Ünsal Özdilek ^*

• Université du Québec à Montréal, Montreal, Canada

This study integrates the Lotka-Volterra prey-predator equations with a probabilistic adaptation of the Gravity model to forecast population dynamics across three regional clusters in Quebec, Canada. By leveraging these models, we capture the nonlinear interdependencies and spatial interactions often overlooked in traditional demographic forecasting methods. Building upon prior works in ecological modeling and spatial interaction theories, our research underscores the importance of embedding robust demographic theories into population estimation practices. Our empirical findings, validated within the Quebec context, highlight the significance of theoretical frameworks, particularly prey-predator interactions, in guiding accurate population forecasts and regional planning strategies. The study explores the intricacies of regional competition and cooperation dynamics, promoting sustainable, balanced, and long-term population growth patterns. By merging advanced mathematical modeling with demographic theory, our research marks a significant advancement in demographic methodologies, offering a comprehensive framework for understanding population changes and their implications for policy and planning. Furthermore, the model's adaptability demonstrates its potential for application in diverse regional contexts worldwide, enhancing the precision and reliability of population forecasting on a global scale.