Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications

Patterson, Denis; Levin, Simon A.; Staver, Carla; Touboul, Jonathan

doi:10.1137/19m1298329

Cited by 16 publications

(25 citation statements)

References 44 publications

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“…Other papers generate similar bistability results using stochastic fire feedbacks (Batllori et al 2015;Baudena et al 2010). Some stochasticity, e.g., Patterson et al (2020), is also captured by continuum models like those in Staver et al (2011a) and Touboul et al (2018). The impulsive model presented in this paper not only has forest-savanna bistability, but forest-grassland bistability and bistability between woodier and grassier savanna coexistence states.…”

Section: Contextualization Of Resultssupporting

confidence: 54%

“…Given the ecological, economic and cultural value of savannas as well as their precarious ecological role, savanna ecosystems are a frequent target of modeling investigations (Accatino et al 2010;Batllori et al 2015;Baudena et al 2010;Beckage et al 2009;Djeumen et al 2021;Goel et al 2020;Patterson et al 2020;Ratajczak et al 2017;Schertzer et al 2015;Staver et al 2011a;Tamen et al 2016Tamen et al , 2017Touboul et al 2018;Wuyts et al 2019;Yatat et al 2018). In tree-grass-fire interaction models of savanna ecosystems, the impact of fire on tree and grass biomass is often represented as a continuous mortality in ordinary differential equation (ODE) models (Accatino et al 2010;Beckage et al 2009;Djeumen et al 2021;Staver et al 2011a;Touboul et al 2018) and in spatial partial differential equations (PDE) models (Goel et al 2020;Wuyts et al 2019;Yatat et al 2018).…”

Section: Introductionmentioning

confidence: 99%

“…Continuous fire is an obvious simplification, and in this paper, we show that it is not equivalent to similar models with discrete fire. Fire is also sometimes represented via a more complicated stochastically applied loss term (Batllori et al 2015;Baudena et al 2010;Patterson et al 2020). Stochastic loss terms lead to some models that are difficult to fully analyze.…”

Section: Introductionmentioning

confidence: 99%

“…Stochastic loss terms lead to some models that are difficult to fully analyze. However, Patterson et al (2020) shows that stochastic loss terms can be used to underpin continuum models, giving a nuanced relationship between the two types of models.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Impulsive Fire Disturbance in a Savanna Model: Tree–Grass Coexistence States, Multiple Stable System States, and Resilience

Hoyer‐Leitzel

Iams

2021

Bull Math Biol

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Savanna ecosystems are shaped by the frequency and intensity of regular fires. We model savannas via an ordinary differential equation (ODE) encoding a one-sided inhibitory Lotka–Volterra interaction between trees and grass. By applying fire as a discrete disturbance, we create an impulsive dynamical system that allows us to identify the impact of variation in fire frequency and intensity. The model exhibits three different bistability regimes: between savanna and grassland; two savanna states; and savanna and woodland. The impulsive model reveals rich bifurcation structures in response to changes in fire intensity and frequency—structures that are largely invisible to analogous ODE models with continuous fire. In addition, by using the amount of grass as an example of a socially valued function of the system state, we examine the resilience of the social value to different disturbance regimes. We find that large transitions (“tipping”) in the valued quantity can be triggered by small changes in disturbance regime.

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Section: Contextualization Of Resultssupporting

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Impulsive Fire Disturbance in a Savanna Model: Tree–Grass Coexistence States, Multiple Stable System States, and Resilience

Hoyer‐Leitzel

Iams

2021

Bull Math Biol

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“…We show the correlation between different parameter through computational simulation and showed a more natural in a sense of the limited resource context. In the future, we will further explore the house hunting behavior with present of geometry structure (distance of from the candidate nest to the old nest), which can be same analysis as mean field theory literature for ecology [27,32] or extension of distributed algorithm literature [33]. This will add in new factor for the decision making and making the merit function more realistic since ant will take the effort into account.…”

Section: Discussionmentioning

confidence: 99%

Population model of Temnothorax albipennis as a distributed dynamical system: I. self-consistent threshold is an emergent property in combination of quorum sensing and chemical perception of limited resource

Qiu

2021

Preprint

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House hunting of ant, such as Temnothorax albipennis, has been shown to be a distributed dynamical system. Such a system includes agent-based algorithm [1], with agents in different roles including nest exploration, nest assessment, quorum sensing, and brood item transportation. Such an algorithm, if used properly, can be applied on artificial intelligent system, like robotic swarms. Despite of its complexity, we are focusing on the quorum sensing mechanism, which is also observed in bacteria model. In bacterial model, multiple biochemical networks co-exist within each cell, including binding of autoinducer and cognate receptors, and phosphorylation-dephosphorylation cycle. In ant hunting, we also have ant commitment to the nest, mimicking binding between autoinducer and cognate receptors. We also have assessment ant specific to one nest and information exchange between two assessment ants corresponding to different nests, which is similar process to the phosphorylation-dephosphorylation cycle in bacteria quorum sensing network. Due to the similarity between the two models, we borrow the idea from bacteria quorum sensing to clarify the definition of quorum threshold through biological plausible mechanism related to limited resource model. We further made use of the contraction analysis to explore the trade-off between decision split and decision consensus within ant population. Our work provides new generation model for understanding how ant adapt to the changing environment during quorum sensing.

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Parallelized integrated nested Laplace approximations for fast Bayesian inference

Gaedke-Merzhäuser

Niekerk²,

Schenk³

et al. 2022

Stat Comput

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There is a growing demand for performing larger-scale Bayesian inference tasks, arising from greater data availability and higher-dimensional model parameter spaces. In this work we present parallelization strategies for the methodology of integrated nested Laplace approximations (INLA), a popular framework for performing approximate Bayesian inference on the class of Latent Gaussian models. Our approach makes use of nested thread-level parallelism, a parallel line search procedure using robust regression in INLA's optimization phase and the state-of-the-art sparse linear solver PARDISO. We leverage mutually independent function evaluations in the algorithm as well as advanced sparse linear algebra techniques. This way we can flexibly utilize the power of today's multi-core architectures. We demonstrate the performance of our new parallelization scheme on a number of different real-world applications. The introduction of parallelism leads to speedups of a factor 10 and more for all larger models. Our work is already integrated in the current version of the open-source R-INLA package, making its improved performance conveniently available to all users.

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Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications

Cited by 16 publications

References 44 publications

Impulsive Fire Disturbance in a Savanna Model: Tree–Grass Coexistence States, Multiple Stable System States, and Resilience

Impulsive Fire Disturbance in a Savanna Model: Tree–Grass Coexistence States, Multiple Stable System States, and Resilience

Population model of Temnothorax albipennis as a distributed dynamical system: I. self-consistent threshold is an emergent property in combination of quorum sensing and chemical perception of limited resource

Parallelized integrated nested Laplace approximations for fast Bayesian inference

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