Results  In total, 1203 participants with omega-3 PUFA treatment (mean age, 43.7 years; mean female proportion, 55.0%; mean omega-3 PUFA dosage, 1605.7 mg/d) and 1037 participants without omega-3 PUFA treatment (mean age, 40.6 years; mean female proportion, 55.0%) showed an association between clinical anxiety symptoms among participants with omega-3 PUFA treatment compared with control arms (Hedges g, 0.374; 95% CI, 0.081-0.666; P = .01). Subgroup analysis showed that the association of treatment with reduced anxiety symptoms was significantly greater in subgroups with specific clinical diagnoses than in subgroups without clinical conditions. The anxiolytic effect of omega-3 PUFAs was significantly better than that of controls only in subgroups with a higher dosage (at least 2000 mg/d) and not in subgroups with a lower dosage (<2000 mg/d).

Giacco, R., Cuomo, V., Vessby, B., Uusitupa, M., Hermansen, K., Meyer, B. J., Riccardi, G., and Rivellese, A. A. Fish oil, insulin sensitivity, insulin secretion and glucose tolerance in healthy people: is there any effect of fish oil supplementation in relation to the type of background diet and habitual dietary intake of n-6 and n-3 fatty acids? Nutr.Metab Cardiovasc.Dis. 2007;17(8):572-580. View abstract.

Founder and currently Executive Editor of Science-Based Medicine Steven Novella, MD is an academic clinical neurologist at the Yale University School of Medicine. He is also the host and producer of the popular weekly science podcast, The Skeptics’ Guide to the Universe, and the author of the NeuroLogicaBlog, a daily blog that covers news and issues in neuroscience, but also general science, scientific skepticism, philosophy of science, critical thinking, and the intersection of science with the media and society. Dr. Novella also has produced two courses with The Great Courses, and published a book on critical thinking - also called The Skeptics Guide to the Universe.
A lot of the benefit of fish oil seems to come from the omega-3 fatty acids that it contains. Interestingly, the body does not produce its own omega-3 fatty acids. Nor can the body make omega-3 fatty acids from omega-6 fatty acids, which are common in the Western diet. A lot of research has been done on EPA and DHA, two types of omega-3 acids that are often included in fish oil supplements.
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