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This work submits the computational modeling of nonlinear coupled reaction–diffusion (RD) models via uniform scale‐2 Haar wavelets (S2HWs) based numerical algorithm. The nonlinear RD models have many applications in mathematical chemistry, chemical and biological processes, etc. In the design of the algorithm, first of all, semi‐discretization is done in time, and after that, the quasi‐linearization process is used for linearization. Finally, the full discretization is done with the help of S2HWs, and the enlisted linear system is solved by LU decomposition method. Also, the convergence analysis of the algorithm has discussed. In the simulation part, different types of patterns such as Turing, pulse‐splitting, self‐replicating pulse patterns, etc. of different models are captured. [ABSTRACT FROM AUTHOR]

A stock-effort dynamical model of a fishery with spatial structure is considered to assess the impacts of reserve size on fishing catch. We study the existence, uniqueness and global character of the solutions. It is shown that when the cost of fishing effort is less than the principal eigenvalue for an elliptic operator defined on a bounded domain corresponding to the fishing zone, then the fishery is viable, while in the opposite case, the fishery is not viable and fishing effort disappears. For both cases, the existence of stable solutions is studied. We perform some numerical simulations to illustrate our results in this paper and give a brief concluding remark. [ABSTRACT FROM AUTHOR]

The bacterial colony is a powerful experimental platform for broad biological research, and reaction–diffusion models are widely used to study the mechanisms of its formation process. However, there are still some crucial factors that drastically affect the colony growth but are not considered in the current models, such as the non-homogeneously distributed nutrient within the colony and the substantially decreasing expansion rate caused by agar dehydration. In our study, we propose two plausible reaction–diffusion models (the VN and MVN models) based on the above two factors and validate them against experimental data. Both models provide a plausible description of the non-homogeneously distributed nutrient within the colony and outperform the classical Fisher–Kolmogorov equation and its variation in better describing experimental data. Moreover, by accounting for agar dehydration, the MVN model captures how a colony’s expansion slows down and the change of a colony’s height profile over time. Furthermore, we demonstrate the existence of a traveling wave solution for the VN model. [ABSTRACT FROM AUTHOR]

We establish the existence of solutions to a class of nonlinear stochastic differential equations of reaction–diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained is the scaling limit of a sequence of interacting particle systems and satisfies the martingale problem corresponding to the target differential equation. [ABSTRACT FROM AUTHOR]

A nonlinear conjugate gradient method is derived for the inverse problem of identifying a treatment parameter in a nonlinear model of reaction–diffusion type corresponding to the evolution of brain tumours under therapy. The treatment parameter is reconstructed from additional information about the tumour taken at a fixed instance of time. Well-posedness of the direct problems used in the iterative method is outlined as well as uniqueness of a solution to the inverse problem. Moreover, the parameter identification is recasted as the minimization of a Tikhonov type functional and the existence of a minimizer to this functional is shown. Finite-difference discretization of the space and time derivatives are employed for the numerical implementation. Numerical simulations on full 3D brain data are included showing that information about a spacewise-dependent treatment parameter can be recovered in a stable way. [ABSTRACT FROM AUTHOR]

In this paper, I develop a template-based analysis to include several elements of processes through which templates are transferred between fields of inquiry. The analysis builds on Justin Price’s identification of the importance of a “landing zone” in the recipient domain, from which “conceptual pressure” may be created. I will argue that conceptual pressure is a characteristic feature of the process of template transfer; that this means that there are costs to the process of transfer as well as benefits; and that it would be reasonable if modelers try to mitigate these costs. I will discuss two such mitigation strategies: ‘conceptual embedding’ and ‘customization’. I illustrate the claims, focusing on the mitigation strategies, with a case study: that of pioneering applications of reaction–diffusion equations in mathematical ecology. [ABSTRACT FROM AUTHOR]

