  A key aim in biology and psychology is to identify fundamental principles
underpinning the behavior of animals, including humans. Analyses of human
language and the behavior of a range of non-human animal species have provided
evidence for a common pattern underlying diverse behavioral phenomena: words
follow Zipf's law of brevity (the tendency of more frequently used words to be
shorter), and conformity to this general pattern has been seen in the behavior
of a number of other animals. It has been argued that the presence of this law
is a sign of efficient coding in the information theoretic sense. However, no
strong direct connection has been demonstrated between the law and compression,
the information theoretic principle of minimizing the expected length of a
code. Here we show that minimizing the expected code length implies that the
length of a word cannot increase as its frequency increases. Furthermore, we
show that the mean code length or duration is significantly small in human
language, and also in the behavior of other species in all cases where
agreement with the law of brevity has been found. We argue that compression is
a general principle of animal behavior, that reflects selection for efficiency
of coding.
