Travelling waves due to negative plant-soil feedbacks in a model including tree life-stages.

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.

Process based modelling of plants-fungus interactions explains fairy ring types and dynamics.

Many mushroom-forming fungi can develop circular colonies affecting the vegetation in a phenomenon named fairy rings. Since the nineteenth century, several hypotheses have been proposed to explain how fairy ring fungi form ring-like shapes instead of disks and why they produce negative or positive effects on the surrounding vegetation. In this context, we present a novel process-based mathematical model aimed at reproducing the mycelial spatial configuration of fairy rings and test different literature-supported hypotheses explaining the suppressive and stimulating effects of fungi on plants. Simulations successfully reproduced the shape of fairy rings through the accumulation of fungal self-inhibitory compounds. Moreover, regarding the negative effects of fungi on vegetation, results suggest that fungal-induced soil hydrophobicity is sufficient to reproduce all observed types of fairy rings, while the potential production of phytotoxins is not. In relation to the positive effects of fungi on plants, results show that the release of phytostimulants is needed to reproduce the vegetation patterns associated to some fairy ring types. Model outputs can guide future experiments and field work to corroborate the considered hypotheses and provide more information for further model improvements.

Modelling how negative plant-soil feedbacks across life stages affect the spatial patterning of trees.

In this work, we theoretically explore how litter decomposition processes and soil-borne pathogens contribute to negative plant-soil feedbacks, in particular in transient and stable spatial organisation of tropical forest trees and seedlings known as Janzen-Connell distributions. By considering soil-borne pathogens and autotoxicity both separately and in combination in a phenomenological model, we can study how both factors may affect transient dynamics and emerging Janzen-Connell distributions. We also identify parameter regimes associated with different long-term behaviours. Moreover, we compare how the strength of negative plant-soil feedbacks was mediated by tree germination and growth strategies, using a combination of analytical approaches and numerical simulations. Our interdisciplinary investigation, motivated by an ecological question, allows us to construct important links between local feedbacks, spatial self-organisation, and community assembly. Our model analyses contribute to understanding the drivers of biodiversity in tropical ecosystems, by disentangling the abilities of two potential mechanisms to generate Janzen-Connell distributions. Furthermore, our theoretical results may help guiding future field data analyses by identifying spatial signatures in adult tree and seedling distribution data that may reflect the presence of particular plant-soil feedback mechanisms.

An Adaptive Generalized Leaky Integrate-and-Fire Model for Hippocampal CA1 Pyramidal Neurons and Interneurons.

Full-scale morphologically and biophysically realistic model networks, aiming at modeling multiple brain areas, provide an invaluable tool to make significant scientific advances from in-silico experiments on cognitive functions to digital twin implementations. Due to the current technical limitations of supercomputer systems in terms of computational power and memory requirements, these networks must be implemented using (at least) simplified neurons. A class of models which achieve a reasonable compromise between accuracy and computational efficiency is given by generalized leaky integrate-and fire models complemented by suitable initial and update conditions. However, we found that these models cannot reproduce the complex and highly variable firing dynamics exhibited by neurons in several brain regions, such as the hippocampus. In this work, we propose an adaptive generalized leaky integrate-and-fire model for hippocampal CA1 neurons and interneurons, in which the nonlinear nature of the firing dynamics is successfully reproduced by linear ordinary differential equations equipped with nonlinear and more realistic initial and update conditions after each spike event, which strictly depends on the external stimulation current. A mathematical analysis of the equilibria stability as well as the monotonicity properties of the analytical solution for the membrane potential allowed (i) to determine general constraints on model parameters, reducing the computational cost of an optimization procedure based on spike times in response to a set of constant currents injections; (ii) to identify additional constraints to quantitatively reproduce and predict the experimental traces from 85 neurons and interneurons in response to any stimulation protocol using constant and piecewise constant current injections. Finally, this approach allows to easily implement a procedure to create infinite copies of neurons with mathematically controlled firing properties, statistically indistinguishable from experiments, to better reproduce the full range and variability of the firing scenarios observed in a real network.

Vegetation pattern formation due to interactions between water availability and toxicity in plant-soil feedback.

Development of a comprehensive theory of the formation of vegetation patterns is still in progress. A prevailing view is to treat water availability as the main causal factor for the emergence of vegetation patterns. While successful in capturing the occurrence of multiple vegetation patterns in arid and semiarid regions, this hypothesis fails to explain the presence of vegetation patterns in humid environments. We explore the rich structure of a toxicity-mediated model of the vegetation pattern formation. This model consists of three PDEs accounting for a dynamic balance between biomass, water, and toxic compounds. Different (ecologically feasible) regions of the model's parameter space give rise to stable spatial vegetation patterns in Turing and non-Turing regimes. Strong negative feedback gives rise to dynamic spatial patterns that continuously move in space while retaining their stable topology.