The purpose of this manuscript is to develop a reaction-diffusion heart model for closed-loop evaluation of heart-pacemaker interaction, and to provide a hardware setup for the implementation of the closed-loop system. The heart model, implemented on a workstation, is based on the cardiac monodomain formulation and a phenomenological model of cardiac cells, which we fitted to the electrophysiological properties of the different cardiac tissues. We modelled the pacemaker as a timed automaton, deployed on an Arduino 2 board. The Arduino and the workstation communicate through a PCI acquisition board. Additionally, we developed a graphical user interface for easy handling of the framework. The myocyte model resembles the electrophysiological properties of atrial and ventricular tissue. The heart model reproduces healthy activation sequence and proved to be computationally efficient (i.e., 1 s simulation requires about 5 s). Furthermore, we successfully simulated the interaction between heart and pacemaker models in three well-known pathological contexts. Our results showed that the PDE formulation is appropriate for the simulation in closed-loop. While computationally more expensive, a PDE model is more flexible and allows to represent more complex scenarios than timed or hybrid automata. Furthermore, users can interact more easily with the framework thanks to the graphical representation of the spatiotemporal evolution of the membrane potentials. By representing the heart as a reaction-diffusion model, the proposed closed-loop system provides a novel and promising framework for the assessment of cardiac pacemakers.

Species distribution models assume that at broad spatial scales, environmental conditions determine species ranges and, as such, source-sink dynamics can be ignored. A rationale behind this assumption is that source-sink dynamics manifest at length scales comparable to species mean dispersal distance, which is much smaller than length scales of species distribution and variation in climate. Using a two-dimensional reaction-diffusion model, we show that species can use sink habitats near the niche limit as stepping-stones to occupy sink habitats much further than the mean dispersal distance, thereby extending the distribution far beyond the environmental niche limit. This mismatch between range and niche limits is mediated by the shape (local curvature) of the niche limit. These curvature effects may be significant for a highly dispersive species with low per capita growth rate sensitivity to changes in the environment. These findings underscore the potential importance of stepping-stone dispersal in determining range limits. [ABSTRACT FROM AUTHOR]

In this study, a synchronization problem for spatio-temporal partial differential systems is addressed and researched within a subjectivist framework. In light of Lyapunov direct method and some proposed nonlinear controllers, a new scheme is established to accomplish a full synchronization between two reaction–diffusion systems of integer- and fractional-order. In particular, a novel vector-valued control law is analytically derived to attain the desired synchronization between two chemical models, namely, the Lengyel–Epstein and Gray–Scott models. To validate the obtained theoretical results, further numerical simulations are carried out in 2D and 3D configurations. [ABSTRACT FROM AUTHOR]

In Southern Italy, since 2013, there has been an ongoing Olive Quick Decline Syndrome (OQDS) outbreak, due to the bacterium Xylella fastidiosa, which has caused a dramatic impact from both socio-economic and environmental points of view. Current agronomic practices are mainly based on uprooting the sick olive trees and their surrounding ones, with later installment of olive cultivars more resistant to the bacterium infection. Unfortunately, both of these practices are having an undesirable impact on the environment and on the economy. Here, a spatially structured mathematical model has been proposed to include a predator Zelus renardii as a possible biocontrol agent of the Xylella epidemic. The fact that Z. renardii has been reported to be a generalist predator implies that its introduction is not an efficient control strategy to eradicate a Xylella epidemic. Instead, a specialist predator, whenever identified, would lead to the eventual eradication of a Xylella epidemic. In either cases it has been confirmed that a significant reduction of the weed biomass can lead to the eradication of the vector population, hence of a Xylella epidemic, independently of the presence of predators. [ABSTRACT FROM AUTHOR]

Abstract In this article, the first part is concerned with the important questions related to the existence and uniqueness of solutions for nonlinear reaction-diffusion systems. Secondly, an efficient positivity-preserving operator splitting nonstandard finite difference scheme (NSFD) is designed for such a class of systems. The presented formulation is unconditionally stable as well as implicit in nature and even time efficient. The proposed NSFD operator splitting technique also preserves all the important properties possessed by continuous systems like positivity, convergence to the fixed points of the system, and boundedness. The proposed algorithm is implicit in nature but more efficient in time than the extensively used Euler method.

