Traditional ecological models in management and organization studies, based on equilibrium assumptions (linearity and predictability), are challenged by the inherent complexity and disequilibrium of real-world systems. Models like the NK model (focusing on search and speed) and the Lotka-Volterra (LV) model (analyzing population interactions) have limitations in capturing the dynamic, interconnected nature of organizations and their environments. While acknowledging the limitations of equilibrium-based models, management research still heavily relies on them, leading to inadequate analysis of disequilibrium and uncertainty. The increasing integration of industries and organizations blurs boundaries, necessitating a framework capable of analyzing diverse ecosystem-level structural configurations and multiple firms simultaneously across scales (from individual agents to ecosystems). This paper addresses this need by developing a patch-dynamics framework and simulation models.

The paper reviews the equilibrium and disequilibrium perspectives in ecological research. The equilibrium perspective, while traditionally dominant, is challenged by the observation that equilibrium is rare in nature. The punctuated equilibrium model in organization studies attempts to address this, but it still relies on equilibrium periods. The disequilibrium perspective highlights the importance of heterogeneity and scale multiplicity. Traditional models like the NK and Lotka-Volterra models, widely used in management studies, are criticized for their limitations in capturing complexity, ignoring factors such as interactions between players, naïve agents (NK), and spatial structure and life history (LV). The literature review points to the need for a framework that can accommodate multiple levels of analysis, uncertainty, and disturbances, highlighting the shortcomings of existing models in dealing with real-world dynamics and complex interactions within and between organizational populations and ecosystems.

The authors develop a patch-dynamics framework that focuses on the mediating role of resources, rather than individual agents, to capture interactions across multiple levels. This framework considers patches as discrete habitat areas accommodating populations or organizations, with all participants having equal access. Two simulation models are developed to test the framework's capabilities: **Model A:** This model extends the Lotka-Volterra model to incorporate a stochastic environment with multiple patches and considers environmental fluctuations (*E_a*(t)), patch-specific (*γ_a*(t)), and population-specific environmental responses (*δ_a*(t)). The model is tested through simulations and sensitivity analysis (using multivariate sensitivity simulation in Vensim DSS) to assess robustness. Narrow confidence bounds suggest the model is stable and robust even with variable input values. **Model B:** This model explicitly considers resource exchange between occupied and empty patches, incorporating two relevant organizational scales: patch and population levels. The equations describe resource dynamics within occupied and empty patches, population dynamics, and spatial patch occupancy. This model is also validated via sensitivity analysis, using the Monte Carlo multivariate sampling simulation (MVSS) method in Vensim, showing robustness to changes in input parameters. The models are validated through structural validity tests (boundary adequacy and dimensional consistency tests) ensuring that significant concepts are addressed endogenously within the model and the measurement units are consistent.

Model A demonstrates the framework's ability to capture sudden environmental changes. The sensitivity analysis of Model A showed the model's robustness. Model B demonstrates the interplay between resources, population density, and environmental fluctuations. Simulations of Model B reveal the following: Initially, resources in the occupied, empty patch, and the environment are stable. A sudden increase in resources from the environment occurs around year 37, peaking at year 39, followed by a decrease. Resources in the empty patch show a converse trend, initially low, then increasing, with a peak around year 40. Resources in the occupied patch exhibit a decrease until year 40, but then increase significantly after year 43, demonstrating a rebound even after decreases in environmental and empty-patch resources. Population density remains stable at a low level initially. After year 36, population density increases, but fluctuates with environmental changes, although with a 2-year delay, illustrating the time needed for organizations to adapt to environmental shifts. A comparison of population density with resources demonstrates a strong correlation after year 36, indicating a direct relationship between environmental resources and population growth. The findings highlight the dynamic interactions between resource availability and population response, demonstrating the framework's power to capture these complex evolutionary patterns over time.

The patch-dynamics framework offers new insights into strategic search processes, going beyond the traditional landscape metaphor and incorporating the complexities of competitive interactions. It bridges the gap between landscape-level analysis and the dynamics of individual organizations and populations. The model shows that organizations and populations do not react immediately to environmental change; there is a time lag in their responses, reflecting learning and adaptation processes. This contrasts with previous research that often focuses on isolated decision-making in strategic search. By including multiple scales and levels of analysis, the patch-dynamics framework allows for a more comprehensive understanding of strategic decision-making and search processes. The results are relevant to the growing field of platform economics and digital ecosystems, where the interplay between multiple actors and resources is critical. The framework helps analyze the sustainability of 'winner-take-all' dynamics and provides a tool for assessing ecosystem fitness and health.

The patch-dynamics framework provides a valuable theoretical and methodological approach to model population and ecosystem dynamics across different scales. It successfully integrates equilibrium and disequilibrium perspectives, co-evolution, uncertainties, and disturbances. This framework is especially relevant in the context of increasing complexity and uncertainty in business environments, opening avenues for future research. Further research should apply the framework to specific industrial ecosystems with real-world data.

Due to data limitations, empirical testing with real-world data was not possible in this study. Future research should conduct more comprehensive behavioral pattern tests to validate the model's ability to mimic real-world behavior and explore the sensitivity of the model to parameter changes. Applying data from specific industrial ecosystems will enhance the framework's applicability and allow for more in-depth analysis.