Is there any information that would explain why there are so few symbionts when there are so many Trills? My only guess is that they have shorter reproduction seasons and longer gestation periods than host Trills, but it seems there would still be more symbionts per Trill because of their long lifespan which I seem to remember is 9 times longer than a host Trill's.
All symbionts are capable of being paired with a host. Not all hosts are capable of being paired with a symbiont. Therefore, the number of joined trills has to naturally be lower than the total number of host trills.
Add to that the fact that when joined trills reproduce, only the host species is reproduced, not the symbiont species. So even though Dax had numerous children, Dax didn't actually produce any symbiont offspring in those cases. And since pretty much all symbionts are joined and probably spend the majority of their life as a joined lifeform, symbionts likely only have an opportunity to reproduce for a very small fraction of their life. AFAIK, the symbionts are only bred on the Trill homeworld prior to their first joining, whereas the host species live and reproduce all over the alpha quadrant and can do so for at least half of their adult lifespan.
Also, symbionts are the more dependant and vulnerable species of the two. When they aren't joined, they have to be kept in stasis or in underground nutrient-rich pools (which apparently only exist on the Trill homeworld). The joining process, screening process, host-replacement infrastructure, as well as the tending of the unjoined symbionts are all undertaken by the host species. So that also increases the ratio of hosts to symbionts.
Lastly, the culture of trill society has evolved (or maybe been carefully engineered) to revere and greatly value symbionts. The joining commission has deliberately misled the public into thinking that only a small fraction of the host species is even capable of being joined (when in reality it's more like half) in order to prevent people fighting over symbionts as possessions. They've also put in place a highly selective screening process that maintains the prestige of being a joined trill, as well as ensuring that only the best and brightest of the host species receive a symbiont.
If Trill culture were different, perhaps the symbionts would be farmed like we farm Chicken or Pigs or Cows. Then the symbionts wouldn't be so rare.
The Trill are a symbiotic species of at least two, possibly three, distinct species; two humanoids and one worm-shaped symbiont. How the two/three species formed their rather unique bond is not known to Federation scientists, so the rationale and processes that determine the rate of adoption of hosts to symbionts is as yet unknown.
The worm-like symbiont is a long-lived species capable of living 300 years or more. One symbiont could outlive seven to ten of its humanoid hosts. There have been at least two species that have been seen to have been Joined Trill.
The first species, known for their forehead protrusions, was seen onboard the Next Generation's Enterprise during a peace treaty event where Riker temporarily hosted the symbiont after the original host, Odan, was killed. The second species, known by their spots, has been best represented by Jadzia Dax onboard the space station, Deep Space Nine.
Trill symbionts are not as rare as is believed by other races of the Federation. The reason the joined Trill are less often seen is because the Trill have increased the screening requirements of hosts to become Joined to prevent potential events similar to those caused by the Host Joran while bonded with the Dax symbiont. Joran was both insane and a murderer who passed the host screening exams. Since the screening process was unable to detect Joran's instability, the Trill opted to reduce the number of Joined Trill, spending years in training and psychological profiling to ensure the successful joining of the two species. All records of Joran's instability have been purged from the program and remain a state secret. As a result, being a host is considered to be an elevated role in their society.
It makes sense that the nearly immortal, worm-like symbionts have a significantly reduced population since they live so long. On Earth, the longer an organism lives, the lower its reproduction rate. This makes sense since long-lived organisms would overrun their environment and consume all of the resources in that environment. It also seems that the symbionts require significant care during their development, which might also keep their numbers rather low.