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I would guess they often just did not have acknowledged children.

Which might be the only way they'd have living descendants at all since wiping out all your family is a pretty common theme. It makes it a selection advantage.

Imagine being a teetotaler and siring a ton of heirs, and people crediting your virtuous abstention from alcohol while not realizing the poisonous lead was the culprit for others.

So it's less a case of having children. Which a lot of Emperors did have. It was a case of having children survive to adulthood in a political world where murdering your enemy was a viable tactic for getting ahead. Augustus had his daughter Julia, who gave him loads of grandchildren, in fact she seemed to have problems not being pregnant. Tiberius also had a son, who died due to interference from the Praetorian Prefect Sejanus. Caligula, his successor, had a daughter who was murdered. Claudius had four and all of them were murdered. And Nero also had a daughter, who died in early childhood.

So it was a very hard environment for children to actually survive. Especially when blood relation to the ruling Emperor and Augustus was very important for maintaining power. But you had the low survival rates combined with the seemingly deadly game of politics combined with various other dangers that come from ruling a state, such as death in warfare or on campaign. It's one of the reasons why adoption was seen as being as legitimate as being blood related, because sometimes you just have bad luck.

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Several reasons:

• Infant Mortality in the ancient world was high.
• Very few contemporary accounts of emperors actually exist- most surviving histories were written well after their reigns and many personal details are lost as a result.
• Many emperors didn't die peacefully in their beds. That meant his children were often murdered in order to secure the successor's throne.

The result is you get someone like Marcus Aurelius. We know Commodus, his son, succeeded him. But what is generally not known is Marcus and his wife had thirteen children. Nine didn't survive infancy or very early childhood, and 3 of the survivors were girls.

BTW, don't put much stock into the lead pipe thing. The Romans knew lead was problematic and used clay pipes most of the time. Additionally, chemical reactions with minerals in the water created calcium carbonate deposits in lead pipes which would prevent the lead from leeching into the water. The studies that looked at the lead in wine (from its production) had some issues, including the failure to account for the fact Romans mixed wine with water and that copper vessels were used in winemaking as well.

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Infant mortality in this era was approximately 50%. There was a significant amount of inbreeding among the elites. And it wasn't just lead pots...but all of the water pipes were made of lead as well.

That doesn't matter so much. That's why you adopt them.

Often the adopted children were nephews/cousins/etc, as well, so practically it was a means of keeping power and prestige in the family even if your own line died off, as well.

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Infant mortality was high (one estimate is that the average Roman woman had to have 5 children just to keep the population constant), and higher still in urban areas. A large urban area like Rome would have been particularly unhealthy. Throw in a very competitive political environment, the tendency of younger emperors to be killed before they could marry and that emperor remained always an office (open to anyone who had enough support among the military 'electorate'), rather than a hereditary position, and 'dynasties' rarely lasted more than 2-3 generations.

Bastards were not as much of a thing in Roman times. Like another comment said, you just adopt. Bastards being an issue in succession were products of other times and other regimes and is not a universal issue in all eras.

Only 1/3rd of Roman emperors died of natural causes, the rest were murdered or killed in battle.

I'm pretty sure the problem was murder, murder, murder, and more murder.

Many children died of illness back in ancient times, so poisoning them was a very effective means of ensuring the current emperor didn't have an heir, and there were so many poisons that just looked like a natural death from disease.

And not to mention a lot of their heirs by blood or adopted heirs were generals and which made "assassination on the field of battle" an option.

So yeah, both biological heirs tended to die en masse and even the adopted ones. Usually by the time the next emperor was selected, it was the emperor's fourth or fifth choice. Not the one they would have preferred.

To add on this, they were murdered by political opponents to the previous regime when they came into power. Any lingering family members from previous leaders represented a real threat from which other actors could rally behind.

Those who did not engage in the practice of killing their old political rivals children often came to regret the decision. Unless they were married into the current regimes family tree with the outward notion of unity.

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Wasn't there some miracle plant that worked so good as a contraceptive that the Romans picked it out of existence?

Silphium, or whatever?