A population which exceeds its carrying capacity and then collapses is represented graphically by a

Analyze the question: It asks which graph shape shows a population that grows beyond its carrying capacity (K) and then crashes.

Concept: Population growth curves in ecology:

• J-shaped (exponential) curve: rapid growth with no limit.
• S-shaped (sigmoid) curve: logistic growth. The population grows slowly, then rapidly, then levels off at the carrying capacity. It does not overshoot and collapse.
• Boom-and-bust (overshoot and crash): the population rises sharply, overshoots K because resources are used up, then falls steeply. On a graph this rises to a peak and then drops, giving a hump or bell-like shape.

Working through the options:

• A. Bell-shaped curve: it rises to a peak and then falls. This matches growth beyond carrying capacity followed by collapse.
• B. Linear curve: a straight line shows constant increase or decrease. This doesn't fit.
• C. Sigmoid curve: this is the normal logistic growth that stabilises at K, with no collapse. This doesn't fit.
• D. Skewed curve: this term describes the asymmetry of a distribution, not the standard name for a population crash. It is not the best choice.

A population that overshoots and then collapses shows a rise, a peak, and a fall. The best description among the options is a bell-shaped curve.

Exam tip: Remember the pattern:

• Sigmoid (S) = growth that levels off at K.
• J-shaped = growth with no limit.
• Bell or hump = boom and crash, rising and then falling.