Step 1: Understand demographic stochasticity.
Demographic stochasticity refers to the random fluctuations in population size and growth due to the random nature of reproduction and survival at the individual level. Populations with small geographical ranges and low population densities are more vulnerable to these fluctuations, making them more likely to face extinction.
Step 2: Evaluate each option.
Option (A): Correct, small range and low population density increase vulnerability to extinction via demographic stochasticity.
Option (B): Larger ranges can reduce vulnerability by allowing for a larger population, even if density is low.
Option (C): High population density can buffer against demographic stochasticity, making this option less likely to cause extinction.
Option (D): Large range and high density would typically protect against stochastic extinction.
Hence, the correct answer is (A).