I don't think you will have long term success using tank water. As others have mentioned, there are too many organisms that either eat or compete with phytoplankton. The fertilizer really isn't that expensive (less than the cost of the salt in the culture medium), and I think you will have much better success using what is referred to as "F/2" fertilizer. For most people, I think that Tetraselmis may be one of the easier/tougher strains to culture - that is the one I would recommend to start with.
It takes some care, but I think that most people can culture phyto if they think it is worth the effort. I think it is definitely beneficial to dose phyto to a reef system. Here is a fairly simple method to culture phytoplankton:
To get started use clear 2L soda bottles with some rigid airline tubing. You will need the bottles, some rigid airline tubing, some regular airline, an air pump, and a light source (fluorescent or LED works fine). Drill a hole in the cap that is a little larger than the rigid tubing (1/4" if you are using 3/16" tubing). The hole should be slightly larger to allow air to escape. I would recommend having two bottles with rigid airline for each culture so that you can have a sterilized bottle ready to go when you split the culture.
Contamination is going to be your main enemy. This can be in the form of bacteria, ciliates/protozoa, or other species of algae. It is important to sterilize the bottles and rigid airline each time before you use them. The simplest way is probably to use bleach. I would always use the same bottles for the same species just in case any cells survive. You will also want to clean your hands when switching from one culture to the next - I use hand sanitizer. If you can filter the air using a very fine filter (less than 1 micron would be ideal), that will be helpful but not mandatory. If you culture pods or especially rotifers, keep your phyto cultures far away and never move from the zooplankton cultures to the phytoplankton cultures.
Put 0.8ml of F/2 (assuming 1ml/2.5L concentration) in each sterilized bottle and fill about half way with clean/fresh (sterilized would be best) artificial sea water. Different species prefer slightly different salinities, but 30ppt will work for everything. Next add the 16oz of phyto. Then, top off with more saltwater stopping a couple of inches from the top. Now insert the rigid airline and adjust the air so that the culture looks like it is boiling gently. Set these bottles about 12-18" from your light (start at about 24" the first time because the phyto has been in the dark and move a few inches closer each day. Have the light on for 12-16 hours per day (I do 16).
The cultures should darken more each day. Once they look dark enough (usually 7-10 days), remove the cap and airline and pour half of the culture into a new sterilized bottle and use the other half to dose your tank. Top off the new culture with clean saltwater and 0.8ml of F/2. Keep repeating, and you have a constant supply of phyto.
Unfortunately, the cultures crash occasionally, or fail to get established. So, you may want to run two cultures of each species, or be sure to keep a fresh start in the fridge. If you want to start two cultures of each species right from the start, just adjust the amounts listed above. Of course, if your cultures crash at some point, I would be glad to sell you some fresh starts - some guys like to get a fresh start occasionally anyway.
Good luck if you decide to try culturing. Let me know if I can help.
