Environmental drivers of marine primary production, such as photosynthetically available radiation, temperature, and mixed-layer depth, can be decomposed into long-term trends, seasonal cycles, and stochastic fluctuations. While most marine ecosystem models account for trends and seasonality, the effects of environmental noise are typically limited to changes in variability, assuming that its influence on the mean state vanishes upon averaging. Here, we show that this assumption is generally incorrect. Using stochastic calculus, specifically Itô's lemma together with Jensen's inequality, we demonstrate that environmental noise introduces second-order corrections that modify the mean state and shift the fixed points of marine primary production models. Surface irradiance variability consistently reduces mean primary production, whereas fluctuations in temperature and mixed-layer depth can either enhance or suppress it, depending on the system's nonlinear response. We interpret these contrasting behaviours through the concepts of fragility and antifragility, which quantify whether stochastic fluctuations decrease or increase system performance. This framework provides a simple way to assess how noise reshapes ecosystem equilibria and stability. The results suggest that changes in environmental variability under climate change may influence marine productivity not only through altered variance but also by shifting mean system states, potentially bringing ecological tipping points closer than deterministic models predict.