Appendix E. Sensitivity analysis.

METHODS

Sensitivity analysis is usually assigned to test the effect of uncertainty in parameters definition on model results (Dunning et al. 1995, Cramer and Portier 2001). In this work, the relative importance of different landscape parameters was also tested. In each sensitivity-test, one parameter or more was changed relative to the parameter set used in the main model.  The changes were of two types: (a) complete removal of one of the parameters to evaluate its relative importance; (b) changing the value of one or several parameters to assess the sensitivity of the model to an error in parameter estimation (Dunning et al. 1995).

Forty tests were conducted in three categories:

(1) Landscape parameters: the relative effect of the habitat availability matrix, the relative effect of vegetation cover vs. topographical slope, the relative effect of the topographical slope values, the relative effect of the vegetation coverage values, and the relative effect of main roads.

(2) Home range parameters: the relative effect of the home range shape and size and the threshold score for establishing a home range.

(3) Movement parameters: the relative effect of road crossing and movement restricted to open land, the relative effect of the shift of the home range, the relative effect of the spatial overlapping between home ranges.

The effect of the change was tested by running the model for five years (30 runs) and by comparing the model results to the results of the baseline model and also to the observations matrix.  The observations matrix represented the annual home ranges of 37 released females that were tracked during the fifth year. We used the same measures described in the methods to evaluate our results.

The relative effect of the landscape templates          

Creating a landscape matrix in which all the pixels received a uniform score greater than the threshold tested the relative effect of the habitat availability matrix on spatial distribution. The values of the V. I. Index and r (amongst the lowest values obtained in all tests) were low and no activity centers were formed.  Canceling also the open land matrix, such that the deer movement in space was not restricted, reduced the correlation relative to observations even more (Table A1).  The importance of human-related landscape elements, such as the built-up areas, roads and buffers around them, is highlighted when these are added to the uniform matrix (Table A1).

Following the deletion of the “real” landscape templates (uniform matrix and the deletion of open land matrix), the spatial movement in the model was affected only by the presence of conspecifics in the area and the total area occupied in the model was larger than in observations (Total area ratio = 1.28). By adding the human-related landscape elements, occupied area decreased (Total area ratio = 1.05, Table A1).

The relative effect of land cover vs. topographical slope

To test the relative importance of the different parameters in the habitat quality matrix – vegetation, topography and human-related landscape structure – each component was deleted separately from the matrix.  The deletion of the vegetation parameter led to a decrease in the values of most of the measures (Table A1), and to disappearance of the western activity center. A noteworthy decline is seen in the r values of the 4 km² and the 16 km² around the release site. In these areas, the vegetation effect may be particularly important given the steep slopes of the ravine around the release site.

By giving an additional weight to the vegetation matrix in creating the habitat availability matrix (twice the weight in comparison to the slope), most of the measures’ values were similar to the base file (Table A1). However, for the area of the 4 km² around the release site (area that included steep slopes), there was a decrease in the r-value. This observation and the increase in the r value of the 4 km² when weighting the scores in favor to the slopes (twice the weight in comparison to the vegetation) indicates the slope is an important factor in the spatial distribution of the deer with a preference towards moderate terrain.

The relative effect of the topographical slope values

The values of the topographical slope parameter were examined by changes in ranking of the topographical slope image. The different slope categories received scores according to different strategies ranging from a sharp to moderate bell shape distribution, as well as a distribution emulating the distribution of the slopes of the home ranges in the second year and in the first and second year combined (Table A2).  The different ranking procedures led to variance in the model outputs (Table A3), and thus the model is sensitive to the strategy in which parameters values are determined.

The relative effect of the vegetation coverage values

The values of the vegetation parameters were also examined by changes in ranking of the vegetation image. The scores for the woodland cover type were varied from a sharp to moderate bell shape curve, and in one case where the vegetation score was determined only by the scrubland and woodland types (Table A3).  The changes in the scores of the woodland (Table A4) led to slight changes in the measures of fit to observations (Table A3). The model is less sensitive to these changes since the woodland type is only one of four vegetation cover components in the final vegetation score. However, when the scores were determined only by the woodland and scrubland (the major components of the home ranges), there was a decrease in the measures’ values and the activity centers were only partially identified (Table A3). Hence all vegetation types are important in habitat selection and should be incorporated in the model.

The relative effect of main roads

The effect of main roads was examined by changing the width of the buffer zone around the roads. A decrease in the buffer width to 300m had minor effects on the output (Table A5), but the western activity center was identified only partially.  Furthermore, the population extended northward beyond its real range suggesting that roads do direct the direction the population radiates. 

