Schroedinger's Woodpecker

Barring dramatic new information, the Ivory-billed Woodpecker situation has once again settled in to stalemate. Various summaries and such will be coming out in the near future, but they will be unlikely to reveal anything major that is not already known. I've got a few big-picture summary points I want to make as well. To begin, I want to review the order-of-magnitude probability issues I have gone over several times in the past.

A fundamental split in opinion can be summarized as follows:

Opinion A. If there were any out there, surely they'd have been adequately documented by now.

Opinion B. Finding a few birds in a large area is extremely difficult, and they could remain undocumented for a very long time even with many people looking.

Biologists are generally a bit math-phobic; ask anyone who has taught undergraduate genetics about the blank stares and panicky fidgeting that fill the classroom as soon as you get to population genetics and write the first equation on the board. People in general are also quite poor at comprehending the very small and the very large. Because of these two factors, most bird people have been arguing Opinions A and B based on not much more than hunch, intuition, and common sense. Those who work in other sciences, in contrast, are much more inclined to try to work with actual numbers when dealing with these matters of the huge and tiny. The order-of-magnitude approximation is a time-honored tool in most natural sciences. So here, once again, I'm going to apply this tool to Opinions A and B.

The question of how much effort it takes to find a bird can be summed up in a simple equation:

D = A*c

Here D is your detection rate, in terms of detections per hour, A is the actual abundance of the bird (birds per km²), and c is the coefficient of detectability. This coefficient is dependent on the species, time of year, habitat, etc., and your criteria for a "detection" (e.g. heard, seen, captured in a mist net, etc.). For a general and reasonable approximation, for a typical forest bird, if there's one per km² an experienced observer moving about through this square kilometer will detect it by sound or sight about once every 10 hours. This means that c has a value of 0.1 if you are dealing with hours and square kilometers. In spite of all the arguments that ivorybills should be either less conspicuous or more conspicuous than average, I'll use this nice round order-of-magnitude number.

Now we need estimates for A, abundance expressed as Ivorybills/km², under various scenarios. Estimates for the total extent of bottomland hardwoods vary, but a value used by The Nature Conservancy of 20,000 km² is typical. Using this number, if there is only one ivorybill out there, its abundance in this habitat is 0.00005 bird/km². This one individual Ivorybill would be "detected" (more on what this means later) about once for every 200,000 hours of birder effort spent in bottomland hardwoods. If there are 100 Ivorybills scattered in this region, this rate becomes once per 2000 hours of effort.

To address the Opinions A vs. B question, we need an estimate for total observer effort within this region. Here I am just going to make up order of magnitude numbers based on my own experiences as an active birder who has lived in or near the historical range of the Ivorybill for most of my life. I'm going to guess that within this region there are roughly 1000 birders who are competent, reliable, and experienced enough to be able to produce an Ivorybill report that could be granted credibility. This is on the order of 100-200 per state. I'm going to guess that each of these observers spends about 1000 hours per year afield; as this is 20 hours per week it is likely a rather generous estimate. Working with orders of magnitude, this gives us 1,000,000 hours of birding time per year in the region.

How much of this time is spent in closed canopy coastal plain bottomland forests? A quite small fraction, actually. The forested bottomlands are not a magnet for birders; in fact they are a bit of a repellant. After getting their Swainson's Warbler for the year, most birders have little additional need for this habitat. That 20,000 km² of bottomlands is about 2% of the land area within the region; most of it is inaccessible, all of it is frequently to occasionally flooded, and rich in biting insects much of the year. Hence, it seems reasonable to guess than only about 1% of this general birding effort is within this habitat, or 10,000 hours per year.

Now to combine these two ballpark numbers:

-- Individual Ivorybill within 20,000 km² of bottomlands detected every 200,000 hours

-- Birders spend 10,000 hours per year in this habitat

It's simple to figure that a lone Ivorybill would be "detected" once every 20 years.

But what does "detected" mean? In the context used so far, for a typical woodland bird, it means heard or seen well enough to "count" an individual of a species that is expected to be within the area. In the case of forest birds, this means "heard" about 90% of the time; sometimes heard faintly, distantly, and/or only once. Only about 10% of these detections will be visual; one might estimate that only about 10% of those visual detections would be "good" ones that would allow for a detailed description or the opportunity for a diagnostic photograph.

