When I was in grade school I hated Story Problems in math class — those word problems without formulas, just a bunch of facts to solve.

But life is full of stories.  I overcame my disgust, learned how to turn word problems into formulas, and became a math major.  Thus when I wrote about starling flocks last Friday I began to wonder…

How did the starling population increase from 100 birds released in Central Park in 1891 to 200 million (or more) in 2013?

Using information on their breeding habits and survival rate, I did some crude mathematics and came up with an answer.  First, the facts:

• Starlings north of the 48th parallel produce only one brood per year, the rest produce two.  (To give you an idea of this location, the western U.S.-Canada border is at the 49th parallel.)
• Female starlings typically lay 5 eggs per nest.
• 50% – 80% of the eggs survive to the fledgling stage.
• 20% of the fledglings survive to adulthood.
• 60% of the adults survive each year.

(Warning!  If math makes your head spin, now’s the time to skip to the end.)

If we started with 100 starlings in Pittsburgh this spring, how many starlings would we have next spring?   To make it simple I made some big assumptions and did a lot of rounding.

• 100 starlings = 50 nesting pairs
• 50 pairs * 2 nests per year * 5 eggs per nest = 500 eggs this year
• 50% to 80% of the eggs will fledge.  I used 65% * 500 eggs = 325 juvenile starlings in August.  I rounded this down to 300.
• 100 adults + 300 juveniles = 400 starlings in August.   This is why we see so many starlings in the fall — and this doesn’t even include the migrants.
• 60% of the adults survive to the next spring = 60% * 100 = 60 adults in March
• 20% of the juvies survive the winter = 20% * 300 = 60 former juveniles in March
• 60 adults + 60 of last year’s juveniles = 120 starlings in March

If I’m right (but I’m not) our starling population increases 400% in August, then winter trims it to an annual increase of 20% by March.

But 20% is too high.  Sixteen pairs survived from the 100 birds released in Central Park in 1891.  If their increase had been uniform it would resemble compound interest over 120 years (1891 to 2011) of about 14%.

(If you skipped the math, resume reading here.)

Interestingly, scientists estimated that the starling population boom in the western U.S. in the 1970’s was 16% per year, so I got close.

Fortunately the starling population seems to have stabilized so their annual increase is now — perhaps — zero.

How’s that for a story problem?

(photo by Bobby Greene)

Yesterday while on my way to somewhere else , I discovered a blog called Goldbird Variations that began when the author started playing music for birds.

Years ago Lisa Rest of Chicago took up the piano again and often played with her window open.  One day a mourning dove flew to the windowsill and sang along.  She didn’t understand what it was doing until later, wanting to share her music with an audience, she rediscovered that the birds were listening outside her window and singing as she played.

Soon she began intentionally playing music for birds, recording their duets and writing about her encounters.  Now she’s hooked on birds and blogging.  I know how that is!

Lisa has perfect pitch and can tell that the birds do too.  Listen to a cardinal sing with her in this post that explains why birds are attracted to music.

Which leads to the nightingale above…

Lisa points out she’s not the only one to play music for birds.   In May 1927 the BBC recorded Beatrice Harrison playing Londonderry Air on her cello in her garden in Surrey as a nightingale sang along.  The bird waits for her phrases and blends in at appropriate times.  Amazing!  Click here to download and play the mp3 recording from the Music And Nature radio program.

I have neither perfect pitch nor musical skill but I’ve encountered birds’ interest in music when I whistle while I hike.  I’m particularly fond of Bach and Beethoven and since I don’t sing well I whistle my favorite tunes.

Their favorite of my repertoire seems to be the second movement of Beethoven’s 6th Symphony, Szene am Bach (Scene at the brook) from his Pastoral Symphony.

Of course the birds like that one!

(photo of a nightingale singing in Berlin.  Click on the image to see the original on Wikimedia Commons.  This post was inspired by the Goldbird Variations)

If you live in North America this fact is amazing:  House sparrows are an endangered species in Britain.

I learned this when I read John Metcalfe’s article called Making Cities More Bird Friendly With Nesting Bricks.  In it he describes a new brick specially designed by Aaron Dunkerton and manufactured in England to provide habitat for nesting house sparrows.  Before mortar is applied it looks like this.  (Click on the bricks to read about them.)

House sparrows are the most widely distributed wild bird on earth.  Why are they so endangered in the U.K. that people invent ways to help them?  Here’s what I found out.

Since 1977 house sparrows have declined by 71% in Britain.  In some locations they are nearly extirpated.  London’s Kensington Park had 2,603 house sparrows in 1925.  By 2000 there were only 18.

Despite many studies a single cause has not been found and no other urban/suburban bird has experienced a similar decline.

In 2005 Kate E. Vincent published a house sparrow population study.  In 2009 Lorna Margaret Shaw investigated the role of neighborhood socio-economic status in house sparrow abundance.  These studies found:

• The greatest house sparrow declines occurred where nestlings starved within a week of hatching or had low fledging weight, both due to lack of insect prey.  The best success occurred where they ate plenty of aphids or spiders.  (Aphids come up again!)
• Because house sparrows nest in holes in buildings, they did well in neighborhoods built before 1919, in neighborhoods where soffitt and fascia were made of wood, and in distressed neighborhoods where the buildings needed repairs.  They avoided neighborhoods built after 1985 because of new construction standards and lack of deterioration.  That’s why Aaron Dunkerton invented the bird brick for new homes.
• House sparrows did poorly in tidy neighborhoods with lots of paving.  Over the years Britons have paved their front yards and removed trees and shrubs so they can park their cars.  This has reduced house sparrow habitat.
• All habitat was not equal.  House sparrows preferred deciduous plants and the insects associated with them.
• House sparrows did not use ornamentals or evergreens.  This lead to a headline that Leylandii hedges were to blame for the house sparrow decline.  (A fascinating topic…more on that tomorrow.)

With so many factors in play there’s no simple answer to the house sparrow’s mysterious disappearance.  In the meantime they continue to decline and Britons miss them terribly.

If it would work I’d package some of ours and send them to England.  We have a house sparrow surplus right now.

(photo of a house sparrow in California from Wikimedia Commons. Nesting bricks by Aaron Dunkerton.  Click on the images to see their originals.)