In general, r represents the per capita birth rate minus the per capita death rate for a population (r=b-d). In this tutorial we call r the intrinsic rate of increase, and we distinguish between two types of r:
 
    WHAT IT MEANS IN EACH MODEL: EXPLANATION:

rmax:

maximum
intrinsic rate of increase
exponential: rmax=(b-d)
rmax is constant
Birth (b) and death (d) rates are constant because the population is unlimited by resources.
    logistic: rmax=(b-d)
rmax is constant
rmax is constant, but it is adjusted to obtain the realized rate (see below).
         
r:
realized
intrinsic rate of increase
exponential: r = rmax
r is contant
The realized is the same as the maximum rate of increase because the population is unlimited by resources.
    logistic: r = rmax[1-(N/K)]
r changes with N
The realized rate of increase, at any moment in time, is obtained by multiplying rmax by the density-dependent term, [1-(N/K)]. This "adjustment" takes into account changes in b and d that happen as density changes.

NOTE: We use the term "intrinsic rate of increase" to avoid confusing r with population growth rate, which is dN/dt. Some authors and ecologists use the words "per capita growth rate" to describe r because of the following mathematical relationship:
   
(logistic equation)
 
Divide both sides by N and you get the growth rate per number of individuals ("per capita"):
 
 
Because r = rmax [1-(N/K)] in the logistic model, we can substitute r:
 
 
Thus, r equals the per capita growth rate.