Final answer:
For the measurement of population sizes, sample counting using a quadrat is best for immobile organisms like bluebonnet flowers and oak trees, while capture-mark-and-release is suitable for mobile organisms like birds and whales.
Step-by-step explanation:
To determine the best method for measuring the population sizes of different organisms such as birds, whales, bluebonnet flowers, and oak trees, one must consider the mobility and behavior of the organisms. Sample counting is ideal for immobile organisms, like the bluebonnet flowers and oak trees, which can be counted using a quadrat. On the other hand, the capture-mark-and-release method, also known as mark and recapture, is suitable for mobile animals like birds and whales. This method involves marking a sample of captured individuals, releasing them to mix with the unmarked population, and later recapturing some individuals to estimate the population size. Factors such as animal behavior and marking effects on survival must be considered to ensure accurate population estimates.