Meta-modeling on detailed geography for accurate prediction of invasive alien species dispersal

Abstract Invasive species are recognized as a significant threat to biodiversity. The mathematical modeling of their spatio-temporal dynamics can provide significant help to environmental managers in devising suitable control strategies. Several mathematical approaches have been proposed in recent decades to efficiently model the dispersal of invasive species. Relying on the assumption that the dispersal of an individual is random, but the density of individuals at the scale of the population can be considered smooth, reaction-diffusion models are a good trade-off between model complexity and flexibility for use in different situations. In this paper we present a continuous reaction-diffusion model coupled with arbitrary Polynomial Chaos (aPC) to assess the impact of uncertainties in the model parameters. We show how the finite elements framework is well-suited to handle important landscape heterogeneities as elevation and the complex geometries associated with the boundaries of an actual geographical region. We demonstrate the main capabilities of the proposed coupled model by assessing the uncertainties in the invasion of an alien species invading the Basque Country region in Northern Spain.

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The influence of density in population dynamics with strong and weak Allee effect

Journal of the Egyptian Mathematical Society ◽

10.1186/s42787-021-00114-x ◽

2021 ◽

Vol 29 (1) ◽

Author(s):

Kamrun Nahar Keya ◽

Md. Kamrujjaman ◽

Md. Shafiqul Islam

Keyword(s):

Population Dynamics ◽

Allee Effect ◽

Global Bifurcation ◽

Reaction Diffusion ◽

Logistic Growth ◽

Allee Effects ◽

Reaction Diffusion Model ◽

Positive Steady States ◽

The Stability ◽

The Impact

AbstractIn this paper, we consider a reaction–diffusion model in population dynamics and study the impact of different types of Allee effects with logistic growth in the heterogeneous closed region. For strong Allee effects, usually, species unconditionally die out and an extinction-survival situation occurs when the effect is weak according to the resource and sparse functions. In particular, we study the impact of the multiplicative Allee effect in classical diffusion when the sparsity is either positive or negative. Negative sparsity implies a weak Allee effect, and the population survives in some domain and diverges otherwise. Positive sparsity gives a strong Allee effect, and the population extinct without any condition. The influence of Allee effects on the existence and persistence of positive steady states as well as global bifurcation diagrams is presented. The method of sub-super solutions is used for analyzing equations. The stability conditions and the region of positive solutions (multiple solutions may exist) are presented. When the diffusion is absent, we consider the model with and without harvesting, which are initial value problems (IVPs) and study the local stability analysis and present bifurcation analysis. We present a number of numerical examples to verify analytical results.

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Managing alien bird species: Time to move beyond “100 of the worst” lists?

Bird Conservation International ◽

10.1017/s0959270915000167 ◽

2015 ◽

Vol 26 (2) ◽

pp. 154-163 ◽

Cited By ~ 14

Author(s):

SABRINA KUMSCHICK ◽

TIM M. BLACKBURN ◽

DAVID M. RICHARDSON

Keyword(s):

Invasive Species ◽

Alien Species ◽

Expert Opinion ◽

Bird Species ◽

Alien Invasive Species ◽

Common Myna ◽

Acridotheres Tristis ◽

Pycnonotus Cafer ◽

Selection Of Species ◽

The Impact

SummaryAlien species can cause severe impacts in their introduced ranges and management is challenging due to the large number of such species and the diverse nature and context of their impacts. Lists of the most harmful species, like the “100 of the World’s Worst” list collated by the Invasive Species Specialist Group of the International Union for Conservation of Nature (IUCN) or the “100 of the Worst” invaders in Europe collated by the Delivering Alien Invasive Species Inventories in Europe (DAISIE) project, raise awareness about these impacts among the public, and can guide management decisions. Such lists are mainly based on expert opinion, but in recent years a more objective comparison of impacts has become possible, even between highly diverse taxa. In this study, we use a semi-quantitative generic impact scoring system to assess impacts of the three birds listed among the “100 of the World’s Worst” IUCN list (IUCN100) and the four birds on the list of “100 of the Worst” European invaders by DAISIE (DAISIE100) and to compare their impacts with those of other alien birds not present on the respective lists. We found that generally, both lists include some of the species with the highest impacts in the respective regions (global or Europe), and these species therefore deserve the dubious honour of being listed among the “worst”. However, there are broad overlaps between some species with regards to the impact mechanisms and the related issues of invasions, especially those of the Common Myna Acridotheres tristis and Red-vented Bulbul Pycnonotus cafer on the IUCN100, are very similar which might not warrant listing both species. To make the selection of species on such lists more transparent we suggest moving beyond lists based on expert opinion to a more transparent and defendable system for listing alien species based on published records of their impacts and related mechanisms.

