Both phosphate and nitrate can and do cause algae. The thing is just isn't because they are present in the aquarium but rather it is when excess phosphate and/or nitrate is present that algae issues arise.
Nitrate and Phosphate have never caused algae, the theory that they do is a long debated issue, they will however accelerate its growth, I bet if you ask Tom Barr now he'll concur, Nitrate and Phosphate are always in an excess in my set up, the same applies to anyone dosing EI, whereby the aim is to keep nutrients at levels so that they're non-limiting, here's my tank, Phosphate at 2PPM, Nitrate at 40PPM (calculated not tested, test kits are not accurate enough) EDIT, just tested, registering at 40PPM on my Salifert test kit and no algae:
Head over to a planted forum and take a look, most set ups where ferts are added contain no algae.
A lack of nutrients is likely to cause algae however, as well as fluctuating or non-existent CO2 and ammonia.
For those of a more scientific bent, or those trying to troubleshoot a specific problem, it is definitely worth buying good-quality test kits for phosphate and nitrate. Beware of inexpensive test kits, however. In many cases you get what you pay for, and inaccurate measurements can be worse than none at all if you base decisions on them. Nitrate levels in a low-light tank can often be as high as 20 milligrams per liter (mg/L) without causing algae problems, while phosphate can sometimes be as high as 2 mg/L under the same conditions without causing algae problems. In a well-lit tank, nitrate usually begins to be a problem if it approaches 10 mg/L, while phosphate can be troublesome even at 0.5 mg/L
http
/bobstropicalplants.com/Chuck/nov1997.html
This was published in 1997, aquascaping has come a long way since then and it's only in the past few years that the 'nitrate and phosphate cause algae' argument has been put to bed, the reasoning is stupid also, the general consensus is that this lake has algae, this lake also has nitrate and phosphate present, oh this must be the cause which simply isn't the case, even anecdotal evidence in this case is valid in my opinion, it simply disproves all of these hypotheses about the causes of algae being nitrate and phosphate. Out of Aquatic plants and Algae, Algae is the more adaptable, which is why this statement doesn't make sense either:
The trick is to provide enough of all nutrients to satisfy the needs of the higher plants, while limiting excess nutrients that could feed unwanted algae.