Greetings Bob:
Fertilization is a valid intermediate stand management tool if it is warranted AND if is applied correctly. There is a fair amount of research out in cyberspace regarding the fertilization of planted hardwood stands; however, I’m not suggesting you go out and randomly apply bags of 12-12-12 fertilizer to your 30 year-old stand of black walnut.
Your black walnut stand may not respond very well to increased nutrient inputs (i.e., fertilization) if your walnut plantation rests within the path of the last glacial episode (Wisconsin Episode) and if your soils are fertile and slightly acidic to neutral. The best way to test tree fertility/nutrition is to conduct foliar analyses (methodically collect leaf samples and send to a lab for analysis). However, this process is a little more time consuming. A simpler, yet less accurate approach is to conduct standard soil tests to check fertility and pH (almost all soil testing standards are based on annual agronomic crops, not perennial trees). Standard soil tests usually include exchangeable nutrients (macros and micros), pH, cation exchange capacity, and % base saturation.
When it comes to high-value hardwood species, I would strongly suggest that you seek the advice of a local professional forester to determine whether or not your site/trees would benefit from fertilization and whether the “investment” is justified and warranted.
Contact your local IN-DNR forester to help you get started :-)
Best, Jay
