An increase or decrease in one population directly affects the other.

Explanation:
Predators and their prey often exhibit similar population cycles, where the populations of both species go through periodic increases and decreases over time. This phenomenon is known as predator-prey cycles or population cycles. The best explanation for this phenomenon is that an increase or decrease in one population directly affects the other.

1. Interdependence between predator and prey populations:
- Predators rely on prey as a source of food. When prey populations are abundant, predators have a sufficient food supply, leading to increased reproduction and population growth.
- However, as the predator population grows, the increased predation pressure causes a decline in the prey population.
- With a decrease in prey availability, predators face food scarcity and reduced reproductive success, leading to a decrease in their population size.

2. Feedback loop:
- The decrease in prey population reduces the food supply for predators, causing their population to decline as well.
- As the predator population decreases, the reduced predation pressure allows the prey population to recover and increase in numbers.
- This increase in prey population then supports the growth of predator populations, creating a feedback loop.

3. Time lag:
- The population cycles between predators and prey are not instantaneous. There is often a time lag between the changes in one population and the response of the other population.
- For example, when prey populations decline, it may take some time for the predator populations to adjust and start declining as well.
- Similarly, when prey populations increase, it takes time for predator populations to respond and increase in numbers.

4. Oscillations in population size:
- This interplay between predator and prey populations leads to oscillations in their population sizes over time.
- When prey populations are low, reduced predation allows them to rebound, leading to an increase in prey populations.
- As prey populations increase, predation pressure intensifies, causing a decline in prey populations and subsequently reducing the food supply for predators.
- This cycle of increase and decrease in population sizes continues.

In conclusion, the interdependence between predator and prey populations and the feedback loop created by their interactions explain why predators and their prey often exhibit similar population cycles. An increase or decrease in one population directly affects the other, leading to oscillations in their population sizes over time.