3.4: Carrying capacity

Population growth models

Mathematical equations that can be used to predict population size at any moment in time.

• Some uses: protect endangered species, manage hunting/harvesting, control pests

Exponential Growth (J Curve)

This means there are no limits making it unsustainable. In natural environment, resources become scarce and harmful waste builds up.

Exponential Growth Formula

A growth model that estimates a population’s future size (N_t ) 
after a period of time (t), 
based on the intrinsic growth rate (r)
and the number of reproducing individuals currently in the population (N₀).

(N_t = N₀e^rt)

Logistic Growth Model

A growth model that describes a population whose growth is initially exponential, but slows as the population approaches the carrying capacity of the environment.

• More realistic because it incorporates environmental limits.

• S-shaped curve

Variations on Logistic Growth Model

If food becomes scarce or other conditions change, a population can experience fluctuations.

• Overshoot - When a population becomes larger than the environment’s carrying capacity.

• Die-off - A rapid decline in a population due to death.

Polynomial Growth

Typical in predator/prey relationships

• With food and low predators, prey grow

• With more prey, predators then grow

• As prey reach carrying capacity, they die off

• As prey die, predators also die

• With less predation and more food, prey population increases again

Limiting resource

A resource that a population cannot live without and that occurs in quantities lower than the population would require to increase in size.

Carrying capacity (K)

The number of individuals the environment can support over a long period of time. Due to limiting resources AND density dependent limiting factors.

Density Independent Limiting Factors

Any factor limiting the size of a population whose effect is not dependent on the number of individuals in the population.

• A factor that could kill all members of the population regardless of whether the population is small or large; things that happen by chance.

• does not determine carrying capacity

Density Independent Factors Examples

• Climate (unseasonable cold snap)

• Natural Disasters – flood, fires, earthquakes, volcanos, tsunamis, hurricanes, etc.

Density Dependent Limiting Factors

Any factor limiting the size of a population whose effect is dependent on the number of individuals in the population.

• A factor where an individual’s chance of survival or reproduction depends on the number of individuals in the same area. Has a greater impact on a population as it grows in size.

• determines carrying capacity

Density Dependent Factors Examples

• Resources – food, shelter, mates

•  Disease

• Predation (more death as population increases)

• Build up of toxins

  • Stress (high density induces stress and makes hormonal changes to animals, reproduce less and die quicker