Across the rich world, almost every state faces a version of the same problem: their people are living longer and having fewer children. Every year, tens of thousands of citizens will hit state pension age or retire, and fewer of us are having enough children to maintain our care-dependency ratio (the number of working people supporting those who are too young, too old or too sick to work themselves) at a point that provides the standard of public services and the levels of tax that modern electorates have grown accustomed to.

Immigration is how states have filled the gap. In the UK, overseas students have allowed universities to stay open even as domestic fees have been subjected to a long period of sharp, real-terms cuts. Immigration has filled vacancies in the country's care and construction sectors, both of which cranked up under Boris Johnson's premiership, alongside the expansion of one-off humanitarian routes for people from Hong Kong and Ukraine. Although being "foreign-born" -- a category that includes, for instance, Johnson, a Brit born in the US -- is an imperfect proxy for immigration, it is a fairly useful one. Most wealthy states now have more immigrants than ever before. David Bull, the chair of the rightwing populist party Reform UK, has himself described immigration as the "lifeblood" of the country.

But politicians have a problem: immigration is the subject of fierce political opposition. Alongside inflation, anger at the Democrats' failure to control the southern border with Mexico was a major reason for Donald Trump's return to power in the US. Trump, who has promised to deport more than 15mn people, is the leader haunting many European policymakers.

In the UK, France and Germany, a party of the nativist right has been leading in polls, in part because of opposition to immigration. Not all opposition to immigration is about prejudice -- very few of us react well to sudden change, which is in part why opposition to immigration tends to be highest not in places with a lot of immigration, but where there has been a sudden increase in the rate of the change.

London is an excellent example -- opposition to immigration was much higher in the 1950s, 1960s and 1970s, when the capital had far less of it than it does today. But now, few Londoners expect anything else than to live in a diverse, multiracial city and so changes in the scale of immigration are much less politically controversial than they were before.

And the societal-wide benefits of immigration do create some losers: migration that fills up holes in the labour market and keeps inflation low benefits essentially everybody, but it does, inevitably, create downward pressures on wages at the bottom of the income distribution, from NHS porters to deliverymen.

Some opposition to immigration is simply based on pure prejudice and hostility to ethnic diversity. Left and centre-left politicos have drawn great hope from research showing that opposition to immigration is highest in areas that feel "rundown" -- but the same study shows that one thing people see as a sign of an area going to the dogs is the arrival of immigration.

The history of immigration in the modern world has long had cycles of opening up and shutting down. When my great-great-grandparents arrived in the UK in the late 19th century from what was then the Russian empire, there were no passports and only the cost of travel separated people from living where they pleased. Opposition among the established population to the arrival of Jewish immigrants like them led governments to introduce the first modern passports. Since then, the history of British immigration policy, and indeed that of much of the rest of the world, has been of borders coming up and being rolled down with the political tide.

The difference now is that rapidly ageing societies' ability to pursue the periods of feast and famine in immigration policy face greater constraints than in the past, precisely because they are older and their need for extra labour greater. At the same time, irregular migration is fuelling opposition to all forms of migration. Frontier states, like Italy or, after Brexit, the UK, have become particularly exercised by maritime crossings, whether across the Mediterranean or the English Channel.

Democracies risk falling into a doom loop, in which restrictions on immigration mean ever greater demands on the purse of the native-born population and ever worse services, which in turn deepens opposition towards immigration and therefore creates yet greater pressures, and so on.

How to break the doom loop? Different countries, and different electorates with different demands, will be able to take different approaches. For decades, Japan has had much lower rates of immigration than other rich countries, something made possible because its pensioners have lower incomes than their peers. In the UK, where the country's elderly voters, the group most opposed to high levels of immigration, have twice revolted at the idea that the winter fuel allowance should be restricted to the poorest pensioners, there is no credible path to trade lower standards of living for lower rates of immigration.

On the centre-left, one country is increasingly talked of as an example of how to do it: Denmark, where the Social Democrats have moved sharply to the right on immigration, and retained power as a result. But there are many reasons why "just do a Denmark" is not an option for most other countries. Denmark is not a frontier state: none of the global movements of migration reach Denmark first, and it is easier for the country to shut its doors. Electorally, the Danish electoral system means that votes gained by the Danish Social Democrats from the right, even at the cost of shedding votes to their left flank, are worth more.

For the British Labour party, which governs a country on the EU's frontier, losing voters to the other parties of the left, such as the Greens, or the centre, like the Liberal Democrats, is not a painless transfer of support across the bloc but a damaging loss of much-needed support. In addition, it is far from clear whether Denmark will be able to continue to maintain its current approach, or if labour shortages will force it to loosen its borders.

On the centre-right, there are two countries that are held up as examples to look at: Australia and Italy. Liberal party-led governments in Australia did manage to "stop the boats", though they were helped by geography and favourable geopolitics. Stopping the boats has rested in part on being able to outsource the problem to Papua New Guinea and the Pacific island of Nauru. Europe's democracies have in a sense already done this, by outsourcing some of their border management to Turkey and to the governments that run parts of Libya.

Italy may well represent a more stable equilibrium. Giorgia Meloni, the prime minister, has kept immigration high but she has managed to hold on to political support and an opinion poll lead by sharply limiting paths to citizenship, and like Denmark, to family reunion. She has in part been able to do this because her party is trusted on immigration, just as the centre-left still was when Denmark's Mette Frederiksen began moving her party to the right on the issue. But most European centre-left parties, whether the German SPD or the British Labour party, are now so untrusted on the topic of immigration that the deal of having large numbers of migrants with limited visas may not be one they can persuade their voters to swallow.

And not every option that polls well in the abstract is one that people welcome in practice. In the UK under Tony Blair, New Labour offered something similar to Meloni's "high immigration, high cruelty" approach: immigration went up, but asylum seekers faced new limitations on their ability to work while their claims were processed. As a result, in the here and now, asylum seekers spend their time waiting for an application holed up in temporary accommodation of one kind or another, in the receipt of heavy public subsidy.

The UK is still an integration success story, across a range of metrics. There are areas where it does not do well, such as the high proportion of people in Bradford's Pakistani community who marry close cousins; even here the numbers are improving. But the long-run success of integration happens in the labour market, and just as Sweden's decision in the 1980s to change how asylum seekers were integrated into the welfare system has created integration challenges, not letting asylum seekers work in the UK is creating problems of its own.

The obsessive focus on raw numbers, and on cutting down on dependants, may mean ministers can boast that essentially everyone who comes to the UK does so to fill a specific vacancy. But it also means more areas where the immigrant population consists of solitary men, who are either single or miles from their families, neither of which local residents want, and is, again, bad for integration. Has Dubai, which has much higher numbers of immigrants but essentially no permanent path to citizenship, really done a better job of integrating people and preserving its identity than the UK has?

What governments need to do is to be clear-eyed and honest about what they are choosing, and that every immigration policy comes with trade-offs, whether in terms of integration, labour market outcomes, or how areas are changed by migration. They need to be willing and able to argue for options that can be delivered in the real world -- not retreat to fantasies that ageing societies can protect their prosperity without immigration, or that any form of immigration policy can be made free of cost or friction.

The truth about immigration