The present invention relates to a method of producing fatty acids, by inoculating a mixture of at least one of cellulose, hemicellulose, and lignin with a microorganism strain and an algae strain, and growing said inoculated strains under successive aerobic-heterotrophic and either anaerobic-phototrophic or anaerobic-heterotrophic conditions creating symbiosis between the strains. Under a first aerobic-heterotrophic condition, the microorganism strain produces extracellulases that hydrolyze cellulose, hemicellulose and lignin, to produce sugars, such as glucose, cellobiose, xylose, mannose, galactose, rhamnose, arabinose or other hemicellulose sugars that are metabolized by the algae strain which also metabolizes acetic acid, glucose and hemicellulose from pretreatment. Then, either under a subsequent anaerobic-heterotrophic condition, the microorganism uses cellulose and produces fermentation products, and the algae strain uses part of the released sugars and exhibits a slower growth rate, or under a further anaerobic-phototrophic condition, the microorganism uses cellulose and produces fermentation products and CO2, and the algae strain uses the CO2 and part of the released sugars and the at least one fermentation product. Under a further aerobic-heterotrophic condition, the algae strain uses the fermentation products produced by the microorganism strain in a previous anaerobic step to produce one or more fatty acids, and the microorganism strain continues to produce extracellulases. The microorganism and algae strains are evolved for tolerance to furfural. The fatty acids can optionally be recovered and used for production of biodiesel fuel.