Phenotypic plasticity: A missing element in the theory of vegetation pattern formation.

Regular spatial patterns of vegetation are a common sight in drylands. Their formation is a population-level response to water stress that increases water availability for the few via partial plant mortality. At the individual level, plants can also adapt to water stress by changing their phenotype. Phenotypic plasticity of individual plants and spatial patterning of plant populations have extensively been studied independently, but the likely interplay between the two robust mechanisms has remained unexplored. In this paper, we incorporate phenotypic plasticity into a multi-level theory of vegetation pattern formation and use a fascinating ecological phenomenon, the Namibian "fairy circles," to demonstrate the need for such a theory. We show that phenotypic changes in the root structure of plants, coupled with pattern-forming feedback within soil layers, can resolve two puzzles that the current theory fails to explain: observations of multi-scale patterns and the absence of theoretically predicted large-scale stripe and spot patterns along the rainfall gradient. Importantly, we find that multi-level responses to stress unveil a wide variety of more effective stress-relaxation pathways, compared to single-level responses, implying a previously underestimated resilience of dryland ecosystems.

Long-distance seed dispersal affects the resilience of banded vegetation patterns in semi-deserts.

Landscape-scale vegetation stripes (tiger bush) observed on the gentle slopes of semi-arid regions are useful indicators of future ecosystem degradation and catastrophic shifts towards desert. Mathematical models like the Klausmeier model-a set of coupled partial differential equations describing vegetation and water densities in space and time-are central to understanding their formation and development. One assumption made for mathematical simplicity is the local dispersal of seeds via a diffusion term. In fact, a large amount of work focuses on fitting dispersal 'kernels', probability density functions for seed dispersal distance, to empirical data of different species and modes of dispersal. In this paper, we address this discrepancy by analysing an extended Klausmeier model that includes long-distance seed dispersal via a non-local convolution term in place of diffusion, and assessing its effect on the resilience of striped patterns. Many authors report a slow uphill migration of stripes; but others report no detectable migration speed. We show that long-distance seed dispersal permits the formation of patterns with a very slow (possibly undetectable) migration speed, and even stationary patterns which could explain the inconsistencies in the empirical data. In general, we show that the resilience of patterns to reduced rainfall may vary significantly depending on the rate of seed dispersal and the width of the dispersal kernel, and compare a selection of ecologically relevant kernels to examine the variation in pattern resilience.

Large scale patterns in mussel beds: stripes or spots?

An aerial view of an intertidal mussel bed often reveals large scale striped patterns aligned perpendicular to the direction of the tide; dense bands of mussels alternate periodically with near bare sediment. Experimental work led to the formulation of a set of coupled partial differential equations modelling a mussel-algae interaction, which proved pivotal in explaining the phenomenon. The key class of model solutions to consider are one-dimensional periodic travelling waves (wavetrains) that encapsulate the abundance of peak and trough mussel densities observed in practice. These solutions may, or may not, be stable to small perturbations, and previous work has focused on determining the ecologically relevant (stable) wavetrain solutions in terms of model parameters. The aim of this paper is to extend this analysis to two space dimensions by considering the full stripe pattern solution in order to study the effect of transverse two-dimensional perturbations-a more true to life problem. Using numerical continuation techniques, we find that some striped patterns that were previously deemed stable via the consideration of the associated wavetrain solution, are in fact unstable to transverse two-dimensional perturbations; and numerical simulation of the model shows that they break up to form regular spotted patterns. In particular, we show that break up of stripes into spots is a consequence of low tidal flow rates. Our consideration of random algal movement via a dispersal term allows us to show that a higher algal dispersal rate facilitates the formation of stripes at lower flow rates, but also encourages their break up into spots. We identify a novel hysteresis effect in mussel beds that is a consequence of transverse perturbations.

Low-frequency ERK and Akt activity dynamics are predictive of stochastic cell division events.

Understanding the dynamics of intracellular signaling pathways, such as ERK1/2 (ERK) and Akt1/2 (Akt), in the context of cell fate decisions is important for advancing our knowledge of cellular processes and diseases, particularly cancer. While previous studies have established associations between ERK and Akt activities and proliferative cell fate, the heterogeneity of single-cell responses adds complexity to this understanding. This study employed a data-driven approach to address this challenge, developing machine learning models trained on a dataset of growth factor-induced ERK and Akt activity time courses in single cells, to predict cell division events. The most predictive models were developed by applying discrete wavelet transforms (DWTs) to extract low-frequency features from the time courses, followed by using Ensemble Integration, a data integration and predictive modeling framework. The results demonstrated that these models effectively predicted cell division events in MCF10A cells (F-measure=0.524, AUC=0.726). ERK dynamics were found to be more predictive than Akt, but the combination of both measurements further enhanced predictive performance. The ERK model`s performance also generalized to predicting division events in RPE cells, indicating the potential applicability of these models and our data-driven methodology for predicting cell division across different biological contexts. Interpretation of these models suggested that ERK dynamics throughout the cell cycle, rather than immediately after growth factor stimulation, were associated with the likelihood of cell division. Overall, this work contributes insights into the predictive power of intra-cellular signaling dynamics for cell fate decisions, and highlights the potential of machine learning approaches in unraveling complex cellular behaviors.

Evidence for scale-dependent root-antation feedback and its role in halting the spread of a pantropical shrub into an endemic sedge.

Vegetation pattern formation is a widespread phenomenon in resource-limited environments, but the driving mechanisms are largely unconfirmed empirically. Combining results of field studies and mathematical modeling, empirical evidence for a generic pattern-formation mechanism is demonstrated with the clonal shrub Guilandina bonduc L. (hereafter Guilandina) on the Brazilian island of Trindade. The mechanism is associated with water conduction by laterally spread roots and root augmentation as the shoot grows-a crucial element in the positive feedback loop that drives spatial patterning. Assuming precipitation-dependent root-shoot relations, the model accounts for the major vegetation landscapes on Trindade Island, substantiating lateral root augmentation as the driving mechanism of Guilandina patterning. Guilandina expands into surrounding communities dominated by the Trindade endemic, Cyperus atlanticus Hemsl. (hereafter Cyperus). It appears to do so by decreasing the water potential in soils below Cyperus through its dense lateral roots, leaving behind a patchy Guilandina-only landscape. We use this system to highlight a novel form of invasion, likely to apply to many other systems where the invasive species is pattern-forming. Depending on the level of water stress, the invasion can take two distinct forms: (i) a complete invasion at low stress that culminates in a patchy Guilandina-only landscape through a spot-replication process, and (ii) an incomplete invasion at high stress that begins but does not spread, forming isolated Guilandina spots of fixed size, surrounded by bare-soil halos, in an otherwise uniform Cyperus grassland. Thus, drier climates may act selectively on pattern-forming invasive species, imposing incomplete invasion and reducing the negative effects on native species.