If we use this more nuanced definition of "detection," we find that once every 20 years or so, this lone Ivorybill will be heard, and not necessarily well. It would be seen about once every 200 years; most of these sightings would be "lousy." To expect a good sighting and a shot for a photo or video, you would be waiting about 2000 years.

This all scales up linearly of course. If we have 100 Ivorybills spread within this area, we still predict only one (probably lousy) sighting every 2 years, and a good sighting or photo every 20 years.

The gist of this is that small populations of mobile forest animals (say less than 100 individuals) spread over very large areas are almost impossible to detect with the typical birder effort. The scenario for 10 birds is indistinguishable from no birds at all, given the reality of honest mistakes and the possibilities of fraud.

There are two extensions to this ballpark analysis I'm going to run through. The first is the matter that all of these 20,000 km² might not be suitable habitat, which conceivably narrows the search range. The second is the matter of intensive targeted searches within smaller areas.

I'll start with the "suitable habitat" question. True, in all likelihood only an unknown fraction of all bottomland forest is actually suitable Ivorybill habitat. It is likely, though, that the "suitable habitat" is less accessible, and hence disproportionately less often visited by birders, than the more accessible, "marginal" habitats. Hence, the numbers get even worse if you try to account for this, not better -- one quarter the area with one tenth the effort, for instance.

Now for the target search scenario. Here people identify an area within which they think there is an especially high probability of finding the bird, and focus effort there. This is of course the usual method that birders and ornithologists use to find rare birds. Here a species-specific complication comes in to play. The overall consensus of historical accounts for the Ivorybill indicated that it was a highly mobile bird with a surprisingly large (and entirely forested) home range. It was generally not described as remaining within any small area for very long. Even nesting pairs were difficult to nail down. A general estimate for the size of this home range would reasonably be 10 mi², or 25 km², an area slightly more than 3 miles on a side and approximately the size of a typical breeding bird atlas block. Those who have atlassing experience might think, "surely if I had an ivorybill within one of my atlas blocks I would have found it!" Or, if you are an Ivorybill searcher, you might think that if you did get within the home range of a bird, you'd have a good chance of nailing that sucker. Think again.

A single observer within a 25 km² home range that contains one bird would expect encounters with the following frequency:

Auditory every 250 hrs
Visual every 2500 hrs
Good sighting or photo op every 25,000 hrs

Note that 25,000 hours is 10 hours a day, every day, for 6.8 years. Under the same circumstances, you'd expect some visual contact every 250 days (about 8 months) and an "I heard something suspicious" encounter every 25 days. Any wonder, then, that Tanner only found his birds with the help of a man who effectively lived in the forest full-time?

What about the Cornell scenario? They had about 10 people in the field, all day, for about 4 months each year. That's about 12,000 hours per field season. What is the expectation there, if all this effort was within the home range of this hypothetical Ivorybill, and all of it was good field time, not preoccupied with other tasks (like servicing field equipment, etc.)? That works out to 48 audio detections, 5 sightings, and a half of a photo. For Cornell's initial secret search, these numbers are somewhat high on the audio, low on the sightings, and about right on the photo (I think the Luneau video can be counted as half a photo...). Considering that I am working in orders of magnitude, it's a pretty good approximation. For comparison, look at our Moss Island searches, where we put in about about 2000 hours of effort. The prediction is for 8 audios, 0.8 sightings, and 0.08 photos. Again, this is a pretty fair agreement. The audio rate was about right, we had three uncertain glimpses (does this total to 0.8 sightings?) and were absolutely skunked on the photo front.

