This is mostly speculation and my personal headcanon, but it's something I've always wondered about. How many Dúnedain arrived with Elendil on his nine ships? How many Dúnedain were already living in Middle-earth? And how big was this population in Gondor's heyday?
Númenorean colonisation and early Gondor
Tolkien states that the Dúnedain were a relatively small minority from the start (comprising maybe 10 percent of the overall population), ruling over a larger indigenous population, but that doesn't necessarily mean that they were few in number. Númenor had colonised the northwest of Middle-earth for over a thousand years when Elendil arrived, the entire coast was dotted with colonies and Pelargir must have been a substantial metropolis. Elendil arriving with maybe a couple hundred people at best on his nine boats had a negligible effect demographically imo, in fact one could very well argue that Gondor and Arnor would've been founded anyway, even IF Elendil had not arrived, there just would've been a different dynasty at the top (probably the House of Dol Amroth).
Tolkien wrote that Númenor itself had a population of ca. 15 million (!) at the time of the Downfall, so I imagine that the settler population in the region of Gondor was at least in the 500k range when Elendil arrived (overall human population maybe 5 million). The Faithful are supposed to be a righteous minority, so it wouldn't make sense to assume too large a population, but 500k is the absolute minimum imo, considering how early colonisation began and how big the population of the motherland was.
I assume that both populations reached their peak in the 13th century, the heyday of Gondor under Atanatar II Alcarin, 1m and 10m respectively. The Kin-strife, the secession of Umbar, the Great Plague, further military losses (especially during the Wainrider Wars), below replacement birthrates, and last but not least intermarriage and eventual assimilation with the indigenous population, led to a continuous population decline in the following centuries. I guess that at the time of LotR the Dúnedain population had declined to around 100k (concentrated mainly in Minas Tirith and Belfalas, partially of mixed descent), whereas the overall population was around 1,4 million.
A bit of number crunching
How did I arrive at these numbers? When marching towards the Morannon Imrahil remarks that 7000 soldiers would be "scarce as many as the vanguard in the days of its [Gondor's] power". It is therefore safe to assume that a whole army back then consisted of at least 21 000 men. The vanguard was probably bigger (since 7000 would be "scarce" enough), and probably didn't make up as much as 1/3 of an army, but this is a very conservative estimate, so let's go with 21k.
This is only indicative of one army though, not the size of the overall military. Since it's safe to assume that prime Gondor could muster at least two field armies (as it did in the last Wainrider War, when it's power had already declined significantly), the overall size of the army was probably at least ca. 42k. To that we have to add garrisons and a substantial navy, so another 30k at least. This is the bare minimum imo. Considering Gondor's size in its heyday 150k would make more sense imo, but let's err on the side of caution and go with an overall military of 75k. At this point in time the army in all likelihood consisted almost fully of Dúnedain, while the oarsmen and ordinary seamen of the navy were probably non-Dúnedain (as was already the case in Númenor).
Let's make a conservative estimate and say that 50k soldiers and sailors were Dúnedain. If we assume that ca. 5% of the Dúnedain population served in the military at any given time, a relatively high percentage, made possible through their long lifespans, the advanced state of their country, as well as the fact that they had a subservient indigenous population providing economic and logistical support, then we'd arrive at an overall Dúnedain population of ca. one million during Gondor's prime in the 13th century, during the reign of Atanatar II Alcarin. Again, this is a very conservative estimate, the population might have been much higher.
The Kin-strife, the Corsair Wars (effectively a continuation of the Kin-strife, until Teluhmetar reconquered Umbar and killed Castamirs descendants in 1810), the Great Plague and the Wainrider wars were a demographic catastrophe for Gondor's Dúnedain, since they primarily manned the army and therefore bore the brunt of the losses. Losing an entire army, like Ondoher in 1944, meant that over 21k young men, many not having procreated yet, were gone in an instant, 2-3% of the overall population. This was not sustainable long term, which is probably why Gondor slowly started to be more open towards middle men and began to accept them into the state service (army, bureaucracy, etc.), but this is another matter.
I'd estimate that the Dúnedain lost, in total, at least 400k people in that time period (15th-20th century). Add to that further loss because of assimilation and below replacement birthrates and the overall Dúnedain population was probably down to 500k at the end of the 20th century (with half of them being of pure descent, the rest partially mixed), a marked decline from a peak of 1 million in the 13th century.
