Interactions between phytoplankton species shape their physiological and evolutionary responses. Yet, studies addressing the evolutionary responses of phytoplankton in changing environments often lack an explicit element of biotic interactions. Here, we ask (1) how the presence of a locally adapted phytoplankton species will affect an invading phytoplankton species' evolutionary response to a physiologically challenging environment; (2) whether this response is conserved across environments varying in quality; and (3) which traits are associated with being a successful invader under climate change scenarios. In a conceptual first step to disentangle these broad questions, we experimentally evolved populations of fresh-and seawater phytoplankton in a novel salinity (the freshwater green algae Chlamydomonas in salt water, and the marine Ostreococcus in freshwater), either as mono-cultures (colonizers) or as co-cultures (invaders: invading a novel salinity occupied by a resident species, for example, Chlamydomonas invading salt water occupied by resident Ostreococcus) for 200 generations. We superimposed a temperature treatment (control (22 C), mild warming (26 C), drastic warming (32 C), and fluctuating (22 C/32 C) warming) as a representative aspect of climate change with the potential to ameliorate or deteriorate existing environmental conditions. Invaders had systematically lower extinction rates and evolved overall higher growth rates, as well as broader salinity and temperature preferences than colonizers. The invading species' evolutionary responses differed from those of colonizers in a replicable way across environments of differing quality. The evolution of small cell size and high reactive oxygen species tolerance may explain the invaders' higher fitness under the scenarios tested here.