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Microbial competition reduces interaction distances to the low µm-range

10.1101/2020.01.22.915835 ◽

2020 ◽

Author(s):

Rinke J. van Tatenhove-Pel ◽

Tomaž Rijavec ◽

Aleš Lapanje ◽

Iris van Swam ◽

Emile Zwering ◽

...

Keyword(s):

Effective Interaction ◽

Three Dimensional ◽

Reaction Diffusion ◽

Dimensional System ◽

Cellular Interactions ◽

Natural Ecosystems ◽

Concentration Gradients ◽

Reaction Diffusion Model ◽

The Impact ◽

Three Dimensional System

AbstractMetabolic interactions between cells affect microbial community compositions and hence their function in ecosystems. It is well-known that under competition for the exchanged metabolite, concentration gradients constrain the distances over which interactions can occur. However, interaction distances are typically quantified in two-dimensional systems or without accounting for competition or other metabolite-removal, conditions which may not very often match natural ecosystems. We here analyze the impact of cell-to-cell distance on unidirectional cross-feeding in a three-dimensional system with competition for the exchanged metabolite. Effective interaction distances were computed with a reaction-diffusion model and experimentally verified by growing a synthetic consortium of 1 µm-sized metabolite producer, receiver and competitor cells in different spatial structures. We show that receivers cannot interact with producers ∼15 µm away from them, as product concentration gradients flatten close to producer cells. We developed an aggregation protocol and created variants of the receiver cells’ import system, to show that within producer-receiver aggregates even low affinity receiver cells could interact with producers. These results show that competition or other metabolite-removal of a public good in a three-dimensional system reduces the interaction distance to the low micrometer-range, highlighting the importance of concentration gradients as physical constraint for cellular interactions.

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Why microbes secrete molecules to modify their environment: the case of iron-chelating siderophores

Journal of The Royal Society Interface ◽

10.1098/rsif.2018.0674 ◽

2019 ◽

Vol 16 (150) ◽

pp. 20180674 ◽

Cited By ~ 15

Author(s):

Gabriel E. Leventhal ◽

Martin Ackermann ◽

Konstanze T. Schiessl

Keyword(s):

Iron Uptake ◽

Large Fraction ◽

Reaction Diffusion ◽

Iron Particles ◽

Diffusion Limitation ◽

Iron Solubility ◽

Reaction Diffusion Model ◽

Particulate Iron ◽

The Impact ◽

Release Strategy

Many microorganisms secrete molecules that interact with resources outside of the cell. This includes, for example, enzymes that degrade polymers like chitin, and chelators that bind trace metals like iron. In contrast to direct uptake via the cell surface, such release strategies entail the risk of losing the secreted molecules to environmental sinks, including ‘cheating’ genotypes. Nevertheless, such secretion strategies are widespread, even in the well-mixed marine environment. Here, we investigate the benefits of a release strategy whose efficiency has frequently been questioned: iron uptake in the ocean by secretion of iron chelators called siderophores. We asked the question whether the release itself is essential for the function of siderophores, which could explain why this risky release strategy is widespread. We developed a reaction–diffusion model to determine the impact of siderophore release on iron uptake from the predominant iron sources in marine environments, colloidal or particulate iron, formed due to poor iron solubility. We found that release of siderophores is essential to accelerate iron uptake, as secreted siderophores transform slowly diffusing large iron particles to small, quickly diffusing iron–siderophore complexes. In addition, we found that cells can synergistically share their siderophores, depending on their distance and the size of the iron sources. Our study helps understand why release of siderophores is so widespread: even though a large fraction of siderophores is lost, the solubilization of iron through secreted siderophores can efficiently increase iron uptake, especially if siderophores are produced cooperatively by several cells. Overall, resource uptake mediated via release of molecules transforming their substrate could be essential to overcome diffusion limitation specifically in the cases of large, aggregated resources. In addition, we find that including the reaction of the released molecule with the substrate can impact the result of cooperative and competitive interactions, making our model also relevant for release-based uptake of other substrates.

