Theoretical analysis of epidemic dynamics has attracted significant attention in the aftermath of the COVID-19 pandemic. In this article, we study dynamic instabilities in a spatiotemporal compartmental epidemic model represented by a stochastic system of coupled partial differential equations (SPDE). Saturation effects in infection spread-anchored in physical considerations-lead to strong nonlinearities in the SPDE. Our goal is to study the onset of dynamic, Turing-type instabilities, and the concomitant emergence of steady-state patterns under the interplay between three critical model parameters-the saturation parameter, the noise intensity, and the transmission rate. Employing a second-order perturbation analysis to investigate stability, we uncover both diffusion-driven and noise-induced instabilities and corresponding self-organized distinct patterns of infection spread in the steady state. We also analyze the effects of the saturation parameter and the transmission rate on the instabilities and the pattern formation. In summary, our results indicate that the nuanced interplay between the three parameters considered has a profound effect on the emergence of dynamical instabilities and therefore on pattern formation in the steady state. Moreover, due to the central role played by the Turing phenomenon in pattern formation in a variety of biological dynamic systems, the results are expected to have broader significance beyond epidemic dynamics.

Under nonequilibrium conditions, inorganic systems can produce a wealth of life-like shapes and patterns which, compared to well-formed crystalline materials, remain widely unexplored. A seemingly simple example is the formation of salt deposits during the evaporation of sessile droplets. These evaporites show great variations in their specific patterns including single rings, creep, small crystals, fractals, and featureless disks. We have explored the patterns of 42 different salts at otherwise constant conditions. Based on 7,500 images, we show that distinct pattern families can be identified and that some salts (e.g., Na2SO4 and NH4NO3) are bifurcated creating two distinct motifs. Family affiliations cannot be predicted a priori from composition alone but rather emerge from the complex interplay of evaporation, crystallization, thermodynamics, capillarity, and fluid flow. Nonetheless, chemical composition can be predicted from the deposit pattern with surprisingly high accuracy even if the set of reference images is small. These findings suggest possible applications including smartphone-based analyses and lightweight tools for space missions.

This work analyzes the effect of wall geometry when a reaction-diffusion system is confined to a narrow channel. In particular, we study the entropy production density in the reversible Gray-Scott system. Using an effective diffusion equation that considers modifications by the channel characteristics, we find that the entropy density changes its value but not its qualitative behavior, which helps explore the structure-formation space.

Decisions to disperse from a habitat stand out among organismal behaviours as pivotal drivers of ecosystem dynamics across scales. Encounters with other species are an important component of adaptive decision-making in dispersal, resulting in widespread behaviours like tracking resources or avoiding consumers in space. Despite this, metacommunity models often treat dispersal as a function of intraspecific density alone. We show, focusing initially on three-species network motifs, that interspecific dispersal rules generally drive a transition in metacommunities from homogeneous steady states to self-organized heterogeneous spatial patterns. However, when ecologically realistic constraints reflecting adaptive behaviours are imposed-prey tracking and predator avoidance-a pronounced homogenizing effect emerges where spatial pattern formation is suppressed. We demonstrate this effect for each motif by computing master stability functions that separate the contributions of local and spatial interactions to pattern formation. We extend this result to species-rich food webs using a random matrix approach, where we find that eventually, webs become large enough to override the homogenizing effect of adaptive dispersal behaviours, leading once again to predominately pattern-forming dynamics. Our results emphasize the critical role of interspecific dispersal rules in shaping spatial patterns across landscapes, highlighting the need to incorporate adaptive behavioural constraints in efforts to link local species interactions and metacommunity structure. This article is part of the theme issue \'Diversity-dependence of dispersal: interspecific interactions determine spatial dynamics\'.

OBJECTIVE: Electrostatically stabilised colloidal particles destabilise when brought into contact with cations causing the particles to aggregate in clusters. When a drop with stabilised colloidal partices is deposited on a liquid film containing cations the delicate balance between the fluid-mechanical and physicochemical properties of the system governs the spreading dynamics and formation of colloidal particle clusters.
METHODS: High-speed imaging and digital holographic microscopy were used to characterise the spreading process.
RESULTS: We reveal that a spreading colloidal drop evolves into a ring-shaped pattern after it is deposited on a thin saline water film. Clustered colloidal particles aggregate into larger trapezoidally-shaped \'supraclusters\'. Using a simple model we show that the trapezoidal shape of the supraclusters is determined by the transition from inertial spreading dynamics to Marangoni flow. These results may be of interest to applications such as wet-on-wet inkjet printing, where particle destabilisation and hydrodynamic flow coexist.

We develop a conceptual framework for geo-evolutionary feedbacks which describes the mutual interplay between landscape change and the evolution of traits of organisms residing on the landscape, with an emphasis on contemporary timeframes. Geo-evolutionary feedbacks can be realized via the direct evolution of geomorphic engineering traits or can be mediated by the evolution of trait variation that affects the population size and distribution of the specific geomorphic engineering organisms involved. Organisms that modify their local environments provide the basis for patch-scale geo-evolutionary feedbacks, whereas spatial self-organization provides a mechanism for geo-evolutionary feedbacks at the landscape scale. Understanding these likely prevalent geo-evolutionary feedbacks, that occur at timescales similar to anthropogenic climate change, will be essential to better predict landscape adaptive capacity and change.

