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Numerical techniques are widely used to simulate population dynamics in space. In vegetation dynamics, these techniques are very useful to investigate how plants grow, compete for resources, and react to environmental factors within the ecosystem. Plant–soil feedback (PSF) refers to the process where plants or a community alter the biotic and abiotic characteristics of soil that affects the growth of plants or community subsequently growing in that soil. During the last three decades, PSF has been recognized as an important driver for the emergence of vegetation patterns. The importance of studying such vegetation patterns is that they provide an insight into potential ecological changes and illustrate the flexibility and resilience of an ecosystem. Despite the fact that water depletion was once thought to be a major factor in the development of vegetation patterns the existence of patterns in ecosystems without water limitations serves as evidence that this is not the case. In this study, we examine how negative plant–soil feedback contributes to the dynamics of plant biomass. We provide a comparison of different reaction–diffusion PDE models explaining the dynamics of plant biomass in the presence of autotoxicity produced by litter decomposition. We introduce different growth terms, including logistic and exponential, along with additional factors such as extra mortality and inhibitor terms, and develop six distinct models to investigate their individual and combined effects on biomass toxicity distribution. By applying appropriate numerical techniques, we solve the proposed reaction–diffusion PDE models in MATLAB to predict the impact of soil toxicity on plant biomass. [ABSTRACT FROM AUTHOR]

Bimatrix evolutionary games are used to model the way Plant-Soil Feedbacks (PSFs) influence the competition between plant species growing in the same soil. This feedback refers to the impact on plant growth caused by the plant’s ability to modify soil conditions, whether abiotic or biotic. Along with a review on the existing literature of modelling PSFs from an Evolutionary Game Theory point of view, we introduce our own contribution on the field, generalising the current models. Our game describes the direct interaction between nplants and their nspecies-specific soil communities and its implied effect to the plants’ competition. For n>2, we treat numerically the Nash Equilibria of the game to find evidence for the possible stable states of the induced population dynamics. Together with a theoretical analysis based on well-known Evolutionary Game Theory results, we address the high complexity of the dynamical system and determine whether PSFs favour the coexistence of species or lead to the absolute dominance of one species. In fact, our results strengthen the general belief that negative PSFs are necessary for plants’ biodiversity.

We perform both analytical and numerical bifurcation analysis of an alternating forest and grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of the value of the forest. The system displays multiple steady states corresponding to different forest densities as well as regimes characterized by both stable and unstable limit cycles. We derive analytically the conditions with respect to the model parameters that give rise to various types of codimension-one criticalities such as transcritical, saddle-node, and Andronov–Hopf bifurcations and codimension-two criticalities such as cusp and Bogdanov–Takens bifurcations at which homoclinic orbits occur. We also perform a numerical continuation of the branches of limit cycles. By doing so, we reveal turning points of limit cycles marking the appearance/disappearance of sustained oscillations. Such critical points that cannot be detected analytically give rise to the abrupt loss of the sustained oscillations, thus leading to another mechanism of catastrophic shifts.

Soil aggregation, a key aspect of soil physical health, is a crucial component of agroecosystem sustainability as it affects numerous soil processes and agroecosystem productivity. Application of organic amendment (OA) plays a vital role in improving soil aggregation. In this review, we provide a comprehensive synthesis and a critical assessment of the current state of knowledge in soil aggregation in relation to OA. We first highlight factors (such as soil texture and clay mineralogy, source and type of OA, OA application rate and frequency, and OA application mode) determining the effect of OA on soil aggregation. Secondly, we review how OA regulates soil aggregation and point out that OA improves soil aggregation mainly via: (i) increasing soil organic carbon (SOC) content where OA acts as an external source of SOC, (ii) promoting soil biotic activity where OA acts as a substrate for microbes, and (iii) increasing soil hydrophobicity, thus reducing aggregate turnover. Finally, we draw reader’s attention to the complex linkages between OA quality and soil aggregation. The OA quality defined by 13C-NMR spectroscopy in terms of organic C type can explain variable effects of OA on soil aggregation better than C/N and lignin/N ratio indices. Considering organic C types, OA rich in carbohydrate C fractions tends to induce rapid but short- and medium-term effects on soil aggregation, while OA riched in aromatic C fractions barely affects soil aggregation. We conclude that soil structure can be significantly modified through better agronomic practices of OA application which will enhance soil aggregation, reduce soil erosion, and subsequently increase overall productivity.

We revisit the theorem stating that it is possible to approximate with any accuracy any real continuous function with a class of relational maps. In other words, relational maps are universal approximators. We review the key works that have proved this property, highlighting their limitations and providing yet another proof that it is not restricted by certain assumptions considered in early proofs. We also show how one can go inversely to approximate these systems with a series of polynomials. This provides us with analytical expressions of these maps which can facilitate a series of important analysis tasks such as modeling and numerical analysis of ill-defined-uncertain complex systems.

ABSTRACTDNA is usually known as the molecule that carries the instructions necessary for cell functioning and genetic inheritance. A recent discovery reported a new functional role for extracellular DNA. After fragmentation, either by natural or artificial decomposition, small DNA molecules (between ∼50 and ∼2000 bp) exert a species specific inhibitory effect on individuals of the same species. Evidence shows that such effect occurs for a wide range of organisms, suggesting a general biological process. In this paper we explore the possible molecular mechanisms behind those findings and discuss the ecological implications, specifically those related to plant species coexistence.

The emergence and maintenance of tree species diversity in tropical forests is commonly attributed to the Janzen–Connell (JC) hypothesis, which states that growth of seedlings is suppressed in the proximity of conspecific adult trees. As a result, a JC distribution due to a density-dependent negative feedback emerges in the form of a (transient) pattern where conspecific seedling density is highest at intermediate distances away from parent trees. Several studies suggest that the required density-dependent feedbacks behind this pattern could result from interactions between trees and soil-borne pathogens. However, negative plant–soil feedback may involve additional mechanisms, including the accumulation of autotoxic compounds generated through tree litter decomposition. An essential task therefore consists in constructing mathematical models incorporating both effects showing the ability to support the emergence of JC distributions. In this work, we develop and analyse a novel reaction–diffusion-ODE model, describing the interactions within tropical tree species across different life stages (seeds, seedlings, and adults) as driven by negative plant–soil feedback. In particular, we show that under strong negative plant–soil feedback travelling wave solutions exist, creating transient distributions of adult trees and seedlings that are in agreement with the Janzen–Connell hypothesis. Moreover, we show that these travelling wave solutions are pulled fronts and a robust feature as they occur over a broad parameter range. Finally, we calculate their linear spreading speed and show its (in)dependence on relevant nondimensional parameters. • Tropical tree species diversity is maintained by seedling growth suppression. • Plant–soil negative feedback explains the Janzen–Connell (JC) seedling distribution. • Our mathematical model supports the JC distribution as a travelling wave. • The JC distribution is a pulled front with well-defined spreading speed. • Sufficiently strong negative plant–soil feedback induces a JC distribution. [ABSTRACT FROM AUTHOR]