Environmental Engineering Reference
In-Depth Information
An individual hunter's profits are the price per kill minus the cost per kill. If the
profit is greater than zero, they go hunting, otherwise they don't. The total harvest
on the prey population is the sum of the number of hunters hunting (
means
sum), because each hunter kills one animal.
This economic model is particularly simple because we have assumed that each
hunter makes just one kill in the time period. The equations for the standard bio-
economic model, in which hunter effort is included as a variable, the Schaefer
model, are in Clark (1990) and many other fisheries textbooks.
Finally, the bio-economic component, where the population size and the eco-
nomics interact—this is through the hunter costs. We include some individual
variability between hunters, which may be due to differences in their opportunity
costs or skill (though note that we don't track individual hunters, as the variation is
uncorrelated between years and individuals). To keep things simple, we assume
that hunter costs are normally distributed around a mean value, and that this mean
value is related to the size of the prey population.
C
t
a
bN
t
c
i
,
t
C
t
(0,
s
)
These equations say that the average cost of killing one animal is a linear function
of the population size (the higher the population size the lower the cost), where
a
and
b
are constants. The cost that an individual hunter faces is the average cost plus
a random component which is taken from a normal distribution with a mean of
zero and standard deviation
s
.
This is the step that people find the biggest barrier to modelling, but with con-
fidence and a methodical approach it is not actually intellectually difficult—the
hard thinking should have been done in the previous step. Here's how to go about
learning to code a model for the first time:
5.3.3.1 Step 1—Developing a spreadsheet model
Find a paper that has used a model similar to the one that you would like to pro-
duce. Ideally the model will be relatively simple, and the data and functional forms
used will be well documented and clearly laid out. Replicate the model equations
in a spreadsheet. You probably won't be able to do a full facsimile of the model, but
you should be able to produce a deterministic non-dynamic version. Make sure
that you are generating the same results as the authors—if the inputs are identical
you should get identical results, and not just similar ones. For example, you could
try re-creating in Figure 5.3 or Figure 1.1. If you don't, dig away at the problem
until you are sure you know why not. Depressingly, often a mistake in the
published paper is to blame—but be sure!
You can get a fair way with a spreadsheet model, especially if you use macros and
add-ins. But the limits come with multiple simulations to carry out sensitivity
