The Allometric Equation
Consider two correlated trait measures:
x & y
A non-linear growth relationship between
them can be expressed: y = mxa
To express this as
proportional change, use a log scale: ln(y) = ln(m)
+
a ln(x)
In this form, the equation is linear and
ln(m) is the y-intercept.
If x is a
general
size measure, then y starts growing with x:
since y =
0 when x = 0, then ln(m) = 0
The
Allometric Equation then simplies to ln(y)
=
a ln(x),
which can then be
rewritten
Y' = a X' , where
a = allometric coefficient