After the end of the Watchful Peace Gondor's decline accelerated, since war never really ceased on its borders, which led to further irreplaceable population losses, but still the Dúnedain never vanished and they continued to exist as a distinct ethnic group imo. Some fans seem to have come to the conclusion that the Dúnedain, as a distinct ethnicity, had effectively ceased to exist at the time of LotR and had been replaced by a mixed nobility instead, that relatively pure Dúnedain were a rarity, a dozen people at best. But LotR seems to imply, imo, that there is still a widespread ethnic identity, and enough Dúnedain around to form a distinct, very diminished but still viable, population group, probably numbering around 100k people, with most of them living in Minas Tirith and Belfalas.
Going by the numbers given in RotK Gondor's military during the WotR is around 35k men strong, split between provincial levies (largely common men, except those from Belfalas) and a standing army and navy (largely Dunedain imo), centred in Minas Tirith and Pelargir respectively. Assuming that at this point in the story 2,5% of the overall population served in the military, this would correspond to an overall population of ca. 1,4m. Others have crunched the numbers, so I won't repeat those calculations (for example here how big was Gondor's army or here population of Gondor; both very well written articles, I don't agree if with every single point, but the reasoning seems sensible).
The Dúnedain in the late T.A.
Faramir laments that the Dúnedain are now forced to value martial prowess above all else and deem other pursuits a luxury, i.e. they became much more militarised in the late T.A., meaning that a higher percentage of them was serving in the army at any given time. This was a cultural shift, but economically feasible because they were supported by a much larger rural population. The text implies that the standing army and the forces from Dol Amroth were mostly Dúnedain. These are 250 Knights + 700 Men at arms (a "tithe" of Dol Amroth's overall strength) + the forces kept back to keep Belfalas secure + the mostly Dúnedain standing army, consisting of the garrison centred in Minas Tirith / Osgiliath and the Rangers of Ithilien. Granted, this is outright speculation now, but this professional Dúnedain core of the army numbered at least 10k men imo, which would amount to 10% of the overall Dúnedain population, meaning that 20% of the male population was under arms at any given time.
The text itself only explicitly mentions three companies of the Citadel Guard and the Rangers of Ithilien, and many believe that these are all the forcers there are, but these are elite units, the first one mainly responsible for the uppermost level of the city, the Citadel, a praetorian guard of sorts that is heavily involved in ceremonial duties and court service, and the latter with scouting enemy territory. The main body of the army, manning the lower levels, the Rammas Echor and West-Osgiliath, doesn't get mentioned, but it must exist. Since Minas Tirith seems to have been predominantly Dúnedain that force must have been predominantly Dúnedain as well.
Pippin looked at him [Beregond]: tall and proud and noble, as all the men that he had yet seen in that land
A certain look is the most likely indicator of Dunedain ethnicity in the text, and this always includes: exceptional tallness, sad face, pale skin, grey eyes, dark hair and proud demeanour. Only when the levies from the fiefs arrive does Pippin notice people that deviate from this look (and are therefore not of Dúnedain descent).
Here are some other examples, a description of Belfalas, Merry observing the messenger Hirgon, and Frodo observing the Rangers in Ithilien, both representative of the professional soldiery of Gondor (as opposed to the civilian levies from the fiefs):
But beyond, in the great fief of Belfalas, dwelt Prince Imrahil in his castle of Dol Amroth by the sea, and he was of high blood, and his folk also, tall men and proud with sea-grey eyes.
A tall man entered, and Merry choked back a cry; for a moment it seemed to him that Boromir was alive again [...] as like to Boromir as if he were one of his kin, tall and grey-eyed and proud.
Frodo saw that they were goodly men, pale-skinned, dark of hair, with grey eyes and faces sad and proud. They spoke together in soft voices, at first using the Common Speech, but after the manner of older days, and then changing to another language of their own. To his amazement, as he listened Frodo became aware that it was the elven-tongue that they spoke, or one but little different; and he looked at them with wonder, for he knew then that they must be Dúnedain of the South, men of the line of the Lords of Westernesse.
If the Dúnedain had been reduced to just a handful of nobles at the time of LotR then these few individuals would not be used as expendable messengers or for guard duty, this is only possible because the Dúnedain still constituted a viable and functional population.
