CSIRO
statistician Dr Mark Bravington has been counting invisible whales in
the Southern Ocean, the ocean that encircles Antarctica.
Can
you count something you can’t see? Statisticians can and they do it all
the time. No, they’re not dreaming! They’re just using some clever
maths.
Help! Some of my data is missing!
Working out
the number of whales in the oceans when you can’t see all of them is a
typical example of the 'missing data' situation that statisticians deal
with a lot of the time.
Statisticians use mathematics to work
out how an entire population can be discovered by studying a small part
of it, called a 'sample'. If you’ve ever filled in a questionnaire, you
will have been in a sample – a group of people whose responses are used
to estimate what the entire population thinks.
Surveying animals
(the non-human sort) is a bit trickier. Animals can’t write on a
questionnaire (Please put one paw print for 'yes', two for 'no'!).
When
studying wildlife populations, for example, biologists sometimes use a
technique called a 'mark-recapture' experiment. It’s a common way of
estimating the size of a particular population of animals (all the
animals that live in an area) by tagging just some (a sample).
Biologists
catch a sample of animals, tag them, and let them go. Later they catch
some more animals and see how many of them are tagged. If there are
very few animals in the population, they will probably re-capture
mostly tagged ones. If there are lots of animals in the population,
they probably won’t.
Counting whales uses a similar technique,
but it’s slightly different because whales can’t really be caught,
tagged, released and re-caught!
Now you see them, now you don’t
Why
count whales at all? One reason is that whales were hunted commercially
for more than a hundred years, and there is a lot of international
debate about whether whale populations are recovering or not. Countries
like Japan and Norway claim some whale species are numerous and should
be hunted; but countries like Australia say they are still endangered.
Who is right? How can you find out how many there really are? You could
try to count them all. But it’s not so easy.
The Southern Ocean
is huge – 20 million square kilometres. Even if you could search the
entire area, whales only come to the surface for air now and again; and
if you pass by too quickly, or if the weather makes it hard to see, you
might miss them.
Dr Mark Bravington from CSIRO has been working
with the Australian Antarctic Division in Hobart to estimate whale
populations from the numbers seen from whale survey ships. Two separate
teams of observers on the deck of the whale survey ship look for whales
through binoculars. When they see a whale, they write down how far away
it was.
The ship travels slowly enough so that every whale in that area comes to the surface to breathe at least once.
'Even
so, it’s likely that some whales close to the ship will be overlooked,
especially if they are in smaller groups, or if conditions are rough.
The first thing to do is to estimate how many nearby whales were
missed,' says Mark.
'We check how many whales were seen by both
teams versus how many were seen by only one team. That lets us estimate
how many whales were seen by neither team – the 'invisible whales'.'
By
solving this mathematical challenge, Mark has provided more reliable
ways of estimating whale numbers, which will help us understand if and
how whale populations are recovering.
By Ms Carrie Bengston
Read more about Antarctica at Polar eyes.