The coupling of the internal mechanisms of cell polarization to cell shape deformations and subsequent cell crawling poses many interdisciplinary scientific challenges. Several mathematical approaches have been proposed to model the coupling of both processes, where one of the most successful methods relies on a phase field that encodes the morphology of the cell, together with the integration of partial differential equations that account for the polarization mechanism inside the cell domain as defined by the phase field. This approach has been previously employed to model the motion of single cells of the social amoeba Dictyostelium discoideum, a widely used model organism to study actin-driven motility and chemotaxis of eukaryotic cells. Besides single cell motility, Dictyostelium discoideum is also well-known for its collective behavior. Here, we extend the previously introduced model for single cell motility to describe the collective motion of large populations of interacting amoebae by including repulsive interactions between the cells. We performed numerical simulations of this model, first characterizing the motion of single cells in terms of their polarity and velocity vectors. We then systematically studied the collisions between two cells that provided the basic interaction scenarios also observed in larger ensembles of interacting amoebae. Finally, the relevance of the cell density was analyzed, revealing a systematic decrease of the motility with density, associated with the formation of transient cell clusters that emerge in this system even though our model does not include any attractive interactions between cells. This model is a prototypical active matter system for the investigation of the emergent collective dynamics of deformable, self-driven cells with a highly complex, nonlinear coupling of cell shape deformations, self-propulsion and repulsive cell-cell interactions. Understanding these self-organization processes of cells like their autonomous aggregation is of high relevance as collective amoeboid motility is part of wound healing, embryonic morphogenesis or pathological processes like the spreading of metastatic cancer cells.

Conservation and management of animal populations requires knowledge of their occurrence and drivers that influence their distribution. Noninvasive survey methods and occupancy models to account for imperfect detection have become the standard tools for this purpose. Simultaneously addressing both occurrence and occurrence–environment relationships, however, presents multiple challenges, particularly for species with reduced ranges or those recovering from historical declines. Here, we present a comprehensive framework to satisfy the assumption of organism–environment equilibrium, map the range of a species, incorporate camera traps and detection dogs as complementary data sources, and make inference about wildlife space use at multiple scales. To meet these goals, we developed a Bayesian spatial occupancy model for Pacific fishers (Pekania pennanti) in Oregon using data from a large‐scale (64,280 km2) empirical effort combining 1240 camera traps (74,219 trap nights) and 196 detector dog surveys (3 × 3 km units, survey average = 17.3 km/unit). We deployed this model with and without a geoadditive term to improve predicted range map generation and covariate inference, respectively. We used reaction–diffusion models to project recovery trajectories to determine both plausible spatial extents for inclusion in our occupancy model and whether the current distribution can be explained by time‐limited population expansion from historical refugia. To assess nonstationary effects where species–habitat relationships vary spatially, we fit separate models within distinct ecological regions. We confirmed the presence of the native and introduced fisher populations, but populations occupy less area than previously believed. The spatial extent of the introduced population was less than expected except under our lowest growth model, suggesting limiting factors were preventing population expansion. The native population extent matched expectations under several growth scenarios, suggesting that the contemporary distribution is plausibly due to time‐limited expansion. The relationship of fisher occupancy to environmental covariates varied with scale, spatial extent, and ecological region, but fishers consistently selected for old forests at fine spatial scales in the detection model across spatial extents and detection modalities. Collectively, we provide an integration of camera traps and detection dogs into spatial occupancy models and demonstrate how to generate plausible spatial extents to improve inferences for species recovering from range contractions. [ABSTRACT FROM AUTHOR]

The theory of dynamical systems and their widespread applications involve, for example, the Lane–Emden-type equations which are known to arise in initial- and boundary-value problems with singularity at the   time   t = 0 . The main objective of this paper is to make use of some mathematical analytic tools and techniques in order to numerically solve some reaction–diffusion equations, which arise in spherical catalysts and spherical biocatalysts, by applying the Chebyshev spectral collocation method. The proposed scheme has good accuracy. The results are demonstrated by means of illustrative graphs and numerical tables. The accuracy of the proposed method is verified by a comparison with the results which are derived by using analytical methods. [ABSTRACT FROM AUTHOR]