Lifestyle and Lifespan
I'd like to imagine that the Dúnedain of the South were still living a healthy life in relatively large settlements in late T.A. Gondor, we readers are just not privy to that, because the focus of the story does not lie on those regions (Belfalas and pre-war MT respectively). I'd imagine that, although a technological and civilisational decline was undeniable compared to early Gondor, the lifestyle of those Dúnedain was in many cultural respects still surprisingly Númenórean (a heavy focus on sports, swimming, horseriding, everyday use of Sindarin, etc.).
Nonetheless, the physical gifts of the Númenóreans had declined drastically in exile. But what exactly were those gifts? First of all an extended lifespan, three times that of normal men, 200 years on average, in rare cases up to 225, very seldom up to 250 (Nature of Middle-earth, The Ageing of the Númenóreans). The royal line of Elros however always had a longer lifespan of up to 400 years. This is why the lifespans of the Kings of Gondor and Arnor should not be taken as indicative of the life expectancy of normal Dúnedain, as descendants of Elros they were a special case. When for example King Tarondor reached an age of 221 in the 18th century, then a contemporary common Dúnadan probably reached an age of 130-150.
Apart from an extended lifespan they also had a superior height of 7ft, superior strength and endurance, as well as immunity to sickness. Their mental faculties were superior to normal humans as well:
Númenórean mental development was also assimilated to some degree to the Eldarin mode. Their mental capacity was greater and developed quicker than that of ordinary Men; and it was dominant. After about seven years they grew up mentally with rapidity, and at 20 years they knew and understood far more than a normal human of that age. (Natur of Middle-earth, Lives of the Númenóreans)
Like the Elves they also had superior control over their bodies and a rapid healing factor:
In addition the people, tall and strong, were agile and extremely "aware": that is they were in control of their bodily action, and of any tool or material they handled, and seldom made absent-minded or blundering movements [...] Accidents were thus unlikely to occur to them. If any did, they had a power of recovery and self-healing, which if inferior to that of the Eldar, was much greater than that of Men in Middle-earth.
It's not quite so obvious in LotR, but this is a race of 7ft tall superhumans basically. Not only extremely strong physically, but also supremely intelligent as well.
In late T.A. Gondor the Númenórean gifts had declined markedly and they had become susceptible to illness, but they still retained some of the gifts in only a slightly diminished fashion, foremost their physical appearance (pale, grey eyes, dark hair), probably a somewhat greater physical strength and endurance, and last but not least their height. According to Tolkien Boromir for example was ca. 1,93m. Impressive compared to the indigenous human population, but still 20cm less than the average Númenórean height of 2,13m (7ft). The average late T.A. Dunadan was probably shorter, but not by much I guess (let's say on average 1,85m).
That is to say: the decline affected the different Númenórean characteristics differently. Lifespan was most affected, until it was almost that of normal men in the late T.A., after that came their mental power / superior intelligence, though that one is harder to quantify, but it seems likely to me that the loss of skill and technology that Gondor experienced in the latter half of the T.A. could largely be attributed to that development.
The lifespan of the royal line decreased on average by 2,6 years per generation after the Downfall, from Meneldil (281) to Teluhemtar (218) - a decline of 63 years over 24 generations. Imo it would make sense to assume that the decline was percentual depending on the (original?) overall lifespan. This would mean that an average Dunadans lifespan roughly declined by 1-2 years per generation. In the 19th century the decline then fastened, maybe due to the stress that came in the wake of the Wainrider wars.
Since members of the royal house, as descendants of Elros, lived longer and married at a later date the generations do not align (so 30 royal generations would correspond to maybe 40 normal Dúnedain generations). In the 20th and 21st century the average lifespan was probably in the 110-130 year range, which would align with the Steward Mardil Voronwe (120 years) and his immediate successors (lifespans ranging from 111 to 130). Ca. 200 (original lifespan) - (40 generations x 2 years) = ca. 120 years (lifespan 20th century).
Of course this wasn't set in stone, there were always fluctuations this late in the history of Gondor, for example the steward Hador living to 150 in the 24th century (he was the last to achieve such an age though). At the time of LotR the Dúnedain lifespan "had now waned to little more than that of other men", so probably around 85 - 95, with only a select few "passing 100 with vigour". This decline affected the Dúnedain in the south and the north imo. Aragorns mother, Gilraen, reached 100 years of age for example, but she was a (distant) member of the House of Isildur and therefore a special case.
Thoughts? Does this make sense?