. The English sparrow has been on this continent little more
than fifty years; it has found the conditions in this country favorable
because few natural enemies like those of its original home have been met,
and as a consequence it has multiplied at an astounding rate so as to
invade nearly all parts of North America, driving out many species of song
birds before it. About twenty years ago David Starr Jordan wrote that if
the English sparrow continued to multiply at the natural rate of that
time, in twenty years more there would be one sparrow to every square inch
of the state of Indiana; but of course nature has seen to it that this
result has not come about. A single conger-eel may produce fifteen million
eggs in a single season, and if this natural rate of increase were
unchecked, the ocean would be filled solid with conger-eels in a few
years. Sometimes a single tapeworm, parasitic in the human body, will
produce three hundred million embryos; the fact that this animal is
relatively rare diverts our attention from the alarming fertility of the
species and the excessive rate of its natural increase. Perhaps the most
amazing figures are those established by the students of bacteria and
other micro-organisms. Many kinds of these primitive creatures are known
where the descendants of a single individual will number sixteen to
seventeen millions after twenty-four hours of development under ordinarily
favorable conditions. Though a single rodlike individual taken as a
starting-point may be less than one five-thousandth of an inch in length,
under natural circumstances it multiplies at a rate which _within five
days_ would cause its descendants _to fill all the oceans to the depth of
one mile_. This is a fact, not a conjecture; the size of one organism is
known, and the rate of its natural increase is known, so that it is merely
a matter of simple arithmetic to find out what the result would be in a
given time.

Even in the case of those animals that reproduce more slowly, an
overcrowding of the earth would follow in a very short time. Darwin wrote
that even the slow-breeding human species had doubled in the preceding
quarter century. An elephant normally lives to the age of one hundred
years; it begins to breed at the age of thirty, and usually produces six
young by the time it is ninety. Beginning with a single pair of elephants
and assuming that each individual born should live a complete life, only
eight hundred years w