title: Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress.
abstract: Populations occasionally experience abrupt changes, such as local extinctions, strong declines in abundance or transitions from stable dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we study changes in the stability of populations under stress across a variety of transitions. Using a Ricker-type model, we simulate shifts from stable point equilibrium dynamics to cyclic and irregular boom-bust oscillations as well as abrupt shifts between alternative attractors. Our aim is to infer the loss of population stability before such shifts based on changes in nonlinearity of population dynamics. We measure nonlinearity by comparing forecast performance between linear and nonlinear models fitted on reconstructed attractors directly from observed time series. We compare nonlinearity to other suggested leading indicators of instability (variance and autocorrelation). We find that nonlinearity and variance increase in a similar way prior to the shifts. By contrast, autocorrelation is strongly affected by oscillations. Finally, we test these theoretical patterns in datasets of fisheries populations. Our results suggest that elevated nonlinearity could be used as an additional indicator to infer changes in the dynamics of populations under stress.
authors.affiliation: Institute of Integrative Biology, Center for Adaptation to a Changing Environment, ETH Zurich, Zurich, Switzerland vasilis.dakos@env.ethz.ch.
authors.forename: Vasilis
authors.identifier: 0000-0001-8862-718X
authors.initials: V
authors.lastname: Dakos
authors.affiliation: Korbel School of International Studies, University of Denver, Denver, USA.|Secure Fisheries, One Earth Future Foundation, Broomfield, CO, USA.
authors.forename: Sarah M
authors.initials: SM
authors.lastname: Glaser
authors.affiliation: Institute of Oceanography, Department of Life Science, National Taiwan University, Taiwan, Republic of China.|Institute of Ecology and Evolutionary Biology, Department of Life Science, National Taiwan University, Taiwan, Republic of China.|Research Center for Environmental Changes, Academia Sinica, Taiwan, Republic of China.
authors.forename: Chih-Hao
authors.initials: CH
authors.lastname: Hsieh
authors.affiliation: Scripps Institution of Oceanography, University of California-San Diego, San Diego, CA, USA.
authors.forename: George
authors.initials: G
authors.lastname: Sugihara
mesh_terms: D000818:Animals; D005399:Fishes / Q000502:physiology*; D008954:Models, Biological; D011157:Population Dynamics
keywords: critical transition; early warning signal; empirical dynamic modelling; population dynamics; resilience; state-dependence