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Another useful population parameter closely related to the net reproductive rate and the intrinsic rate of increase is the so-called finite rate of increase, λ, defined as the rate of increase per individual per unit time.
In the model, the rate at which a population grows is described by the population growth rate, often represented by the symbol lambda (\(\lambda\)). Higher values of \(\lambda\) indicate rapid population growth, while smaller values suggest slow growth.
The quantity (λ + R) is called the finite rate of increase, λ. Thus, we can write where N is the number of individuals present in the population, and t is a time interval of interest.
The symbol \(r\) is called the instantaneous rate of increase or the intrinsic rate of increase. The parameters \(r\) and \(r_d\) are not equal, although they are related, as we will show below.
λ is also called the finite rate of increase. Therefore, by induction, we obtain the expression of the population size at time t: = where λ t is the finite rate of increase raised to the power of the number of generations. This last expression is more convenient than the previous one, because it is explicit.
Under many circumstances it's valuable to have a 'finite' rate of increase, or the rate/unit time in the same time units used to calculate r and the generation time. The finite rate of increase is called lambda, and = e r (= 1.14 for this life table).
We can determine this by computing the net reproductive rate (R 0). To predict long-term changes in population size, we must use this net reproductive rate to estimate the intrinsic rate of increase (r).
