The current global Tiger population is roughly 5100 according to Wikipedia. With habitat destruction and poaching continuing and no effective improvement in conservation, most likely the Tiger population will continue to decrease. I'm wondering what is the theoretical maximum population to which the Tiger species could be restored. Suppose poaching and habitat destruction stopped today and conservation efforts were increased drastically, so the only factors limiting population growth are the natural dynamics between the species and its prey. Could we then restore the global population of tigers to its pre-20th century level of 100,000?
I don't think your core question can be answered exactly, namely "...the theoretical maximum population to which the Tiger species could be restored", since there are too many variables to consider. However, the comment from @Remi.b is apt, in the sense that it shows that population growth rate per se (or reproductive rate) should not be the limiting factor. The bottleneck will probably be some concept of carrying capacity (the number of tigers that the current tiger habitats can sustain). This number will naturally depend on many factors, for instance whether all hunting of tigers and their prey is removed from the remaining habitats.
You could arrive at a ballpark estimate of the current "theoretical" maximum population size by finding the area of suitable tiger habitat and dividing this by the average size of tiger territories. However, the size of tiger territories differ quite a bit between males and females and between areas with different prey densities, and probably also between different tiger subspecies (which will covary with average prey density to some extent - Siberian tigers generally live in habitats with lower prey densities). Looking at estimates from the Smithsonian and wikipedia, territory sizes seems to range between 20 to 510 km2, with maybe even larger male territories in Siberia (so quite a big range). The IUCN Red list assessment of tigers state that the current tiger range is to 1.185 million km2 (from Sanderson et al. 2006 as "Tiger Conservation Landscapes"). It is however unclear whether this number corresponds to the total range extent or to the actual amount of suitable habitat (probably the former though). Nevertheless, lets say that the average territory size is 265km2 (probably way to high on average), that the estimated area from IUCN is correct, and lets assume that territories never overlap (which they do; male territories overlap with several female territories and female territories can also overlap to some extent). In that case, we will arrive at an estimated theoretical popultion size of ~4500 tigers. If we instead use a more modest territory size of 40km2 we will arrive at a population size of ~30000 tigers. Since territories can overlap, these estimates should be biased low, given their other assumptions.
Sanderson et al. (2006) however also includes a summary of "Effective Potential Habitat" of tigers, which sum to 5.65 million km2. If this number is used to calculate the estimated theoretical popultion size you will arrive at ~21300 or 141000 tigers, using the same territory sizes as above. However, this completely ignores issues such as landscape connectivity, and that tigers are completely missing from large parts of their former distribution (these factors, and others, were used to define the "Tiger Conservation Landscapes"). Also note that much of the potential habitat lies in low-productivity areas (Russia and parts of China), where territory sizes are relatively large.
Another perspective would be to use the historical population size pre-20th century and the amount of decrease in tiger habitat to estimate a theoretical population size. I don't know anything about the historical population size, but let's say that your 100000 is accurate (source?). Dinerstein et al (2007) state that current tiger ranges correspond to 7% of historical ranges. Using only these numbers, you could arrive at a current theoretical population size of 7000 tigers (100000*0.07), assuming that the tiger population should directly mirror the amount of available habitat. However, the current 7% of historical ranges include range contractions due to hunting, so this estimate should be biased low (maybe strongly so) with respect to the possible population size that could be obtained if all hunting stopped.
These calculations should show that the current Tiger populations could probably be increased quite a bit with strong and effective conservation efforts (in your words: if "poaching and habitat destruction stopped today and conservation efforts were increased drastically"), but that 100000 will probably be extremely hard to obtain, given that so much of the historical range has been lost. With reintroduction programmes and a long timeframe it doesn't appear to be impossible though, but this is ignoring potential future problems such as increased tiger-human conflicts. Also note that I don't know much about Tiger biology, that these are merely rough back-of-an-envelope calculations, and an expert could certainly give you a more detailed and accurate answer.
- Dinerstein et al. 2007. The Fate of Wild Tigers. Bioscience 57 (6): 508-514. doi: 10.1641/B570608
- Sanderson et al. 2006. Setting Priorities for the Conservation and Recovery of Wild Tigers: 2005-2015. The Technical Assessment. WCS, WWF, Smithsonian, and NFWF-STF, New York – Washington, D.C.
- The Smithsonian: Tigers
- Wikipedia: Tiger
- IUCN Red List: Panthera tigris