The change in distribution of precipitation will have a significant effect on total biomass.  This of course will also affect species composition and diversity significantly.  Some of these effects can be estimated by coupling vegetation models to global climate models during climate change experiments.  This plot shows the change in simulated total live vegetation (biomass) between last decade of the 21st century and 1961-1990 from two different climate models (Bachelet et al. 2001)