  In this paper we study networks of nodes characterised by binary traits that
change both endogenously and through nearest-neighbour interaction. Our
analytical results show that those traits can be ranked according to the
noisiness of their transmission using only measures of order in the stationary
state. Crucially, this ranking is independent of network topology. As an
example, we explain why, in line with a long-standing hypothesis, the relative
stability of the structural traits of languages can be estimated from their
geospatial distribution. We conjecture that similar inferences may be possible
in a more general class of Markovian systems. Consequently, in many empirical
domains where longitudinal information is not easily available the propensities
of traits to change could be estimated from spatial data alone.
