Construction of a trophically complex near-shore Antarctic food web model using the Conservative Normal framework with structural coexistence

Bates, Margaret L.; Nash, Susan Bengtson; Hawker, Darryl William; Norbury, John W.; Stark, Jonathan S.; Cropp, Roger Allan

doi:10.1016/j.jmarsys.2014.12.002

Cited by 15 publications

(16 citation statements)

References 48 publications

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“…The BEN method proceeds by integrating the model to steady state. (Note that substantial numerical analysis of models with structural coexistence has suggested that having a stable interior equilibrium point is a property of such models (Cropp and Norbury 2012b, 2013, Bates et al 2015 but we have yet to prove this. Having a stable steady state is no more crucial to the success of the BEN method than it is to any other calibration method, however, it does shorten the integration times required.)…”

Section: The Boundary Eigenvalue Nudging (Ben) Methodsmentioning

confidence: 80%

Parameter estimation in complex plankton models using the Boundary Eigenvalue Nudging – Genetic Algorithm (BENGA) Method

Cropp

Norbury²

2015

Weber, T., McPhee, M.J. And Anderssen, R.S. (Eds) MODSIM2015, 21st International Congress on Modelling and Simulation

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The analysis of trophically complex mathematical ecosystem models is typically carried out using numerical techniques because it is considered that the number and nonlinear nature of the equations involved makes the use of analytic techniques virtually impossible. In particular, building such models is a notoriously difficult task; most competing populations in many ecosystem models collapse (i.e. have multiple spurious extinctions). This is a realisation in silico of the Principle of Competitive Exclusion (Gause 1932, 1934) that stipulates that only as many competing populations can coexist as there are resources to support them. The incongruity of Gause's laboratory findings with the natural world led Hutchinson (1961) to propose the Paradox of the Plankton. This paradox articulated the observation that many populations of plankton coexisted in the ocean in apparent contradiction of Gause's Principle and the predictions of the simple theoretical models of the day. Whilst many solutions to the Paradox of the Plankton of varying robustness have been proposed (for example, Huisman and Weissing 1999, Schippers et al. 2001, Cropp and Norbury 2012b) the parameterization of complex ecosystem models remains a significant practical challenge (Cropp and Norbury 2013) that applied modelers need to overcome (for example, Gabric et al. 2008). The conservative normal (CN) framework articulates a number of ecological axioms that govern ecosystems by exploiting the properties of systems that are written in Kolmogorov form. Previous work has shown that trophically simple models developed within the CN framework are mathematically tractable, simplifying analysis. By exploiting the properties of Kolmogorov ecological systems it is possible to ensure models have particular properties, such as all populations remaining extant, into an ecological model. Here we demonstrate the usefulness of analytical results known for models of Kolmogorov form to construct a trophically complex ecosystem model. We also show that the properties of Kolmogorov ecological systems can be exploited to create ecosystem models with structural coexistence, that is, models for which no population goes extinct for all realistic (i.e. positive) parameter sets. We utilize this property in conjunction the key attribute of Kolmogorov systems, that closed form analytical expressions for the eigenvalues associated with populations that are zero at an equilibrium point are trivially obtained, to provide a computationally efficient method for the refinement of model parameters. Genetic Algorithms (GAs) are commonly used to estimate parameter sets that allow ecological models to reproduce observed data or theoretical objectives (Kristensen et al. 2003). It is a well-known property of GAs and other optimization approaches that convergence slows as the dimension of the solution space increases (Fournier et al. 2011), that is, as the number of parameters required to be estimated increases. We combine the properties of Kolmogorov systems with a GA to increase the rate of ...

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Section: The Boundary Eigenvalue Nudging (Ben) Methodsmentioning

confidence: 80%

Parameter estimation in complex plankton models using the Boundary Eigenvalue Nudging – Genetic Algorithm (BENGA) Method

Cropp

Norbury²

2015

Weber, T., McPhee, M.J. And Anderssen, R.S. (Eds) MODSIM2015, 21st International Congress on Modelling and Simulation

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“…Moreover, the new design adopts the population perspective and estimates pollution exchange rates between the environment and organisms. The accumulated pollutant in each compartment is expressed as [ 9 , 17 , 20 ]:

Where

represents the mass of PCBs accumulated in compartment

;

is the volume of compartment

;

(mol/Pa m 3 ) is the fugacity capacity of compartment

;

is the PCBs fugacity which represents the level of PCBs in compartment

. Thus, the dynamic change of PCBs in compartment

is estimated as:

…”

Section: Methods Detailsmentioning

confidence: 99%

A population-based simultaneous fugacity model design for polychlorinated biphenyls (PCBs) transport in an aquatic system

Sun

Small

2018

MethodsX

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“…The model is deliberately abstracted and simplified in order that key attributes of the trophic interactions may be discerned. For a detailed model of an Antarctic ecosystem, that also informed the development of this model, the reader is referred to Bates et al [2].…”

Section: The Southern Ocean Ecosystem Model (Soem)mentioning

confidence: 99%

The Role of Mixotrophy in Southern Ocean Ecosystems

Norbury

Moroz

Cropp

2019

Environ Model Assess

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We investigate the influence of mixotrophy on the dynamical properties of a six population model of a three trophic level Southern Ocean ecosystem. We find that including mixotrophic interactions between the lowest trophic level populations can significantly influence the dynamics of the highest trophic level populations, and in extreme cases lead to extinctions. Significantly, not only is the strength of the mixotrophic interaction important, it matters how it is included in the model, as a specialist or generalist grazer. We note in particular that the generalist formulation is inappropriate for "green" mixotrophs that fuel the majority of their growth by photosynthesis. The model can have complicated dynamics when subject to large amplitude, regular forcing, suggesting the sea ice-salps link may be obfuscated by endogenous population oscillations. Further, we observe that constructing the model within the Conservative Normal framework allows insights into the bifurcation behaviour of the model.

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Construction of a trophically complex near-shore Antarctic food web model using the Conservative Normal framework with structural coexistence

Cited by 15 publications

References 48 publications

Parameter estimation in complex plankton models using the Boundary Eigenvalue Nudging – Genetic Algorithm (BENGA) Method

Parameter estimation in complex plankton models using the Boundary Eigenvalue Nudging – Genetic Algorithm (BENGA) Method

A population-based simultaneous fugacity model design for polychlorinated biphenyls (PCBs) transport in an aquatic system

The Role of Mixotrophy in Southern Ocean Ecosystems

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