387than ten are sampled in practice because few appropriate experts are available
(Czembor et al. 2011 ).
System stochasticity was a moderate source of variance in the model results for
the Eucalyptus example. In VDDT, this variance reflects the stochastic sequence of
disturbances over repeated simulations (i.e., transitions occur at random times
within simulations, but with the same average probability through time across simu-
lations). While stochasticity in the rate of disturbances over time was not evaluated
in the Eucalyptus example, this source of uncertainty can be incorporated into “tem-
poral multipliers” (see Sect. 13.3). Temporal transition multipliers were used to
parameterize uncertainty in a study of the effects of the exotic annual grasses,
B. tectorum, Taeniatherum caput-medusae L (medusahead), and Ventenata dubia
(Leers) Coss. (North Africa grass), on native plant species in sagebrush steppe eco-
systems across years differing in wildfire occurrence (Creutzburg et al. 2014 ).
The variance in model results due to imperfect knowledge was the least impor-
tant source of uncertainty in this case study. The example incorporated imperfect
knowledge using replicate models that used ranges of values for transition rates, but
Fig. 13.5 Bar plots showing the variance due to among-expert uncertainty, imperfect knowledge,
and system stochasticity every 10 years for 150 years. A 95 % Confidence Interval that corre-
sponds to a logit transformed variance of 0.73 (the among-expert variance at timestep 150) would
span 3–46 % of modeled cells in the desired vegetation state. Results adapted from Czembor et al.
( 2011 )
13 State-and-Transition Models: Conceptual Versus Simulation Perspectives...