Effect of Density on Populations
The Logistic Growth Model
- The exponential growth model assumes unrestricted growth in the population
- An unrestricted scenario is unlikely in nature and so populations rarely follow the J-curve for exponential growth
- Instead, populations are impacted by
- Density-dependent factors - These are factors which exert a stronger effect as the population increases e.g. competition for resources, predation and disease
- Density-independent factors - These are factors which restrict growth regardless of size or density e.g. natural disasters, extreme weather events or habitat destruction
- The logistic model produces a population growth curve which is sigmoid, or S shaped
- Such curves contain three phases:
- Exponential phase
- Also known as the logarithmic phase
- Here there are no factors that limit population growth, so the population increases exponentially
- The number of individuals increases, and so does the rate of growth
- This part of the curve is J shaped
- Transition phase
- As the population size increases, the density may increase past the threshold that can be supported by the system resource availability
- Limiting factors start to act on the population, eg. competition increases and predators are attracted to large prey populations
- The rate of growth slows, though the population is still increasing
- Plateau phase
- Also known as the stationary phase
- Limiting factors cause the death rate to equal the birth rate and population growth stops
- This plateau occurs at the carrying capacity
- The population size often fluctuates slightly around the carrying capacity
- Exponential phase
Population Growth Curve Graph
Sigmoidal population growth curves show an exponential (J-shaped) growth phase, a transitional phase and a plateau phase
- As limits to growth are imposed upon a population (as density changes), a new mathematical model emerges:
where:
dt = change in time
N = population size
rmax = maximum per capita growth rate of the population
K = carrying capacity
- The essence of this equation is that when N is large (near to the carrying capacity), then the term in brackets will be close to zero, so the growth rate will be small
An Example of a Logistic Growth Model
- Population growth curves can generally be seen in any newly established or recovering population, eg.
- Antarctic fur seals were hunted extensively during the 1800s and underwent a population recovery following the end of this practice
- The recovery of the seal population in some locations follows a classic growth curve, eg. in the graph below for seals on Cape Shirreff, Antarctica
- Pup count is used to represent the size of the seal population
- Note that this recovery has not continued throughout the early 21st century, with climate change having since caused severe declines in many seal populations
Antarctic Fur Seal Population Growth Curve Graph
The Antarctic fur seal population in Cape Shirreff, Antarctica, followed a classic growth curve between 1960 and the early 2000s