#=============================================================================
#  wolf moose graph version 20101225.R
#  R program to plot the average kill rate of moose per wolf (average number
#  of moose killed per wolf per 100 day; vertical axis) with the density of
#  moose (average number per 1000 square km; horizontal axis), along with the
#  model equation for predation rate from ecological theory.
#
#  Data are from Messier, F. 1994. Ungulate population models with predation:
#  a case study with the North American moose. Ecology 75:478-488.
#=============================================================================

#---------------------------------------
#  Enter data into two R-vectors.
#---------------------------------------
moose.density=c(.17,.23,.23,.26,.37,.42,.66,.80,1.11,1.30,1.37,
1.41,1.73,2.49)
kill.rate=c(.37,.47,1.90,2.04,1.12,1.74,2.78,1.85,1.88,1.96,
1.80,2.44,2.81,3.75)

#--------------------------------------
#  Draw a scatterplot of the data.
#--------------------------------------
plot(moose.density,kill.rate,type="p")

#--------------------------------------
# Calculate predation rate equation over a range of moose
# densities and store in two vectors, m and k.
#--------------------------------------
m=2.5*(0:100)/100  # Range of moose densities from 0 to 2.5.
a=3.37             # Prey density at which kill is half of
                   # maximum.
b=0.47             # Maximum kill rate.
k=a*m/(b+m)        # Model equation calculated for all values
                   # contained in the vector m.
#--------------------------------------
# Plot the predation rate equation data as a line plot.
#--------------------------------------
points(m,k,type="l")