2 Population growth

Imagine a few rabbits introduced to a new place that has plenty of food and no competitors:

1. At first, the rabbits adjust to the new place.
2. They begin to reproduce.
3. With abundant food, the population rises quickly.
4. As numbers rise, food begins to run out.
5. Competition increases and the growth slows down.
6. The population reaches a relatively stable size balanced with its environment.

The growth curve has four phases: lag phase (slow start), exponential growth phase (rapid increase), slowing-down phase, and stationary phase (at the carrying capacity).

Exponential growth. Under ideal conditions a population can multiply rapidly: 2 → 4 → 8 → 16 → 32 …, i.e. 2¹, 2², 2³, 2⁴, 2⁵ …

Worked example 1

A culture of bacteria doubles every hour starting from 1 cell. After 1 hour: 2 cells (2¹); after 2 hours: 4 (2²); after 5 hours: 2⁵ = 32; after 10 hours: 2¹⁰ = 1024 cells. If it starts from 3 cells, after 4 hours there are 3 × 2⁴ = 48 cells.

Environmental resistance.

• In nature, growth cannot go on for ever because resources (food, water, space) are limited.
• The factors that limit population growth are called environmental resistance:

• depletion of resources,
• increased competition among individuals,
• fast spread of diseases and parasites (and predators).

• Because of environmental resistance, the population stops growing at the carrying capacity: the maximum number of individuals of a species that an environment can support continuously without damaging its resources.
• If a population goes above the carrying capacity, resources are exhausted, so deaths exceed births and the number falls back.

Application. In nature reserves, scientists determine the carrying capacity of each species and intervene if a population grows too much or declines sharply, to maintain the balance of the ecosystem.