Disequilibrium and complexity across scales: a patch-dynamics framework for organizational ecology

The paper addresses the limitations of traditional equilibrium-based ecological models (notably NK and Lotka–Volterra) in management and organization studies, especially their inability to incorporate multi-level dynamics, heterogeneity, uncertainty, and stochastic disturbances. The authors propose a patch-dynamics framework that emphasizes the mediating role of resources across multiple organizational scales (patch and population levels) to capture co-evolutionary dynamics under disequilibrium. The purpose is to integrate equilibrium and disequilibrium perspectives and provide modelling tools that reflect complex, dynamic business environments. The study’s importance lies in offering a multi-level, disturbance-aware approach for organizational ecology and strategic organizing where prior tools often reduce complexity to average behaviors and single-scale analyses.

The theoretical background contrasts equilibrium and disequilibrium perspectives. Equilibrium-based views (e.g., punctuated equilibrium, dynamic equilibrium models) have informed organizational change theories but struggle with heterogeneity and multi-scale complexity. In ecology, the balance-of-nature assumption has been challenged; equilibrium is rare, and prior metacommunity models often assume stability, limiting analysis of true dynamics. Classic models used in management—Lotka–Volterra (LV) and NK—are critiqued for limited capacity to represent multi-species interactions, spatial structure, life histories (LV), and for assuming predefined landscapes with full information and single-scale focus (NK). The literature points to the need for frameworks accommodating spatial heterogeneity, uncertainty, and interactions across levels. Patch-dynamics, originating from community and landscape ecology, decomposes landscapes into discrete patches that can support populations/communities and can operate from cells to large landscapes. It has evolved into landscape ecology and metacommunity perspectives, enabling integration of local and regional processes and disturbances. The framework is suited to capture environmental variability, spatial occupancy, dispersal, and disturbance regimes, and is increasingly used to assess persistence and viability, but remains underexplored in management studies. Uncertainty and disturbance are central in organizational contexts; disturbances shape stability, resilience, and coexistence, and patch-dynamics explicitly incorporates stochasticity and disturbance effects propagating via patches. The authors thus position patch-dynamics as a tool to bridge gaps in organizational ecology by capturing multi-scale dynamics, uncertainty, and resource-mediated interactions.

The study develops two simulation models to instantiate patch-dynamics for organizational ecosystems, focusing on patch- and population-level dynamics with resource mediation and disturbance. Model A extends LV dynamics to multi-patch, stochastic environments (after Wang and Loreau, 2016). General dynamics for species a in patch i: dN_ai/dt = r_ai N_ai [1 − (Σ_j N_ji / K_ai) − Σ_k c_aij N_ji] + (−d_a N_ai + Σ_p d_a N_ap) + N_ai Σ_j α_ij(t), where N_ai is population density, r_ai growth rate, K_ai carrying capacity, c coefficients capture competition, d_a dispersal/emigration rate, and the final term captures environmental responses. Environmental response E_a(t) = γ_a(t) + δ_a(t) + ρ γ_a(t)δ_a(t) incorporates patch-specific and population-specific responses and their interaction (ρ). Simulation settings for Model A: Initial Time=0, Final Time=492, Time Step=1 (months). Sensitivity analysis: Vensim DSS multivariate sensitivity with 1000 runs; noise seed=10; parameters varied (e.g., number of patches m broadened to (0,10); N_ap randomized Uniform(0,20); variations in N_b and ρ). Robustness assessed via confidence bounds of N_a in patch 1. Model B operationalizes a resource-centered patch-dynamics example across two scales. Resource dynamics in occupied patches: dN_i/dt = R − α N_i − Σ_{i≠j} α_ij N_i Q_ij − L(N_i − N_c); empty patch resources: dN_c/dt = R − α N_c − L(N_c − N_c); population quantities: dQ_ai/dt = α_ij N_i Q_ai − α_ij Q_ai (with death-related term); regional average resources: N = p N_i + (1 − p) N_c, where p is spatial occupancy. Spatial occupancy dynamics: dρ_i = c ρ_i (1 − Σ_j ρ_j) − m ρ_i − Σ_j c ρ_i ρ_j, with m disturbance rate and c colonization rate (resources per population × Q_ij). Causal loop diagrams clarify feedbacks among resource inputs, consumption, losses, disturbance, and environmental responses. Sensitivity/robustness for Model B: Monte Carlo multivariate sampling simulation (MVSS) with 2000 runs, noise seed=1234; broadened parameter ranges up to 10×; randomized Uniform(0,10) for resource consumption rate α and resource loss L; Vensim generated random samples. Validation: structural validation via boundary adequacy (endogenizing time-varying parameters; indirect boundary adequacy via sensitivity behavior), and dimensional consistency (variables treated as dimensionless, ensuring consistent equations). Time units for Model B set to years to reflect longer-term dynamics.