The relative effect of the home range shape and size

We tested the sensitivity of the model to how home range was delineated into two ways: (1) comparing between the observations matrix and a matrix depicting a 17 × 17 grid square around the real home range centers (as determined by the 10% isopleth of the adaptive kernel technique - Worton 1989), and (2) changes in the home range size.

When using the square home ranges around the real centers the correlation (r) with the observations matrix was 0.58. In addition the ratio between the occupied areas between these two matrices was 0.69.  Thus, the use of a constant home range size, while having no impact on predicting the spatial expansion pattern of the population by itself, contributes much of the deviation of the model from observations. Whereas the individual home ranges of the reintroduced animal varied considerably in size, we found no relationship between home range size and slope or scrubland cover (P > 0.05, linear regression, df = 33). We did find a significant negative correlation between home range size and the presence of woodland in the home range (P = 0.005, linear regression, df = 33).  However, the correlation coefficient was too low (r² = 0.17) to be a useful parameter in the model. 

The changes in the home range size affected mainly the measures of the total occupied area. A smaller home range size (15 × 15 pixels) led to a decrease in the total occupied area to 68% of observations, while increasing the area to 19 × 19 pixels led to an increase in the area even more than in observations (Table A5). However, in all cases the activity centers were identified. Thus, although the model is sensitive to the home range size, this parameter does not influence establishment of home ranges in the preferred habitats. Moreover, as the population increases and disperses, the effect of variance in home range size relative to the whole occupied area will decrease.

The threshold score for establishing a home range

Based on model definitions, an individual will settle in a home range only if the threshold score exceeds 4.25. We tested the sensitivity of the model to this score using four other values: 3, 5.5, 7 and 8.5.  Threshold scores of 3, 5.5, and 7, had little effect of the model’s output and the formation of activity centers.  By model definitions, the deer has the opportunity to “improve” its home range during the first two years post release, and this has a major affect on the spatial distribution pattern (see below). The expansion pattern seen after five years in the model outputs includes the improvement of four release groups and therefore the threshold score doesn’t have a major effect. A change in the threshold to an extreme situation (8.5) led to a decrease in most of the fit measures between the model’s output and observations, mostly because there were far fewer pixels that could function as a home range center number, i.e., fewer available home ranges.   However even in this situation the activity centers were recognized.

The effect of the shift of the home range

Canceling the opportunity to improve the home range (shift) to areas in which the conditions are better during the first two years post release led to a decrease in all the measures of fit to observations. Moreover, the total occupied area decreased and the western activity center disappeared (Table A5). Without the “opportunity” to shift home range, deer in the model remained relatively near to the release site (Fig. A1).

The effect of the spatial overlapping between home ranges

Limiting the spatial overlap between home ranges influences the spatial dynamics of the population. In reality, limited overlap may be due to social interaction between individuals in the area and restricted resources. When we studied two extreme situations in the model, a maximum of one animal overlapping with no more than two others, and a maximum of one animal overlapping with up to 14 animals the difference was most notable in the total occupied area:  an 100% increase and 40% decrease, respectively, in the area occupied by the simulated population relative to observations (Table A6). We note that the range of the population in the simulation with the minimum overlap was larger than in any other simulation we performed (Fig. A2). Although this is, to a certain degree, self-evident, it highlights the importance of spatial interactions between individuals as a driving force of population expansion.

We tested whether the amount of overlap in observations is affected by habitat condition by determining the amount of overlap in the model as a function of habitat conditions: when habitat conditions were good (score > 7), an individual could overlap with more individuals than in bad conditions (Table A6). In this test the central activity center was clearly visible, but the western activity center was only partially recognized.  Thus habitat conditions by themselves can’t explain the variability in overlap.

With the increase in the amount of overlapping between individuals in the model the values of r, SMC, and V.I. Index increased as well. However, the other measures (area ratio and the presence of activity centers) indicated a decrease in the fit to observations. This outcome is not surprising as correlations are strongly influenced by extreme values (in this case the maximum number of individuals in pixel).

