The carrying capacity of a population is determined by its

Concept. Carrying capacity, written K, is the largest population of a species that a particular habitat can support indefinitely. Nature does not supply unlimited food, water, space or nutrients, so every habitat holds only a finite stock of these essentials, and by Liebig’s law of the minimum the essential in shortest supply relative to demand sets the ceiling. In the logistic model dN/dt = rN(K − N)/K, K is that resource-imposed ceiling: it is a property of the habitat’s resource supply, not of any rate the population happens to be showing.

Application. The stem asks what fixes K for a population. Work through what each candidate is:

1. Identify the essentials the population must draw from its habitat — food, water, breeding space, mineral nutrients.

2. Ask which of them the habitat can supply only in limited amount; that scarcest essential is the limiting resource.

3. The number of individuals that limited supply can maintain is K. Add more resource and K rises; take resource away and K falls.

So the carrying capacity is determined by the limiting resources of the habitat — that is the value limiting resources.

Contrast with the other values.

• population growth rate — dN/dt is an outcome, not a cause. As N approaches K the growth rate falls to zero; it is K that shapes the growth rate, not the other way round. A population can grow fast or slowly in the same habitat without changing the ceiling that habitat can support.

• natality — births per unit population per unit time is one of the four demographic parameters that change population density (with mortality, immigration and emigration). Raising natality makes a population reach the ceiling sooner; it does not raise the ceiling, because the extra individuals still have to be fed from the same finite stock.

• More than one of the listed options — this would need at least two of the three named items to fix K, but neither the growth rate nor natality fixes it, so only one of them does.

• None of the listed options — rejected, because one of the listed items, the limiting resources, does fix K.

Cross-check. NCERT Class XII Biology, Organisms and Populations, states that a population growing in a habitat with limited resources shows logistic growth and that every habitat has a limit, nature’s carrying capacity (K), beyond which no further growth is possible — the limit being set by the limited resources of that habitat. A quick test confirms it: two ponds of identical size, one nutrient-rich and one nutrient-poor, support very different maximum fish populations even though birth rates are the same.

Answer: limiting resources.