What exasperated or overworked parent hasn't declared to a child at least once: "You'll be the death of me!"

Now we know — with unprecedented precision — just how true that can be.

A pair of researchers, drawing on the experience of nearly 22,000 couples in the 19th century, has measured the "fitness cost" of human reproduction. This is the price that parents pay in their own health and longevity for the privilege of having their genes live on in future generations. The findings, published last month in the Proceedings of the National Academy of Sciences, are both predictable and surprising.

Not surprisingly, women paid a bigger price than men. Older mothers were four times as likely to die in the year after having a child than their mates. Having lots of children was especially risky. A mother of 12 had five times the risk of dying prematurely as a mother of three.

Even after their child-bearing years came to an end, women who had many children died earlier than women who had few.

The price of parenthood wasn't trivial for men, either. Despite avoiding the hazards of childbirth, fathering more children meant more risk of dying before their time, too.

Why does child-rearing erode parents' longevity? The answer must involve physiology, because it occurs in both sexes and in women who survive childbirth.

One theory is that physical and psychological stress causes people to grow old before their time.

But it wasn't only parents who paid the "fitness cost" of reproduction.

Later-born children in very large families had less chance than their older brothers and sisters of surviving into adulthood and having children themselves. Losing a mother raised every child's risk of dying young.

The findings begin to provide for human beings what's been learned about fruit flies, guppies and mice — namely, a measure of the trade-offs between unchecked procreation and individual survival in evolution's calculus.

As raw material, the researchers, Dustin J. Penn, of the Austrian Academy of Sciences in Vienna, and Ken R. Smith, of the University of Utah, used a database of genealogical information kept by the Church of Jesus Christ of Latter-day Saints in Salt Lake City. They examined the reproductive history and survival of 21,684 couples married between 1860 and 1895. Each person was married only once, and polygamists were excluded.

Altogether, the couples bore nearly 175,000 children — slightly more than eight each. The women's average age at the birth of the last child was 39 years. About 1,400 of them died within a year of delivering their last baby, and 2,400 within five years. For men, the corresponding numbers were about 600 and 1,700. About 18 percent of the children died by age 18.

The data sample is the largest used to estimate the cost of human procreation. It covers a wide spectrum of society — most men in previous studies were aristocrats — and a period largely before modern hygiene and medicine greatly reduced maternal and childhood mortality.

"These are basically pioneers, and the mortality is probably more like what it was before the Industrial Revolution," said Penn, who heads the Konrad Lorenz Institute for Ethology but had previously been at the University of Utah.

When Penn and Smith examined their data, a clear and unmistakable trend stood out. The bigger the family, the smaller the chance that the parents would live into old age. Both mothers and fathers paid a price for having lots of children, with mothers always paying more, regardless of family size.

For example, 1.5 percent of mothers who bore one to three children were dead within a year of the last child, but only 0.4 percent of fathers were. Among women who had 12 or more babies, 6 percent were dead within a year of the last birth, compared with 2.5 percent of men.

Big families were hard on children, too. Twenty percent of children in the largest families died before age 18, compared with 10 percent in the smallest. About 15 percent of first-born children died by 18, compared with nearly 25 percent of 12th-borns.

Why would being in a large family, or being at the end of the birth order, be hazardous to a child's health? One reason is that those children are more likely to have their mother die — and small children without mothers are more likely to die themselves.

Children who lost a mother before their fifth birthdays had a 78 percent higher chance of dying before they turned age 18 than children whose mothers survived. The same effect was seen — again, less dramatically — after the death of a father. Children who lost a father by age 5 had a 14 percent higher risk of dying in childhood.

The findings also provide an explanation for menopause, which ends a woman's reproductive capacity but not her mate's.

Every human child has a stake in his or her mother's survival. Every mother has a stake in her children's survival. Menopause appears to be a way of protecting a mother's life and helping ensure she will live long enough to raise her last child to reproductive age.