A key factor to determine the expansion dynamics and future distribution of non-native species is their physiological response to abiotic factors and their changes over time. For this study we developed a spatially explicit, agent-based model of population growth to represent the complex population dynamics of invasive marine macroalgae with heteromorphic biphasic life cycles. The model framework represents this complex life cycle by treating the individual developmental stages (gametophytes/sporophytes) as autonomous agents with unique behaviour/growth parameters. It was parameterised to represent a well-documented invasive algal species, the Asian kelp Undaria pinnatifida, and validated against field results from an in situ population in Brittany, France, showing good quantitative agreement in terms of seasonal changes in abundance/recruitment and growth dynamics. It was then used to explore how local environmental parameters (light availability, temperature and day length) affect the population dynamics of the individual developmental stages and the overall population growth. This type of modelling approach represents a promising tool for understanding the population dynamics of macroalgae from the bottom-up in terms of the individual interactions between the independent life history stages (both microscopic and macroscopic). It can be used to trace back the behaviour of the population as a whole to the underlying physiological and environmental processes impacting each developmental stage and give insights into the roles these play in invasion success.