Does each incarnation of the Doctor have a different natural lifespan depending on how "old" they look?

Question

As we know the Doctor, regardless of his total age, has the ability to regenerate into the form of a body seemingly older or younger (in terms of physical appearance) than the previous one (Doctors such as the 11th, 10th and 5th started out looking rather "young", while other incarnations such as the 12th and 3rd began with their bodies appearing "older" from the start).

The 11th Doctor's 2013 Christmas special The Time of the Doctor story made it clear that if one incarnation lives long enough without regeneration, the body will physically age (I'm aware this is either demonstrated or implied in earlier stories, but I'm just going with the most obvious example); Eleven can be seen transitioning from the appearance of a young man to that of a much older man towards the end of the episode, but what if the 12th or the 3rd were in that scenario? Would they have died of old age much sooner than Eleven, as they had older bodies from the start, or would something else have happened?

Answer 1

The Doctor's physical appearance is neither linked with their actual age nor their accumulated age since the last regeneration. How old they look in human terms after regeneration (presumably along with other physical changes) is apparently some kind of subconscious choice to address a need. The Twelfth Doctor realised firstly that he had subconsciously taken the face of someone he had previously rescued as a reminder that "nobody gets left behind", but there is also a suggestion when he speaks to Clara that he took an older appearance in order to clarify their relationship ("Clara, I'm not your boyfriend.")

As to the question of whether each regeneration has a lifespan dictated by their physical age - to date, only three Doctors have regenerated due to old age. The First Doctor, the War Doctor (both said their bodies were "wearing thin") and the Eleventh Doctor who was about to die of old age before he was given a new regeneration cycle and immediately regenerated.

Take the First Doctor as an example - it is calculated that when he regenerated he was somewhere between 400-450 years old. He regenerated because of that age, combined with whatever stress and ordeals he had gone through to wear him out, not because he had the physical age of 58 (Hartnell's age at the time he bowed out).

The War Doctor had apparently fought in the Time War for 100 years when he decided "no more", and in that time he had physically aged 34 years, from roughly 39 (Hurt's age in 1979, when most people believe the brief image seen in Night of the Doctor was taken) to 73 (his age at the time of filming Day of the Doctor). This means he physically aged faster than, for example, Eleven who went from 907 at the start of his run to 1103 in The Impossible Astronaut and didn't look a day older.

By contrast, the Eleventh Doctor looked waaaay older than either the First or the War Doctor when he regenerated. Eleven gave his age as 907 when he first met Amy, and his age at his regeneration is calculated to be 2,100, meaning that regeneration lived 1,193 years.

So it is established that a regeneration can die of old age; the apparent physical age and the rate of ageing of each regeneration are based on more than the passage of time and may be related to physical stresses such as fighting in the Time War, and there appears to be no set time-limit on each regeneration - they wear out when they wear out.

Answer 2

How old the Doctor looks seems to have no true bearing on the lifespan of the present incarnation, and seems to be more of a reflection of his state of mind than anything else.

Time of the Doctor is also a special case, because, when we see 11 as an old man, he is at the end of his last regeneration, as the Daleks point out when they finally attack the planet. It is possible that Timelords only begin to truly age physically when they run out of regenerations, and not before. Though it is to be noted that they still have long timespans, as he's been living on Trenzalore for about 300 years by that time.

At the same time, on The Impossible Astronaut, we see 11 looking quite the same when he first says that he's 1103 years old, while the whole gang is enjoying their picnic by the lake, then when they meet a younger version of him later at the dinner and he says that he's 909 years old.

We could also mention the War Doctor, who looks much older than any of the incarnations seen since the reboot and the first appearance of 9, and who seems to have had a quite long life fighting in the Time War.

Another example is 12, who looks older again than 10 or 11, and who is, clearly, a tortured Doctor, much angrier and haunted by his past than 10 or 11 could have been. He states that he chose his new face specifically during his regeneration, basing it on the face of someone he previously encountered.

That hints that he may have a degree of control over how his physical appearance changes during his regeneration. Although it might subconscious since 11 said to 10 that 'regeneration is a lottery' in Time of the Doctor and no recent incarnation ever managed to be ginger despite truly wanting to.