Not beyond dispute at all. There's a huge number of confounding factors involved in comparing all the different datasets used over the time period concerned. On

Not beyond dispute at all. There's a huge number of confounding factors involved in comparing all the different datasets used over the time period concerned. One example is that older tests famously overestimated sperm counts. Additionally, many of the older data is from observational studies of people presenting at early fertility clinics. This paper attempts to control those factors and while I haven't seen any particular criticism of their methods it's an incredibly difficult problem to deal with. Especially when sperm count appears to be so responsive to small environmental variations to begin with. It'll be interesting to see more research in the field, probably spurred on by this study. Questions that need to be answered include, why only Western countries? Does that imply a correlation between technological development and fertility? What are the trends in Korea and Japan looking like considering they modernised a while before many of their neighbours? Halving counts sounds like a lot, but it isn't really and teasing out the ultimate causes is probably going to be incredibly difficult.