Final answer:
The study of how predator and prey population sizes change over time is called predator-prey dynamics, a crucial part of population ecology and demography that helps us understand ecosystem balance.
Step-by-step explanation:
Studying how the changing sizes of predator and prey populations vary over time is known as predator-prey dynamics. This field of biology examines the fluctuations of these populations as they affect each other. For example, when a prey population increases, it provides more food for predators, which can then also increase in number. However, as predators become more numerous, they begin to reduce the prey population through increased predation, which in turn may lead to a decrease in the predator population due to a shortage of food. These interactions can result in cyclic patterns of population sizes, such as the well-known cycle between the lynx (predator) and the snowshoe hare (prey) which lasts approximately ten years.
The study of these interactions and the factors influencing population sizes, including environmental changes and natural disasters, is a subfield of population ecology known as demography. Demography uses mathematical tools to investigate how populations respond to biotic and abiotic changes in their environments. The predator-prey dynamic is a classic example of this study and plays an essential role in understanding the balance and health of ecosystems.