Wednesday, June 15, 2011

Calculating Our Chances of Getting Zebra Mussels

What are the odds Oregon will become infested with zebra or quagga mussels? These invasive freshwater mussels spread quickly in the East after being introduced to the Great Lakes in the 1980s. In 2007, they appeared in Western waters, and since then, they have spread to several western states. To date, Oregon has been lucky; as of today, we don’t know of any bodies of water in Oregon that are infested. We also know that mussels are excellent hitchhikers on trailored boats. What are the odds we can keep Oregon zebra/quagga mussel free? Are we doomed, or can we keep them out? It would be nice to know. Maybe we can calculate the odds.

Since I read my first science fiction book as a boy, I have been fascinated with the idea that there might be life elsewhere in the universe. Frank Drake is famous for his 1961 equation to calculate the number of other civilizations in our galaxy. The equation looks like this:
                                    N = N *  fp * ne * fl * fi  * fc * fL  
N = number of stars in our  galaxy
fp = fraction of stars that have planets
ne = number of planets per star capable of sustaining life
fl = fraction of planets in ne where life evolves
fi = fraction of fl where intelligent life evolves
fc = fraction of fi that communicate
fL = fraction of planet’s life during which communicating civilizations live

Because there are no data for any of these factors except the first one, it isn’t a reliable estimate, but it sure stimulates the imagination! There is even a calculator on the Internet that allows you to input values that make sense to you and see what the odds are that we have galactic neighbors:

We can use a similar approach to estimate our chances of getting zebra/quagga mussels. Here is my amaterish attempt:
                                    P = (N * fo * fz * fd * fin * fa * fe) * 100
                        P = probability the zebra or quagga mussels will become established in Oregon in any                           particular year
                        N = number of boats launches in the state/year
                        fo = fraction of launched boats coming from out-of-state
                        fz = fraction of out-of-state boats infested with zebra/quagga mussels
                        fd = fraction of infested boats not cleaned by owners
                        fin = fraction of infested, non-cleaned boats not intercepted/cleaned at check stations
                        fa = fraction of mussels on dirty boats that are alive at the time of relaunch
                        fe = fraction of mussel introductions that result in established populations

Now comes the fun part. Just like a someone searching for extraterrestrial intelligence, we can take the meager amount of data available, make a series of assumptions, and see what pops out of the equation. Here goes:

N = 375,000 (average of best estimates from Glenn Dolphin, Oregon Marine Board and Rick Boatner, Oregon Department of Fish and Wildlife; there are 46,000 launches during the Lower Willamette River Spring Chinook fishery season alone; 151,691 boats are registered in Oregon)
fo = 1/6 (based on 20% of boats that stopped for inspections in 2010 were from out-of-state, but most of the data came from inspection sites near Oregon’s borders)
fz = 1/5,000 (my guess based on 2,852 boats inspected last year*; none had zebra/quagga mussels, yet we have had two cases of infested boats reported in OR)
fd = ¾ (my guess that only a quarter of boats are cleaned by owners between launches)
fin = 9/10 (my guess that only 1 in 10 infested boats are intercepted and cleaned at inspection stations)
fa = ½ (my guess that half the time mussels on infested boats dry out and die before relaunch)
fe = 1/10 (my guess that 90% of introductions don’t result in reproducing populations)

                        P = (375,000 * .17 * .0002 * .75 * .9 * .5 * .1) * 100
                        P =  43% chance zebra mussels will become established in Oregon this year

Based on this admittedly simple analysis, it shouldn’t surprise anyone if zebra/quagga mussels become established in Oregon sometime in the next few years. Of course, the odds could change. If the fraction of boats coming into the state infested with mussels increases, our odds of avoiding infestation go down. This is likely to happen as water bodies closer and closer to Oregon become infested. On the other hand, if we increase the number of people cleaning their boats between launches, we can improve our odds of staying zebra/quagga mussel-free.

Imagine if 99% of people cleaned their boats between launchings (fd = .01). Keeping all other factors the same, this equation predicts that the probability of establishment would drop to just 0.57% per year. I like those odds better! Let’s all clean our boats between launchings. It’s not that hard. The Marine Board has excellent information on how to do it right at :

Dan Hilburn 

*Dolphin, G. & R. Boatner. 2010. Oregon Aquatic Invasive Species Prevention Program. 2010 Program Report. Oregon State Marine Board, Oregon Department of Fish & Wildlife. Feb. 2011. 22pp.




  1. According to the recent report "Economic Risk Associated with the Potential Establishment of Zebra and Quagga Mussels in the Columbia River Basin" every year that we can keep the zebra and quagga mussels from establishing in the Columbia River basin will save us between $34 to $41 million dollars a year.

    So if 99% vs. 25% of boat owners followed the clean boating " clean, drain and dry" recommendation, the odds of infestation from quagga and zebra mussels due to boats in any year will drop from probability 1 in every 2.3 years to about 1 in every 180 years.

    These are odds that can make us feel like multi-billionaires!

  2. A qualification to my earlier post:

    "every year that we can keep the zebra and quagga mussels from establishing in the Columbia River basin will save us between $34 to $41 million dollars a year."

    That's an annual savings of $34 to $41 million in damage/maintence costs from zebra and quagga mussels for only the hydroelectric dams on the Columbia/Snake River Systems!