Glioblastoma multiforme (GBM) is an aggressive primary brain cancer with a grim prognosis. Its morphology is heterogeneous, but prototypically consists of an inner, largely necrotic core surrounded by an outer, contrast-enhancing rim, and often extensive tumor-associated edema beyond. This structure is usually demonstrated by magnetic resonance imaging (MRI). To help relate the three highly idealized components of GBMs (i.e., necrotic core, enhancing rim, and maximum edema extent) to the underlying growth "laws, " a mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. This model generates a traveling-wave solution that mimics tumor progression. We develop several novel methods to approximate key characteristics of the wave profile, which can be compared with MRI data. Several simplified forms of growth and death terms and their parameter identifiability are studied. We use several test cases of MRI data of GBM patients to yield personalized parameterizations of the model, and the biological and clinical implications are discussed.

In a recent paper by one of the authors and collaborators, motivated by the Olive Quick Decline Syndrome (OQDS) outbreak, which has been ongoing in Southern Italy since 2013, a simple epidemiological model describing this epidemic was presented. Beside the bacterium Xylella fastidiosa, the main players considered in the model are its insect vectors, Philaenus spumarius, and the host plants (olive trees and weeds) of the insects and of the bacterium. The model was based on a system of ordinary differential equations, the analysis of which provided interesting results about possible equilibria of the epidemic system and guidelines for its numerical simulations. Although the model presented there was mathematically rather simplified, its analysis has highlighted threshold parameters that could be the target of control strategies within an integrated pest management framework, not requiring the removal of the productive resource represented by the olive trees. Indeed, numerical simulations support the outcomes of the mathematical analysis, according to which the removal of a suitable amount of weed biomass (reservoir of Xylella fastidiosa) from olive orchards and surrounding areas resulted in the most efficient strategy to control the spread of the OQDS. In addition, as expected, the adoption of more resistant olive tree cultivars has been shown to be a good strategy, though less cost-effective, in controlling the pathogen. In this paper for a more realistic description and a clearer interpretation of the proposed control measures, a spatial structure of the epidemic system has been included, but, in order to keep mathematical technicalities to a minimum, only two players have been described in a dynamical way, trees and insects, while the weed biomass is taken to be a given quantity. The control measures have been introduced only on a subregion of the whole habitat, in order to contain costs of intervention. We show that such a practice can lead to the eradication of an epidemic outbreak. Numerical simulations confirm both the results of the previous paper and the theoretical results of the model with a spatial structure, though subject to regional control only. [ABSTRACT FROM AUTHOR]

In this work, we consider a reaction–diffusion system, modeling the interaction between nutrients, phytoplankton, and zooplankton. Using a semigroup approach in L2, we prove global existence, uniqueness, and positivity of the solutions. The nonlinearity is handled by providing estimates in L∞, allowing to deal with most of the functional responses that describe predator/prey interactions (Holling I, II, III, Ivlev) in ecology. The paper finally exhibits some time asymptotic properties of the solutions. [ABSTRACT FROM AUTHOR]

Mathematical immunology is the branch of mathematics dealing with the application of mathematical methods and computational algorithms to explore the structure, dynamics, organization and regulation of the immune system in health and disease. We review the conceptual and mathematical foundation of modelling in immunology formulated by Guri I. Marchuk. The current frontier studies concerning the development of multiscale multiphysics integrative models of the immune system are presented. [ABSTRACT FROM AUTHOR]

In this paper, five different models for five different kinds of diseases occurring in wildlife populations are introduced. In all models, a logistic growth term is taken into account and the disease is transmitted to the susceptible population indirectly through an environment reservoir. The time evolution of these diseases is described together with its spatial propagation. The character of spatial homogeneous equilibria against the uniform and non-uniform perturbations together with the occurrence of Hopf bifurcations are discussed through a linear stability analysis. No Turing instability is observed. The partial differential field equations are also integrated numerically to validate the stability results herein obtained and to extract additional information on the temporal and spatial behavior of the different diseases. [ABSTRACT FROM AUTHOR]

