# Multipliers

Many ecological processes are influenced by several factors together. For example, plant growth may be influenced by temperature, radiation, and soil water content. It is often difficult to know how to combine the effect of these factors.

One method is to envisage each factor as having some optimum value: when all the influencing factors are at this optimum, then the process (e.g. growth) proceeds at some maximum rate. When a factor is not at its optimum value, then the rate of the process is reduced. Thus, a general solution is to use an expression of the form:

flow = flowmax*m1*m2*m3

where:

• flow is the calculated flow rate
• flowmax is the max flow rate if all influencing factors have their optimum values
• m1, m2 etc are multipliers for each influencing factor (e.g. m1 could be the temperature multiplier)

To calculate the multipliers, you might use the abs function to find out the difference between a factor and its optimum value. You then need to scale the multiplier so that it lies between zero and one. Alternatively, suppose that plants do not grow at all below Tmin nor above Tmax. Then the following expression would work:

q=(Topt-Tmin)/(Tmax-Topt),
if ((T>Tmin)&&(T<Tmax)) then
(((T-Tmin)^q) * (Tmax-T)) / (((Topt-Tmin)^q) * (Tmax-Topt))
else
0

You may notice that the above expression involves an intermediate variable q. It is a valuable feature of Simile’s equation language that expressions can often be simplified by calculating a sub-expression that is used more than once and assigning it to an intermediate variable.

The expression is also formatted to make it easier to read. The equation dialogue box preserves the formatting you enter. It doesn’t affect the parsing of the equation, but it does make it easier for the user.