The carrying capacity of an area refers to the maximum number of individuals of a given species that can be sustained indefinitely in a particular area. This means that it is the limit of population size that can be supported by the available resources and environmental conditions.

Option 1, which states that carrying capacity is the increase in population size by even larger amounts per unit time, is incorrect. Carrying capacity does not describe the rate of increase in population, but rather the maximum number of individuals that can be supported without depleting resources or causing environmental degradation.

Option 2, which mentions that carrying capacity is dependent on birth, death, immigration, and emigration rates, is partially correct. These factors do influence the carrying capacity of an area, as an increase in birth or immigration rates can increase the population size and potentially exceed the carrying capacity. However, carrying capacity is not solely dependent on these rates, but also on factors such as resource availability and environmental factors.

Option 4, which suggests that carrying capacity is a demographic expression of the rate of natural increase in a population, is also incorrect. Carrying capacity is not a measure of the rate of increase, but rather the maximum population size that can be sustained.

Therefore, option 3 is the correct answer as