In this article, the first part is concerned with the important questions related to the existence and uniqueness of solutions for nonlinear reaction-diffusion systems. Secondly, an efficient positivity-preserving operator splitting nonstandard finite difference scheme (NSFD) is designed for such a class of systems. The presented formulation is unconditionally stable as well as implicit in nature and even time efficient. The proposed NSFD operator splitting technique also preserves all the important properties possessed by continuous systems like positivity, convergence to the fixed points of the system, and boundedness. The proposed algorithm is implicit in nature but more efficient in time than the extensively used Euler method. [ABSTRACT FROM AUTHOR]

Summary: The conductance of carbon dioxide (CO2) from the substomatal cavities to the initial sites of CO2 fixation (gm) can significantly reduce the availability of CO2 for photosynthesis. There have been many recent reviews on: (i) the importance of gm for accurately modelling net rates of CO2 assimilation, (ii) on how leaf biochemical and anatomical factors influence gm, (iii) the technical limitation of estimating gm, which cannot be directly measured, and (iv) how gm responds to long‐ and short‐term changes in growth and measurement environmental conditions. Therefore, this review will highlight these previous publications but will attempt not to repeat what has already been published. We will instead initially focus on the recent developments on the two‐resistance model of gm that describe the potential of photorespiratory and respiratory CO2 released within the mitochondria to diffuse directly into both the chloroplast and the cytosol. Subsequently, we summarize recent developments in the three‐dimensional (3‐D) reaction‐diffusion models and 3‐D image analysis that are providing new insights into how the complex structure and organization of the leaf influences gm. Finally, because most of the reviews and literature on gm have traditionally focused on C3 plants we review in the final sections some of the recent developments, current understanding and measurement techniques of gm in C4 and crassulacean acid metabolism (CAM) plants. These plants have both specialized leaf anatomy and either a spatially or temporally separated CO2 concentrating mechanisms (C4 and CAM, respectively) that influence how we interpret and estimate gm compared with a C3 plants. Significance Statement: This review discusses new developments regarding mesophyll CO2 conductance in C3, C4, and CAM plants. [ABSTRACT FROM AUTHOR]

The theory of dynamical systems and their widespread applications involve, for example, the Lane–Emden-type equations which are known to arise in initial- and boundary-value problems with singularity at the time t=0. The main objective of this paper is to make use of some mathematical analytic tools and techniques in order to numerically solve some reaction–diffusion equations, which arise in spherical catalysts and spherical biocatalysts, by applying the Chebyshev spectral collocation method. The proposed scheme has good accuracy. The results are demonstrated by means of illustrative graphs and numerical tables. The accuracy of the proposed method is verified by a comparison with the results which are derived by using analytical methods.

Let V be any finite set and p (⋅ , ⋅) a transition kernel on it. We present a construction of a family of Reaction–Diffusion models that converge after scaling to the solution to the | V | -dimensional SDE: d ζ t = [ Δ p ζ t − β ⋅ ζ t k ] d t + α ⋅ ζ t ℓ d B t with arbitrary initial condition ζ 0 ∈ R V. Here, Δ p is the diffusion on V corresponding to p , α , β are positive real numbers and k , ℓ are positive integers. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical (finite volume) approximation of reaction–diffusion systems with relaxation, among which the hyperbolic extension of the Allen–Cahn equation – given by τ ∂ t t u + (1 − τ f ′ (u)) ∂ t u − μ ∂ x x u = f (u) , where τ , μ > 0 and f is a cubic-like function with three zeros – represents a notable prototype. Appropriate discretizations are constructed starting from the kinetic interpretation of the model as a particular case of reactive jump process, given by the substitution of the Fourier's law with the Maxwell–Cattaneo's law. A corresponding pseudo-kinetic scheme is also proposed for the Guyer–Krumhansl's law. For the Maxwell–Cattaneo case, numerical experiments 1 are provided for exemplifying the theoretical analysis (previously developed by the same authors) concerning the stability of traveling waves under a sign condition on the damping term g : = 1 − τ f ′. Moreover, important evidence of the validity of those results beyond the formal hypotheses g (u) > 0 for any u is numerically established. [ABSTRACT FROM AUTHOR]

