Thinking Point
	Can you think of a natural or man-made catastrophe, other than the Exxon Valdez oil spill, that has seriously damaged a marine ecosystem?

We know up front that there are a variety of different catastrophes that are going to compromise the effectiveness of reserves, and the establishment of networks of reserves can do nothing to stop these. There are both man-made catastrophes, which we are all familiar with, and there are a number of natural catastrophes. You might ask: Why do natural catastrophes play the same role here as human-based catastrophes? I think they do because when we reduce the average population size of a marine species to the point that they need the protection from something like marine reserves then natural catastrophes take on a different role than they would in a pristine ecosystem.

To clarify, if you have to maintain some spawning stock biomass within a particular species and you use the reserves to set a lower boundary on that stock, the effectiveness of that lower boundary is going to be influenced by natural catastrophes that reduce population sizes within reserves in exactly the same way that they would in human-based catastrophes. So we really have to think about both types of catastrophes and how they might influence reserves.

One of the ways we can look at events that are relatively rare and infrequent is by thinking about them as a return time. How long do you have to wait, on average, until you see an event of a particular size. When we think about floods or storms, for example, we think about 100-year floods or 50-year storms, or things like that. This is the way we talk about rare events. You can look at catastrophes in exactly the same way. If you look at oil spill data over the last 20 years, you see there's enormous range in terms of volume spills, but the surprising thing to see is that spills the size of the Exxon Valdez have a return time of about a year over this 20-year period. That obviously was a huge catastrophic event that had a greater shoreline impact than other spills of comparable size, but it shows that large catastrophes with this kind of human-induced event are quite common. They are also widespread. Widespread pattern of spills along the coasts of California and Oregon shows that there are clearly areas that have a higher frequency of spills than others, but there are no areas of the coastlines that are completely devoid of this as a threat.

Photo courtesy of the Exxon Valdez Oil Spill Trustee Council. An oily sheen covers the surface of an intertidal habitat with aquatic plants (Fucus sp.) following the Exxon Valdez oil spill in Prince William Sound.

Photo courtesy of the Exxon Valdez Oil Spill Trustee Council. A spill worker with respirator hoses Quayle Beach, Smith Island after the Exxon Valdez oil spill.

Reserve size, spacing and area
From the perspective of catastrophes, there are three issues regarding reserves that I'd like to mention: individual reserve size, reserve spacing and total reserve area.

We can imagine some simple guidelines that we want to have a reserve size on average that is greater than the catastrophe size. This is one way that you can limit the likelihood that a single catastrophe could compromise the effectiveness of an entire reserve. That's fine, but the spatial extent of certain catastrophes can be enormous. Just looking at the extent of the Exxon Valdez catastrophe demonstrates that there are no reserves that size and likely never will be at that sort of scale.

The second thing is that the spacing of these reserves should be greater than the scale of the catastrophe. Again, this is simply because you don't want a single catastrophic event to compromise multiple reserves at the same time. This is fine as long as the scale of catastrophes doesn't get too large, because then you start compromising the function of the reserves in terms of whether there is any potential connectivity between one reserve and the next.

If we look at the pattern of oil spill sizes for a couple of different events we can see that these guidelines can be useful in some cases. For West Coast oil spills, the vast majority of spills are along the order of 10 kilometers or less of shoreline affected. That also turns out to be true for the Gulf of Mexico. This is the type of catastrophe where a simple rule of thumb in terms of the size of reserves and spacing could potentially play an important role, because the size of the catastrophe is small enough that you can have reserves that are larger than this and you can have spacing between reserves that is larger than this. Plus, you can still have a functioning network of connectivity.

If we look at another kind of catastrophe, the spatial scale for shoreline impact of hurricanes, it's a totally different ballgame. Those simple rules would never be able to deal with these kinds of large spatial scales. As a consequence, for many potential catastrophes it's impractical to make reserves large enough to be resistant to them. If you make the spacing large enough to avoid simultaneous catastrophes, then you are very likely to compromise other aspects of the reserve function based upon the biology and physics.

Reserve insurance
So what do we do? One possible solution to this is to "buy" insurance for reserves. We've talked a lot about reserves themselves as insurance for a variety of other activities. We can flip this on its head and think about the problem of buying reserve insurance rather than using reserves as insurance.

Just to develop this in an oversimplified manner, imagine that we have a network of reserves covering 30 percent of the coastline. This leads to rapid increases in population size within these reserves. Let's suppose, just for the sake of calculation, that 10 percent of the coastline is hit by catastrophe each year. We've now lost that contribution to this network in terms of enhanced biomass and production. Year Two we lose another reserve. Year Three we lose another reserve. But, in Year Three the reserve that was hit two years ago now has recovered, so what happens is that eventually you're going to get new losses being counteracted by recovery from reserves from previous catastrophes.

There are two key parameters to thinking about what are really going to affect what fraction of the reserve system is going to be in a recovered state in any one time. One is going to be the fraction of the shoreline that is affected by the catastrophe each year, so we'll just call that h, and the other is the average recovery time--how long does it take after a catastrophe before the reserve gets back up to where it is contributing to the fisheries or conservation benefits that it was established for?

Insurance multiplier equation
It turns out there is a very simple way in which you can go from these two parameters to what you can call an insurance multiplier. If fraction h is affected by the shoreline each year, then in a single year the unaffected fraction is 1-h. And if it takes t years for this to recover, then the unaffected fraction at any one time is going to be 1-h raised to the t power. This is because over those cumulative effects of each of the t years, you are losing-- without gaining back--recovered reserves. If that's the amount that's going to be unaffected, then if you want to maintain a certain area or certain fraction of the population size by your reserves, then you have to have this multiplier (1 over u), which is additional reserves you have to set up in the beginning to counteract the long-term consequences of catastrophes.

If you have 1 percent of the shoreline affected and a recovery time of two years, there's a relatively small multiplier--the value is just a little above one, which means you don't have to worry about the catastrophe. Whereas if you have 1 percent of the shoreline affected and a recovery time of 50 years the multiplier is over 1.5. That means even though it is a rare event, only a 1 percent event, the fact that it takes a long recovery time from the catastrophe means you have to initially set up 50 percent more than you anticipate is needed to maintain a level for your goals over a long period of time. This is buying the insurance. We can't stop the catastrophes by setting up the reserves, so we effectively counter them by setting up more reserves than the catastrophes are going to be able to wipe out.

There is great variability within regions in terms of getting hit with catastrophes such as oil spills, so average numbers should be looked at cautiously. Some places along the California coast had 0 percent catastrophes within the 20-year period for which we had data, and other places had up to 4 percent, so that of course affects the multiplier within each section of coastline.

Another important point to remember is that this looks at only one type of catastrophe and does not include other types occurring within a single year. So you have to look at recovery time, frequency of catastrophes, and the types of catastrophes within a given area and take all these into account. The bottom line is that all these increase the insurance you have to buy up front in order to maintain the levels of the reserves to meet your goals.

To summarize, these reserves are going to be embedded within disturbance regions that compromise their effectiveness, and there's nothing that we can do about enforcement of the reserves that is going to stop that. So reserve insurance provides a conceptually simple solution to a failure of marine reserves. The key thing is that based on preliminary analyses of existing types of disturbances, sometimes you need a lot of insurance. There are a variety of ways in which you can deal with this, but the overall answer is that optimal solutions, even when they exist, are not sufficient. In the long run, you have to set aside more than you initially think you'll need to achieve your goals.