Friday, January 20, 2006

Woodpecker math

Let's put this to rest, and I'll go off the woodpecker theme here for a while. An Ivory-billed woodpecker need not be especially wary, nor in an extremely remote habitat, to avoid detection for many years. It just has to be RARE.

The density of Pileated Woodpeckers in the area where the Ivorybills were sighted in Arkansas has been reported as 40/mi2. And the total area of the Big Woods is called 250 mi2 in a frequently bandied number. So lets be generous and give the Big Woods 5 Ivorybills, or one per 50mi2. And let's assume that is it as conspicuous as the Pileated. Given this, you would expect to detect one Ivorybill for every 2000 Pileateds.

But wait, that is just a detection. As we all know, we do "80% of our birding by ear." And is a heard-only Ivorybill good enough? Of course not. Is a quick glimpse of a big woodpecker with a general impression of how much white it has enough? It's enough to count a Pileated, but not for an Ivorybill. No, we need a good look. So again being a bit generous let's say 10% of these "detections" would be good enough for you to even consider making a public announcement that "Oh my god I am pretty sure I just saw an Ivorybill!" Now we are at one Ivorybill per 20,000 Pileateds.

To put this in context: that is a Pileated a day for over 50 years. It is nearly 40 times the number of Pileateds EVER recorded on the White River NWR Christmas Bird Count in the 35 years it has been conducted. In the Big Woods, I detected about 2 pileateds per hour (mostly by voice). Laura Erickson has been reporting about 1-2 per hour on her trip too it seems. So that is one glimpse of an Ivorybill per 10,000-20,000 observer hours. 10,000 observer hours is 10 hours a day, every day, for three years. Even someone who lives and works at the refuge, with all his or her other duties, would probably not chalk up 20,000 Pileateds in a decade even if they were a birder and trying to pay attention. I know here at home I detect about one pileated per 1-2 hours when I am birding, only about one a day (or less) when I am going about my regular farm chores.

But even after all that, all we have is a sight record. Quite probably a brief one that would still leave much detail to be desired. Events of the last year prove you need a photo or video, and indeed a good photo or video. Laura hasn't gotten even one decent Pileated photo per day on her trip. So, realistically, we might need to add another order of magnitude here and say one acceptably photographed and unequivocally documented Ivorybill per 200,000 Pileateds, or 100,000 observer hours, and only if that observer is carrying a camera.

A hundred thousand observer hours. Ten hours a day, every day, for 30 years. Ten hours a weekend for 200 years. About a full years' worth of christmas counts.. and I mean all the christmas counts, every single party hour on every christmas count conducted anywhere in the continent, all transplanted to the Big Woods. And everyone carrying a camera. Or more realistically, 10 camera-equipped parties spending 10 hours a day in the field every day... for three years.

So the "skeptics" can already start rejoicing. Odds are, even if there are five Ivorybills in the Big Woods, and even if they are no more wary than Pileateds, there will not be an unequivocal photograph taken this year. Or next. There will be some sightings, a few of them probably even pretty good ones. There will likely be a fair number of maybe's, might-have-been's, and sure-sounded-like-one's -- all of which would be enough to count a common bird on a CBC but not enough to document an Ivorybill.

The bird does not have to be extinct, or especially wary, or living only at the ends of the earth, to have avoided having its portrait snapped for all these years. It just has to have had a very low population density.


At 7:22 PM, Anonymous Anonymous said...

I don't think we need math to determine the odds of finding an Ivory-bill.

"Using traditional methods, we have some experience with how long it takes to find a rare bird ... and it is a lot less (time) than they are spending," Richard Prum, Curator of Ornithology, Peabody Museum, Yale University.

1941, Dr. and Mrs. Tanner (Singer Tract) see and document 5 Ivory-bills.

1943-1944, Richard Pough, Singer Tract. As far as I know, he was by himself. He found, apparently many times, a single Ivory-bill.

1944, Don Eckelberry and Jesse Laird, Singer Tract. They relocate, many times, what was apparently that same single Ivory-bill.

If you look at the history of the Ivory-bill, you'll see how the population appeared to be plunging rapidly. In the last few years ('41-'44), scores of good, well-documented, sightings were made, along with plenty of SOLID PROOF.

According to your math, if you found an Ivory-bill, it would likely take 30 years to get another good look. Once the above people were in the right area, they usually could find their birds in a few days.

No proof proof like that has been found in the last 62 years. I don't think the experience of the above people is reflected in your math. And even if your math were correct, someone still needs to prove there are living birds out there.

Hopeful Skeptic

At 8:37 PM, Blogger Bill Pulliam said...

Once you find a nest the whole game changes.

At 8:38 PM, Blogger Bill Pulliam said...

And, you can always find an expert to quote who has said anything.

At 6:30 AM, Blogger Bill Pulliam said...

Overnight reflection...

If you don't like the conclusion, challenge the assumptions. They are clearly spelled out. Don't just say "Well but so and so said otherwise and such and such found something completely different in another time and place under fundamentally different circumstances."

Singer tract: much higher population densities than 0.02/mi2 (nesting pairs and family groups in territories far smaller than 50 square miles). I also assumed random distribution and movement within the entire area. Until you can identify where and when clumps are likely to occur, that is what you are dealing with.

