This letter focuses on open challenges in the fields of environmental data analysis and ecological complex systems. It highlights relations between research problems in stochastic population dynamics, machine learning and big data research, and statistical physics. Recent and current developments in statistical modeling of spatiotemporal data and in population dynamics are briefly reviewed. The presentation emphasizes stochastic fluctuations, including their statistical representation, data-based estimation, prediction, and impact on the physics of the underlying systems. Guided by the common thread of stochasticity, a deeper and improved understanding of environmental processes and ecosystems can be achieved by forging stronger interdisciplinary connections between statistical physics, spatiotemporal data modeling, and ecology.