When DNA test results shattered everything Lavinia and Michelle thought they knew about their family history, they also revealed something never before documented in the UK

I like being a twin. It defines who I am,” Lavinia Osbourne tells me on the 49th birthday she shares with her sister, Michelle. “It’s amazing to have a twin and have a built-in friend for ever,” Michelle says. “I’ve been really blessed to go through this journey with someone else.”

Lavinia and Michelle know that those of us who haven’t shared a womb with a sibling can be fascinated by twins: their similarities, how they differ, whether there’s any kind of mysterious synergy between them.

The social and economic impact of people living longer and having fewer babies is hitting countries worldwide. Adaptation is key

In Japan, there are now companies that specialise in cleaning the apartments of elderly people who have died alone and gone undiscovered for weeks or months, while adult incontinence pads have outstripped nappy sales for more than a decade. In Italy, depopulating villages are selling homes for €1 to attract new residents and keep services running. In the UK, falling pupil numbers are already closing schools and classrooms in parts of London.

These are not isolated curiosities, but signs of a broader shift taking place across much of the developed world. “In the EU in 2024, 21 of 27 countries had more deaths than births,” said Prof Sarah Harper, the director of the Oxford Institute of Population Ageing. Across Asia and the Americas, too – from Japan and South Korea, to Cuba and Uruguay – many countries are seeing the same pattern.

Josh, 30, a video game designer, meets Hannah, 31, an architectural lighting designer

What were you hoping for?
A fun evening and easy chat with an interesting and unique human being.

The East West Rail project linking Oxford to Milton Keynes was finished in 2024. There’s just one hitch: no services

The rumbling noise in the night, still enough to waken the unhabituated, is what really goads some people living in Winslow, Buckinghamshire. Freight trains running through the new station since late 2024 prove this stretch of railway is operational. But the long-promised passenger services have yet to appear – and there is no sign of any arriving soon.

Welcome to East West Rail, open or not. For well over a decade, ministers have talked up a new railway linking Oxford to Cambridge via Milton Keynes to accelerate the drive for housing, jobs and growth – an arc of tech industry hailed as the UK’s answer to Silicon Valley.

Charles III’s subtle, much needed history lesson delivered the US some tough love. But will Trump get the message?

Of the many jokes cracked by King Charles during his visit to Washington, the one recalling the definitive 18th-century Anglo-French contest for dominion over the New World was the most pointed. Speaking at a state banquet in the White House, Charles turned to Donald Trump and said: “You recently commented, Mr President, that if it were not for the United States, European countries would be speaking German. Dare I say that, if it wasn’t for us, you’d be speaking French!”

Did Trump get it? Who knows? Broadly speaking, history, even their own, is not most Americans’ favourite subject. A forward-looking people, they do not dwell on the past, nor hanker after the illusory felicities of former glories. While generations of Britons still wallow in nostalgia for Spitfires, Churchill and Vera Lynn (and beating the French), Americans typically seek new metaphorical mountains to climb. Theirs is a positive outlook, on the whole. Except, under Trump, it has twisted into a revived, ugly version of US “manifest destiny” imperialism.

Simon Tisdall is a Guardian foreign affairs commentator

With a fast-expanding membership and electoral gains in sight, the Israel–Palestine debate is testing party unity

A Green party member for more than 30 years, Elise Benjamin admits to bittersweet feelings even as fellow activists anticipate a historic breakthrough in next week’s elections.

Benjamin was involved in drawing up the party’s guidance on antisemitism, which she describes as comprehensive. But the former Green councillor in Oxford now wonders whether further guidance is needed: “Now that we have such a large membership, I think there needs to be an urgent review of how to make our complaints process fit for purpose.”

Exclusive: Greater Manchester mayor said to have identified seats where MPs would step aside to allow leadership bid

• ‘No other plan comes close’: Labour MPs turn to Burnham as pressure mounts on Starmer

Andy Burnham has a credible plan to return to Westminster “within weeks”, his allies have said, with the Greater Manchester mayor expected to use a byelection fight to set out a new agenda for government.

Burnham, who was blocked by Labour’s ruling body from running in February’s Gorton and Denton byelection, has identified several seats where MPs are prepared to step aside for his leadership bid.

US president says European countries are ‘absolutely horrible’ to refuse to support operations in strait of Hormuz

• Why does the US have military bases in Germany?

• Trump tells Merz to ‘fix his broken country’ in new attack on German chancellor

The US is withdrawing 5,000 troops from Germany, the Pentagon announced on Friday, as Donald Trump also threatened Italy and Spain for not helping to reopen the strait of Hormuz.

The president’s move to reduce the number of personnel deployed in Germany came after the country’s chancellor, Friedrich Merz, said the US was being “humiliated” by Iran.

Green leader apologises for sharing post that said officers were ‘repeatedly and violently kicking a mentally ill man in the head’ and says he had did so ‘in haste’

Keir Starmer has condemned Zack Polanski as “disgraceful” and unfit to head a political party after the Greens’ leader shared a social media post critical of the way police tackled the suspect in the Golders Green stabbings.

The prime minister said any criticism of the police involved in the arrest was unfair on officers having to make split-second decisions in a moment of potentially grave danger.

Staff warned news operations face 15% cut, above BBC-wide 10% target, as corporation pushes through £600m savings plan

The BBC’s news operation is to cut costs by a steeper-than-expected 15%, with staff told to expect heavy redundancies.

The division, home to about a quarter of all BBC staff, is being saddled with one of the highest cost-cutting targets as the corporation attempts to cut as many as 2,000 jobs in the biggest downsizing of the public service broadcaster in 15 years.