Leave the dam beavers alone!
I do not see the point of constantly tearing up the beaver dams. By constantly tearing out the dams, what you are accomplishing is akin to chasing your own tails like a rabid dog, inflicting cruelty on animals, causing continued destruction of the area trees and erosion of the riverbanks. I suspect nobody in charge of this program has any real knowledge or information about beavers or beaver habits, otherwise you would not be acting like rednecks on a witch hunt.
Please educate yourselves.
Most of this is common sense, the rest I learned from a two-minute Google search.
If you leave the dams alone and stop tearing them out, the beavers will only take wood to repair the dams. If you keep tearing up the dams and/or exterminating the beavers, guess what, will rebuild and/or repopulate. Eventually there will be no trees left. I suppose that might make the beavers go elsewhere eventually…
Peaceful Coexistence with Beavers: http://www.hawriver.org/?p=688
“Problems with lethal trapping — Lethal trapping is expensive, and has been proven to provide only temporary relief…. trapping beavers can actually increase the immediate beaver population. Beavers are the largest member of the rodent family, and research has shown that rodents begin breeding at earlier ages and produce more offspring in response to an abrupt decline in population levels.
If your problem is flooding — When beavers go house-hunting they are looking for an area that is easily dammed and will provide an adequately-sized pond. Such areas include drainpipes and culverts. Clogged pipes and culverts can cause extensive flooding, and can result in roads washing out. The best way of dealing with this problem is by installing a device known as a beaver baffler. There are several different beaver baffler designs in use today and they involve installing a 15- to 30-foot wire cage-like device on the upstream side. A screen is placed over the upstream entrance to the cylinder and over the exit hole on the opposite side of the road. The device is actually made of two wire cylinders, one inside the other. Beaver bafflers prevent beavers from being able to plug the culvert or drain pipe, and cut down on the maintenance costs from regular cleaning of the pipes.
Why not just relocate the beavers? One of the first things people ask me is “Why can’t you just move beavers that are causing problems?” The reason why simple relocation doesn’t work is the same reason why trapping doesn’t work.
If you have beaver habitat, you’re going to have beavers. If there is a way they can make a pond, and there’s a suitable food supply, beavers will continue to repopulate an area.”
Water quality and beavers — Beaver ponds and the wetlands that succeed them, remove sediments and pollutants from waterways, including total suspended solids, total nitrogen, phosphates, carbon and silicates. 
The term “beaver fever” is a misnomer coined by the American press in the 1970s, following findings that the parasite giardia lamblia, which causes giardiasis, is carried by beavers. However, further research has shown that many animals and birds carry this parasite, and the major source of water contamination is by other humans.  Norway has many beaver but has not historically had giardia and New Zealand has giardia but no beaver. Recent concerns point to domestic animals as a significant vector of giardia with young calves in dairy herds testing as high as 100 per cent positive for giardia.  In addition, fecal coliform and streptococci bacteria excreted into streams by grazing cattle have been shown to be reduced by beaver ponds, where the bacteria are trapped in bottom sediments. ”
If the beavers have dammed up a stream, another kind of device known as a beaver limiter is needed. Beaver limiters are made of PVC pipe and are placed through the dam to reduce and control the amount of water backed up behind the dam. Note that if you drain all the water, the beavers will just move and build another dam a few feet away. However, many homeowners are willing to let beavers stay if they can just minimize the flooding. Limiters do this quite well, and are used successfully all across the country.”
I hope whoever it is that apparently has “beaver fever” in Ponoka will take the time to educate themselves and then act accordingly.