Integrating Lotka-Volterra dynamics and gravity modeling for regional population forecasting

Introduction

Forecasting population dynamics is crucial for effective urban and regional planning. Traditional demographic methods, such as Cohort Component Analysis, often do not capture nonlinear interactions and spatial dependencies among regions. To address these limitations, this study integrates Lotka—Volterra prey—predator equations with a probabilistic adaptation of the Gravity model, providing a more robust theoretical and methodological framework for regional population forecasting.

Methods

We adapt the Lotka—Volterra model—originally rooted in ecological theory—by introducing carrying capacities and region-specific parameters, then embed a probabilistic Gravity model to capture interregional mobility. This unified approach leverages population data and migration flows from three major clusters in Quebec, Canada, calibrating model parameters to reflect observed demographic trends. The resulting system of equations was iteratively solved and tested using population data from 2021 through 2023.

Results

The combined model effectively captured competitive and cooperative population interactions, revealing how spatial connectivity and resource constraints shape long-term growth patterns across the three regions. Calibrated forecasts aligned well with observed trends, demonstrating the framework’s capacity to reflect real-world interdependencies in regional population flows. Key findings highlight the importance of prey—predator—like dynamics in producing stable or shifting equilibria, offering deeper insights into regional competition, cooperation, and demographic sustainability.

Discussion

By merging ecological modeling principles with spatial interaction theories, this work underscores the added value of grounding demographic forecasting in well-established theoretical constructs. Compared to more traditional approaches, the integrated Lotka–Volterra and Gravity model provides a clearer picture of how regional populations evolve under nonlinear and spatially linked influences. This approach is readily adaptable to diverse contexts, potentially enhancing forecast precision and guiding policy interventions in urban development, resource allocation, and strategic planning on a broader scale.