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Effect of Bulk Composition on the Heterogeneous Oxidation of Semi-Solid Atmospheric Aerosols

Atmosphere ◽

10.3390/atmos10120791 ◽

2019 ◽

Vol 10 (12) ◽

pp. 791

Author(s):

Hanyu Fan ◽

Fabien Goulay

Keyword(s):

Atmospheric Aerosols ◽

Bulk Composition ◽

Particle Surface ◽

Reaction Diffusion ◽

Solid Particles ◽

Molar Ratio ◽

Heterogeneous Oxidation ◽

Reaction Diffusion Model ◽

Semi Solid ◽

The Impact

The OH-initiated heterogeneous oxidation of semi-solid saccharide particles with varying bulk compositions was investigated in an atmospheric pressure flow tube at 30% relative humidity. Reactive uptake coefficients were determined from the rate loss of the saccharide reactants measured by mass spectrometry at different monosaccharide (methyl-β-d-glucopyranoside, C7H14O6) and disaccharide (lactose, C12H22O11) molar ratios. The reactive uptake for the monosaccharide was found to decrease from 0.53 ± 0.10 to 0.05 ± 0.06 as the mono-to-disaccharide molar ratio changed from 8:1 to 1:1. A reaction–diffusion model was developed in order to determine the effect of chemical composition on the reactive uptake. The observed decays can be reproduced using a Vignes relationship to predict the composition dependence of the reactant diffusion coefficients. The experimental data and model results suggest that the addition of the disaccharide significantly increases the particle viscosity leading to slower mass transport phenomena from the bulk to the particle surface and to a decreased reactivity. These findings illustrate the impact of bulk composition on reactant bulk diffusivity which determines the rate-limiting step during the chemical transformation of semi-solid particles in the atmosphere.

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A Study of Impacts of Coupled Model Initial Shocks and State–Parameter Optimization on Climate Predictions Using a Simple Pycnocline Prediction Model

Journal of Climate ◽

10.1175/jcli-d-10-05003.1 ◽

2011 ◽

Vol 24 (23) ◽

pp. 6210-6226 ◽

Cited By ~ 33

Author(s):

S. Zhang

Keyword(s):

Time Scales ◽

Parameter Optimization ◽

Time Scale ◽

Model Simulation ◽

Coupled Model ◽

State Parameter ◽

Model Parameters ◽

Forecast Errors ◽

Long Time ◽

The Impact

Abstract A skillful decadal prediction that foretells varying regional climate conditions over seasonal–interannual to multidecadal time scales is of societal significance. However, predictions initialized from the climate-observing system tend to drift away from observed states toward the imperfect model climate because of the model biases arising from imperfect model equations, numeric schemes, and physical parameterizations, as well as the errors in the values of model parameters. Here, a simple coupled model that simulates the fundamental features of the real climate system and a “twin” experiment framework are designed to study the impact of initialization and parameter optimization on decadal predictions. One model simulation is treated as “truth” and sampled to produce “observations” that are assimilated into other simulations to produce observation-estimated states and parameters. The degree to which the model forecasts based on different estimates recover the truth is an assessment of the impact of coupled initial shocks and parameter optimization on climate predictions of interests. The results show that the coupled model initialization through coupled data assimilation in which all coupled model components are coherently adjusted by observations minimizes the initial coupling shocks that reduce the forecast errors on seasonal–interannual time scales. Model parameter optimization with observations effectively mitigates the model bias, thus constraining the model drift in long time-scale predictions. The coupled model state–parameter optimization greatly enhances the model predictability. While valid “atmospheric” forecasts are extended 5 times, the decadal predictability of the “deep ocean” is almost doubled. The coherence of optimized model parameters and states is critical to improve the long time-scale predictions.

