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The intrinsic rate of increase, as defined in the exponential equation, is not a constant number at all but rather is itself a function of the density of the population.
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In a closed population the intrinsic rate of increase is defined as the instantaneous per capita birth rate, b, minus the instantaneous per capita death rate, d. [Similarly, in an open population r is equal to (births + immigration) – (deaths + emigration).]
The algebraic symbols b, d and r stand for the rates of birth, death, and the rate of change per individual in the general population, the intrinsic rate of increase. This formula can be read as the rate of change in the population ( dN / dt ) is equal to births minus deaths ( B − D ).
Intrinsic Rate of Increase. We can use our knowledge of exponential population growth and our value of R 0 to estimate the intrinsic rate of increase (r) (Gotelli 2001). The size of an exponentially growing population at some arbitrary time t is N t = N 0 ert, where e is the base of the natural logarithms and r is the
Therefore, we use a lowercase \ (r\) instead of \ (r_d\) to distinguish the continuous-time exponential model from the discrete-time geometric model. The symbol \ (r\) is called the instantaneous rate of increase or the intrinsic rate of increase.
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.
The population growth rate (sometimes called the rate of increase or per capita growth rate, r) equals the birth rate (b) minus the death rate (d) divided by the initial population size (N 0). Another method of calculating the population growth rate involves final and initial population size (figure 14.2.2).
