Monthly Archives: February 2012

208 – Ecological thresholds, uncertainty and decision making

The concept of thresholds features prominently in ecology and resilience theory. The idea is that if a variable crosses a threshold value, an ecological system can change abruptly and substantially. How this affects decisions made by rational environmental managers can depend greatly on how uncertain they are about the value of the threshold.

The Resilience Alliance has an online database of “Thresholds and Alternate States in Ecological and Social-Ecological Systems”. It contains many examples including:

  • Coral bleaching on the Great Barrier Reef when temperature rises beyond a threshold level.
  • Hypoxia (reduced oxygen concentration dissolved in water) in the Gulf of Mexico when the concentrations of nitrogen and phosphorus (largely originating from agricultural fertilizers) exceed thresholds.
  • A switch from woodland to grassland in the Chobe National Park of Botswana when elephant numbers exceed a threshold.

Thresholds are often talked about as if they are pretty black and white. If the variable is on one side of the threshold, the probability of a bad outcome is zero, whereas, if it is on the other side, the bad outcome is certain to occur (Figure 1). If you know that you are close to such a threshold, the benefits of taking action to avoid crossing it could be very  high.

For example, the decision might be, should we invest in actions to stop the management variable increasing slightly (moving to the right in Figure 1). If we know for sure that the variable currently has a value just below the threshold (e.g. 0.49 in this example), the benefits of investing in actions look high, as we can totally avoid the bad outcome.

In reality, though, when thinking about a decision that needs to be made about future management, we usually don’t know for sure whether there really is a clear-cut threshold, and even if we are willing to assume that there is one, we don’t know its value.

Instead, we might feel that there is a range of values that the threshold might take, and that these different values have different probabilities of actually being the threshold. In other words, we may be able to subjectively specify a probability distribution for the threshold.

To illustrate, Figure 2 shows how the cumulative probability of a bad outcome might look for a case where we believe there is a sharp threshold and our best-bet value for the threshold is 0.5, but we have high uncertainty about what the threshold value really is. In this case, the cumulative probability of a bad outcome increases smoothly and steadily until it reaches 1.

Decision theory was developed for just such a case. It’s a way to account rigorously for uncertainty about a variable when trying to make a decision about what to do. It says that we should weight the outcomes of our decisions by their probabilities of occurring, and base decisions on the “expected value” of the outcomes. “Expected value” means the weighted average, allowing for different possible outcomes and their probabilities.

If we apply that to a case where we are uncertain about what the threshold is (like Figure 2), then the expected value of avoiding a small increase in the management variable is not  large, even if its current value is just below the best-bet value for the threshold. For example, in the numerical example in Figure 2, preventing an increase in the variable from 0.49 to 0.51 would reduce the probability of a bad outcome by only 4% (compared to 100% in Figure 1).

If allowing for  uncertainty about the value of the threshold  means that the estimated benefits of a management decision are very different, then the optimal decision about what to do could be quite different too.

Interestingly, even if you believe that there really is a sharp threshold, the effect of allowing for uncertainty about the value of the threshold is to smooth things out, so that the decision is no longer black and white, but is a shade of grey. The result is that the decision problem is rather similar to what it would be like if there wasn’t a sharp threshold at all, but a smooth transition between good and bad states.

To my mind, recognising realistic uncertainties about thresholds reduces their potency as an influence on decision making. It may result in reasonable decision makers choosing to take more measured actions than they would feel compelled to take if they believed that the problem was black and white.

Appendix

The following two figures are referred to in my reply to a comment below by Thomas Brinsmead. Ignore them unless you are reading that reply. The first figure is for a risk-neutral decision maker and the second one is for a risk-averse decision maker.

207 – Are sharks more valuable dead or alive?

After 2011, when Western Australia suffered 25% of all shark fatalities in the world (3 out of 12), it’s hard for a West Australian to imagine people paying for the pleasure of swimming with sharks. But large numbers do. I was part of a project to estimate the economic benefits of shark-based tourism to the small island state of Palau. It turns out that shark diving is really quite a significant part of the Palauan economy.

Palau is in the Pacific Ocean, about 800 km east of The Philippines. It has a population of about 21,000 people. Most of its economic activity relates to tourism, fishing or subsistence agriculture.

In 2009, Palau announced a ban on fishing for sharks in its waters – the world’s first shark sanctuary. The motivation was to protect a growing tourism industry based on diving with sharks.

