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The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
Monitoring urban structure and development requires high-quality data at high spatiotemporal resolution. While traditional censuses have provided foundational insights into demographic and socioeconomic aspects of urban life, their pace may…
Different statistical samples (e.g., from different locations) offer populations and learning systems observations with distinct statistical properties. Samples under (1) 'Unconfounded' growth preserve systems' ability to determine the…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
System dynamics (SD) is an effective approach for helping reveal the temporal behavior of complex systems. Although there have been recent developments in expanding SD to include systems' spatial dependencies, most applications have been…
Enhancement of the predictive power and robustness of nonlinear population dynamics models allows ecologists to make more reliable forecasts about species' long term survival. However, the limited availability of detailed ecological data,…
Swarms of large numbers of agents appear in many biological and engineering fields. Dynamic bi-stability of co-existing spatio-temporal patterns has been observed in many models of large population swarms. However, many reduced models for…
We develop a data-driven model discovery and system identification technique for spatially-dependent boundary value problems (BVPs). Specifically, we leverage the sparse identification of nonlinear dynamics (SINDy) algorithm and group…
Self-arrangement of individuals into spatial patterns often accompanies and promotes species diversity in ecological systems. Here, we investigate pattern formation arising from cyclic dominance of three species, operating near a…
We develop an theoretical approach for predicting biodiversity in multi-dimensional niche spaces, arising due to ecological drivers such as competitive exclusion. The novelty of our approach relies on the fact that ecological niches are…
Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional methods frequently struggle with the inherent complexity,…
This paper addresses mechanisms for boundedly rational decision makers in discrete choice problem. First, we introduce two mathematical models of population dynamics with conformity biases. We next analyze the models in terms of…
We propose a general model to study the interplay between spatial dispersal and environment spatiotemporal fluctuations in metapopulation dynamics. An ecological landscape of favorable patches is generated like a L\'{e}vy dust, which allows…
Deep generative models are increasingly used to gain insights in the geospatial data domain, e.g., for climate data. However, most existing approaches work with temporal snapshots or assume 1D time-series; few are able to capture…
Speciation is fundamental to the huge diversity of life on Earth. Evidence suggests reproductive isolation arises most commonly in allopatry with a higher speciation rate in small populations. Current theory does not address this dependence…
The discovery of governing differential equations from data is an open frontier in machine learning. The sparse identification of nonlinear dynamics (SINDy) \citep{brunton_discovering_2016} framework enables data-driven discovery of…
This paper is mainly devoted to lay an empirical foundation for further research on complex spatial dynamics of two-population interaction. Based on the US population census data, a rural and urban population interaction model is developed.…
The strong Allee effect plays an important role on the evolution of population in ecological systems. One important concept is the Allee threshold that determines the persistence or extinction of the population in a long time. In general, a…
Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional data-driven methods face challenges in capturing inherently…
Many dynamical systems exhibit oscillatory behavior that can be modeled with differential equations. Recently, these equations have increasingly been derived through data-driven methods, including the transparent technique known as Sparse…