Realistically, in the very low density situation I describe, those weak and possible encounters (sounds, glimpses) would allow you over time to target your effort within a much smaller area and greatly increase the odds off an encounter given two conditions are BOTH met:

1. These uncertain sightings are paid attention to and given serious consideration

2. The birds do in fact clump within the area

Condition 1 has most definitely NOT been met over most of the last 60 years. Only now is it beginning to be met. Condition 2 is quite probably true, fortunately, but is unhelpful without Condition 1.

At 7:27 AM, Anonymous Anonymous said...

I see some problems.

One is this: once you find a nest, you are likely to get as many good views as you like. The Christmas bird count isn't done during nesting season. Odds are you'll locate a roost or nesting site fairly early on in a search, but only if birds are in the area.

Another flaw is that the searchers are looking SPECIFICALLY for Ivory-bills, while on the Christmas bird count they are not specifically looking for Pileateds. Makes a big, big difference.

Another is that, judging from Cornell's team, camo and ghillie suits and stealth are very important. Cornell has a huge advantage there.

Another is the days are much shorter in December than they are later in the year. Adds up fast.

Another is there are remote cameras set up in the very most promising feeding areas, roosting sites and the like. 24 hours a day, tireless, with a very high probability of getting very good shots if an ivory-bill shows.

Another flaw is that if my examples of people actually looking for and finding ivory-bills don't count, certainly extrapolating Laura Erickson's results from her brief visit, thus boosting "the order of magnitude" doesn't count for anything.

Another flaw is that, at least for me, this debate is about the Ivory-bill nationwide. It's not just searchers who are aware of what's going on around them in the forest, there are thousands and thousands of birders, hunters, and other outdoorsman out there.

Also of course, if there are no living birds, we'll never get photos!

Hopeful Skeptic

At 8:07 AM, Blogger Bill Pulliam said...

All valid points, though I take exception to one. Laura is working in the same habitat. The earlier studies did not.

The back of the envelope calculation is a powerful tool in science for order of magnitude estimations and getting an idea of context and practicality. I would never claim it as definite.

At 4:50 PM, Anonymous Anonymous said...

Do you have any actual data to support a home range size estimate of 50 square miles?!

Another Hopeful Skeptic

At 7:50 PM, Blogger Bill Pulliam said...

No data at all. It doesn't actually have to have a home range of 50 square miles. It just has to be somewhere within a 50 square mile area, but you don't know where. It could be ranging only within 1 mile of the roost tree, but it still would take you 2000 pileateds (on avergage) before you first encountered it if you had no idea where that roost tree was. Actually, all five of them could be clumped within the same square mile within the entire 250 square mile area, and the estimate remains the same. Of course in that hypothetical, the followup on the initial (probably pretty lousy) sighting would be far easier!

The whole point is this: A very small number of birds of moderate detectability, spread over a fairly large area, can take a very long time and a lot of effort before someone is able to get a decent photo of one. It's only an order of magnitude calculation (if even that), dudes. And it actually applies more to the situation prior to 2004, when there was not a large-scale organized search going on; rather there were just people in the area who might have encountered one by chance. Which is also the current situation in all the other places that an Ivorybill or two would seem just as likely (or unlikely) to still be lurking. Don't pick apart the details and miss the overall general point: the woods are big, the bird are small, much more so than we generally comprehend. And us birders tend to WAY overestimate how thoroughly we cover the planet.

At 10:50 AM, Anonymous Anonymous said...

How does the math account for Tanner, Pough and Eckelberry "winning the lottery" scores of times?

Hopeful Skeptic

At 10:14 PM, Blogger Bill Pulliam said...

Larger number of birds in a smaller area, and nest tree(s) located. Didn't the Singer tract have something like one Ivorybill per 40 pileateds, not one per 2000? So crank all these numbers up by two orders of magnitude.

I just looked through the Singer Tract photos. All appear to be near or on the nest tree. In the absence of a found nest those birds would probably have never been photographed at all.

At 11:21 AM, Anonymous Anonymous said...

My understanding is the same as Bill's, that the reason so many were seen by a few observers in the past was, in every case, that they had located a nest.

As far as vocalizations, I've long observed that birds vocalize with increasing frequency as their population goes up. You hear one Pileated call, and more often than not another answers. When my neighborhood had a large robin population, with four different pairs sharing my bird bath, back in the 80s, very often a male would sing the entire night through during nesting season. Now at most I have only 2 pairs sharing the bird bath because the local population has dropped, and in the past four or five years not once have I heard a male singing after dark. I think it's a fair assumption that with such a tiny population (perhaps, frighteningly, only one bird) in the Arkansas river bottomlands, vocalizations are probably just not happening very often, decreasing the probability of detection even further.

At 12:57 PM, Anonymous Anonymous said...

Larger number of birds in a smaller area, and nest tree(s) located.

Nope. In 1943, two years after the Tanner's, Pough located a single female. Repeatedly. In 1944, Eckelberry located that same female. Again, repeatedly.

If the math stands up, they were "winning the lottery" with some consistency.

Hopeful Skeptic

At 2:20 PM, Blogger Bill Pulliam said...

How many acres was the Singer tract?

At 10:48 PM, Anonymous Anonymous said...

"How many acres was the Singer tract?"

I don't know, but unless we know how big of an area the Arkansas Ivory-Bill(s) is/are ranging in, which we don't, I'm not sure it's relevant.



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