The R-function describes the feedback structure acting on a population when ⁺feedback due to the 1^st principle has been removed by converting the growth process to logarithms. Starting with a description of the exponential growth feedback function (the 1^st principle),

and converting population density to natural logarithms, we obtain

which shows that population change is now independent of population density. In other words, when population density is expressed in logarithms, the ⁺feedback due to the 1^st principle disappears! With this simple transformation, we can avoid the trivial process of exponential growth, and concentrate our attention on the more complicated aspects of feedback acting through the per-capita rate of change, R. Thus, a general feedback function with ⁺feedback due to the 1^st principle removed is

Note that this equation also describes a feedback process because if R is a function of N so too is . This general feedback function is called the reproduction function or R-function (sometimes also called a regulation function because, as we shall see, it defines the process of population regulation). R-functions describe the nontrivial feedback structures of population systems according to the following conditions: