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Population Ecology

Author(s): Evan Siemann, PhD

Density-independent Population Growth

Continuous population growth models use differential equations (population growth rate is represented as dN/dt=rN0). Discrete models employ  difference equations (time at some number of time steps in the future is a function of the current population size - Nt+1=λNt). In these simple equations, r and λ depend only on immigration, emigration, births and deaths.

The dynamics of these models also are simple. If births exceed deaths (λ>1 or r>0), the population increases exponentially to infinity. If births are the same as deaths, the population stays constant. If deaths exceed births (λ<1 or r<0), the population decreases asymptotically to zero. The only difference in the dynamics of these two models is the shape of the population growth curve: smooth with continuous reproduction and stair-step when reproduction is discrete.