Environmental Engineering Reference
In-Depth Information
It is then possible to play around with the fecundity function, plotting up its
shape each time you change
a
or
b
, and with the values of the other parameters. How
much hunting is required to bring the population below two individuals? Can
you alter the model so that you have discrete individuals rather than fractions of
an individual, and which would be more realistic? What effect does this have? Can
you alter it to make survival into a coin-tossing exercise rather than a proportion, so
that for each individual, you use a random number to decide whether it lives or dies?
Hunter model—spreadsheet version
In the first column we put the values of the constants in our model. Let's have as an
example:
Price (
p
)
105
Carrying capacity (
K
)
1000
Intrinsic rate of increase (
r
max
)
0.2
Hunter cost intercept (
a
)
200
Hunter cost slope (
b
)
0.2
Cost standard deviation (
s
)
10
Then there should be a column for each year up to, say, 30 years, with a row each
for the population size,
N
t
, (starting with, say, 500 individuals), the productivity,
P
t
, the average cost,
C
t
, and the number of animals caught,
H
t
. To work out
H
t
for
a given year (column), we first need a cost,
c
i,t
, row for each of, say, 200 hunters. In
Excel, the function for generating a normally distributed random number
is
NORMINV(rand(), mean, standard deviation). In our case, the mean is
C
t
and the standard deviation is
s
. Then below this, for each hunter decide whether
hunting is profitable or not, with a row for each
h
i,t
value [use the formula
IF
(
c
i,t
p
,0,1)], and add up the number killed to get a value for
H
t
. The final step is
to seed the next year (column) with a new population size, which is
N
t
P
t
H
t
.
Each time you press F9 you will get a different set of values for your model, as the
individual costs are recalculated. You can then play with the model, and see how
changing the values of the variables affects the equilibrium population size.
5.3.3.2 Step 2—Programming language
Next you will replicate your validated spreadsheet model in a programming lan-
guage (Box 5.1). One way to do this is to use the macro function in Excel as a way
of learning visual basic, but this is fairly limiting. If you have already learnt R for
statistical modelling, then you can carry on using R for this type of modelling too.
R is adequate for most simple models, though it struggles with large models such
as spatial or individual-based ones. If you have no prior preferences, then use
C
, as it is a powerful and generic language. Once you have learnt one pro-
gramming language you will find others easier to pick up, so the decision is not
something to agonise over.
