Biology · Ch 13 — Organisms and Populations
Population Growth
Population Growth
The density of a population in a given habitat, over a given period, fluctuates because of four basic processes. New births (B) and immigration (I) both act to increase population density, while deaths (D) and emigration (E) both act to decrease it. Immigration is the number of individuals of the same species that have entered the habitat from elsewhere over the time period under consideration, while emigration is the number of individuals of the population that have left the habitat over that same period. If Nₜ is the population density at time t, then the density one time-step later, at time t+1, can be calculated as:
Nₜ₊₁ = Nₜ + [(B + I) − (D + E)]
Ecologists recognise two broad models describing how a population's size changes with time.
i. Exponential growth: resources such as food and space are essential for any population to grow. When resources in a habitat are effectively unlimited, a species can fully realise its innate reproductive potential, and the population grows in an exponential, or geometric, proportion. Darwin famously illustrated this by showing how even a slow-breeding animal like the elephant could, given unlimited food and space, eventually reach enormous numbers. Plotted against time, this produces a continuously accelerating, J-shaped curve (Fig. 13.4), rising ever more steeply the larger the population becomes. …
What this figure shows. A simple two-axis line graph with time along the horizontal axis and population size along the vertical axis. The plotted curve rises only gently at first and then climbs ever more steeply, tracing a smooth, continuously accelerating, upward-sweeping J-shaped curve that never levels off within the plotted range. It illustrates that when resources are unlimited, a population increases at a rate proportional to its own current size, so the pace of g …
What this figure shows. A graph of population growth (plotted as size or weight of the organism) against time, drawn as an S-shaped (sigmoid) curve made up of four labelled phases occurring in sequence along the curve: first a lag phase where the increase is slow, then a log or exponential phase where growth accelerates rapidly, followed by a diminishing-growth phase where the rate of increase slows down as resources become limiting, and finally a stationary phase where the curve flattens out once t …