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Pattern Formation and Oscillations in Reaction–Diffusion Model with p53-Mdm2 Feedback Loop

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419300404 ◽

2019 ◽

Vol 29 (14) ◽

pp. 1930040 ◽

Cited By ~ 5

Author(s):

Qianqian Zheng ◽

Jianwei Shen ◽

Zhijie Wang

Keyword(s):

Pattern Formation ◽

Feedback Loop ◽

Reaction Diffusion ◽

Vital Role ◽

Reaction Diffusion Equation ◽

Biological Mechanism ◽

Reaction Diffusion Model ◽

The Impact ◽

Theoretical Results ◽

Diffusive System

P53 plays a vital role in DNA repair, and several mathematical models of the p53-Mdm2 feedback loop were used to explain the biological mechanism. In this paper, a p53-Mdm2 model described by a delay reaction–diffusion equation is studied both analytically and numerically. This research aims to provide an understanding of the impact of delay and sustained pressure on the p53-Mdm2 dynamics and tries to explain some biological mechanism. It is found that the type of pattern formation is affected by Hopf bifurcation. Also, the amplitude equation in delay diffusive system is derived and it is shown that sustained stress plays an essential role in the function of p53. Finally, simulation is used to verify the theoretical results.

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Optimal control of an invasive species using a reaction-diffusion model and linear programming

Ecosphere ◽

10.1002/ecs2.1979 ◽

2017 ◽

Vol 8 (10) ◽

pp. e01979 ◽

Cited By ~ 2

Author(s):

Mathieu Bonneau ◽

Fred A. Johnson ◽

Brian J. Smith ◽

Christina M. Romagosa ◽

Julien Martin ◽

...

Keyword(s):

Optimal Control ◽

Invasive Species ◽

Linear Programming ◽

Diffusion Model ◽

Reaction Diffusion ◽

Reaction Diffusion Model

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A COMPUTATIONAL ANALYSIS OF BONE FORMATION IN THE CRANIAL VAULT USING A COUPLED REACTION–DIFFUSION-STRAIN MODEL

Journal of Mechanics in Medicine and Biology ◽

10.1142/s0219519417500737 ◽

2017 ◽

Vol 17 (04) ◽

pp. 1750073 ◽

Cited By ~ 6

Author(s):

CHANYOUNG LEE ◽

JOAN T. RICHTSMEIER ◽

REUBEN H. KRAFT

Keyword(s):

Bone Formation ◽

Mechanical Strain ◽

Mathematical Formulation ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Cranial Vault ◽

Model Parameters ◽

Computational Domain ◽

Reaction Diffusion Model

Bones of the murine cranial vault are formed by differentiation of mesenchymal cells into osteoblasts, a process that is primarily understood to be controlled by a cascade of reactions between extracellular molecules and cells. We assume that the process can be modeled using Turing's reaction–diffusion equations, a mathematical model describing the pattern formation controlled by two interacting molecules (activator and inhibitor). In addition to the processes modeled by reaction–diffusion equations, we hypothesize that mechanical stimuli of the cells due to growth of the underlying brain contribute significantly to the process of cell differentiation in cranial vault development. Structural analysis of the surface of the brain was conducted to explore the effects of the mechanical strain on bone formation. We propose a mechanobiological model for the formation of cranial vault bones by coupling the reaction-–diffusion model with structural mechanics. The mathematical formulation was solved using the finite volume method. The computational domain and model parameters are determined using a large collection of experimental data that provide precise three-dimensional (3D) measures of murine cranial geometry and cranial vault bone formation for specific embryonic time points. The results of this study suggest that mechanical strain contributes information to specific aspects of bone formation. Our mechanobiological model predicts some key features of cranial vault bone formation that were verified by experimental observations including the relative location of ossification centers of individual vault bones, the pattern of cranial vault bone growth over time, and the position of cranial vault sutures.

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