OK, here is the final version, hopefully:
ammonia or ammonium: A toxic product (chemical formula NH3 or NH4+) produced by uneaten food and feces in an aquarium. The ideal ammonia level in a well-established aquarium is zero. See [cycling].
nitrite: A toxic product (chemical formula NO2-) of the breakdown of [ammonia] in an aquarium. The ideal level of nitrite in a well-established aquarium is zero. See [cycling].
nitrate: The non-toxic product (chemical formula NO3) produced by the breakdown of [ammonia] and [nitrite] in an aquarium. While not toxic, high nitrate levels (>50 ppm) in an aquarium indicate the need for larger partial water changes on a regular basis. See [cycling].
cycling (1): The breakdown of waste products in an aquarium. Waste products produce [ammonia], which is subsequently broken down by beneficial bacteria in the presence of oxygen. The ammonia is converted to [nitrite] and then into [nitrate]. An aquarium is considered to be "cycling" (or "cycled") when the beneficial bacteria have become well-established, a process that takes one month or more after a new aquarium has been set up. See [link to cycling article].
cycling (2): The seasonal changes that prepare an animal for reproduction. For example, a salamander may need to be exposed to a cold winter and decreased sunlight in order to be properly cycled for breeding in the spring.