DenOz,
1.) Do they cycle? Yes. Zebra mussels are a boom and bust species meaning that they can increase in numbers exponentially until carrying capacity is exceeded and then their numbers crash.
2). Have their ups and downs once they are in these waters? Yes. Once the population crashes they will begin to build their population density again. This is where it gets a little tricky. We really don't know how long it takes the species to reach a level for the first crash or how long it will take for the population to start rebuilding in numbers. For example, zebra mussels were discovered at El Dorado in 2003. The population peaked in 2006. The first 'crash'/large die-off occurred in 2007. During the 2008, 2009, and 2010 growing seasons the zebra mussels remained at very low densities with very few young of the year zebra mussels (veligers) produced. But during 2011, shoreline encrustation by adults increased as veliger densities increased to over 100 veligers per liter of lake water over the 4-6 veligers per liter of lake water that was seen during 2008-2010. The big question now is will we reach the densities we saw in 2006, will the population crash as it did before, will a higher population density be maintained for a longer period? There are many factors that can influence the zebra mussel populations so it is difficult to predict what the outcome will be.
3). Will they completely die naturally without the body of water chemically treated? No. As stated above we expect the zebra mussel populations to naturally cycle from very high levels to low levels. Even when at their lowest levels after infestation there will still be adequate numbers of mussels to sustain the species and continue the 'boom and bust' population cycling so they will never die out completely. Predicting the cycle is the tricky part as each water body and the factors affecting them vary each year. Researchers continue to look for ways to control zebra mussels in open water systems but right now there is no feasible way to apply treatment to kill zebra mussels over 1,000's of acres of open water found in our reservoirs.