Final answer:
The population size can increase without migration when the birth rate rises and the death rate falls, which is option (C) Birthrate increases; death rate decreases.
Step-by-step explanation:
The conditions under which the size of a population can increase without the influences of migration depend on the rates of births and deaths within that population. In the absence of migration, if the birth rate is larger than the death rate, the population will experience growth. Specifically, when the birth rate increases and the death rate decreases, the population sees a positive growth. Therefore, the correct answer to the question would be (C) Birthrate increases; death rate decreases.
Throughout the demographic transition stages, we can observe how fluctuations in birth and death rates affect population growth. For instance, in Stage 2, we see a decline in death rates while birth rates remain high, resulting in faster population growth. Studies like life tables can help us understand these dynamics by shedding light on demographic characteristics that influence population changes, such as life expectancy and its impacts on resources, reproduction, and health.