BurrliOZ
A Flexible Approach to
Species Protection
 Environmental
Managers responsible for implementing the Australian and New Zealand Water
Quality Guidelines for Fresh and Marine Waters need to generate 'trigger
values' (ie the maximum concentration of a chemical that should permit the
integrity and function of aquatic environments to be maintained) for local
conditions within Australia. To do this, they will utilise toxicant data
and a statistical software package, BurrliOZ, developed by the CSIRO
Environmetrics Group for Environment Australia. Another software package
that calculates trigger values using the Aldenberg and Slob (1993)
approach exists, however this has been shown to be a special case of the
approach implemented in BurrliOZ (Shao, 2000). BurrliOZ uses a flexible
family of distributions, the Burr Type III, to estimate the concentrations
of chemicals such that a given percentage of species will survive.
This project makes available to the public, free of charge and subject
to certain restrictions, a new software packages including both the 'Web' and a CD-ROM suitable for delivery with the
Guidelines document. This software and delivery format addresses concerns
raised during the 1999 public comment period. Download
Burrlioz software.
The work is expected to facilitate approval of the final Water Quality
Guidelines by the Australian and New Zealand Environment and Conservation
Council (ANZECC) and the Agriculture and Resource Management Council of
Australia and New Zealand (ARMCANZ) Ministers and also accelerate
effective implementation of the Water Quality Guidelines. This work
represents a significant advance in the methods used to derive water
quality guidelines and it should have international implications and uses.
A screen shot of
what BurrliOZ looks like
The Method
The protecting concentrations are estimated by fitting the Burr Type
III distribution to the No Observed Effect Concentration (NOEC) data,
collected for a range of species. This distribution is
required by the Environment Protection Authority. Other distributions are
fitted to the data, including the log-normal and log-logistic as these are
familiar to environmental managers. However, they are provided only as a
reference and are not used for the estimation of protecting
concentrations.
The Burr III distribution is a very flexible three-parameter
distribution, which can provide good approximations to many commonly used
distributions such as the log-normal, log-triangular and Weibull. The
cumulative distribution function for the Burr III distribution is
The three-parameters of the Burr III distribution, b, c,
and k are estimated by maximum likelihood using the Nelder-Mead
simplex algorithm, a derivative free optimisation technique.
A feature of the Burr Type III distribution is that as some of the
parameters tend to limiting values the Burr Type III distribution
tends to one of a set of limiting distribution (Shao, 2000).
For example, as  the Burr III
distribution tends to the reciprocal Weibull distribution. As 
the Burr III distribution tends to the reciprocal Pareto distribution. In
practice, if k is estimated to be greater than 100 in a fit of
the Burr distribution, then the parameter estimation is
repeated, a reciprocal Weibull is fitted. Similarly if c is
estimated to be greater than 80 then the reciprocal Pareto distribution is
fitted.
Estimating the protecting concentration
The protecting concentration, PC(q), is calculated from the Burr Type
III distribution, or an associated limiting distribution. The user
requires the concentration corresponding to the statement that ``q% of the
species should be protected if the concentration of the chemical is less
than the estimated protecting concentration". Thus, for a given value
for q, the protecting concentration is estimated from the Burr III
distribution fit as
Typical values for q are 80, 85, 90 or 95.
Estimating a confidence interval for the protecting concentration
Unlike the estimation of the protecting concentration, there is no
theoretically derived equation for estimating the lower bound of a
confidence interval (CI) about the protecting concentration etimate,
though Shao (1998) has shown that a delta method approximation works
sometimes, particularly for large samples. Instead, a technique known as
bootstrapping is used to estimate the lower bound of the CI.
Bootstrapping is a standard statistical approach in situations where
theoretical results are difficult to obtain, or require unrealistic
assumptions (Efron and Tibshirani, 1993).
To perform the bootstrapping, a new dataset of the same size as the
original dataset is created by selecting values from the original set at
random, but with replacement. The PC(q) is estimated from this new dataset
as above. This process is repeated many times. This gives a large set of
estimates for the PC(q) which, in essence, is a representation of the
distribution of the PC(q). The lower bound of a 90% confidence interval
(for example) for the PC(q) can then be estimated by ordering all the PC(q)
values and selecting the value that is ranked at 5%.
It should be noted that the estimated lower bound to the CI is based on
a random sampling method and will not be exactly the same if the bootstrap
procedure is repeated.
References:
Aldenberg, T. and Slob, W. (1993). Confidence limits for hazardous
concentrations based on logistically distributed NOEC toxicity data. Ecotoxicology
and Environmental Safety, 25, 48-63
Efron, B. and Tibshirani, R.J. (1993). An introduction to the
Bootstrap. New York: Chapman & Hall.
Shao, Q. (1998). Statistical Review and Assessment of Water
Quality Guidelines, CSIRO Mathematical and Information Sciences
Report No CMIS98/21
Shao, Q. (2000). Estimation for hazardous concentrations based on NOEC
toxicity data: an alternative approach. (accepted by Environmetrics)
Contact Details: burrlioz@cmis.csiro.au
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