Predator-prey feedback in a gyrfalcon-ptarmigan system?

Frédéric Barraquand,Ólafur K Nielsen

doi:10.1002/ece3.4563

Abstract

Specialist predators with oscillating dynamics are often strongly affected by the population dynamics of their prey, yet they are not always the cause of prey cycling. Only those that exert strong (delayed) regulation of their prey can be. Inferring predator–prey coupling from time series therefore requires contrasting models with top‐down versus bottom‐up predator–prey dynamics. We study here 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. We infer the degree of coupling between populations, as well as forcing by abiotic variables, using multivariate autoregressive models MAR(p), with p = 1 and 2 time lags. MAR(2) models, allowing for species to cycle independently from each other, further suggest alternative scenarios where a cyclic prey influences its predator but not the other way around (i.e., bottom‐up scenarios). The classical MAR(1) model predicts that the time series exhibit predator–prey feedback (i.e., reciprocal dynamic influence between prey and predator), and that weather effects are weak and only affecting the gyrfalcon population. Bottom‐up MAR(2) models produced 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 more likely to be misidentified as bottom‐up dynamics than vice versa. We therefore conclude that predator–prey feedback in the gyrfalcon–ptarmigan system is likely the main cause of observed oscillations, though bottom‐up dynamics cannot yet be excluded with certainty. Overall, we showed how to make more out of ecological time series by using simulations to gauge the quality of model identification, and paved the way for more mechanistic modeling of this system by narrowing the set of important biotic and abiotic drivers.

Highlights

Theoretical ecology predicts that among predators, specialists are the most likely to shape the dynamics of their prey (e.g. Andersson& Erlinge, 1977; Gilg, Hanski, & Sittler, 2003; Turchin & Hanski, 1997)
The full 2 × 2 interaction ma‐ trix in a Multivariate Autoregressive (MAR)(1) framework provided a better model than a diagonal matrix, meaning there was causality between prey and predator dynamics in the sense of Granger (1969): The addition of the predator and prey variables reduced the residual variances of the time series models for the prey and predator, respectively
We found, in agreement with Lütkepohl (2005), that time series of around 100 points are needed to allow for fairly reliable inference of top‐down versus bottom‐up dynamics in systems of 2 cyclic species

Summary

| INTRODUCTION

Theoretical ecology predicts that among predators, specialists are the most likely to shape the dynamics of their prey While there is a convincing array of evidence showing that lynx has a dynamical impact on hare (Vik et al, 2008), and wolf has an impact on moose (Vucetich et al, 2011), there is evidence that weather and other drivers have often a strong forcing influence on prey dy‐ namics (Vucetich & Peterson, 2004; Yan, Stenseth, Krebs, & Zhang, 2013) Even in such strongly interacting systems that fascinate the imagination by demonstrating strong oscillations, it has been sug‐ gested that the presence of an ubiquitous external forcing hardly warrants to view such systems as a pair of autonomous coupled dif‐ ferential equations (Barraquand et al, 2017; Nisbet & Gurney, 1976), despite the pivotal role of autonomous and deterministic dynamical systems in ecological theory (see e.g., McCann, 2011). MAR modeling has been largely developed in econometrics (Granger, 1969; Lütkepohl, 2005), where it is primarily used to estab‐ lish causal relationships in the sense of prediction (i.e., a variable has causal influence if it helps improving predictions about the future, Granger, 1969), which is the statistical philosophy that we adopt here

| MATERIALS AND METHODS

Findings

| DISCUSSION

| CONCLUSION