Question

Explain the two patterns of growth observed in a population, based on the availability of resources? [5 marks]

Answer 1

There are two patterns of growth based on the availability of resources:

i) Exponential or J-shaped growth form [½ mark]
When resources in the habitat are in abundance, each species in the population grows exponentially. Any species which is growing exponentially under unlimited conditions can reach an enormous population in a short span of time. [½ mark]
It is represented by: dN/dt = rN, [½ mark]
where
dN/dt = the increase or decrease in a size of population (N) during a unit time period (t)
r = the ‘intrinsic rate of natural increase’ and is calculated by r = b-d, where b is the per capita births and d is the per capita deaths
R is an important parameter which is chosen for determining the impacts of any biotic or abiotic factor on population growth. [½ mark]
The above equation shows an exponential or geometric growth pattern of a population and forms a J-shaped curve when we plot N in relation to time. [½ mark]

ii) Logistic or S-shaped growth form [½ mark]
For a given habitat, there is a limit to the resources that can support a maximum possible number. This is known as nature’s carrying capacity for a species in a particular habitat and beyond this no further growth is possible. [½ mark]
It is described by the following equation:
dN/dt = rN[(K-N)/K], [½ mark]
where,
N = Population density at time t
R = Intrinsic rate of natural increase
K = Carrying capacity [½ mark]

A plot of N with respect to time (t) results in a sigmoid growth curve. [½ mark]

Fig. Graph: J-shaped growth curve (blue) and S-shaped growth curve (red)