage reaches its assumed carrying capacity of 54.31% of the restocked reef (Figure 8). Project net present values for 50,000 staghorn colonies outplanted annually for 30 years are presented in Table 35. Values were derived by extrapolating adjusted WTP values to the various relevant populations and accounting for costs of production, outplanting, and two years of monitoring (Coral Restoration Foundation, personal communication). Corresponding benefit-cost ratios and sensitivity analysis are presented in Table 36. Results suggest project values may be substantial, and benefit-cost ratios may be greater than one, suggesting economic efficiency, depending on the relevant population considered. A description of all the ecosystem services supported by staghorn corals is contained in Table 29. As noted previously, the services valued with this study represent a subsample of those supported by staghorn corals.