Long transients in ecology: Theory and applications

Морозов, А.; Abbott, Karen C.; Cuddington, Kim; Francis, Tessa B.; Gellner, Gabriel; Hastings, Alan; Lai, Ying Cheng; Petrovskii, Sergei; Scranton, Katherine; Zeeman, Mary Lou

doi:10.1016/j.plrev.2019.09.004

Cited by 152 publications

(136 citation statements)

References 151 publications

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“…The once popular idea that ecosystems are at, or moving towards, Lyapunov stability is considered passé (e.g., Morozov et al, 2019). The growing appreciation amongst ecologists that ecosystems and communities are dominated by nonlinear processes often outside of equilibrium (Rominger, et al, 2017) suggests that our tool kits to understand ecosystems need to evolve along with our analogies of them.…”

Section: Discussionmentioning

confidence: 99%

Viewing communities as coupled oscillators: elementary forms from Lotka and Volterra to Kuramoto

Hajian‐Forooshani

Vandermeer

2020

Preprint

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Ecosystems and their embedded ecological communities are almost always by definition collections of oscillating populations. This is apparent given the qualitative reality that oscillations emerge from consumer-resource interactions, which are the simple building blocks for ecological communities. It is also likely always the case that oscillatory consumer-resource pairs will be connected to one another via trophic cross-feeding with shared resources or via competitive interactions among resources. Thus, one approach to understanding the dynamics of communities conceptualizes them as collections of oscillators coupled in various arrangements. Here we look to the pioneering work of Kuramoto on coupled oscillators and ask to what extent can his insights and approaches be translated to ecological systems. We explore all possible coupling arrangements of the simple case of three oscillator systems with both the Kuramoto model and with the classical Lotka-Volterra equations that are foundational to ecology. Our results show that the six-dimensional analogous Lotka-Volterra systems behave strikingly similarly to that of the corresponding Kuramoto systems across all possible coupling combinations. This qualitative similarity in the results between these two approaches suggests that a vast literature on coupled oscillators that has largely been ignored by ecologists may in fact be relevant in furthering our understanding of ecosystem and community organization.

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Section: Discussionmentioning

confidence: 99%

Viewing communities as coupled oscillators: elementary forms from Lotka and Volterra to Kuramoto

Hajian‐Forooshani

Vandermeer

2020

Preprint

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“…Other suggested mechanisms responsible for transients are chaotic saddles responsible for transient chaos [38,39], spatial systems [40], linear systems with varying time scales, coupled oscillators, and stochasticity [41] (see also Refs. [42][43][44] 1: (a) Habitat loss is an important ecological handicap for species persistence. Here we display the percentages of habitat loss divided in terrestrial eco-regions (source: http://habitatlossfragmentation.weebly.com/habitat-loss.html).…”

Section: Introductionmentioning

confidence: 99%

Habitat loss causes long transients in small trophic chains

Vidiella

Valverde

Fontich

et al. 2020

Preprint

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Transients in ecology are extremely important since they determine how equilibria are approached. The debate on the dynamic stability of ecosystems has been largely focused on equilibrium states. However, since ecosystems are constantly changing due to climate conditions or to perturbations such as the climate crisis or anthropogenic actions (habitat destruction, deforestation, or defaunation), it is important to study how dynamics can proceed till equilibria. In this contribution we investigate dynamics and transient phenomena in small food chains using mathematical models. We are interested in the impact of habitat loss in ecosystems with vegetation undergoing facilitation. We provide a thorough dynamical study of a small food chain system given by three trophic levels: vegetation, herbivores, and predators. The dynamics of the vegetation alone suffers a saddle-node bifurcation, causing extremely long transients. The addition of a herbivore introduces a remarkable number of new phenomena. Specifically, we show that, apart from the saddle node involving the extinction of the full system, a transcritical and a supercritical Hopf-Andronov bifurcation allow for the coexistence of vegetation and herbivores via non-oscillatory and oscillatory dynamics, respectively. Furthermore, a global transition given by a heteroclinic bifurcation is also shown to cause a full extinction. The addition of a predator species to the previous systems introduces further complexity and dynamics, also allowing for the coupling of different transient phenomena such as ghost transients and transient oscillations after the heteroclinic bifurcation. Our study shows how the increase of ecological complexity via addition of new trophic levels and their associated nonlinear interactions may modify dynamics, bifurcations, and transient phenomena.

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“…as arising from a saddle-node bifurcation: for parameter values just past their bifurcation value, the system mimics its steady state dynamics prior to the bifurcation), crawl-bys (slow changes near saddle points) and slow-fast dynamics (different processes take place on different time scale); for more details, see (Hastings et al, 2018). In spatial systems, there are additional mechanisms that include travelling waves and formation of transient spatiotemporal patterns (Lai and Tél, 2011, Morozov et al, 2019, Petrovskii et al, 2005.…”

Section: Introductionmentioning

confidence: 99%

The Yellow Vests Movement - a case of long transient dynamics?

Морозов¹,

Petrovskii²,

Gavrilets³

2019

Preprint

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Understanding the dynamics of protests and social unrest is important in order to ensure a stable, sustainable development of the society. Mathematical models of social dynamics have been increasingly recognised as a powerful research tool in achieving this goal. Here, motivated by the fact that the dynamics of the ongoing Yellow Vest Movement in France exhibit anomalously long duration (currently it is in 30th week), we explore whether this can be a result of a dynamical systems phenomenon known as long transients. To this end, we build and study a hierarchy of mathematical models describing the "population dynamics" of the movement, i.e. how the number of protesters changes with time. We show that in these models long transients appear via two roots: via a ghost attractor and via an interaction of the slow and fast dynamics. We demonstrate that long transients are also present in some earlier models of social protests. Interestingly, our models predict that the Yellow Vest Movement should end abruptly by, at the latest, mid-summer 2019 without any interference from the French government. More generally, we argue that long transients are a generic feature of dynamical models describing social processes in the same way as they are in models of physical, ecological, and evolutionary systems.

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Long transients in ecology: Theory and applications

Cited by 152 publications

References 151 publications

Viewing communities as coupled oscillators: elementary forms from Lotka and Volterra to Kuramoto

Viewing communities as coupled oscillators: elementary forms from Lotka and Volterra to Kuramoto

Habitat loss causes long transients in small trophic chains

The Yellow Vests Movement - a case of long transient dynamics?

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