||Sign graph diagrams
Format for a sign graph diagram
This type of diagram was first used in the biological sciences
in the early part of the Twentieth Century. They are used to represent and investigate
the relationships between variables in a given situation and in particular to
identify positive and negative feedback loops driving the system’s behaviour.
Hence it is good for thinking about the likely effects of changes and, in particular,
of interventions in systems. A sign graph is often drawn to establish the structure
of planned quantitative models. They can be developed directly from a multiple
- arrows labelled with either a plus or minus sign;
phrases (e.g. aaa, bbb, ccc, ddd, etc.) shown refer to variables (so phrases
like ‘number of’ ‘cost of’ ‘speed of’ ‘level of’ are often found in
phrases should not themselves refer to variations (so do not use ‘more/less’ or
‘increase/decrease’ in the phrases).
- Use a
minus sign by an arrow where a change in the variable at the tail of the arrow
produces an opposite change in the variable at the head. So, in the figure
above, an increase in ccc will lead to an decrease in ddd, and a decrease in ccc
will lead to an increase in ddd (see guideline 2).
- Use a
plus sign by an arrow where a change in the variable at the tail produces a similar
change in the variable at the head. So, in the figure above, an increase in aaa will
lead to an increase in ccc and a decrease in aaa will lead to a
decrease in ccc (see guideline 2).
- A system boundary can be used but is usually not included.
- A title defining the system of interest is essential.
off with the simplest diagram you can, and then elaborate it as necessary. In
that way you can be sure that you understand the meaning and implications lif
your diagram before it becomes too complex.
checking that you’ve got the signs right on your arrows, it helps to read
through the diagram asking ‘Does more of (insert first variable) lead to more
of (insert second variable)?’ in which case put a plus sign on the arrow or
‘Does more (or less) of (insert first variable) lead to less (or more) of
(insert second variable)? in which case use a minus sign on the arrow.
- Where there are loops of variables in the
sign graph, you can check whether they represent positive or negative feedback
loops by looking at the signs.
- First, check that it really is a
continuous loop in which the arrows follow each other around the loop (i.e. all
clockwise or all anti-clockwise).
- Then count the number of minus signs
(it doesn't matter how many plus signs there are). If there is an odd number of
minus signs (1, 3, 5 etc.) then it is a negative feedback loop. Otherwise it is
a positive feedback loop.
- The figure above shows only two feedback
loops: a positive feedback loop from aaa to ccc to bbb and back to aaa, and a
negative feedback loop from ccc to bbb and back to ccc.
diagram can be built up from the end, as multiple-cause diagrams, or from a
variable which you imagine to be very important following its ramifications.