To keep the models as simple as possible, we made two assumptions common to both. First, we represented damselfly movement over landscapes by a random series of habitat-specific move lengths and turn angles. Moves were defined as the straight-line distance traveled during a 1-minute interval. This time step corresponds to empirical measures of damselfly movement (Jonsen and Taylor 2000). Second, we assumed that Calopteryx aequabilis and Calopteryx maculata used only stream and forest as habitats and moved through all other elements of the landscape as they do through pasture. For the purpose of this study, we treated all nonhabitat elements as though they were pasture. We did this for two reasons: (1) pasture was the only nonhabitat element for which we had movement data, and (2) pasture dominated (about 65%) the nonhabitat components on all 15 landscapes. Other nonhabitat elements presented on some landscapes included houses, hay and small-grain fields, and clearcuts.

At the outset of each simulation run, 100 damselflies were placed randomly along a central portion of the stream habitat. Damselflies were constrained to move in discrete steps of 1-minute intervals. The former condition was intended to mimic the initial distribution of emerging adults at the beginning of the breeding season, i.e., adult emergence occurs solely along streams (Martin 1939, Johnson 1962), whereas the latter condition mimicked an empirical analysis of damselfly movement (Jonsen and Taylor 200).

In both models (VISCOSITY and PERMEABILITY), move lengths and turn angles were drawn randomly from empirically determined distributions for each habitat type. In the VISCOSITY model, individuals redistributed themselves freely over the landscape according to habitat-specific movement parameters. In the PERMEABILITY model, movements away from streams were restricted so that, in any time step, the probability of individual damselflies moving off stream matched an empirically observed probability (P _mv). Once a damselfly moved off stream, it moved freely over the landscape (as in the VISCOSITY model), unless it re-encountered the stream.

Movement pathways were represented as a series of connected vectors, each of length M and direction T. At the end of each move, the vector defined by the scalars M_R and T_R was converted to x, y integers to correspond with the landscape grid. The habitat type of the cell at position x, y was evaluated, and the appropriate move and turn distributions were specified for the next move. Successive moves (M_i, T_i) were added onto the resultant M_R, T_R calculated in the previous time step (not the x, y integer position) (see Appendix 4 for a visualization). At the end of each simulation run, we calculated the proportions of damselflies occupying stream and forest habitats and compared them with observed proportions from our survey data. Damselflies occupying pasture at the end of simulations were removed (i.e., assumed to be dead), and proportions in stream and forest were adjusted accordingly.

The use of vector-based movements has one potential limitation: vector-based moves can pass directly through a habitat patch if the move does not begin or terminate in that patch. In other words, damselflies moving through a patch do not alter their behavior unless the current move terminates and a new move initiates in that patch. Despite this potential limitation, we chose to use vector- rather than cell-based movement because it related directly to (1) damselfly movements measured in the field (Jonsen and Taylor 2000) and (2) correlated random walk processes, which are often used as null models of insect movement (Turchin 1998).

Based on model calibration tests (not presented), we chose 480 time steps (8 h) as a maximum duration for simulation runs. This approximated the daily activity period for both C. aequabilis and C. maculata (Waage 1972). We used reflecting borders for all simulations.

To correspond with our survey design (no transects through pasture), we corrected the predicted proportions of damselfly in stream and forest for individuals that were in pasture at the end of simulation runs. We did this by subtracting the number in pasture from 100 and using this difference to calculate the proportions in stream and forest habitats. Thus, the proportions of C. aequabilis and C. maculata in forest were equal to 1 minus the proportions along streams. For brevity, we present only data pertaining to stream habitat.

Although our models predicted the proportions of damselflies in stream and forest habitats, our observed proportions were based on damselfly counts along stream and forest transects. Because our forest transects sampled a smaller proportion of habitat than did our stream transects, we adjusted counts in forest relative to the proportion of total stream area sampled as follows:

(1200 m²/total area of stream) x total area of forest x (observed counts in forest/2000 m²)

where1200 m² and 2000 m² are the areas encompassed by stream and forest transects, respectively.