Chapter 14. Chapter 14 Graphic Content

The graph shows how a population’s size changes over time. Based on the graph’s title, “Managing Natural Resources,” it also is intended to reveal something about how knowledge of population growth can help resource managers be more effective. Specifically, it shows the size at which a population can most effectively be utilized for natural resources, which may involve cutting down some trees for wood or catching some lobsters for food, for example.

As a population gets closer to the carrying capacity of its environment, its growth slows and plateaus at that point.

A population can stay at the same size if the number of individuals arriving (through birth or immigration) is exactly the same as the number of individuals leaving (through death or emigration). This situation can persist indefinitely, even as organisms continue dying.

No data points appear on the graph. This suggests that perhaps the graph just presents a theoretical relationship. In this case, it appears to be the relationship between population size and time, when a population is growing logistically, calculated as: rN [ (K – N ) / K ].

It would be helpful if some real data were presented for actual populations, showing how they grow over time. The data points could be overlaid on the graph, perhaps with points for different populations shown in different colors. This would give insight into how well the logistic growth equation predicts the actual growth of natural populations.

Implicit assumptions are, first, that carrying capacity does not change over time, and second, that a population’s growth is restrained with perfect efficiency as it approaches its carrying capacity. In other words, growth slows exactly as required to avoid exceeding the carrying capacity—as opposed to the population growing so quickly that it overshoots its carrying capacity, after which it grows more slowly, possibly undershooting K, and ultimately oscillating around it.

The graph described in the question will show a sort of inverted "U," with the low points of growth rate at population sizes 0 and K, and with the maximum in the middle of the x-axis at K / 2. The population grows fastest when it is at half its carrying capacity.