Question

Does the growth of a population with time show any specific and predictable pattern?

Answer 1

The population does show a specific growth pattern depending on the resources available to it.
There are two types of population growth pattern-

• Exponential growth
• Logistic growth

The population grows in a geometric and exponential manner when available resources are plenty. This usually occurs in laboratory conditions.
It can be given as: dN/dt = rN
where, N = Population size,
r = (b-d) is the intrinsic rate of natural increase (b is birth rate and d is death rate)
t = time period
The integral form of this equation is Nt = N0ert
Graph: J-shaped curve when we plot N in relation to time.

Fig: Exponential growth

Logistic population growth takes place when the resources are limited. The curve of the graph is sigmoid in nature or S-shaped as the population has the following growth pattern:-

• Lag phase: The population is getting adjusted to the environment.
• Log phase: The second part of the curve shows an exponential increase in the population as the resources are available. There are three phases between lag phase and stationary phase are as follows:
• Positive acceleration phase: Limited growth in population.
• Exponential growth phase: Suddenly and very rapid growth of population.
• Negative acceleration phase: Decrease in the growth rate.
• Stationary phase: As population density increases, resources become a limiting factor resulting in growth slowing down. The population reaches the carrying capacity (K) of the environment.

The following equation represents the dN/dt = rN{(K-N)/K} Where N = Population density at time t
t = Time
r = Intrinsic rate of natural increase
K = Carrying capacity (maximum possible number of organisms in an environment, beyond which no further increase can take place)