Some non-intuitive properties of simple extensions of the chemostat model

Rapaport, Alain

doi:10.1016/j.ecocom.2017.02.003

Cited by 11 publications

(8 citation statements)

References 34 publications

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“…3A; it happens when the growth rate ρ( R ) intersects the mortality rate m (see the mathematical derivation in Appendix or elsewhere in the literature, e.g., Ranjan and Bagchi 2016, Harmand et al. 2017, Rapaport 2018). In contrast to standard monotonic growth functions in consumer–resource systems, such as linear or Monod, the humped shape of ρ leads not to one, but two zero net growth concentrations, denoted R * and R c here, with R * < R c .…”

Section: Negative and Positive Feedbacks Between A Single Species And Its Environment: The Fundamental Nichementioning

confidence: 99%

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From competition to facilitation and mutualism: a general theory of the niche

Koffel

Daufresne

Klausmeier

2021

Ecological Monographs

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Niche Theory is a central framework in ecology based on the recognition that most interactions between organisms are indirect, mediated by the biotic and abiotic dynamical environment these organisms live in. Despite its potential generality, the theory still mostly focuses on how resource–consumer dynamics mediate competition in ecological communities. However, it is being increasingly recognized that positive interactions between organisms also play an important role in driving the structure and functioning of ecological communities, from plants to microbes. In this paper, we present a unified theory of the niche that applies to both positive and negative interactions between organisms, mediated by one or two environmental factors. We show that classical concepts such as niche differences and fundamental and realized niches can naturally be expanded to facilitative and mutualistic interactions. In addition, we introduce and formalize new general niche concepts that appear exclusively in the presence of positive interactions: (1) the Allee niche, a region of environmental conditions for which a species can persist but not invade from low densities and (2) niche facilitation, when the presence of a species expands the set of environmental conditions under which a second species can invade and/or persist. To show the broad applicability of this theory, we illustrate these concepts using a diverse set of theoretical examples, from bacteria feeding on an inhibiting substrate, to nitrogen‐fixing plants and the indirect mutualism between a plant and a carnivore species. In sum, our work shows how Niche Theory provides a natural framework for positive interactions in ecology, bringing a unified perspective and new conceptual tools to study ecological systems where these positive interactions occur.

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Section: Negative and Positive Feedbacks Between A Single Species And Its Environment: The Fundamental Nichementioning

confidence: 99%

“…2017, Koffel et al. 2018 a , Rapaport 2018), is the following: by definition, the facultative N fixer cannot invade in its Allee niche as soil N levels are too low. However, if P levels are high enough, the obligate N fixer can invade there.…”

Section: Positive Interactions Between Species: Niche Expansion and The Realized Niche(s)mentioning

confidence: 99%

From competition to facilitation and mutualism: a general theory of the niche

Koffel

Daufresne

Klausmeier

2021

Ecological Monographs

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“…When this happens, the presence of the resident F facilitated the establishment of

F^{'}

, by making the invasion of the latter possible (Gerla et al . ; Rapaport ). We call such an invader‐resident replacement a facilitation‐driven successional step.…”

Section: Community Assembly Dynamicsmentioning

confidence: 99%

Facilitation‐ vs. competition‐driven succession: the key role of resource‐ratio

et al. 2018

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Symbiotic nitrogen (N)-fixing plants are abundant during primary succession, as typical bedrocks lack available N. In turn, fixed N accumulates in soils through biomass turnover and recycling, favouring more nitrophilous organisms. Yet, it is unclear how this facilitation mechanism interacts with competition for other limiting nutrients such as phosphorus (P) and how this affects succession. Here, we introduce a resource-explicit, community assembly model of N-fixing species and analyze successional trajectories along resource availability gradients using contemporary niche theory. We show that facilitation-driven succession occurs under low N and high enough P availabilities, and is characterised by autogenic ecosystem development and relatively ordered trajectories. We show that late facilitation-driven succession is sensitive to catastrophic shifts, highlighting the need to invoke other mechanisms to explain ecosystem stability near the climax. Put together with competition-driven succession, these results lead to an enriched version of Tilman's resource-ratio theory of succession.

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“…The first examples of such models, known as compartment models, represent a reactor as a network of interconnected well-mixed zones and thus use systems of ordinary differential equations (ODE), which facilitates analysis and simulation [1], [2], [3].…”

Section: Introductionmentioning

confidence: 99%

Simulation of spatially distributed intensive biological systems

Haddon

Alcaraz-González

Hmissi

et al. 2020

2020 European Control Conference (ECC)

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We introduce a new type of bioreactor model that offers a representation of the spatial features of a pilot scale upflow fixed bed reactor. This model couples fluid dynamics and biological activity in order to obtain the internal gradient of substrate and biomass concentrations. We take advantage of reactor geometry to reduce the model to a single spatial dimension in the section containing the fixed bed but in other sections, we consider a 3D model with Navier-Stokes equations for the fluid dynamics. To represent the biological activity, we use a 2 step model and for the substrates, advectiondiffusion-reaction equations. We only consider the biomasses that are attached in the fixed bed section and to take into account crowding effects, we model their growth with a density dependent function. We show that this model can reproduce the spatial gradient of experimental data and helps to better understand the internal dynamics of the reactor.

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Some non-intuitive properties of simple extensions of the chemostat model

Cited by 11 publications

References 34 publications

From competition to facilitation and mutualism: a general theory of the niche

From competition to facilitation and mutualism: a general theory of the niche

Facilitation‐ vs. competition‐driven succession: the key role of resource‐ratio

Simulation of spatially distributed intensive biological systems

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