Emergent spatial organization of competing species under environmental stress and cooperation
Ton Viet Ta
TL;DR
This work develops a unified spatial model that couples population dynamics to four environmental drivers—temperature, pollution, resources, and cooperation—through a dynamic carrying capacity $K_i(x,y,t)$. It combines a reaction–diffusion population equation with linear diffusion–reaction PDEs for $P$, $R$, $T$, and $C$, capturing feedbacks between abiotic forcing and social behavior. Numerically, it reveals emergent persistent spatial patterns and a quasi-stationary dominance structure, with metrics such as boundary length and fractal dimension quantifying pattern simplification over time. To address data sparsity, it introduces a Swin Transformer–based inverse framework that infers high-dimensional parameters from two spatial snapshots, achieving accurate short-term spatial predictions but limited long-term forecasts due to intrinsic nonlinear sensitivity of the system.
Abstract
Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability, pollution, resource heterogeneity, and cooperation. Here, temperature follows low-frequency oscillations, while pollution and resources diffuse from localized sources. Growth is governed by a dynamic carrying capacity integrating abiotic stress with an endogenous, pollution-sensitive cooperation field. Numerical simulations reveal the spontaneous emergence of persistent spatial organization, including dominance segregation and stable competitive boundaries. Quantitative analyses-using boundary geometry, fractal dimension, and spatial entropy-demonstrate a transition from intermixed initial states to low-complexity, quasi-stationary configurations. Coexistence occurs through distinct strategies: one species occupies more area, while the other maintains higher local densities. Cooperation enhances resilience but collapses in polluted zones, creating heterogeneous "social buffering." We further introduce a hybrid inverse modeling framework using a Swin Transformer to infer high-dimensional parameters from only two temporal snapshots. Trained on synthetic data, the model accurately recovers demographic, diffusive, and environmental-sensitivity parameters. While it achieves reliable short-term spatial predictions, long-term forecasts diverge due to the intrinsic sensitivity of nonlinear systems. This unified framework links sparse observations to mechanistic dynamics, advancing biodiversity forecasting under accelerating global change.