Using the phase shift for assessing the causation of population cycles

The occurrence of an appreciable phase shift between the predator and prey curves is a characteristic signature of predator–prey cycles. The magnitude of the phase shift can be used for assessing whether the direct effect of predation is likely to cause the observed cyclic dynamics. The statistical estimation of the phase shift requires having simultaneous, long-term data series for predator and prey in the same locality, a condition that is almost never satisfied by long-term data of most cyclic populations. A method for estimating the magnitude of the phase shift between the predator and prey trajectories using only single species data. This method is applied to two cases in which predation has been suggested to be the ecological cause of the cycles: the lynx–hare cycles in boreal Canada and the gyrfalcon–ptarmigan cycles in northern Iceland. The estimates of the phase shift indicate that while the lynx–hare cycles are unlikely to be due by the direct effect of lynx predation, those of gyrfalcon–ptarmigan are consistent with predator–prey causation.