Why 'K' Matters

Whereas 'r' is the driver of population growth, so 'K', the carrying capacity of the environment, is the handbrake to limit total population size.

Last August we posted about exponential population growth where a constant rate of population growth, ‘r’, drives bigger and bigger increases in population size to give the classic ‘J’ shaped curve of population size.

While this scenario is usually only theoretical, or reserved for controlled lab experiments, it can be observed in natural populations that grow quickly from a narrow base, such as when a small number of founders colonise a new habitat.

So if ‘r’ is the accelerator of population growth then what acts as the brake to slow down the rate of population growth?

The answer is ‘K’, the carrying capacity of the environment. This expresses itself as limiting factors that cap population size to an upper limit. These limiting factors can be many and varied and may include food availability, or living space, or the availability of mates to breed with. As the size of the growing population approaches this carrying capacity then population growth slows down to generate the distinctive ‘S’ shaped curve of logistic population growth.

As the population size approaches the environmental carrying capacity, one of a number of outcomes may occur:

• the population stabilises and shows little variation in size from year to year gradually oscillating around the carrying capacity
• the population is able to escape the limiting factor and continues growing until it reaches another limiting factor that checks population size at a higher level
• the population growth rate is so high and the population is growing so fast that it overshoots the carrying capacity leading to environmental damage that actually lowers carrying capacity and leads to a crash in population size as it is dragged down to the reduced carrying capacity of the environment.

The first of these outcomes usually occurs with long lived animals that breed quite slowly, such as cattle on a farm.  Unless the farmer can find ways of feeding larger numbers of animals using supplementary feed the farm will support roughly the same size herd from year to year. The global human population is an example of the second outcome. Colonisation of new lands, increased food production and improved medical care, especially leading to higher child survival, has led to a booming number of people on Planet Earth since the Industrial Revolution in the 18th Century that still shows little sign of slowing down after 300 years of runaway growth.

The third outcome is a possibility when invasive animals arrive in a new habitat, such as on an island. Here they may escape from the limiting factors that affect them in their existing habitat, plus they can exhibit exponential growth to skyrocket in numbers. Just such an event happened on Taukihepa / Big South Cape Island off the southern tip of Stewart Island during the late 1950’s when rats colonised the predator free island by getting ashore along a boat’s mooring line then exploded in numbers.

Rat numbers got so high they denuded the forest of undergrowth, they caused the extinction of two species of bird and one species of bat and even took to eating the bedding and the wallpaper on the walls in a hut on the island. Only emergency translocations saved the South Island Saddleback from joining the Bush Wren, South Island Snipe and Greater Short-tailed Bat on the list of New Zealand’s extinct animals. Big South Cape is now free of rats after a successful eradication project undertaken in 2006.

​Whereas ‘r’ can be the enemy of pest and predator management while it is a positive number and drives population growth, ‘K’ can be a friend if it is paired up with ‘r’ as a negative number and turned into a sinking lid.

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