When Agatha Christie was a child, she would wake in the night convinced her father had died. She describes in her Autobiography how she would get up and creep to his bedroom and linger outside the door until she heard a reassuring snore. Only then could she go back to sleep.
I recognise this fear. It is a fear felt by many children who have older fathers. Mine was 56 when I was born, and he is 81 now, and I felt - and still feel - that same kind of vigilant, anxious devotion. Sometimes, I am secretly and irrationally afraid of answering the phone in case it will be bad news about him.
The number of children born to men over 50 is growing; this year it was 6,850, which works out at roughly 1 per cent of births. We learned this week that Gordon Brown, 55, is to become a father for the second time. Rod Stewart had his sixth at the end of last year at 60. Paul McCartney had his youngest in 2003 when he was 61 and David Jason had his first child, at 61, five years ago.
The list goes on - John Humphrys, Eric Clapton, Michael Douglas, Ken Livingstone and Des O'Connor all know the pleasures and trials of older fatherhood.
And their children will know them too. "I suppose it was an unconventional way to grow up," says Karen, 28, whose father is 76. "I never knew how old he was until I was half way through university. My parents never told me their age; I think they didn't want me to tell other people at school in case I was teased."
Professor Lorraine Sherr, of University College medical school, believes there is a stigma attached to "Saga dads". "Society is judgemental about childbirth," she says. "We're always saying people do it too young, or too old. But the fact is that with older fathers, we don't know.
"We know there are lots of good things associated with older mothers: they breastfeed for longer, their children have higher IQ measurements because they are stimulated and nurtured, their children tend to feel wanted. I believe this also applies to older fathers, although research is limited."
But an interesting older father is much more special than a young, hearty one. I am lucky to have a father who can sing me 1930s hits, tell me what it was like to be an officer in the Navy during the war, and explain to me exactly what the Suez crisis was. I sometimes treat him as a living encyclopaedia. I'm fiercely proud of the life he lived before I was born, if sometimes slightly disappointed I wasn't around to be part of it. But others I spoke to feel differently.
Roderick, 49, says: "I was always embarrassed by my father being born in 1897. The other kids couldn't believe it. They thought he was ancient history. I feel slightly as if I skipped a generation. I grew up in a basically Victorian household, church, discipline, my father handing his pay to my mother every week, sometimes giving me the odd whack with the hairbrush. It's a bit as if I've got the outlook of a much older person."
Can you spot children of elder parents? I have begun to think I have a radar for them. Often they know weird things someone of their age shouldn't know, say, the words to the songs of the 1954 musical Salad Days, or they have an old-fashioned style and over-decorous table manners.
Roderick has regrets about his father. "When I was a boy, I wasn't interested in talking to him about family history, or how he was sent home wounded from the Somme. Now I would love to have a great long chat with him. But he died when I was in my 20s. His death was difficult for me to come to terms with."
Like lots of children with an older father, Roderick was the first in his peer group to lose a parent. "Commonality of experience makes trauma a lot easier," says Lorraine Sherr. "It's always harder when no one else you know is going through what you're going through."
Being part of a minority of 1 per cent is bound to be lonely. And it can be tough, caring for an ageing parent in your twenties. If you're lucky, there may be other siblings to share the burden.
Equally, the child who arrives on the scene last often gets more quality time than the children who came before. "I can give him my full attention, because I've achieved everything I want to achieve in my work," one father in his fifties told me. Older fathers naturally tend to focus on the benefits of their maturity. But in a private moment, some will admit a sense of anxiety.
Michael, father to a baby boy at 53, has two older children from his first marriage. "Often men in my situation might not particularly want a baby, especially if they've already had children," he says. "But they wouldn't want to impose a childless relationship on their new wife, who might be in her thirties. Having a child in my fifties has been an overwhelmingly wonderful thing. Still, under the surface, you think, 'Is what I'm doing quite natural'?"
