How to find simple nonlocal stability and resilience measures

Lundström, Niklas L. P.

doi:10.1007/s11071-018-4234-x

Cited by 19 publications

(23 citation statements)

References 35 publications

(76 reference statements)

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“…Indeed, non-linearities can have a strong effect on the short-term response, but leave the long-term response essentially unchanged, because the latter corresponds to small displacements for which the linear approximation is accurate. When allowing for stronger perturbations, the ecosystem might be pushed to a different state (e.g., to another equilibrium), and the notion of ecosystem recovery itself becomes meaningless (for concrete proposals of how to deal with this case, see Menck et al, 2013 and Lundström, 2017). Finally, it should be noted that ecosystem stability has also been analyzed in the absence of perturbations.…”

Section: Discussionmentioning

confidence: 99%

How ecosystems recover from pulse perturbations: A theory of short- to long-term responses

Arnoldi

Bideault

Loreau

et al. 2018

Journal of Theoretical Biology

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Quantifying stability properties of ecosystems is an important problem in ecology. A common approach is based on the recovery from pulse perturbations, and posits that the faster an ecosystem return to its pre-perturbation state, the more stable it is. Theoretical studies often collapse the recovery dynamics into a single quantity: the long-term rate of return, called asymptotic resilience. However, empirical studies typically measure the recovery dynamics at much shorter time scales. In this paper we explain why asymptotic resilience is rarely representative of the short-term recovery. First, we show that, in contrast to asymptotic resilience, short-term return rates depend on features of the perturbation, in particular on the way its intensity is distributed over species. We argue that empirically relevant predictions can be obtained by considering the median response over a set of perturbations, for which we provide explicit formulas. Next, we show that the recovery dynamics are controlled through time by different species: abundant species tend to govern the short-term recovery, while rare species often dominate the long-term recovery. This shift from abundant to rare species typically causes short-term return rates to be unrelated to asymptotic resilience. We illustrate that asymptotic resilience can be determined by rare species that have almost no effect on the observable part of the recovery dynamics. Finally, we discuss how these findings can help to better connect empirical observations and theoretical predictions.

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Section: Discussionmentioning

confidence: 99%

How ecosystems recover from pulse perturbations: A theory of short- to long-term responses

Arnoldi

Bideault

Loreau

et al. 2018

Journal of Theoretical Biology

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“…A large and convex basin-time set should then reflect high resilience. Therefore, both the size and the shape of the basin-time constitute natural candidates for measuring resilience (Lundström 2018). We will consider the size of the basin-time set as a resilience measure.…”

Section: Basin-time Resilience and Further Investigations Of The Stagmentioning

confidence: 99%

Meeting Yield and Conservation Objectives by Harvesting Both Juveniles and Adults

Lundström¹,

Loeuille²,

Meng³

et al. 2019

The American Naturalist

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Sustainable yields that are at least 80% of the maximum sustainable yield are sometimes referred to as pretty good yield (PGY). The range of PGY harvesting strategies is generally broad and thus leaves room to account for additional objectives besides high yield. Here, we analyze stage-dependent harvesting strategies that realize PGY with conservation as a second objective. We show that (1) PGY harvesting strategies can give large conservation benefits and (2) equal harvesting rates of juveniles and adults is often a good strategy. These conclusions are based on trade-off curves between yield and four measures of conservation that form in two established population models, one age-structured and one stage-structured model, when considering different harvesting rates of juveniles and adults. These conclusions hold for a broad range of parameter settings, though our investigation of robustness also reveals that (3) predictions of the age-structured model are more sensitive to variations in parameter values than those of the stage-structured model. Finally, we find that (4) measures of stability that are often quite difficult to assess in the field (e.g. basic reproduction ratio and resilience) are systematically negatively correlated with impacts on biomass and impact on size structure, so that these later quantities can provide integrative signals to detect possible collapses.Similarly, we consider impact on size-structure through the expression Impact on size-structure = which equals the relative change in the fraction of juvenile biomass following harvesting. If the impact on size-structure is positive (negative), then harvesting has increased (decreased) the fraction of juveniles in the population.Resilience, basic reproduction ratio and recovery potential as risk measures Resilience as a risk measure is increasingly used in ecology (Pimm and Lawton 1977; Loreau and Behera 1999; Petchey et al. 2002; Montoya et al. 2006; Loeuille 2010; Valdovinos et al.

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“…When the local stability condition of the endemic equilibrium point is met, the endemic equilibrium point is asymptotically stable, but may only attract a very small part of the state space. Therefore, studying the size of the basin of attraction of the endemic equilibrium point is relevant [31]. However, we do not discuss the basin of attraction of the endemic equilibrium point in this article.…”

Section: Theorem 8 Endemic Equilibrium Point E Bmentioning

confidence: 99%

Schistosomiasis Model Incorporating Snail Predator as Biological Control Agent

et al. 2021

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Schistosomiasis is a parasitic disease caused by the schistosoma worm. A snail can act as the intermediate host for the parasite. Snail-population control is considered to be an effective way to control schistosomiasis spread. In this paper, we discuss the schistosomiasis model incorporating a snail predator as a biological control agent. We prove that the solutions of the model are non-negative and bounded. The existence condition of equilibrium points is investigated. We determine the basic reproduction number when the predator goes to extinction and when the predator survives. The local stability condition of disease-free equilibrium point is proved using linearization, and the Lienard–Chipart and Routh–Hurwitz criteria. We use center-manifold theory to prove the local stability condition of the endemic equilibrium points. Furthermore, we constructed a Lyapunov function to investigate the global stability condition of the disease-free equilibrium points. To support the analytical results, we presented some numerical simulation results. Our findings suggest that a snail predator as a biological control agent can reduce schistosomiasis prevalence. Moreover, the snail-predator birth rate plays an essential role in controlling schistosomiasis spread.

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How to find simple nonlocal stability and resilience measures

Cited by 19 publications

References 35 publications

How ecosystems recover from pulse perturbations: A theory of short- to long-term responses

How ecosystems recover from pulse perturbations: A theory of short- to long-term responses

Meeting Yield and Conservation Objectives by Harvesting Both Juveniles and Adults

Schistosomiasis Model Incorporating Snail Predator as Biological Control Agent

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