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The spatial distribution of species is mediated by a combination of biotic interactions and environmental conditions. Understanding the relative importance of these factors and how they interact is particularly important for predicting the spread of non-native species and their impact on resident communities. * We used a 3-species Lotka-Volterra model parameterized with field and experimental data to understand the potential for continued spread by an introduced, non-native, dune-building beach grass (Ammophila breviligulata) and whether this invasion will result in coexistence or displacement in the resident beach grass communities (native Elymus mollis and introduced, non-native Ammophila arenaria) of the US Pacific Northwest. * We also used the model to investigate to what extent different rates of ocean-driven sand supply mediate the outcomes of beach grass species interactions. * Our model suggests that A. breviligulata could invade and dominate dunes across the range of sand supply rates observed in the region. We found that sand supply influenced intra- vs. interspecific interactions, the strength of positive and indirect effects among beach grasses and the long-term abundances of the beach grass species themselves. * Of the two non-natives, A. breviligulata is the inferior dune-building species. Thus, our results suggest that further invasions by A. breviligulata could reduce the coastal protection services afforded by tall dunes currently dominated by A. arenaria. * Synthesis: In systems with strong environmental forcing and stressful conditions such as coastal dunes, environmentally mediated positive and indirect species interactions can govern invasion success and long-term native-non-native coexistence. In doing so, these interactions ultimately shape community structure and ecosystem function. Understanding the joint effects of environmental forcing and species interactions on community assembly is particularly important in cases where species introductions can alter ecosystem services, such as coastal protection, which are vulnerable to the effects of climate change.