At first, there are more lynx than rabbits. This is shown by the fact the orange curve is above the blue curve. Because there are more predators than prey, some predators will unfortunately go without food and starve (this assumes that rabbits are the lynx only food source). This die-off explains why the orange curve goes down or decreases.
As the predators die off, the prey has time to flourish. The rabbit population grows or increases. Note the blue curve going uphill as the orange curve goes downhill. The blue curve hits a peak point and it then goes down. This is due to the lynx population rebounding. There's more food for the lynx and the lynx population will increase. The lynx then eat the rabbits to bring the hare population down.
In short, as one population increases, the other decreases, and vice versa. This back and forth cycles indefinitely. This keeps things in balance so one population doesn't overwhelm a location. Keep in mind that I'm only focused on these two populations and no other animal species. Also, I'm not considering any other factors such as habitat loss. So this is a very simplistic view of what's going on in nature. It's considered a predator-prey model to give biologists a rough sense of what's going on.
The chart shows that we do have a cyclic up and down pattern for each population. For the most part, the peak rabbit populations seem to coincide with the lynx population increasing. Also, when the rabbit population is at its lowest, the lynx population is on the decline. Furthermore, when the lynx population is at its peak, the hare population is on the decline. The lynx population being at its lowest seems to coincide with the hare population increasing.
The exceptions to this general rule seem to be at around 1885, 1895, and 1905. During these time frames, it appears that the two populations are in lockstep together. In other words, they seem rise and fall at the same time. What could explain this is something like habitat loss that I mentioned earlier. Habitat loss would explain why a population decreases. Also, people hunting either animal would explain the population decrease if the hunting is intense enough. If the population gets too low, then governments may step in to enact endangered species laws to protect the animals so that the population could rebound again.
