Iodine

Rat Study: Excess Iodine Reduces Testosterone
https://www.ncbi.nlm.nih.gov/pubmed/26701334
1) Iodine accumulates in the testis resulting in reactive oxygen species.
2) It stimulates the secretion of corticosterone which inhibits LH release. This may only be a problem in rats corticosterone
3) It causes hypothyroidism.

Rat Study: Iodine supplementation reduces sperm count
https://www.ncbi.nlm.nih.gov/pubmed/18604636?dopt=Abstract

https://www.ncbi.nlm.nih.gov/pubmed/18728126?dopt=Abstract

http://link.springer.com/article/10.1134/S1990750807010088

https://www.ncbi.nlm.nih.gov/pubmed/3403362?dopt=Abstract
"These results indicate that thyroid hormone therapy increases plasma SHBG levels in both normal and hypothyroid patients and that this increase precedes the expected elevation of plasma T in males."

Rat study: Iodine and/or Selenium deficiency impacts on rat reproductive function
https://www.ncbi.nlm.nih.gov/pubmed/17290749

Rat study: Potassium Iodide, thyroid and testosterone
https://www.ncbi.nlm.nih.gov/pubmed/1684642

"Men with primary hypothyroidism have subnormal responses of luteinizing hormone (LH) to gonadotropin-releasing hormone (GnRH) administration and normal response to human chorionic gonadotropin (hCG)."
https://www.ncbi.nlm.nih.gov/pubmed/15142373

iodine also proved to mediate the dehydrogenation of testosterone (testosterone into 4-androstene-3,17-dione)
https://www.ncbi.nlm.nih.gov/pubmed/26913544
What does this mean?

Bull Study: Potassium Iodide increases testosterone in bulls
http://www.bu.edu.eg/portal/uploads/openLearning/The%20Effect%20Iodine%20Supplement%20on%20the%20Sexual%20Activity%20And%20Semen%20Characteristics%20of%20Friesian%20Bulls_paper_en.pdf