#=========================================================
# Figure 15.1.R.
# R script to draw a scatterplot of sustainable yield vs.
# harvesting effort for shrimp data from the Gulf of Mexico,
# with parabolic yield-effort curve fitted and superimposed.
#=========================================================

#---------------------------------------------------------
# 1.  Read and plot the data.
#  (a data file named shrimp_yield_effort_data.txt is assumed
#  to be in the working directory of R)
#---------------------------------------------------------
df=read.table("shrimp_yield_effort_data.txt",header=TRUE)
attach(df)
plot(effort,yield,type="p",xlab="harvest effort",ylab="sustainable yield")

#---------------------------------------------------------
# 2.  Fit parabolic yield-effort curve with least squares.
#---------------------------------------------------------
X=cbind(effort,effort^2)  # First column of matrix X is effort.
                          # Second column is effort squared.
b=solve(t(X)%*%X,t(X)%*%yield)  # Least squares solution.
h=b[1,]          # Coefficient of effort.
g=b[2,]          # Coefficient of effort squared.


#---------------------------------------------------------
# 3.  Overlay fitted quadratic model on scatterplot.
#---------------------------------------------------------
elo=100            # Low value of effort for calculating quadratic.
ehi=350            # High value of effort.
eff=elo+(0:100)*(ehi-elo)/100  # Range of effort values
sy=h*eff+g*eff^2   # Sustainable yield calculated for range of
                   #  effort values.
points(eff,sy,type="l")  #  Add the quadratic model to the plot.

#---------------------------------------------------------

x0=effort
y0=yield
x1=effort
y1=h*effort+g*effort^2
segments(x0,y0,x1,y1,lty=2)
detach(df)