Report on Rule-Based Systems for Carrying Capacity
ECASA Internal Report (Draft)
William Silvert, 16 February 2016
Introduction
The ICES Working Group on Environmental Interactions of Mariculture (WGEIM)
produced a “Review of recent development in carrying capacity models for shellfish
and recommendations for future directions” at its 2005 meeting. This review provides
a good basis for ECASA work on carrying capacity models for shellfish. This report
develops a set of rules based on the WGEIM review and illustrates both the working
of a rule-based system and the advantages of using fuzzy rules. It can serve as a
prototype for further work based on the results of the ongoing work packages.
The WGEIM review identified four different kinds of carrying capacity that need to
be evaluated in order to develop a comprehensive model of shellfish carrying
capacity. These are as follows:
1. Physical Carrying Capacity - the total area of marine farms that can be
accommodated in the available physical space,
2. Production Carrying Capacity - the stocking density of bivalves at which
harvests are maximized, nutrients, phytoplankton, zooplankton, the farmed
species, and detritus as well as varying levels of complexity of interactions
among these components (feedbacks among these variables, temperaturedependent interactions
3. Ecological Carrying Capacity - the stocking or farm density which causes
unacceptable ecological impacts, infaunal trophic index (ITI)
4. Social Carrying Capacity - the level of farm development that causes
unacceptable social impacts.
Along with these they provide detailed information on the relevant variables and how
the different carrying capacities are determined.
The WGEIM Decision Model
The interaction between these four kinds of carrying capacity is represented by the
decision process shown in Figure 1. Each of the four capacities is evaluated in
sequence, and since Ecological Carrying Capacity reflects social values and concerns,
there is feedback from Social Carrying Capacity to Ecological Carrying Capacity. We
can represent this process (omitting the feedback loop for the present for simplicity)
by the sequence of rules:
IF F<F0 THEN REJECT ELSE
IF P<P0 THEN REJECT ELSE
IF E<E0 THEN REJECT ELSE
IF S<S0 THEN REJECT ELSE
[feedback loop to E]
ACCEPT
where F, P, E and S refer to Physical, Production, Ecological and Social Carrying
Capacities respectively, and F0, P0, E0 and S0 are threshold values. These thresholds
are described in the way shown in Figure 2, which is discussed later.
Physical carrying capacity
Water depth
Currents
Temperature
etc...
Production carrying capacity
Plankton
Detritus
Nutrients
etc...
Ecological carrying capacity
Community structure
DEPOMOD
Mass balance models
etc...
guidance/feedback
Social carrying capacity
Traditional fisheries
Recreation
Charismatic species
etc...
Figure 1. WGEIM Decision Model.
This type of decision framework is relatively straightforward to implement, as it
goes step by step until the final feedback loop – once the Physical Carrying Capacity
F has been checked it no longer needs to be considered. This however is a major
disadvantage of this approach, since a slight inadequacy at one step of the way may
block consideration of further very favourable factors. If F is just slightly below F0 but
the other three carrying capacities are well above theirs, we would in reality probably
accept the site. This is in fact a very common practice when even all three levels F, P
and E are at unsatisfactory low levels but S is very high (as when there is strong
political pressure to allow aquaculture because it has influential support or would
meet a need for job creation). In other words, this kind of decision model does not
allow for trade-offs between favourable and unfavourable indicators, which is not the
way that decisions are made in the real world.
Response Variables in the WGEIM Model
The thresholds used in the WGEIM report are based on the analysis shown in
Figure 2. A response variable, which can be interpreted as a measure of acceptability,
is plotted against the production level, and as production goes up, the response
variable decreases. Typical response variables might be water quality, area available
to wild fisheries, freedom of motion of water skiers, and scenic beauty. The values
indicated in the figure for “acceptable level of response variable”, defined as “the
level of the indicator that has been determined to be acceptable by managers” are
difficult to ascertain, and the methodology for that reason is not very robust. In the
example given previously where F is slightly less than F0 while P, E and S are very
high, a slight decrease in the somewhat arbitrary value of F0 might make the
difference between rejecting and accepting a site.
response variable
However an interesting point about the report is that in describing how acceptability
is determined they produce a figure which shows a typical fuzzy membership
function, where the response variable can be interpreted as the membership in the set
of acceptable environmental impacts. If we transform the response variables into an
acceptability measure in such a way that the acceptable levels are normalised to 50%,
then we can interpret the WGEIM decision model as requiring that all four carrying
capacities have acceptabilities above 50% - however we can also impose more liberal
requirements, such as an average acceptability of 50%, or a more stringent
requirement like an average acceptability of 60% and no values below 40%.
acceptable level of
response variable
acceptable level of
production
production level
Figure 2. Hypothetical response curve of environmental variable under the
influence of varying levels of bivalve culture production.
We can implement this latter condition with a set of fuzzy rules that are similar to
the rules used in the WGEIM report, as follows:
IF μ(F) < 40% THEN REJECT ELSE
IF μ(P) < 40% THEN REJECT ELSE
IF μ(E) < 40% THEN REJECT ELSE
IF μ(S) < 40% THEN REJECT ELSE
[feedback loop to E]
IF [μ(F) + μ(P) + μ(E) + μ(S)]/4 < 60% THEN REJECT ELSE
APPROVE
where the symbol μ is the acceptability of the corresponding carrying capacity, or, in
the language of fuzzy set theory, the membership in the set of acceptable levels.
Of course this is a very simplified example and any number of generalisations are
possible. The threshold values need not be the same, and, for example, environmental
groups would probably fight over any value of μ(E) less than 50%. Furthermore fuzzy
rule sets are usually enumerated in more linguistic terms and in greater detail than
this, for example:
IF μ(E) is low and μ(S) is not high THEN REJECT
which states that a low ecological acceptability is grounds for rejection no matter how
acceptable the physical and production carrying capacities, unless the social carrying
capacity is high.
Pros and Cons of Fuzzy Rules
While the normal rule-based decision system described in the WGEIM report is
clearly easier to set up and implement, the vagueness of the threshold values can lead
to arbitrary decisions in borderline cases and thus the system lacks robustness. The
fuzzy system is more complex but offers a more nuanced way to balance conflicting
factors.
The chief advantage of using fuzzy rules for decision-making is that they permit the
balancing of favourable and unfavourable factors in the same way that human
decision-makers do. While the use of traditional threshold criteria may seem more
objective and scientific, they are often less likely to be acceptable to all stakeholders,
which ultimately means that they are less effective. Fuzzy rules come closer to
capturing the complexity of how decisions are actually made.