Introduction: European mistletoe (Viscum album L.) has been gaining increasing interest in the field of oncology as a clinically relevant adjunctive treatment in many forms of cancer. In the field of phytopharmacology, harvesting time is pivotal. In the last century, a form of metabolomic fingerprinting based on pattern formation was proposed as a way to determine optimal harvesting times to ensure high quality of mistletoe as raw material for pharmaceutical use. In order to further evaluate the information obtained with this metabolomic fingerprinting method, we analysed a large time series of previously undigitised daily mistletoe chromatograms dating back to the 1950s. Methods: These chromatograms were scanned and evaluated using computerized image analysis, resulting in 12 descriptors for each individual chromatogram. We performed a statistical analysis of the data obtained, investigating statistical distributions, cross-correlations and time self-correlations. Results: The analysed dataset spanning about 27 years, contains 19,037 evaluable chromatograms in daily resolution. Based on the distribution and cross-correlation analyses, the 12 descriptors could be clustered into six independent groups describing different aspects of the chromatograms. One descriptor was found to mirror the annual rhythm being well correlated with temperature and a phase shift of 10 days. The time self-correlation analysis showed that most other descriptors had a characteristic self-correlation of ∼50 days, which points to further infradian rhythms (i.e., more than 24 h). Discussion: To our knowledge, this dataset is the largest of its type. The combination of this form of metabolomic fingerprinting with the proposed computer analysis seems to be a promising tool to characterise biological variations of mistletoe. Additional research is underway to further analyse the different rhythms present in this dataset.

Reaction-diffusion equations serve as fundamental tools in describing pattern formation in biology. In these models, nonuniform steady states often represent stationary spatial patterns. Notably, these steady states are not unique, and unveiling them mathematically presents challenges. In this paper, we introduce a framework based on bifurcation theory to address pattern formation problems, specifically examining whether nonuniform steady states can bifurcate from trivial ones. Furthermore, we employ linear stability analysis to investigate the stability of the trivial steady-state solutions. We apply the method to two classic reaction-diffusion models: the Schnakenberg model and the Gray-Scott model. For both models, our approach effectively reveals many nonuniform steady states and assesses the stability of the trivial solution. Numerical computations are also presented to validate the solution structures for these models.

Decline of the dissolved oxygen in the ocean is a growing concern, as it may eventually lead to global anoxia, an elevated mortality of marine fauna and even a mass extinction. Deoxygenation of the ocean often results in the formation of oxygen minimum zones (OMZ): large domains where the abundance of oxygen is much lower than that in the surrounding ocean environment. Factors and processes resulting in the OMZ formation remain controversial. We consider a conceptual model of coupled plankton-oxygen dynamics that, apart from the plankton growth and the oxygen production by phytoplankton, also accounts for the difference in the timescales for phyto- and zooplankton (making it a \"slow-fast system\") and for the implicit effect of upper trophic levels resulting in density dependent (nonlinear) zooplankton mortality. The model is investigated using a combination of analytical techniques and numerical simulations. The slow-fast system is decomposed into its slow and fast subsystems. The critical manifold of the slow-fast system and its stability is then studied by analyzing the bifurcation structure of the fast subsystem. We obtain the canard cycles of the slow-fast system for a range of parameter values. However, the system does not allow for persistent relaxation oscillations; instead, the blowup of the canard cycle results in plankton extinction and oxygen depletion. For the spatially explicit model, the earlier works in this direction did not take into account the density dependent mortality rate of the zooplankton, and thus could exhibit Turing pattern. However, the inclusion of the density dependent mortality into the system can lead to stationary Turing patterns. The dynamics of the system is then studied near the Turing bifurcation threshold. We further consider the effect of the self-movement of the zooplankton along with the turbulent mixing. We show that an initial non-uniform perturbation can lead to the formation of an OMZ, which then grows in size and spreads over space. For a sufficiently large timescale separation, the spread of the OMZ can result in global anoxia.

During neural tube (NT) development, the notochord induces an organizer, the floorplate, which secretes Sonic Hedgehog (SHH) to pattern neural progenitors. Conversely, NT organoids (NTOs) from embryonic stem cells (ESCs) spontaneously form floorplates without the notochord, demonstrating that stem cells can self-organize without embryonic inducers. Here, we investigated floorplate self-organization in clonal mouse NTOs. Expression of the floorplate marker FOXA2 was initially spatially scattered before resolving into multiple clusters, which underwent competition and sorting, resulting in a stable \"winning\" floorplate. We identified that BMP signaling governed long-range cluster competition. FOXA2+ clusters expressed BMP4, suppressing FOXA2 in receiving cells while simultaneously expressing the BMP-inhibitor NOGGIN, promoting cluster persistence. Noggin mutation perturbed floorplate formation in NTOs and in the NT in vivo at mid/hindbrain regions, demonstrating how the floorplate can form autonomously without the notochord. Identifying the pathways governing organizer self-organization is critical for harnessing the developmental plasticity of stem cells in tissue engineering.