LUCAS takes a multidisciplinary approach to simulate change in a landscape. Ecologists and economists used knowledge from both disciplines to develop a land management simulation. Many discrete and continuous ecological and sociological variables were used empirically in calculating the probability of change in land cover (a discrete variable): land-cover type (vegetation), slope, aspect, elevation, land ownership, population density, distance to nearest road, distance to nearest economic market center (town), and the age of trees. For an analysis of the influence of these economic and environmental factors on landscape change see [36]. Each variable corresponds to a spatially explicit map layer stored in the GIS (see Section 2). A vector of all of these values for a given grid cell is called the landscape condition label [8,9]. An example landscape condition label (LCL) is shown in Table 3.
Figure 2: Relationship among LUCAS modules
Table 3: Example Landscape Condition Label in the Hoh Watershed on
the Olympic Peninsula
Each element of the LCL 
is used to determine the probability of change using the
multinomial logit equation found in Equation (1)
[39,38,3].
where n is the number of cover types, 
is a 
column vector composed of elements 
of the
LCL 
in Table 3, 
is a
vector of logit coefficients, 
is a scalar intercept,
and Pr
is the probability of unvegetated land cover
remaining the same (
) at time t+1 or changing to
another cover class (i.e., j=1,2,3). The land ownership
(
) determines which table of logit coefficients should be
used and the tree age (
), used only for coniferous forest
cover types, determines if the trees have aged sufficiently to be
harvested, i.e., change to another cover type. The
null-transition or probability of no land cover change is defined
by Equation 2.
where the symbols have the same meaning as in Equation (1). Example vectors of coefficients for the Hoh Watershed are shown in Table 4.
Table 4: Example Multinomial Logit Equation Coefficients for
unvegetated land cover in the Hoh Watershed on the Olympic
Peninsula
The multinomial logit coefficients and intercept values were
calculated empirically by Wear et al. [39] from
existing historical data stored in the GRASS database (see
Figure 2). The table of all probabilities generated
by applying Equation (1) to all cover types is called the
transition probability matrix (TPM), an example of which can
be found in Table 5. If the TPM in Table 5
were used, for example, a random number from the closed interval
less than 0.5839 would change the land cover to grass/brushy,
otherwise the land cover would remain unvegetated. For a discussion
of logistic regression and a basis for Equation (1) see
[34].
Table 5: Example Transition Probability Matrix based on the
example multinomial logit coefficients.
