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37
february2014
© 2014 The Royal Statistical Society
And it even seems to apply to the wealth and pov-
erty distribution of the world as a whole – see Visualisa-
tion on page 39 of this issue.
e phenomenon occurs so often it is now known
either as the “Pareto principle” or “Pareto’s 80–20 rule”
or, even, with a philosophical bent, “the law of the vital
few”. You could say that 80% of wealth is often owned
by 20% of the population; but it seems more general
than that. One economist has even said that 80% of
complaints to a company come from 20% of its cus-
tomers. (He added that companies should ditch such
customers, but we need not go there.) Stated in simple
terms, Pareto’s heuristic states that 80% of the outcomes
of interest are often due to 20% of the possible causes.
Although the Pareto principle (or, more generally,
the Pareto distribution) has been observed numerous
times in management and economics (a quick Google
search will convince you), more recently it is also being
used in scientific studies. Ecologists Seuront and Mitch-
ell3 have used Pareto laws to study marine ecology. ey
list phytoplankton growth processes and differential
grazing by zooplankton among the interactive systems
to which Pareto applies.
Which is where our small case study comes in. We
examined the results of the Brookhaven National Labo-
ratory bird data set that we mentioned at the start. e
Brookhaven survey site is a small one. It occupies only
8.23 square miles. We also examined the comprehensive
Even birds follow
Pareto’s 80–20 rule
Bird watching is massively popular throughout the
world. According to the Cornell Lab of Ornithology,
there are over 800 species of birds just in the United
States and Canada1. In New York State there are at least
185 species of birds present. Bird sampling, a formal
form of bird watching, is an important technique used
by environmentalists to help assess environmental ac-
tivity. In a 13-year ongoing survey at Brookhaven Na-
tional Laboratory, researchers have so far noted roughly
125 different species. However, only a relatively small
percentage of the species accounted for a large percent-
age of the total observed bird population. Does that
sound familiar?
In an entirely different intellectual domain, ana-
lysts often point to the “Pareto principle” to get across a
similar notion in a competitive economic environment.
Vilfredo Pareto (1848–1923), an Italian economist,
made the observation that 80% of the wealth in Italy
is owned by 20% of the population. is principle has
also been noted in much older economies. A paper
in Nature bears the title “Few had wealth in ancient
Egypt”2. e author studied the remains of the city of
Akhetaten, which briefly flourished in the 14th century
. ey gauged the wealth of its people from the floor
area of their houses. And – guess what? e 80–20
ratio turned up there as well. e biggest houses – the
top 20% of them – took up 80% of the housing area of
the city
Vilfredo Pareto noted in 1906 that 80% of the land in Italy was
owned by 20% of the population – and that the ratio seemed to
apply to many countries, many time periods, and many economies.
But is it more than a useful rule of thumb? Pareto also observed that
20% of the pea pods in his garden contained 80% of the peas. His
ratio seems to pop up everywhere. Fred J. Rispoli, Suhua Zeng,
Tim Green and Jennifer Higbie try telling it to the birds.
Is it a
fundamental law
of competition, or
just an oddity that
crops up? Either
way, bird-watchers
could take note
38 february2014
North American Breeding Bird Survey4, to
look at the much larger area of New York State,
which covers 54 000 square miles. We studied
the yearly data, which covered the 13 years from
2000 to 2012. And we found the Pareto 80–20
rule holding true: 80% of the birds that were
seen belonged to 20% of the species that were
seen. It held on a year-by-year basis, and for the
whole time period; and it held on the small scale
of the Brookhaven site, and on a much larger
scale in the New York State data set. A sum-
mary of our data set is given in Table 1.
Whether it is people competing for finan-
cial resources or birds competing for natural
resources, an unequal, skewed distribution is
inevitable. What is so surprising is how often
the top 20% of the species, or causes, is respon-
sible for very close to 80% of the population, or
outcomes. It appears that the Pareto principle
may be a fundamental law of competition.
References
1. http://cams.allaboutbirds.
org/
2. Ball, P. (2002) Few had wealth in ancient
Egypt. Nature online. doi:10.1038/news021125-8.
3. Seuront, L. and Mitchell, J.G. (2008)
Towards a seascape typology. I. Zipf versus Pareto
law. Journal of Marine Systems, 69, 310–327.
4. Sauer, J. R., Hines, J. E., Fallon, J. E.,
Pardieck, K. L., Ziolkowski Jr., D. J. and Link,
W. A. (2011) e North American Breeding Bird
Survey, Results and Analysis 1966–2010. Version
12.07.2011. Laurel, MD: USGS Patuxent Wildlife
Research Center.
Fred J. Rispoli is Professor of Maths and Computer
Science at Dowling College, Long Island, New York.
Suhua Zeng is at the Department of Mathematics, New
York City College of Technology. Tim Green and Jen-
nifer Higbie are at Brookhaven National Laboratory,
Long Island, New York.
Table 1. We looked at data each year during the period 2000–2012, identified the 20% of the species with the
largest populations at the Brookhaven National Laboratory (BNL) and New York State (NYS) sites, and then
determined what percentage of the total population is due to the top 20% of the species
Year Percentage of BNL population
from top 20% of species
Percentage of NYS population
from top 20% of species
2000 73% 81%
2001 77% 81%
2002 76% 80%
2003 80% 80%
2004 77% 81%
2005 74% 80%
2006 79% 81%
2007 75% 81%
2008 77% 80%
2009 74% 80%
2010 71% 81%
2011 73% 80%
2012 76% 80%
A blue jay (Cyanocitta cristata), one of the 20% of common species that make up 80% of bird sightings. Photo: Saforrest
