How sustainable is timber housing?
Building with timber is more sustainable than building with concrete at least in terms of the production of green house gases.  A timber building is using a raw material, trees, that have been sequestering carbon till they are cut.   Cement, or concrete, on the other hand is made by cooking off carbon dioxide from the calcium carbonate, limestone, to produce the lime which makes up a large part of the concrete.  In the production of lime you have CO2 released from the limestone and from the fuels used to heat the limestone, see Lime in Wikipedia.  In addition the timber panels are significantly lighter than the cement components which should also make the timber construction more sustainable.

Most trees used for timber production are grown in sites that are not generally ideal for other types of agriculture, though this is a gross generalization.  They get their phosphorous through local sources, primarily the soil, so forest growth wouldn't have an impact on the phosphorous used for agricultural processes.

The following quote from the North Carolina State University project site summarizes the overall impact on timber construction.  It is important to note that until the advent of CLT, cross laminated timber, it was effectively impossible to build larger structures out of wood.


  CLT paneling is also thermally efficient, requiring 1/3 the heating and cooling energy compared to other traditional building systems. CLT paneling is also beneficial to the environment.  Wood is the only major building material that grows naturally and is renewable, CLT also outperforms steel and concrete in terms of embodied energy required to make the product. It also has a less of an effect on air pollution (stores carbon) and water pollution. CLT Panels USA