Predator-prey feedback in a gyrfalcon-ptarmigan system?

Specialist predators with oscillating dynamics are often strongly affected by the population dynamics of their prey, yet they do not always participate in a predator-prey cycle. Only those that exert strong population regulation of their prey do so. Inferring the strength and direction of the predator-prey coupling from time series therefore requires contrasting models with top-down versus bottom-up predator-prey dynamics. We examine such population-level coupling using multivariate autoregressive models. The models translate several hypotheses for the joint dynamics of population densities of the Icelandic gyrfalcon Falco rusticolus, and its prey, the rock ptarmigan Lagopus muta. The dynamics of both species are likely not only linked to each other but also to stochastic weather variables acting as confounding factors on the joint dynamics. The classical MAR(1) model, used most often in ecology, predicts that the times series exhibit predator-prey feedback (i.e., Granger causality): the predator helps to explain prey dynamics and the prey helps to explain predator dynamics. Weather, in the form of spring temperature, influences gyrfalcon population growth but not ptarmigan population growth, despite individual-level evidence that ptarmigan chicks can be strongly affected by weather. MAR(2) models, allowing for species to cycle independently from each other, further suggests alternative scenarios where a cyclic prey influence its predator but not the other way around; such bottom-up models produce a better fit but less realistic cross-correlation patterns. Simulations of MAR(1) and MAR(2) models further demonstrate that the top-down MAR(1) models are most likely to be misidentified as bottom-up dynamics than vice-versa. We therefore conclude that predator-prey feedback in the gyrfalcon-ptarmigan system is very likely, though bottom-up dynamics cannot be excluded with certainty. We finally discuss what sort of information is needed to advance the characterization of joint predator-prey dynamics in birds and other vertebrates.