Predator and prey: the cycle that never settles

Predator and prey populations rise and fall in a cycle that never settles down, with the predators always lagging behind. It is one of the few patterns in ecology with a clean mathematical form, and the reason it never reaches equilibrium is the same reason a thermostat overshoots.

The lag is the mechanism

Follow one turn of the loop. Prey are abundant, so predators are well fed and produce more predators. But that takes time, so predator numbers keep climbing after prey have started to fall. The now-numerous predators overexploit the diminished prey, which crash. The predators then starve, but again with a delay, so their decline continues after prey have begun to recover. Prey rebound into a landscape with few predators left, and the cycle restarts.

At no point does either population sit still, and neither is failing to adjust. Both are responding correctly to conditions that have already changed by the time the response arrives.

Two equations, and their honest limits

Lotka and Volterra wrote this down independently in the 1920s as a pair of coupled equations: prey grow on their own and are eaten at a rate proportional to how often the two meet; predators die on their own and reproduce in proportion to the same meeting rate. That is enough to produce permanent cycles.

It also produces a genuinely counterintuitive prediction that turns out to be right. Kill both species indiscriminately, and the average prey population goes *up* while predators go down. Volterra derived this to explain why Adriatic fish catches during the First World War, when fishing largely stopped, contained a higher proportion of predatory species. Reduced fishing helped the predators more than the prey.

The model is also wrong in ways worth naming. It has no carrying capacity, so prey grow without limit when predators are scarce. It assumes predators never get full. It has no spatial structure, no refuges, no age classes. Its cycles are neutrally stable, which means a nudge moves the system to a different cycle permanently, and real populations are not that delicate. It is a clear demonstration of a mechanism, not a description of any actual ecosystem.

The evidence, including the awkward part

The famous data is the Hudson's Bay Company's fur records for snowshoe hare and Canada lynx, nearly a century of counts showing both species cycling with a period of about ten years and the lynx lagging behind.

It is a genuinely striking record and it does not straightforwardly confirm the model. Hare cycles continue on islands with no lynx at all, which means predation is not the sole driver: food supply and the hares' own stress physiology contribute. The lynx track the hares closely, but the hares are not simply tracking the lynx. A textbook that presents this as a clean confirmation is overstating it, and the more honest reading is that coupled cycles are real and their causes are plural.

Why this world has no such cycle

This is worth being precise about, because the components look closer to present than they are.

There is a biological ingestion mechanism here, so one organism consuming another is not impossible in principle. What has not been demonstrated is a stable predator level: a lineage that persistently makes its living from other organisms, sitting above a herbivore level that makes its living from the environment. Without that, there is nothing for a predator-prey cycle to be a cycle *of*.

The population oscillation you can actually watch is the single-species kind: organisms against a regrowing resource, which produces overshoot and crash for the delayed-feedback reason described in why populations boom and crash. The mechanism is the same family, one trophic level short.