This paper is concerned with a late stage of lymphangiogenesis in the trunk of the zebrafish embryo. At 48 hours post-fertilisation (HPF), a pool of parachordal lymphangioblasts (PLs) lies in the horizontal myoseptum. Between 48 and 168 HPF, the PLs spread from the horizontal myoseptum to form the thoracic duct, dorsal longitudinal lymphatic vessel, and parachordal lymphatic vessel. This paper deals with the potential of vascular endothelial growth factor C (VEGFC) to guide the differentiation of PLs into the mature lymphatic endothelial cells that form the vessels. We built a mathematical model to describe the biochemical interactions between VEGFC, collagen I, and matrix metalloproteinase 2 (MMP2). We also carried out a linear stability analysis of the model and computer simulations of VEGFC patterning. The results suggest that VEGFC can form Turing patterns due to its relations with MMP2 and collagen I, but the zebrafish embryo needs a separate control mechanism to create the right physiological conditions. Furthermore, this control mechanism must ensure that the VEGFC patterns are useful for lymphangiogenesis: stationary, steep gradients, and reasonably fast forming. Generally, the combination of a patterning species, a matrix protein, and a remodelling species is a new patterning mechanism. [ABSTRACT FROM AUTHOR]

Highlights • Noise can determine invasion success in competition-diffusion models. • Different density dependencies change the impact of noise on wave pinning. • Results are independent on the chosen growth function. • Numerical results show extreme parameter restrictions for wave pinning. • Wave pinning is unstable against environmental perturbations in one dimension. Abstract Numerical results on conditions for the emergence of propagation failure of diffusive fronts in two-species competition models for populations with either logistic growth or strong Allee effect are presented. Particularly, the stability against environmental perturbations is investigated. Two different density dependencies of the noise intensities are considered. They mimic a differential functional response of the competitors to the variable environment. Assuming classical linearly density-dependent noise intensities, stochastic wave pinning can occur. This is an ecologically important finding regarding biological invasion as it means that the invasion speed can be reduced by environmental perturbations even yielding a reversal of the invasion wave. However, this depends on the form of the functional per-capita noise response. [ABSTRACT FROM AUTHOR]

The dynamics and stability of ecological communities are intimately linked with the specific interactions--like cooperation or predation--between constituent species. In microbial communities, like those found in soils or the mammalian gut, physical anisotropies produced by fluid flow and chemical gradients impact community structure and ecological dynamics, even in structurally isotropic environments. Although natural communities existing in physically unstructured environments are rare, the role of environmental structure in determining community dynamics and stability remains poorly studied. To address this gap, we used modified Lotka-Volterra simulations of competitive microbial communities to characterize the effects of surface structure on community dynamics. We find that environmental structure has profound effects on communities, in a manner dependent on the specific pattern of interactions between community members. For two mutually competing species, eventual extinction of one competitor is effectively guaranteed in isotropic environments. However, addition of environmental structure enables long-term coexistence of both species via local "pinning" of competition interfaces, even when one species has a significant competitive advantage. In contrast, while three species competing in an intransitive loop (as in a game of rock-paper-scissors) coexist stably in isotropic environments, structural anisotropy disrupts the spatial patterns on which coexistence depends, causing chaotic population fluctuations and subsequent extinction cascades. These results indicate that the stability of microbial communities strongly depends on the structural environment in which they reside. Therefore, a more complete ecological understanding, including effective manipulation and interventions in natural communities of interest, must account for the physical structure of the environment. [ABSTRACT FROM AUTHOR]

The present work is inspired by the recent developments in laboratory experiments made on chips, where the culturing of multiple cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis and takes into account the interactions among cell populations and the possibility of drug administration for drug testing effects. Our effort is devoted to the development of a simulation tool that is able to reproduce the chemotactic movement and the interactions between different cell species (immune and cancer cells) living in a microfluidic chip environment. The main issues faced in this work are the introduction of mass-preserving and positivity-preserving conditions, involving the balancing of incoming and outgoing fluxes passing through interfaces between 2D and 1D domains of the chip and the development of mass-preserving and positivity preserving numerical conditions at the external boundaries and at the interfaces between 2D and 1D domains.

