Population-level scaling in ecological systems arises from individual growth and death with competitive constraints. We build on a minimal dynamical model of metabolic growth where the tension between individual growth and mortality determines population size distribution. We then separately include resource competition based on shared capture area. By varying rates of growth, death, and competitive attrition, we connect regular and random spatial patterns across sessile organisms from forests to ants, termites, and fairy circles. Then, we consider transient temporal dynamics in the context of asymmetric competition, such as canopy shading or large colony dominance, whose effects primarily weaken the smaller of two competitors. When such competition couples slow timescales of growth to fast competitive death, it generates population shocks and demographic oscillations similar to those observed in forest data. Our minimal quantitative theory unifies spatiotemporal patterns across sessile organisms through local competition mediated by the laws of metabolic growth, which in turn, are the result of long-term evolutionary dynamics.

Parameter estimation for nonlinear dynamic system models, represented by ordinary differential equations (ODEs), using noisy and sparse data, is a vital task in many fields. We propose a fast and accurate method, manifold-constrained Gaussian process inference (MAGI), for this task. MAGI uses a Gaussian process model over time series data, explicitly conditioned on the manifold constraint that derivatives of the Gaussian process must satisfy the ODE system. By doing so, we completely bypass the need for numerical integration and achieve substantial savings in computational time. MAGI is also suitable for inference with unobserved system components, which often occur in real experiments. MAGI is distinct from existing approaches as we provide a principled statistical construction under a Bayesian framework, which incorporates the ODE system through the manifold constraint. We demonstrate the accuracy and speed of MAGI using realistic examples based on physical experiments.

Honeybee swarms are a landmark example of collective behavior. To become a coherent swarm, bees locate their queen by tracking her pheromones. But how can distant individuals exploit these chemical signals, which decay rapidly in space and time? Here, we combine a behavioral assay with the machine vision detection of organism location and scenting (pheromone propagation via wing fanning) behavior to track the search and aggregation dynamics of the honeybee Apis mellifera L. We find that bees collectively create a scenting-mediated communication network by arranging in a specific spatial distribution where there is a characteristic distance between individuals and directional signaling away from the queen. To better understand such a flow-mediated directional communication strategy, we developed an agent-based model where bee agents obeying simple, local behavioral rules exist in a flow environment in which the chemical signals diffuse and decay. Our model serves as a guide to exploring how physical parameters affect the collective scenting behavior and shows that increased directional bias in scenting leads to a more efficient aggregation process that avoids local equilibrium configurations of isotropic (nondirectional and axisymmetric) communication, such as small bee clusters that persist throughout the simulation. Our results highlight an example of extended classical stigmergy: Rather than depositing static information in the environment, individual bees locally sense and globally manipulate the physical fields of chemical concentration and airflow.

Human cancers are biologically and morphologically heterogeneous. A variety of clonal populations emerge within these neoplasms and their interaction leads to complex spatiotemporal dynamics during tumor growth. We studied the reshaping of metabolic activity in human cancers by means of continuous and discrete mathematical models and matched the results to positron emission tomography (PET) imaging data. Our models revealed that the location of increasingly active proliferative cellular spots progressively drifted from the center of the tumor to the periphery, as a result of the competition between gradually more aggressive phenotypes. This computational finding led to the development of a metric, normalized distance from ¹⁸F-fluorodeoxyglucose (¹⁸F-FDG) hotspot to centroid (NHOC), based on the separation from the location of the activity (proliferation) hotspot to the tumor centroid. The NHOC metric can be computed for patients using ¹⁸F-FDG PET–computed tomography (PET/CT) images where the voxel of maximum uptake (standardized uptake value [SUV]_max) is taken as the activity hotspot. Two datasets of ¹⁸F-FDG PET/CT images were collected, one from 61 breast cancer patients and another from 161 non–small-cell lung cancer patients. In both cohorts, survival analyses were carried out for the NHOC and for other classical PET/CT-based biomarkers, finding that the former had a high prognostic value, outperforming the latter. In summary, our work offers additional insights into the evolutionary mechanisms behind tumor progression, provides a different PET/CT-based biomarker, and reveals that an activity hotspot closer to the tumor periphery is associated to a worst patient outcome.

Over one third of the estimated 3 million people with epilepsy in the United States are medication resistant. Responsive neurostimulation from chronically implanted electrodes provides a promising treatment alternative to resective surgery. However, determining optimal personalized stimulation parameters, including when and where to intervene to guarantee a positive patient outcome, is a major open challenge. Network neuroscience and control theory offer useful tools that may guide improvements in parameter selection for control of anomalous neural activity. Here we use a method to characterize dynamic controllability across consecutive effective connectivity (EC) networks based on regularized partial correlations between implanted electrodes during the onset, propagation, and termination regimes of 34 seizures. We estimate regularized partial correlation adjacency matrices from 1-s time windows of intracranial electrocorticography recordings using the Graphical Least Absolute Shrinkage and Selection Operator (GLASSO). Average and modal controllability metrics calculated from each resulting EC network track the time-varying controllability of the brain on an evolving landscape of conditionally dependent network interactions. We show that average controllability increases throughout a seizure and is negatively correlated with modal controllability throughout. Our results support the hypothesis that the energy required to drive the brain to a seizure-free state from an ictal state is smallest during seizure onset, yet we find that applying control energy at electrodes in the seizure onset zone may not always be energetically favorable. Our work suggests that a low-complexity model of time-evolving controllability may offer insights for developing and improving control strategies targeting seizure suppression.