The GOM provides data to replicate the Gulf of Mexico Reef Fish example in Fenichel and Abbott (2014).
This dataset is consisted of parameters and functions.From Fenichel and Abboott(2014),
catch effort: \(x(s)=ys^\gamma\),
harvest: \(h(s,x)=q((ys^\gamma)^\alpha)s=q(y^\alpha)(s^{\gamma\alpha})\),
profit: \(w(s,x)=price \cdot h(s,x) - cost \cdot x(s)\), and
sdot: \(\dot{s} = rs \left( 1 - \frac{s}{k} \right) - q(y^\alpha)(s^{\gamma \alpha + 1})\).
The parameters in detal are in below.
## Load dataset
data("GOM")
## Demonstration of example
# demo(GOM, package="capn")
## R-script location
# system.file("demo", "GOM.R", package = "capn")param: a data.frame of parameters
r intrinsic growth rate (=0.3847)
k carrying capacity (=359016000)
q catchability coefficient (=0.00031729344157311126)
price price (=2.70)
cost cost (=153.0)
alpha technology parameter (=0.5436459179063678)
gamma pre-ITQ management parameter (=0.7882)
y system equivalence parameter (=0.15745573410462155)
delta discount rate (=0.02)
order Chebyshev polynomial order (=50)
upperK upper bound of Chebyshev polynomial nodes (=k)
lowerK lower bound of Chebyshev polynomial nodes (=5*10^6)
nodes the number of Chebyshev polynomial nodes (=50)
functions: functions for generate simulation data for each nodes
effort effort function
catch catch function
profit profit function (w in Fenichel and Abbott (2014))
sdot evaluated \(\frac{dst}{dt}\)
dsdotds evaluated \(\frac{dsdot}{ds}\)
dsdotdss evaluated \(\frac{d}{ds}(\frac{dsdot}{ds})\)
dwds evaluated \(\frac{dw}{ds}\)
dwdss evaluated \(\frac{d}{ds}(\frac{dw}{ds})\)
Fenichel, Eli P. and Joshua K. Abbott. (2014) "Natural Capital: From Metaphor to Measurement." Journal of the Association of Environmental Economists. 1(1/2):1-27.