A good knowledge about species traits variability in relation to their environment is the cornerstone of landscape-oriented species management studies. One way to infer this relationship is to compare species signatures in space and time from field data with spatially explicit population dynamics models outputs. However, the inference robustness relies on the available field data, and thus on the quality of the underlying sampling strategy. Field sampling is constrained by several factors, such as the number of landscape replicates, possible number of temporal sessions and number of sample locations, that need to be accounted for prior to field sampling. We set and illustrate a heuristic method to answer the question of optimal sampling conditioned by these landscape-induced constraints. First we studied a real agricultural landscape to determine its mean properties in terms of configuration and composition. The real landscape properties were used as constraints in a landscape model to generate a collection of landscapes with similar properties. On the other hand, we formulated population dynamics models (hereafter noted Process Models ( PM )) carrying competing hypotheses about two ecological processes—population growth and dispersal—in relation to spatial covariates for Pterostichus melanarius , a carabid species involved in pest regulation. We simulated these spatially explicit models and extracted their sampling-dependent signatures, i.e. metrics computed on different population samples. We defined a sampling design quality as its ability to capture the contrasts between the PM signatures, summarised by the performance of a classification procedure. The most relevant sampling design was selected on the basis of classification performance and in situ feasibility. Finally we explored the effects of the a priori ecological hypotheses quality on classification performances, through a sensitivity analysis of the PM parameters. While some improvements remain to be achieved before being fully operational for landscape ecologists, our framework contributes to bringing closer sampling theory and its application on the field. It endorses the use of landscape modelling to design sampling prior to field experiment to bring out the best from sampled data. [ABSTRACT FROM AUTHOR]

We analyze the effects of cross-diffusion on pattern formation in a PDE reaction-diffusion system introduced in Bozzini et al. 2013 to describe metal growth in an electrodeposition process. For this morphochemical model - which refers to the physico-chemical problem of coupling of growth morphology and surface chemistry - we have found that negative cross-diffusion in the morphological elements as well as positive cross-diffusion in the surface chemistry produce larger Turing parameter spaces and favor a tendency to stripeness that is not found in the case without cross-diffusion. The impact of cross-diffusion on pattern selection has been also discussed by the means of a stripeness index. Our theoretical findings are validated by an extensive gallery of numerical simulations that allow to better clarify the role of cross-diffusion both on Turing parameter spaces and on pattern selection. Experimental evidence of cross-diffusion in electrodeposition as well as a physico-chemical discussion of the expected impact of cross diffusion-controlled pattern formation in alloy electrodeposition processes complete the study. [ABSTRACT FROM AUTHOR]

Spatial structure can decisively influence the way evolutionary processes unfold. To date, several methods have been used to study evolution in spatial systems, including population genetics, quantitative genetics, moment-closure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabilizing/disruptive selection that apply both in continuous space and to metacommunities with symmetrical dispersal between patches. For directional selection on a quantitative trait, this yields a way to integrate local directional selection across space and determine whether the trait value will increase or decrease. The robustness of this prediction is validated against quantitative genetics. For stabilizing/disruptive selection, we show that spatial heterogeneity always contributes to disruptive selection and hence always promotes evolutionary branching. The expression for directional selection is numerically very efficient and hence lends itself to simulation studies of evolutionary community assembly. We illustrate the application and utility of the expressions for this purpose with two examples of the evolution of resource utilization. Finally, we outline the domain of applicability of reaction-diffusion equations as a modeling framework and discuss their limitations. [ABSTRACT FROM AUTHOR]

We formulate a general impulsive reaction-diffusion equation model to describe the population dynamics of species with distinct reproductive and dispersal stages. The seasonal reproduction is modeled by a discrete-time map, while the dispersal is modeled by a reaction-diffusion partial differential equation. Study of this model requires a sim ultaneous analysis of the differential equation and the recurrence relation. When boundary conditions are hostile we provide critical domain results showing how extinction versus persistence of the species arises, depending on the size and geometry of the domain. We show that there exists an extreme volume size such that if |Ω| falls below this size the species is driven extinct, regardless of the geometry of the domain. To construct such extreme volume sizes and critical domain sizes, we apply Schwarz symmetrization rearrangement arguments, the classical Rayleigh--Faber--Krahn inequality, and the spectrum of uniformly elliptic operators. The critical domain results provide qualitative insight regarding long-term dynamics for the model. Last, we provide applications of our main results to certain biological reaction-diffusion models regarding marine reserve, terrestrial reserve, insect pest outbreak, and population subject to climate change. [ABSTRACT FROM AUTHOR]

