Environmental Engineering Reference
In-Depth Information
research has focused on trying to predict how fish with different biology respond
to MPAs; what happens if adults rather than larvae disperse, for example, or if fish
have particular areas where they go to spawn or forage at particular times of year?
On the human side, researchers are exploring the way in which individual fishers
respond to restrictions on their activities, and how they cooperate to find fish
(Smith and Wilen 2003; Branch
et al
. 2006).
Dynamic bio-economic models can become very complex because of the neces-
sity to include both the human and biological components of the system.
Improved computing power means, though, that it is realistic to think of carrying
out simulations that go back to first principles, and use simple decision rules by
both people and prey, rather than having to solve these models analytically. This
would involve building on simple models such as our hunter example above,
though models involving large numbers of individuals and great spatial detail can
soon become unmanageably large and slow to run on the current generation of
personal computers.
Bayesian modelling approaches are very widely used nowadays, particularly in
fisheries managament, although they are also being advocated for conservation and
natural resource management more generally (e.g. Wade 2000; Dorazio and
Johnson 2003; Ghazoul and McAllister 2003). Ten years ago, McAllister and
Kirkwood (1998) gave an excellent and accessible review of the uses of Bayesian
models in fisheries, and said that these methods were still relatively inaccessible to
most scientists. Nowadays, there are software packages available such as WinBUGS,
which make the actual programming of models easier (see Resources section), but
the mathematical understanding required is still conceptually difficult. The basic
maths is
Bayes' theorem
, which is a standard simple equation in probability
theory. However, although this is the engine of Bayesian modelling, it doesn't take
the novice far in working out how to actually implement a Bayesian model.
Bayesian probability is an alternative to classical frequentist probability theory.
In frequentist theory, you assess the likelihood that a hypothesis is true given your
data. For example, based on a sample of 10,000 tosses of a coin I can say that the
probability of a coin toss producing heads is almost exactly 0.5. However, if I only
tossed the coin twice and produce two heads, I would estimate that the probability
of getting heads is 1. I could then use standard statistical techniques to test whether
the outcome of my experiment allows me to reject the null hypothesis that I have a
fair coin with a probability of 0.5 of getting heads (I clearly couldn't reject it in this
case, because my sample size is so small).
Bayesian statistics works the other way round—you assess how likely your data
are given a hypothesis. This may seem like a subtle difference, but it allows a very
important change in approach—you can test your ideas using more information
than just your data. In the example above, my data suggested that the probability
of getting heads was 1, but my friend says that the probability is 0.5 based on her
reading of the frequentist literature. Given this prior information, I could assign a
