Iron
Rat study: Iron deficiency does not effect testosterone or LH
http://m.ajcn.nutrition.org/content/48/3/641.abstract
Observational study: Anaemia associated with low testosterone in kidney patients
https://www.ncbi.nlm.nih.gov/m/pubmed/21617198/
Causation not demonstrated. Indeed there is a good possibility causation works in the opposite direction as the men in the study with lower testosterone were less likely to be helped by erythropoietin-stimulating agents.
Observational study: Men taking exogenous testosterone had more hematocrit
https://www.ncbi.nlm.nih.gov/m/pubmed/12744356
22mg of Zinc reduces copper and iron satus in adolescents
https://www.ncbi.nlm.nih.gov/pubmed/19277992