The reserve had counted five hundred nesting birds in its first survey. Four years later, after two dry summers, the count was three hundred. That is a fall of forty percent, and it was reported as such in the annual report.
Then the wet years returned and the birds came back. The next survey found four hundred and twenty — a recovery of forty percent on the previous count.
A local newspaper ran the two figures together and wrote that the population had fallen forty percent and recovered forty percent, and was therefore back where it started.
It was not. Four hundred and twenty is not five hundred. The reserve's ecologist wrote a short letter explaining why, and she did not use a single formula.
The first forty percent, she wrote, was forty percent of five hundred — two hundred birds. The second forty percent was forty percent of three hundred — only a hundred and twenty. The loss and the gain carry the same percentage and completely different numbers of birds, because they are measured against different starting points.
She added one line at the end, because she knew it would be quoted: a percentage without its base is not a fact, it is half of one.
The population is at eighty-four percent of the original. That is genuinely good news after two dry summers. It is not the same as a return, and the reserve's funding depends on the difference.