Numbers of birds from nocturnal flight calls: two kinds of bird density.
John Black, (black@brocku.ca), Brock University
I recently read the posting of Bill Evans’ reply to Jay Withgott and the posted link by
Guy Monty to an article by Andrew Farnsworth in the Auk: http://www.aou.org/persp1223.pdf.
I would like to make some additional comments on the question by Jay's reader, "How
can I come up with an accurate estimate of number of birds passing over, based on the number of
calls I hear?"
Consider a particular species. Let the ground speed of the bird be v miles per hour and the
calling rate be R calls per hour. To facilitate our discussion we introduce a quantity D, the
distance in miles traveled by a bird between calls, which is v/R. Now suppose that the distance
the bird travels when crossing through the beam of an acoustic microphone is d miles. The
probability that it will call as it crosses that distance is then d/D; that is, if d were half of D, then
50% of all birds crossing the beam along that distance d would be heard.
For the moment let us consider cases where d is less than D in the entire microphone
beam. This would seem to be a suitable approach to the seminal work of Graber and Cochran
(1959). They mentioned that in the majority of cases where a bird was heard in their microphone,
each recorded call represented a different bird. Graber and Cochran’s captive thrush calling rates
are instructive here; the most frequent calling rate was 30 calls per hour. They suggested a
reasonable ground speed for the thrushes would be 35 miles/hour, so that D= v/R = 1.17 miles
per call. They estimated the maximum distance across their microphone beam as d = 0.17 miles.
We then have d/D = 0.15, so that only 15% of these thrushes would be heard as they traversed
the maximum distance in the microphone beam.
How did Graber and Cochran get from the number of calls heard to the number of
thrushes passing over? They treated each bird heard in the microphone as if each bird had been
seen crossing the moon. They then used an approach developed by Lowery (1951) to compute a
flight call density-- the number of birds per hour crossing an imaginary cylinder one mile in
diameter which extended from the ground vertically above their microphone. While it is true that
each bird they heard crossed the cylinder above their microphone, it is somewhat misleading, as
it suggests that they were measuring a flow of birds just as Lowery did with his flight density.
The difference is that every bird that crossed in front of the moon was seen, but not every bird
that passed through the microphone was heard. Therefore, their calculated flight call density is
less than the actual flight density or flow of birds passing over.
How much less is the flight call density than the actual flight density? The answer is a
surprising one. At a location of arrival in the microphone beam of a bird, where the distance
across the beam is d, there will be a certain number of birds arriving each hour. This number will
depend on the product of the volume density and the speed of the birds. (The distinction here
between volume density, so many birds in a cubic mile, and the flight density of Lowery is an
important one.) The number of calls per hour from that length d of the beam would then be the
product of the number of birds arriving per hour and the probability that a bird calls as it
traverses the beam. The resulting product contains the volume density of the birds times R. What
is surprising is that this product does not have the speed in it. This seems counterintuitive at first
sight, but think of it this way: if you double the speed of the birds, you double the number of
birds arriving at the microphone beam each hour; however, they traverse the microphone twice
as quickly, so your chance of hearing them is halved! (If v is doubled, then D is doubled, so d/D
is halved.) Extending the calculation to the entire microphone beam, you find that the calls per
hour heard from the microphone beam equals the bird volume density times the volume of the
microphone beam times the calling rate of each bird. To sum up these ideas, if d/D is less than
one, then you can learn something about volume density from the calls alone but not much about
flight density except a lower limit, which is, strangely enough, insensitive to the speed of the
birds.
Now consider the case where d /D is two or more in the entire microphone beam. All
birds crossing through the beam would be heard. If each bird heard were distinguishable, then
the number of individuals heard calling per hour could be used to estimate a flight density in the
same manner as was done by Lowery. So in this case we can learn something about the flight
density of the birds, and no knowledge of R is required except to know that the birds are calling
more than once as they traverse the beam. Note that the formula derived above for calls heard
when d/D is less than one (volume density times beam volume times R) still gives the total
number of calls from the beam per hour if one does not distinguish individual birds. Therefore,
one can estimate volume density in this case also.
In practice d/D would be greater than 1 in some parts of the beam of most microphones
and less than 1 in other parts of the beam, for most species and speeds. Moreover, the simple
formula given above involving the volume of the beam applies no longer if calling rate and
volume density depend on height. See Black (1997) for details. To sum up then, there are two
kinds of bird density detected in nocturnal monitoring. The kind detected depends on the value of
the ratio d/D. The flight density of birds is what matters when one is considering impacts with
the blades of wind turbines. This is also a quantity that permits a measure of the total migration
over the migration period. The volume density of birds is useful when you are comparing birds
on the ground in the morning with numbers of call notes heard the previous night. It is also the
quantity observed on the WSR-88D weather radars in use at many airports.
Literature Cited
Black, J. E. 1997. The relation between the number of calls of a nocturnally migrating bird
species heard and the actual number of individuals of that species passing overhead. Physics
Department, Brock University, St. Catharines, Ontario, Canada, PR-1997-3.
Graber, R. R., and W. W. Cochran. 1959. An audio technique for the study of nocturnal
migration of birds. Wilson Bulletin 71,220-236.
Lowery, G. H., Jr. 1951. A quantitative study of the Nocturnal Migration of Birds. Univ. Kans.
Publ. Mus. Nat. Hist., 3, 361-472.