Some colleagues in the Oceans Institute at the University of Western Australia were keen to look at the economic benefits of shark diving at Palau, in the hope that it would be a good news story that could be told in other places and encourage other nations to also protect their sharks.

Why would they be concerned about that? Because over-fishing of sharks is a serious problem world-wide. Apart from endangering a number of shark species, it is feared that the effective removal of the top predators from marine ecosystems could have serious consequences. The widespread practice of removing sharks’ fins but discarding the rest of their body, to meet demands for shark fin soup in China, is a major contributor to over-fishing. The fact that shark fins consist of tasteless cartilage makes the practice even more tragic.

So the question for us was whether Palau made more money from using sharks to attract tourists than it would from killing them and selling their products.

The analysis was based on extensive surveys in Palau (conducted by Gabe Vianna), collecting information from tourists, dive  operators, dive guides and fishers.  We were careful to limit results to tourists who stated that they went to Palau specifically to dive with sharks.

The results were quite remarkable. To quote from the paper:

“… we show that shark diving is a major contributor to the economy of Palau, generating US$18 million per year and accounting for approximately 8% of the gross domestic product of the country. Annually, shark diving was responsible for the disbursement of US$1.2 million in salaries to the local community, and generated US$1.5 million in taxes to the government.”

The answer to the question of whether it would be more profitable to catch the sharks was clear-cut:

“If the population of approximately 100 sharks that interact with tourists at popular dive sites was harvested by fishers, their economic value would be at most US$10 800, a fraction of the worth of these animals as a non-consumptive resource. Fishers earn more selling fish for consumption by shark divers than they would gain by catching sharks.”

There was a lot of interest in these results. We even got an article in the New York Times about them.

Now Gabe is repeating the study in Fiji, and there seems to be interest in it being done in other places as well.

Further Reading

Vianna, G.M.S., Meekan, M.G., Pannell, D.J., Marsh, S.P. and Meeuwig, J.J. (2012). Socio-economic and community benefits from shark diving by tourists in Palau: a sustainable use of reef shark populations, Biological Conservation 145(1): 267-277. Abstract at journal web site.

206 – Award for Pannell Discussions

I mentioned in PD#200 that, to mark the milestone of reaching 200 posts, I was nominating Pannell Discussions for an award. The award was the “Quality of Research Communication” prize of the Australian Agricultural and Resource Economics Society (AARES). The results were announced last week at the AARES national conference in Perth and, happily, the nomination was successful (as a joint winner).

I’d particularly like to thank readers who have in the past sent me nice emails about one Pannell Discussion or another. I quoted a number of these emails in the nomination.

205 – Chinese television

Much of Chinese television seems to be pretty low brow. Of course most Australian TV is too, but perhaps this is another area where the Chinese have overtaken us.

My experience of Chinese TV was gained during a visit there last October. I didn’t watch much, just enough to get a biased impression probably, but what I did see (mainly in public areas) was gold.

The best was a soapy based around beach volleyball and kung fu. Ridiculously attractive, tall, western-looking Chinese girls wearing tiny bikinis play each other at beach volleyball. It seems to be professional, as there are big crowds watching, but it could just be that they are so attractive, I suppose. There are plenty of slow-motion shots and close-ups of body parts. One of the teams is “good” (sweet, poor, excellent at kung fu) and the other team is “evil” (bitchy, rich, with henchmen to do the kung fu for them). In between volleyball matches, when they are not dancing or hanging out at the beach, kung fu fights break out between the teams, with the good girls and their friends on one side and the evil girls’ henchmen on the other. The evil girls need to get better henchmen because they always lose the kung fu, even though they are dressed up like Men in Black, there are more of them, and they are fighting a couple of willowy girls. There is a touching love interest, with the incredibly handsome brother of the evil girls being in love with one of the good girls, and vice verse, but of course this makes things complicated! The boy’s mother and sisters are not happy about his taste in girlfriends because she is poor. They regularly order him to leave her, which he gallantly refuses. This gives the evils an excuse to send in the henchmen whenever they feel like it, only to see them humiliated yet again.

One of the airlines on an internal flight thoughtfully provided two episodes of this excellent show, to distract us from the fact that the plane with us in it was delayed at the departure gate for 90 minutes. It was riveting. Why can’t we have programs of this quality and interest in Australia?

If anybody knows the name of the program, I’d love to know.