Harmful algae at the complex nexus of eutrophication and climate change

•Projections for climate for the coming years have more certainty than for nutrients.•Nutrient pollution is altering stoichiometry and dominant nitrogen forms.•Collective effects of climate and nutrient changes may disfavor diatoms.•Collective effects of climate and nutrient changes may favor mixotrophs.•Without further control of nitrogen, more HABs can be expected in a future ocean. Climate projections suggest–with substantial certainty–that global warming >1.5 °C will occur by mid-century (2050). Population is also projected to increase, amplifying the demands for food, fuel, water and sanitation, which, in turn, escalate nutrient pollution. Global projections of nutrient pollution, however, are less certain than those of climate as there are regionally decreasing trends projected in Europe, and stabilization of nutrient use in North America and Australia. In this review of the effects of eutrophication and climate on harmful algae, some of the complex, subtle, and non-intuitive effects and interactions on the physiology of both harmful and non-harmful taxa are emphasized. In a future ocean, non-harmful diatoms may be disproportionately stressed and mixotrophs advantaged due to changing nutrient stoichiometry and forms of nutrients, temperature, stratification and oceanic pH. Modeling is advancing, but there is much yet to be understood, in terms of physiology, biogeochemistry and trophodynamics and how both harmful and nonharmful taxa may change in an uncertain future driven by anthropogenic activities.