Population is a changing entity. Its size composition is ever-Changing. The changes in size and composition are dependent on growth rate. Population shows characteristic patterns of increase which are known as growth patterns.
Basically these are differentiated into two types:
1. J-Shaped Growth Pattern - The J-shaped growth pattern of a population is characterized by the following features -
In the beginning the density of population increases rapidly in compound interest fashion and then stops abruptly as the environmental factors becomes effective. The factors may be food or space or some seasonal factor or if the reproductive season terminates. In this pattern of growth, the density reaches the upper limits, remains at the level for a time and then declines producing a 'relaxation' pattern. This could by represented by the following equation:
dN / dt = rN
Where,
N = Population size,
r = coefficient of population growth.
2. S-Shaped or Signoid Growth Pattern - In this type of growth pattern initially the population increases slowly, then more rapidly and then slows down gradually as the environmental resistance increases until an equilibrium level is reached and maintained. This type of growth is seen more frequently. If a graph is plotted for the density of population against time on arithmetic scale the population growth presents a distinct S-shaped curve. This is known as 'sigmoid curve'. This could be expressed by the following equation:
dN / dt = rN (K-N/K)
Where,
dN/dt = the rate of population growth,
N = the possible size (number)
r = intrinsic rate of population growth,
K = the maximum population size possible.
The rapid increase in number results in over crowding of the population and therefore, adds to the environmental resistance. This brings down the rate of reproduction.
Theories of population growth
The growth of a population can be described by simple mathematical models for the organisms both with discrete generation and with overlapping generations. However if the reproductive rate is constant geometric population growth occurs. The population growth can be explained by various theories. Some important ones are as follows:
(a) Mathematical theory - It applies to those populations exhibiting discrete generations as well as overlapping ones.
(b) Logistic theory - It is applied to those populations growing in limited space.
In it, a logistic curve or S-shaped curve is obtained having upper asymptote and smooth upper maximal level. This theory was first proposed by Verhurst in 1838 and later revived by Pearl Read (1920) to describe the growth of human population. Under logistic theory, two variant approaches have been proposed to explain growth of natural population
(a) Time lag models - Such models have been constructed to describe the population growth of complex organisms. The introduction of time lags into population growth causes the stable asymptote of logistic curve to be replaced by -
- A converging oscillation towards equilibrium,
- A stable oscillation about equilibrium level
- A smooth approach to equilibrium density. Besides, time lags produce a divergent oscillation which are unstable and leads to the extinction of the population.
Regulation of Population Growth
The inherent tendency of all animal populations is to increase in number. But this increase in number is, however, not infinite since the carrying capacity of the environment always imposes a restriction upon it. The regulation of population growth is caused by the following factors:
1. Density Dependent Factors - Density dependent factors are those that vary in the intensity of their action with the size or density of the population. The concept of density dependent factors indicates that all populations are regulated automatically. In the words of the Australian ecologist A.J. Nicholson, "Populations are self governing systems. They regulate their densities in relation to their own properties and those of their environments." Populations become stabilized by density dependent factors whose effect increases in intensity as the population level rises and decreases as the population level declines.
2. Density Stabilizing Factors - These are as under:
- Interactions - The size of a population is determined by interactions either among its members or with other species of competitors, predators or parasites. The role of competition in regulating the population is directly effective by causing mortalities, nest destruction and lobs of food supplies. Regulation by predators or parasities is another possibility. The explosive increase of some species when their predators were removed shows that they had been regulated by their predators.
- Reproductively - It is also a density-stabilizing factor. The birth and death rates have the important roles in regulation of population size.
- Emigration - The pressure of over populations can be relieved by mass emigrations of individuals from particular localities. Emigrations under normal conditions occur when there is overcrowding in the migratory locust, lemming. grouse, snowy owl, snowshoe rabbit, etc.
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