Population Growth and Natural Resources - class-XI

The carrying capacity of an organism is the maximum population size of the species that the environment can sustain indefinitely beyond which there is no further growth. When the population reaches the carrying capacity then mortality becomes greater than natality.

Population growth rate measures the number of individuals in a population (N) over time (t). When the conditions are ideal, the type of growth is known as exponential form of growth which is expressed by the equation, (dN)/(dt)= rN. When the limiting factors is restricted, the growth pattern is known as logistic growth model. This model is described by the differential equation (dN)/(dt)= rN(K-N)/K, where K is the carrying capacity and r is the maximum per capita growth. 

A logistic growth curve that is limited by a definite carrying capacity is shaped like the letter 'S' or a sigmoid curve, which is differentiated into three parts the Lag phase, the Log phase or the exponential growth phase and the stationary or plateau phase. At this phase the amount of resources cannot support the growing population, due to which the number of members in the population is prevented from increasing

The rate of change in a population can be defined as the ratio of total change in population and time taken for that change. Change in population size can be defined as difference in population size at the end and between the beginning of a particular time period

In ecological formulas, N typically represents the total population size and S represents the area or space, so N/S represents population density.

a) Pacific salmon Fish of the genus Oncorhynchus is an individual that reproduces only once in its lifetime. 

In logistic growth, the asymptote (carrying capacity K) is reached when N = K (population equals carrying capacity). At this point, population growth stops because resources limit further growth. When K > N, population is still growing. Option C has garbled formatting but would represent K < N, which is impossible.

The concept that 'population tends to increase geometrically while food supply increases arithmetically were put forward by Thomas Malthus. In his theory of natural selection, Charles Darwin was greatly influenced by the English clergyman Thomas Malthus. Malthus published a book in 17981798 stating that populations with unlimited natural resources grow very rapidly, after which population growth decreases as resources become depleted. This accelerating pattern of increasing population size is called exponential growth.

Carrying capacity is the maximum size of the population of a species that a certain environment can support for an extended period of time. Once population overshoots the carrying capacity, it starts decreasing as at this point, the different environmental resistances start operating and population dies because of the struggle for existence. Among the given options, option B shows that carrying capacity of pasture was exceeded turning it into the barren land. The increase in grasses or weight gain of cow suggests growth of grassland.

The logistic growth equation is dN/dt = rN(1 - N/K), where r is the intrinsic rate of increase, N is population size, and K is carrying capacity.