• Model A captures sudden environmental changes: the trajectory of population density in a focal patch responds to environmental fluctuations embedded via E_a(t). Sensitivity analyses (1000 simulations; noise seed=10; parameters m, N_ap, N_b, ρ varied including Uniform distributions) yield narrow confidence bounds for N_a, indicating stability and robustness of dynamics to parameter uncertainty. - Model B robustness: MVSS with 2000 runs (noise seed=1234), with broadened ranges and Uniform(0,10) for resource consumption α and resource loss L, shows trajectories largely invariant to parameter variation, indicating model robustness. - Resource dynamics over time (years): From Year 0 to 37, resources in environment, empty, and occupied patches remain stable. A sudden environmental resource increase occurs at Year 37, peaks around Year 39. Resources in empty patches follow similar trend with ~1-year delay (increase lasting to Year 40). Resources in occupied patches decrease until Year 40 due to consumption; after Year 43, both environmental and occupied-patch resources increase as populations contribute resources back to the system. Environmental resources decline after their peak, while empty-patch resources continue to grow for ~1 additional year (until Year 48). - Population–environment lag: Population density in a patch exhibits a consistent ~2-year lag relative to environmental fluctuations (e.g., environmental response peaks at Year 37; population density peaks at Year 39). Early stage shows stable low population density during frequent environmental changes; density increases markedly around Year 36–39, tracking environmental dynamics with the lag. - Coupled dynamics and resilience: When environmental and empty-patch resources decrease after Year 45, occupied-patch resources remain higher (post-Year 43 rebound), helping population density recover from a low at Year 46 and rebound thereafter. This illustrates how within-patch processes and resource feedbacks can buffer populations against external declines. - Multi-level integration: The patch-dynamics framework simultaneously captures interactions across patch- and population-level processes, including dispersal, colonization, disturbance, and resource flows between occupied and empty patches, demonstrating an ability to model disequilibrium dynamics and uncertainty not handled by NK/LV alone.

The findings demonstrate that a resource-mediated patch-dynamics framework can integrate equilibrium and disequilibrium perspectives across multiple organizational levels, addressing limitations of NK and LV models. By explicitly modelling disturbances, stochastic environmental responses, spatial occupancy, and resource exchanges between occupied and empty patches, the approach captures delayed population responses, buffering, and feedbacks that are characteristic of complex organizational ecosystems. For strategy and behavioral theory, the framework extends beyond static fitness landscapes to account for resource dynamics and interdependencies among organizations/populations across patches, offering a richer lens on search, exploration–exploitation tradeoffs, and adaptive responses to shocks. The ability to incorporate uncertainty and disturbances has implications for analyzing platform and digital ecosystems where heterogeneity and power asymmetries challenge equilibrium outcomes. The framework supports assessing ecosystem health (resilience, diversity, recovery) by tracking resources and occupancies, informing governance and policy debates on sustainability in complex business environments.

The study proposes a general patch-dynamics framework and simulation methodology to model organizational population and ecosystem dynamics across scales, integrating equilibrium and disequilibrium perspectives, uncertainty, and disturbances. Two models illustrate feasibility and robustness, showing delayed but coherent population responses to environmental fluctuations and resource-mediated buffering across patches. The approach is positioned as a tool to analyze sustainability and ecosystem health, particularly relevant amid shocks like COVID-19. Future research directions include applying the framework with empirical data from specific industrial ecosystems, conducting behavioral pattern and sensitivity tests to compare simulated and real-world dynamics, and expanding to multi-species/multi-firm settings to evaluate governance and policy interventions in platform and digital ecosystems.

The study is based on simulation models without empirical real-world data; parameterization and behaviors are illustrative. Empirical testing is beyond scope due to data limitations. Future work should conduct behavioral pattern tests to assess how well the model reproduces real system behaviors, examine sensitivity of model-based recommendations to parameter uncertainty, and validate the framework in specific industry ecosystems. Additionally, while variables are treated as dimensionless for internal consistency, real-world applications will require careful measurement and calibration.