Selenium 100mcg - The jury is still out on whether or not Selenium helps with arthritis, the thought process was that people with RA typically have low levels of selenium in their blood, but the literature currently suggests that supplementing it doesn't support joint tissue health in this case. [1] In terms of general joint pain it's not a terrible inclusion, as it does have some benefits to helping the joints withstand free radical damage, but it's not a very big deal and there are far better ingredients. [2]
Glucosamine HCL 1500mg - Glucosamine HCL is a good inclusion, and 1500mg is the highest end of the effective dosage, unfortunately this high dosage does commonly cause nausea, but it is the most effective dose in many cases to support connective tissue health. [3]
Tissue Blend 794mg (Turmeric, Boswellia, Ginger) - All three of these ingredients are actually very good for a joint supplement. The problem is that the active ingredient in Turmeric is curcumin, which must be dosed at 500mg or above to be effective [4] to reduce inflammation and improve joint mobility. And Curcumin is only about 20% of turmeric, and it doesn't take too great a skill with mathematics to understand that we can't fit 2500mg of turmeric in this blend. Boswellia could be correctly dosed as it only requires 200mg, and it is effective at improving joint and cartilage health, [5] but it's one of the cheapest ingredients for joint health and is in pretty much every other joint supplement, including ones a lot cheaper than FYI Ultra Garden Of Life. And Ginger, this requires 3 grams to be effective of a specific extract, which is relatively uncommon and even that requires 255mg, [6] and as it's the lowest on this list in terms of size we consider this even more unlikely that they'd include it and not list it.
Antioxidant Blend 301mg (Pomegranate Skin, Astaxanthin, Olive Leaf Extract) - There's currently some speculation around pomegranate skin having some preventative impact on developing OA or RA at all, but this is all correlation data and there isn't currently any substantial generation in terms of trials [7]. Astaxanthin could be interesting, but requires 20mg/kg of body weight as trialled [8] meaning that a 200lb person would need 1.8 grams which is more than 6 times the entire blend. Olive Leaf is also not possibly in any effective range as 150mg [9] was the lowest dose trialled to do anything and as the smallest ingredient in the garden of life fyi ultimate joint formula it can't possibly be above 98mg.
References
1 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7601319/
2 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7423502/
3 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2686334/
4 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5003001/
5 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7368679/
6 - https://www.ncbi.nlm.nih.gov/books/NBK92775/
7 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4825888/
8 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6914430/
9 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8777337/