One way to increase potential crop yield could be increasing mesophyll conductance g m . This variable determines the difference between the CO 2 partial pressure in the intercellular air spaces ( C i ) and that near Rubisco ( C c ). Various methods can determine g m from gas exchange measurements, often combined with measurements of chlorophyll fluorescence or carbon isotope discrimination. g m lumps all biochemical and physical factors that cause the difference between C c and C i . g m appears to vary with C i . This variability indicates that g m does not satisfy the physical definition of a conductance according to Fick’s first law and is thus an apparent parameter. Uncertainty about the mechanisms that determine g m can be limited to some extent by using analytical models that partition g m into separate conductances. Such models are still only capable of describing the CO 2 diffusion pathway to a limited extent, as they make implicit assumptions about the position of mitochondria in the cells, which affect the re-assimilation of (photo)respired CO 2 . Alternatively, reaction-diffusion models may be used. Rather than quantifying g m , these models explicitly account for factors that affect the efficiency of CO 2 transport in the mesophyll. These models provide a better mechanistic description of the CO 2 diffusion pathways than mesophyll conductance models. Therefore, we argue that reaction-diffusion models should be used as an alternative to mesophyll conductance models, in case the aim of such a study is to identify traits that can be improved to increase g m . [ABSTRACT FROM AUTHOR]

We study an individual-based model in which two spatially distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in terms of reproduction rate. In the second case, resources are not uniformly distributed in space. In the third case, the two species are transported by a fluid flow. In all these cases, at varying the parameters, we observe a transition from a regime in which diffusing faster confers an effective selective advantage to one in which it constitutes a disadvantage. We analytically estimate the magnitude of this advantage (or disadvantage) and test it by measuring fixation probabilities in simulations of the individual-based model. Our results provide a framework to quantify evolutionary pressure for increased or decreased dispersal in a given environment. [ABSTRACT FROM AUTHOR]

In this paper, we investigate from a theoretical point of view the 2D reaction-diffusion system for electrodeposition coupling morphology and surface chemistry, presented and experimentally validated in Bozzini et al. (2013J. Solid State Electr.17, 467–479). We analyse the mechanisms responsible for spatio-temporal organization. As a first step, spatially uniform dynamics is discussed and the occurrence of a supercritical Hopf bifurcation for the local kinetics is proved. In the spatial case, initiation of morphological patterns induced by diffusion is shown to occur in a suitable region of the parameter space. The intriguing interplay between Hopf and Turing instability is also considered, by investigating the spatio-temporal behaviour of the system in the neighbourhood of the codimension-two Turing--Hopf bifurcation point. An ADI (Alternating Direction Implicit) scheme based on high-order finite differences in space is applied to obtain numerical approximations of Turing patterns at the steady state and for the simulation of the oscillating Turing–Hopf dynamics. [ABSTRACT FROM PUBLISHER]

The jaguar (Panthera onca) inhabits most of the lowlands (<2000 m) of central and South America in small and numerous fragmented populations. This species now occupies only 50% of its historic range and is included in ICUN red list. Current conservation and management plans rely on the identification and preservation of corridors and potential areas for species dispersion that provide gene flow. Over the last decade, expert-based knowledge consolidation and computational modeling complemented with radio-telemetry and camera-trapping analysis defined suitable areas for jaguar long-term survival and corridors for preserving jaguar connectivity. However, none of these static models incorporate jaguar population dynamics and assume that current population distribution is at steady state equilibrium. Here, we analyze jaguar metapopulation dynamics with a spatially explicit stochastic dispersal model to predict jaguar population distribution and density at a continental level. We also incorporate other biological features in the model such as gender differences regarding movement patterns and include the effect of human-jaguar conflict. This dynamic model provides a good framework for jaguar conservation analysis by providing new insights into jaguar migration and species viability. [ABSTRACT FROM AUTHOR]