When Should You Stop Looking for a Possibly-Extinct Species?

When you’ve found two of everything else.

That’s the conclusion of a fascinating, if disappointing, paper about the ivory-billed woodpecker in the latest issue of Conservation Biology. Most experts believe the “Lord God” bird was driven to extinction in the middle of the twentieth century. Occasional reports of sightings, however, have kept some hope alive. A report from Arkansas in 2004, for example, inspired detailed censuses of several areas with promising habitat. Sadly, no unambiguous evidence of IBWPs appeared.

Which raises an important question: when should you stop looking? Nicholas, J. Gotelli, Anne Chao, Robert K. Colwell, Wen-Han Hwang, and Gary R. Graves used statistics and cost-benefit analysis to derive a simple stopping rule:

We evaluated whether the census efforts at these localities were sufficient to discover an Ivory-billed Woodpecker if it had been present and derived a practical stopping rule for deciding when to abandon the search in a particular site. An efficient stopping rule that incorporates rewards of discovery and costs of additional sampling should be triggered at the smallest sample size q satisfying f1/q < c/R, where f1 is the number of singletons (species observed exactly once during a census), c is the cost of making a single observation, and R is the reward for detecting each previously undetected species (Rasmussen & Starr 1979). Because R for an Ivory-billed Woodpecker is extremely large relative to c, c/R is close to zero. Thus, a simple, empirical stopping rule is to stop searching when each observed species is represented by at least 2 individuals in the sample (f1= 0). The same stopping rule can be derived independently from theorems originally developed by Turing and Good for cryptographic analyses (Good 1953, 2000). Both derivations imply that when f1= 0, the probability of detecting a new species approaches zero. We applied this stopping rule to the census data for the set of species that regularly winter in bottomland forest, such as the Ivory-billed Woodpecker, which was sedentary and occupied year-round territories.

According to that stopping rule, the search should be called off at one location (Congaree River, South Carolina) and is close to hopeless in the other three (Choctawhatchee River, Florida; Pearl River, Louisiana and Mississippi; and Pascagoula River, Mississippi).

Based on these and other data, the authors conclude that the probability that ivory-billed woodpeckers still inhabit the southeastern United States are less than 1 in 10,000.

A Sunday Numeracy Quiz

My Sunday reading turned up three examples of glaring numeracy errors. I make plenty of my own errors, so I have sympathy for the perpetrators. But I did want to highlight them as examples of what can happen when quantitative thinking runs off the rails. And the need to remain mathematically vigilant in your daily life.

So please take this short numeracy quiz. My answers after the fold.

1. How much has teen drinking declined?

In today’s New York Times Magazine, Tara Parker-Pope makes the case that teenagers are more conservative than their parents were. For example, the fraction of high-school seniors who reported that they had recently consumed alcohol fell from 72% in 1980 to 40% in 2011.

I have no beef with those statistics (or that trend), but I do wonder about the chart used to illustrate it. Do you see anything wrong in this visual?

2. What’s a fair way for students to hedge their bets on today’s Super Bowl?

A few pages later (in the ink-and-paper edition), the NYT’s Ethicist, Ariel Kaminer receives a letter from a parent whose child was offered a bet on the Super Bowl … by their school. Leaving aside the propriety of book-making in the class room, what do you think of this wager?

My school charged a dollar for students to bet, or “predict,” which team would win the Super Bowl. It was $1 for one team, and if you won, you would get a candy bar. If you bet $3, you could choose both teams and guarantee your candy bar. Is this legal or even morally right?

3. How much does federal compensation exceed private compensation?

In Friday’s Wall Street Journal, finally, Steve Moore makes the case that federal workers are overpaid. What’s wrong in the following excerpt? (ht: Brad DeLong)

Federal workers on balance still receive much better benefits and pay packages than comparable private sector workers, the Congressional Budget Office reports. The report says that on average the compensation paid to federal workers is nearly 50% higher than in the private sector, though even that figure understates the premium paid to federal bureaucrats.

CBO found that federal salaries were slightly higher (2%) on average, while benefits — including health insurance, retirement and paid vacation — are much more generous (48% higher) than what same-skilled private sector workers get.

Continue reading “A Sunday Numeracy Quiz”

The U.S. Economy is Uncertain, Fragile, and … Growing

Over at the Kauffman Foundation, Tim Kane has released his latest quarterly survey of economic bloggers. Here’s the usual word cloud reflecting the adjectives (up to five per respondent) that we econobloggers offered up to describe the U.S. economy:

That’s much better than last quarter, when you needed a magnifying glass to find any optimistic sentiments:

As usual, the survey also includes various questions about economics, policy, and haiku. Yes, the survey solicited haiku about the European debt crisis. My inner muse didn’t speak that day, so I don’t have my own to share. So let me offer up Jeff Miller’s (A Dash of Insight) as food for thought … and not just for Europe:

When the task is great

take but one step at a time

Compromise builds strength