Even if you are in the right place, documenting a thinly spread forest bird is daunting. It's nearly impossible for a single observer; and challenging for a group of 10 observers. If you look at the total birding community over the entire historical range of this bird, it would be hard to distinguish even as many as 10-100 residual birds from the background noise of honest misidentifications and weird occurrences, with photo ops coming only a few times a century, if even that much. Some will doubtless try to turn this inside out and say "See, that proves the bird is extinct and all these reports are bogus!" which is certainly a bit of backwards logic. What it actually demonstrates is that those of Opinion A who say "If they were out there, we'd surely have found them by now" are in fact mistaken. Between 10 and 100 surviving birds is far from extinct, yet even this many birds would easily avoid "firm confirmation" of their existence for decade after decade. Thinly spread forest creatures, with very large areas within which they might be scattered, are destined to remain phantoms. Their existence will always be extremely challenging to confirm; their extinction will be essentially impossible to establish. Like it or not, this is the way of things.

What one does about this is a matter of policy, resource allocation, etc. That's a different matter. But anyone who declares that the species is "extinct" or "probably extinct" based on existing information is just voicing a personal belief. From a scientific perspective, this is not knowable. Sibley and Kaufmann were in error in concluding that the extinction of this species (and two others) was certain enough that it did not need to be included in "comprehensive" North American field guides. Of course, the same is true of those who declare that the species is definitely extant. Even if the Arkansas video were undeniably an ivorybill, and even if those double knocks I heard at Moss Island in 2009 were absolutely accepted as being the real deal, well, those two spots are only about 100 miles apart, and it's been over a year since then. Conceivably, it might have all been the same bird, it might have been the last bird, and it might be dead now. Far fetched, but not impossible. The only way this will ever be resolved is if the population manages to rebound in at least one area to a point that firm sightings and good photos can be obtained regularly. I think everyone will agree that this would be a great day; I think most would also agree that this day is not likely coming any time soon.

Schroedinger's Woodpecker is still locked up tight in that box.

"Who could have foreseen..."

"...that our air travel network would be brought to its knees by a volcano in Iceland??"

A refrain I have heard several times by jabbering voices on the radio lately. The answer to this question:

ANY competent vulcanologist, hell, any geologist of any subspecies, along with millions upon millions of better-informed lay people could have told you that this was not just a possibility, but an eventual inevitability! This is up there with "who knew the levees would fail?" It still boggles the mind how deep the capacity of human societies is to imagine that their infrastructure is divinely ordained, immortal, and invincible, and therefore they need not waste a passing thought on what happens if some "act of god" (i.e. entirely ordinary and fully anticipatable natural phenomenon) interferes with it. Even in the face of breakdowns, it is all viewed as freaks and special cases, without the larger picture (society ultimately is at the mercy of nature, it does not have dominion over it) and lessons (if you can't function without one of your major social subsystems, you better do something pretty f-ing quickly to change this!) ever being noticed by any but the "fringes."

The Financial Economy

According to the Late Great Douglas Adams, we have been doing this for millions of years. In this excerpt from "The Restaurant at the End of the Universe," he recounts humanity's first Financial Bubble, and the highly effective strategy that was devised to recover from it.

To set the scene -- the Golgafrincham B-Ark has crash-landed on the Earth, 2 million years before the present. The B-Ark was a clever ruse by which the Gogafrinchans rid themselves of a useless third of their population -- all the middlemen, financial planners, telephone sanitzers, etc. They concocted tales of planetary doom, and divided their population into three portions. Each would travel to a new world in a great Ark. The A-Ark would take all the great leaders and thinkers; the C-Ark would take all the people who made things and did things with real skills, and the B-Ark would take everyone else. In a grand show of kindness, the B-Ark was sent off first. The other two-thirds of the population then remained happily at home on Golgafrincham. In this scene, the Golgafrinchans (who will become the progenitors of all earthly humanity) are holding a council meeting as they attempt to build a new civilization on this pristine world. The matter of "money" has just come up; a Management Consultant is speaking, and responding to the assertion that money "does not grow on trees":

"'...since we decided a few weeks ago to adopt the leaf as legal tender, we have, of course, all become immensly rich.' ... 'But we have also,' continued the Managment Consultant, 'run into a small inflation problem on account of the high level of leaf availability, which means that, I gather, the current going rate has something like three decidous forests buying one ship's peanut. ... So in order to obviate this problem and effectively revalue the leaf, we are about to embark on a massive defoliation campaign, and ... er, burn down all the forests. I think you'll all agree that's a sensible move under the circumstances."

Things have not changed much in the intervening 2000 millennia...