Can a country put a fixed limit on its population? That is the question Switzerland will be answering on Sunday when voters go the polls to decide on a proposal to cap their population at 10 million, a move that has exposed divisions about immigration in the Alpine nation.

The move is backed by the right-wing Swiss People's Party, which describes it as a "sustainability initiative" aimed at easing pressure on housing, public services and the environment.

Dubbing it a "chaos initiative", the government, other political parties, business leaders and trade unions argue it will deprive hospitals and hotels of much needed staff, and damage hard-won relations with the European Union, leaving non-EU member Switzerland isolated in a very risky world.

Switzerland's population has grown rapidly since 2002, when it stood at 7.3 million. Now it is 9.1 million, 27% of whom are Swiss residents who were born abroad.

Switzerland's system of direct democracy means all major decisions are taken via the ballot box. Campaigners simply have to gather 100,000 signatures to ensure a nationwide vote.

Many voters are concerned by overcrowded trains, expensive apartments and rising health costs.

The latest opinion polls indicate this could be a very close vote.

They suggest voters are inching towards a no vote by a wafer thin margin, with 52% opposed - but polls remain divided, with 45% saying they are in favour of the proposal and a significant number of voters still undecided.

Helin Genis and Nils Fiechter have a good deal in common, but their diametrically opposed views on limiting the Swiss population are indicative of the polarised nature of this referendum.

Both are young local politicians from immigrant families. Fiechter is 29 and Genis is 31. Helin's parents are originally from Turkey, while Nils's mother is from Canada and he holds dual citizenship.

"We have lost control," complains Fiechter, who represents the Swiss People's Party in canton Bern's parliament. "Unchecked immigration is leading to Switzerland no longer being Switzerland."

He believes Switzerland's problems, which he says include a "housing shortage, gridlocked traffic, overburdened schools and strained social services", are a direct result of immigration.

Genis, who is a Social Democrat elected to Bern city council, dismisses these arguments as scapegoating.

She tells BBC News: "It is not migrants who determine rent levels. It is not migrants who raise health insurance premiums. Nor is it migrants who make political decisions on housing, infrastructure or social investment."

Viewing problems '"through the lens of migration does not lead to solutions, but to division", she adds.

For voters who have not yet made up their minds, a key question is how exactly a population cap would work.

Putting a hard limit on the number of residents is not a measure any other country has tried, although China, through its now abandoned one-child limit, did try to slow population growth.

The Swiss proposal says the population must not exceed 10 million before 2050, and orders the government to take measures once the figure of 9.5 million is reached.

Such plans could include limiting the number of people granted asylum in Switzerland, and ending family reunification rights for foreign workers.

If the 10 million cap were to be reached, international agreements which Switzerland has signed up to, including the EU's free movement of people, would have to be terminated.

This prospect has caused alarm at Switzerland's business association, Economiesuisse.

Its chief economist Rudolf Minsch says that if the motion is passed, Switzerland "could face challenges in our relations with the European Union".

That is because Brussels has long warned non-EU members that they cannot simply cherry-pick the advantages of the EU's single market, and wriggle out of commitments like free movement of people.

"The EU is still by far the most important trading partner for Switzerland," explains Minsch, adding that is it is "in our interest to have stable and clear relationships with our main trading partner".

Swiss employers are also worried about labour shortages, and losing access to a Europe-wide pool of skilled workers.

Half of all those who work in Switzerland's hotels are immigrants. Hospitals and care homes are also reliant on foreign workers.

The Swiss People's Party argues that immigration to Switzerland is simply fuelling an ever-increasing demand for more hospital beds and more places in schools, and that limiting immigration would ease the pressure.

Opponents say this is unrealistic, pointing to 20% of the Swiss population now being over 65.

Young workers, and young taxpayers, are required to staff and fund the needs of an ageing population – and Switzerland is not creating those young workers itself, they warn.

Jon Pult, a member of parliament for the Social Democrats, says his biggest fear about a population cap is being "alone in this unstable and dangerous world".

Switzerland, like its neighbours in Europe, is spending more on defence, and despite its neutrality, is planning closer defence ties with its neighbours.

It has been affected by rising fuel prices because of both Russia's invasion of Ukraine, and the conflict in Iran. It has also seen its products hit with punitive US tariffs.

Switzerland could jeopardise its treaties with the EU, and possibly lose goodwill from Brussels along with them, Pult warns.

Fiechter dismisses this as fearmongering, saying he is "certain that the EU will not allow this to happen", and arguing that the agreements with Switzerland are "entirely in the EU's own interest".

But fear of isolation may be a deciding factor for some voters.

The Swiss were horrified when Washington slapped 39% tariffs on Swiss goods, and an agreement to get them lowered to 15% has still not been finalised.

Now, posters urging voters to reject the population cap show a leering US President Donald Trump, with the shadowy profiles of Russia's Vladimir Putin and China's Xi Jinping behind him.

"Break with Europe, at a time like this?" the poster's headline asks.

Fiechter insists capping the population is all about protecting a way of life.

He said: "Anyone who loves Switzerland, whether with or without a migrant background, wants it to remain a place worth living in, safe and prosperous. That is exactly what this initiative is about."

But Genis cannot see anything positive about it: "The key question is not how to exclude people... [it is] how we create enough affordable housing, ensure good working conditions, and invest in a strong public service.

"That's why I am convinced this initiative does more harm than good to Switzerland."