To limit plant growth in the water column (algae, etc), the nutrients that are of most concern are the various forms of nitrogen (ammonia, nitrite, nitrate) and phosphorus.
The natural approach to pond management relies on bacteria to consume these nutrients; and in order for them to operate at peak efficiency they require minerals.
Many of the complex reactions that occur in nature will not happen without the required trace minerals being present.
This absence is a key reason that many ponds cannot breakdown nitrogen & phosphorus quickly/efficiently enough to prevent the over-growth of algae.
Providing the bacteria with the support that they need to thrive will accelerate the breakdown of these nutrients; thereby limiting the population of algae and alike.
Other helpful techniques include sufficient aeration (monitoring dissolved oxygen levels) and the addition of pond dye that inhibits UV rays, thereby preventing algae growth.