Please check the following link and PDF attachment.

http://www.sciencedirect.com/science/article/pii/S1439179106000430

As Arvind said, see: Large altitudinal increase in tree root/shoot ratio in tropical mountain forests of Ecuador, Plant and Soil 378(1-2) · May 2014, DOI: 10.1007/s11104-013-2009-1 by  Christoph Leuschner et al. on this site.

Tropical rain forests decrease in tree height and above-ground biomass (AGB) with increasing elevation. The above paper investigates the reasons :-) 

Factors affecting root shoot ratio in tree species are

1. Species and genetic makeup

2.Soil factor : Soil depth, Soil moisture, Soil nutrient availability

3. Spacing : Closer spacing encourages growth of tall trees in light demanders

4. Competition: Competition for moisture, water, light growing space is important from the point of root development in trees  

It depend on what type of species is this, it is fast growing or slow growing species. Soil fertility can affect the growth behavior and thus affect root shoot ratio. Obviously planting spacing is an important factor that can affect the ratio.   

Thank you all for the input

An increase in available N usually results in an increase in shoot to root ratio. Fire which results in a short-term increase in available N or the application of N fertilizer could stimulate an increase in shoot to root ratio.