Step 1: Understand island biogeography.
Island biogeography suggests that small islands typically support fewer species because they have fewer resources, lower environmental heterogeneity, and smaller populations.
Step 2: Evaluate each option.
Option (A): Correct, small islands have smaller populations and fewer resources, which increases the likelihood of extinction.
Option (B): Correct, smaller islands typically have less environmental variation, limiting the diversity of species they can support.
Option (C): Correct, smaller islands support fewer individuals, which increases the risk of extinction due to random events.
Option (D): Incorrect, smaller islands typically have lower speciation rates due to fewer ecological opportunities.
Hence, the correct answers are (A), (B), and (C).