TABLE A1. Sensitivity analysis – the effect of the landscape template. Comparison between model’s projections under different scenarios – a matrix that represents the females’ distribution at the end of five time steps (average of 30 runs) – to the observations matrix that represents the actual annual home ranges of the reintroduced females, five years since project’s onset. The measurements are: V.I. Index; Simple Matching Coefficient (SMC); Correlation Coefficient (r) between different parts of the matrixes: the full matrix, and 100 km², 16 km² and 4 km² around the release site; Area Ratio (AR); Occupied Pixels in Observations projected by the model (OPO); Occupied Pixels in model that are occupied in observations (OPM).  For the area ratio calculations, only the pixels in which there was a value higher than 0.5 (i.e., in at least half of the runs they were populated) were taken into account beside the Total Area Ratio measure (TAR), which included the occupied pixels in the matrixes including all occupied pixels in the model matrix that were occupied in at least one run (the value>0). Activity Centers (AC) – the identification of the main centers: The central (AC center) and the western (AC west).

TABLE A2. Ranks for the mean topographical slopes of home ranges in the different sensitivity tests. Scores were determined using different strategies: (1) sharp bell shape – large differences between the scores; (2) mediocre bell shape – mediocre differences between the scores; (3) moderate bell shape – a moderate difference between the scores; (4) Based on the distribution of the slopes of the second year; and, (5) Based on the distribution of the slopes in the first and second year.

TABLE A3. Sensitivity analysis - effect of changes in the ranking strategies of the topographical slope and woodland values on model outputs. The comparison was between the results of the model and the matrix that presents observations. Comparison between model projections under different scenarios – a matrix that represents the females’ distribution at the end of five time steps (average of 30 runs) – to the observations matrix that represents the real annual home ranges of the reintroduced females, five years since project’s onset. The measures’ codes are as described in Table A1.

TABLE A4. Ranks for the woodland cover type of the home ranges in the different sensitivity tests. The scores were determined using different strategies: (1) sharp bell shape – large differences between the scores; (2) mediocre bell shape – mediocre differences between the scores; (3) moderate bell shape – a moderate difference between the scores.

TABLE A5. Sensitivity analysis - Effect of changes in the home range’s characteristics and movement parameters. Comparison between model projections under different scenarios – a matrix that represents the females distribution at the end of five time steps (average of 30 runs) – to the observations matrix that represents the real annual home ranges of the reintroduced females, five years since project’s onset. The measures’ codes are as described in Table A1.

TABLE A6. Sensitivity analysis - Effect of changes in the spatial overlapping between home ranges. Comparison between model’s projections under different scenarios, a matrix that represents the females distribution at the end of five time steps (average of 30 runs), to the observations matrix that represents the real annual home ranges of the reintroduced females, five years since project’s onset. The measures’ codes are as described in Table A1. The sign “2!” represents  complete recognition of activity center. *For  good habitat conditions (score above 7) there is an overlapping probability with nine individuals. In other conditions (above threshold) with maximum 5 individuals. ** At good habitat conditions (score above 7) there is an overlapping probability with nine individuals. In other conditions (above threshold) the probability of overlapping with 5–9 individuals is 0.5. *** Overlapping with two more individuals is in probability of 0.5, with 1 more in any condition.

a). Model projection                                                              b). Observations

FIG. A1: Spatial expansion of a reintroduced population of Persian fallow deer: Patterns are based on: model projection (average of 30 outputs) to the end of five years since the onset of the project after canceling the opportunity to improve the home range (shift) to areas in which the conditions are better: (a) observations at the end of five years since the onset of the project (37 studied females’ annual home ranges) and (b) pixel represents 100 by 100 m (total of 130 by 160 pixels). Color represents the number of individual home ranges of which the pixel is part. An arrow represents the release site.

a). Model projection (Max. 2 deer)         b). Model projection (Max. 14 deer)         c). Observations

FIG. A2: Spatial expansion of a reintroduced population of Persian fallow deer: Patterns are based on: model projection (average of 30 outputs) to the end of five years since the onset of the project after limiting the spatial overlap between home ranges to a maximum of one animal overlapping with no more than two others (a), and to a maximum of one animal overlapping with up to 14 animals (b), and observations at the end of five years since the onset of the project (37 studied females’ annual home ranges) (c). Pixel represents 100 by 100 m (total of 130 by 160 pixels). Color represents the number of individual home ranges of which the pixel is part. An arrow represents the release site.

LITERATURE CITED

Cramer, P. C., and K. M. Portier. 2001. Modelling Florida panther movements in response to human attributes of the landscape and ecological settings. Ecological Modelling 140:51–80.

Dunning, J. B., D. J. Stewart, B. J. Danielson, B. R. Noon, T. L. Root, R. H. Lamberson, and E. E. Stevens. 1995. Spatially explicit population models: current forms and future uses. Ecological Applications 5:3–11.