14 | New Scientist | 21 September 2019News
Biodiversity MathsMichael Le Page Ben SkuseWE ALMOST have a solution to
a fiendishly tricky mathematical
riddle first posed 82 years ago.
The Collatz conjecture is easy to
state. Start with any positive whole
number. If it is even, divide it by 2.
If it is odd, triple it and add 1.
Whatever the result, follow the
same steps as before, again and
again, building a sequence. The
conjecture says that whatever
number you start with, you
eventually get 1 as the answer.
The sequence can be depicted
visually to show lines all wiggling
their way back to the same spot.
This looks a bit like fronds of waving
seaweed or a pile of wiggly worms.
The conjecture has been verified
up to the starting number of 10^20
(100 quintillion). However, proving
it absolutely involves not just
checking more numbers but also
finding a reasoned mathematical
explanation that it is always true.
Now Terence Tao at the
University of California, Los
Angeles, seems to have almost
got that. His work builds on that of
other researchers, who proved that
almost all sequences were at least
able to reach an intermediate value
between their starting number n
and 1. This means they can’t
balloon to infinity.
Tao has managed to go further
(arxiv.org/abs/1909.03562).
“I showed that one could move
this intermediate milestone to be
as close as one wishes to the final
goal 1 for almost all n,” he says.
Jeffrey Lagarias at the University
of Michigan says Tao’s work is “the
most significant progress on the
problem in many years”.
However, Tao says there is little
hope of using his methods to find
a complete proof. He writes that
this is “well beyond [the] reach of
current methods”. This is because
he relies heavily on techniques from
probability theory, meaning there
is always a small chance of failure. ❚Riddle that looks
like a pile of worms
is nearly crackedBEES can be harmed by low
levels of neonicotinoid
pesticides, and now it seems
birds can too. Migrating white-
crowned sparrows have been
found to lose weight after eating
seeds treated with one of these
chemicals, imidacloprid,
delaying their onward
migration by several days.
Such a delay could hamper
their chances of successfully
breeding. However, the main
manufacturer of the pesticide
disputes the findings.
The latest twist in the debate
over neonicotinoids is the result
of work by Christy Morrissey at
the University of Saskatchewan
in Canada and her team. They
caught migrating sparrows,
tagged them with tiny radio
transmitters and gave them
feed containing imidacloprid
or an alternative without the
chemical. The birds given the
pesticide lost up to 6 per centof their body weight in the
6 hours before release, whereas
the other birds hardly lost any.
Scans also showed a decline in
body fat among the first group.
When released, the birds not
fed imidacloprid continued
their migration after half a day.
Those given the pesticide took
four days, on average, to do the
same (Science, doi.org/dbg6).Morrissey says she also has
unpublished evidence that
two other neonicotinoids
have similar effects.
Birds that arrive late at
breeding grounds are less
likely to raise young successfully
and may not breed at all, says
Morrissey. “This has serious
impacts on populations.”The study shows sublethal
doses of neonicotinoids
can have adverse effects on
seed-eating birds as well as
on beneficial insects such as
bees, says Caspar Hallmann
of Radboud University in the
Netherlands. “Birds – especially
small birds – are really
dependent on having sufficient
body fat during migration.”
The findings are disputed by
Bayer, the main manufacturer
of imidacloprid. Real-world
neonicotinoid exposure levels
are far below those that disrupt
migratory behaviour, and the
pesticides are safe when applied
according to instructions, says
a Bayer spokesperson.
Morrissey says the birds were
given realistic amounts. They
could get the highest dose given
in the study by eating just one-
tenth of a treated maize seed,
a fifth of a soya bean or three
canola seeds, for instance. “It’s
tiny, tiny amounts,” she says.
In North America, 57 of the
77 bird species associated with
farmland are in decline, with
neonicotinoids one possible
factor. However, Morrissey says
that banning these pesticides
isn’t the answer because
farmers will just use alternatives
that may turn out to be as bad.
Instead, we need to find ways
of farming that don’t rely on
quick chemical fixes, she says.
“The regulatory system
keeps failing, by allowing new
harmful chemicals into use,”
says Dave Goulson at the
University of Sussex in the
UK. “The only long-term
solution is to move away from
a reliance on pesticides to solve
every problem.” ❚Pesticides could be partly
to blame for bird decline
KURT STRICKER/GETTY
The white-crowned
sparrow is a native of
North America57
out of 77 species of farmland bird
in North America are in decline