The S-shaped growth curve

The number of organisms in a natural population changes with time in a definite pattern. Plotted as a graph, it gives a sigmoid (S-shaped) growth curve with four main phases.

t	0	0.5	1	1.5	2	2.5	3	3.5	4	4.5	5	5.5	6	6.5	7	7.5	8	8.5	9	9.5	10
N	0.04	0.07	0.12	0.21	0.36	0.6	1	1.61	2.5	3.66	5	6.34	7.5	8.39	9	9.4	9.64	9.79	9.88	9.93	9.96

Figure 15.4 — the population growth curve: number N against time t, with the carrying capacity dashed. The guides separate phases 1 to 4.

Phase 1 — lag phase

Numbers begin to rise, but slowly, because few organisms are breeding and they are spread over a wide range.

Phase 2 — exponential phase

The fastest growth: organisms have adapted well, more mature ones are breeding, conditions are favourable and food is plentiful. The birth rate is higher than the death rate.

Phase 3 — decelerating phase

Growth slows because of limiting factors: competition for limited resources, food shortage, disease, predation and parasitism.

Phase 4 — stabilising phase

Numbers change until the population fits what the environment can hold; then births and deaths balance, a dynamic equilibrium, and growth is taken as zero.

Carrying capacity

The number of organisms in a population once it has reached this equilibrium is its carrying capacity.

Why the curve bends twice

At first there are few parents, so even a high birth rate adds few young. As numbers grow, there are more parents and each generation adds more than the last, so the curve turns steeply upward. But the habitat has only so much food, space and water. As the population approaches that limit, each extra animal makes food scarcer for all, disease spreads more easily in crowds, and predators find prey more often, so the curve bends over and levels off. The carrying capacity is not fixed: a drought can lower it, and good rains raise it.

Slow, fast, slowing, steady

A natural population grows in an S-curve: lag, exponential, decelerating and stabilising phases, levelling off at the carrying capacity.