Mothers are warned that giving birth later in life means their children risk adverse health effects. But older fathers have been getting a rap too. In 2001, Professor Dolores Malaspina, of Columbia University, said she could prove there is a male biological clock after a study indicated that children born to men over 50 are three times as likely to have schizophrenia. Approximately 20 birth disorders, including Down's syndrome, are associated with older fathers.
Some older fathers worry the flesh is weak. "What if I can't run as fast as he wants me to be able to run?" says Michael, now 57. Jeremy, 43 is so concerned about this that he says if he has not had his first child by the time he is 50, he will not have any.
But Jack O'Sullivan, co-founder of Fathers Direct, the online advice site, says: "It doesn't matter; he can just give his son a cuddle instead."
Gabrielle, 32, whose father is 86, says: "He is a very interesting man and a former colonel. I find as a result I have to be in a relationship with a strong man.
"At the same time, I do feel a kind of invisible pressure to have children in time for my father to be able to enjoy being a grandfather."
Roderick feels another kind of pressure. "I always thought I didn't want to be an older father. It was difficult for me having one and I wouldn't want to repeat that. But I'm 49 now and something extraordinary might happen." Family structures, it seems, replicate themselves. After all, the best preparation for being an old dad is to have had one.
John Simpson: 'When my son goes to university, I shall be 80'
John Simpson, the BBC's World Affairs Editor, became a father again at the age of 61 last week. The boy, who has yet to be named, is a year younger than his youngest grandchild. Mr Simpson has two daughters in their thirties from his first marriage. His wife, Dee, is 19 years his junior.
"It's lovely. I appreciate it much, much more now than when I did when I was in my twenties and my first two children were born. Everybody I knew had children and it was just what everybody did. Now I realise the uniqueness of the whole thing. It's a wonderful, but absolutely exhausting experience.
"I now know what's what: how precious human life is. My wife said to me this morning: 'I can see your father and mother in him.' My father has been dead for 25 years and my mother for 23, and so the thought that I might see them in my child is a wonderful, wonderful thing.
"I can now give him a more rounded person, less spiky, less upset by trivia, much calmer and more understanding of the nature of human beings and love for each other.
"There are lots of disadvantages about being 61 and some carry over into fatherhood. I'm not a huge enthusiast of the thought that if and when he goes to university I shall be 80. But 80 isn't what it was when I was growing up. Eighty now probably equates to about 65 before, and I hope I shall still be working then. My friend and colleague Charles Wheeler is 82 and he turned out one of the best reports on BBC television news that other day that I've ever seen. So it doesn't have to be complete collapse and decay of everything. But I will not be playing football with him with the same abandon as if I was in my thirties.
"I don't worry about dying while he's still young, but it makes me more aware of the need to establish a really good, deep, contented, peaceable, loving relationship with him right away. He's going to be one of the two or three most important things in my life and I'm damn well going to show it. I'm not going to just let him realise that 30 years later, as happens to most of us. I'm going to make certain he knows that now. In some ways the realisation that time is short actually makes it better. I'm appalled by how much I've forgotten about looking after babies. It was a different world when my two daughters were born in '69 and '71. Nappies are now superbly easy compared with what they were then.
"I expect to be a part of the baby's cleaning, feeding and sleeping process in a way I would not have even thought about in 1969 when midwives and nurses regarded you as a completely unnecessary adjunct to the whole thing. You were just a nuisance then - in the way, clumsy and awkward. I'm still clumsy and awkward but I think everybody - my wife, the hospital people and I myself - all regard my function as being different now.
"I remember very well when my first child was born feeling as if I had been handed this enormously complex piece of equipment and nobody had given me the instruction manual, and I thought what the hell am I going to do with it? How do I do it? That's the only sad thing: it's such a long time since my two previous kids were at this age and I've unfortunately forgotten the instruction manual myself and I can't remember how to do it. But it'll come back.
"I don't think we'll have any more. My wife went through four miscarriages before this. We are hugely, hugely lucky and quite emotional about the whole thing. It's so perfect, so wonderful to have wiped away those five years of real pain."
John Simpson was talking to Julia Stuart