Some South African rangers grimly call it the "Christmas shopping" season for rhino poachers.

They are referring to an annual phenomenon in which poacher incursions into Kruger National Park, South Africa's flagship wildlife reserve, escalate in the final months of the year before tapering off around the year-end holiday season.

Reflecting that trend, rangers killed three in the past week in a flurry of shootouts in Kruger, the national parks service said. Three poachers were wounded and arrested in another firefight. Six others escaped in the various incidents.

"There is definitely an increase compared to previous months in the number of poachers coming into the Kruger park," Paul Daphne, a parks spokesman, said Saturday. "It's not unusual for this time of year."

Many poachers cross into Kruger from neighboring Mozambique. Demand for rhino horn is surging in parts of Asia where it is seen as a status symbol and a cure for illness despite a lack of evidence that it can heal. The horn is made of keratin, a protein also found in human fingernails.

More than 1,000 rhinos have been killed this year in South Africa, two-thirds of them in Kruger park, according to government figures. South Africa is home to most of the world's rhinos.

The surge in poaching and then the drop at year-end could be linked partly to the holiday period when people spend time with family, according to conservationists. Also poachers prefer to operate in the southern African summer months toward the end of the year, when there is more foliage to hide in and rain showers can cover poachers' tracks, said Daphne. Poaching tends to increase sharply after any Christmastime dip, he said, while the rate drops again in the midyear winter when it is dry and there is less bush cover.

Some 164 suspected poachers have been arrested in Kruger park in 2014, about 30 more than last year, according to the government. More are arrested outside the 's boundaries.

Some criminals are "redirecting their attentions" to rhino poaching because they believe the rewards are greater, said Daphne.