Environmental Engineering Reference
In-Depth Information
certainty equivalence
of stochastic models. There is also an interaction between
hunting mortality and environmental variation, such that in general, the higher
the hunting mortality the higher the variability in population size, and the further
below the deterministically predicted population size the real population size
will be—a stochastic model can capture this effect (Hsieh
et al
. 2006). It's also
important to consider the degree to which environmental variation is correlated in
space and time, as this can have a major impact on the sustainability of harvesting
(Jonzen
et al
. 2002).
5.3.5.1 Practicalities of using stochastic models
Even if you have decided that a stochastic model is appropriate for your system, it
is worth starting model exploration with a deterministic model, so that variation
in parameter values doesn't obscure your investigations of model behaviour. When
you carry out the full stochastic analyses, you need to ensure that you have run the
model for long enough and enough times to produce meaningful results. You need
to run the model for long enough in each simulation to ensure that any
transient
behaviour
on the way to equilibrium has run through before you start recording
data. If you start the model from a near-equilibrium point, the transient period
will be shorter. The number of times you need to run the model should be enough
that you are getting robust estimates of your output parameters—several hundred
simulations will be necessary for most systems you will be modelling.
Which distribution to choose to represent the variation in a parameter depends
on the data available and
a priori
theoretical considerations. If the species is poorly
known you may only be able to specify a range of values within which the para-
meter is likely to fall (i.e. use a uniform distribution), while if there are more data you
might be able to fit a statistical distribution to the data. Previous studies on similar
species may have fitted distributions to data, and you could then use the same
distribution. People tend to use the
Normal distribution
as a default. The main
theoretical issue is that the variation in the parameter in question should be likely
to be Normal or near-Normal, and the main programming issue is to ensure that
the value that you get when you pick from the distribution is within the bounds of
the parameter in nature. For example, values in a Normal distribution may fall
below zero, which is biologically impossible for parameters such as survival or
fecundity, while parameters such as survival can't exceed 1. A crude way to deal
with this is to have a line in the code saying that if the parameter exceeds 1, it is set
to 1. This is OK if the situation is rare, but otherwise, you should consider other
distributions. Hilborn and Mangel (1997) have useful pseudocode for generating
some of the common distributions.
5.3.5.2 What can I do if my data are really poor?
One of the main reasons people give for not developing a model is that their data
are too poor, or they don't have an estimate for one of the parameter values.
However, models are particularly useful in these situations, because they allow you
