Norfolk Islanders are deeply concerned about the 2016 census, which shows the number of residents with Pitcairn Island heritage has declined dramatically in the past five years.

They are suspicious of the result, and say it hurts their attempt to challenge the Australian government’s abolition of their parliament and laws.

They say the United Nations process they are engaged in, which may result in the community being entitled to self-determination, hinges on them being able to argue that the Norfolk Island community is ethnically and culturally distinct from Australia.

But the 2016 census could undermine their efforts because it shows there are only 484 people on the island who claim Pitcairn descent, down from 690 people in 2011 – representing a 30% decline in five years, which they refute.

In an official response to questions about the census, an Australian Bureau of Statistics (ABS) spokesman said the results were “broadly in line” with previous censuses on the island.

Norfolk Island controversially ceased being an autonomous territory on 1 July 2016 following a takeover of the island by the federal government.

The island’s population is now governed by the laws of New South Wales, but has no say in those laws. Its residents can only vote in federal elections in Canberra.

The 2016 census was the first time the ABS has included Norfolk Island in Australia’s official population count.

The last census on the island, in 2011, was run by the now-abolished Norfolk Island government.

Andre Nobbs, a former chief minister of the Norfolk Island government, says the 2016 census is contentious because it shows a huge decline in the number of people on the island who claim Pitcairn descent.

He says the result could hurt Norfolk Island’s attempt to challenge the Australian government’s recolonisation through the United Nations.

Nobbs says the census does not account for the political reality on Norfolk Island, where islanders are being forced to become Australian citizens before they can access Australia’s welfare system.

He says there is a suspicion that people who marked their ancestry as “Norfolk Island” in the census were simply counted as Australian, which suits the needs of Australia’s government.

“The census has picked up on the fact that all these people have suddenly become Australian citizens, so they’re no longer Norfolk Islanders ... which is not the case,” Nobbs said. “I think there’s a degree of willingness to misrepresent the situation.”

Norfolk Island’s business community is also concerned about the methodology used by the ABS to count the island’s population.

An email circulated by the Norfolk Island Chamber of Commerce in recent weeks, seen by Guardian Australia, says ABS officials who visited the island recently were unable to explain why the proportion of people on the island who claim Pitcairn descent fell so dramatically between 2011 and 2016.

It says an ABS official told the chamber that the ABS may re-examine the issue, and consider publishing a separate paper with adjustments and corrections.

An ABS spokesman told Guardian Australia that discussions between ABS officials and the Norfolk Island community were continuing, so nothing had been resolved.

“There were a number of differences between the 2011 Norfolk Island census and the 2016 Australian census, including in the way the census was collected, the census form, data processing and language and ancestry classifications,” the spokesman told Guardian Australia. “The ABS used the standard Australian form and process on Norfolk Island.

“The ABS provided additional supporting materials to Norfolk Island residents to help them respond to questions about ancestry and language, and undertook local engagement activities prior to census night to support full community participation.

“The results from the 2016 census on Norfolk Island are broadly in line with previous censuses on the island and the ABS is confident in the quality of the Norfolk Island census data.

“Following the recent census data seminars on Norfolk Island, the ABS has undertaken to work with the Norfolk Island community to assist with understanding of the census results and will provide further information through additional briefings.”