International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
29 explanatory variables
Moving window
(56m radius circle)
Figure 4. Moving window approach within the 56 m radius
circle as applied for all 1- 29 explanatory variables
2.3 Model development
The choice of the "right" model should be carefully made
considering possible advantages and disadvantages. According
to Austin and Gaywood (1994) a model used for biodiversity
assessment should not only be precise but also ecologically
sensible, meaningful and interpretable. An important statistical
development of the last 30 years has been the advance in
regression analysis provided by various linear models (Yee and
Mackenzie 2002). Linear least-square regression can be
generalized by transforming the dependent variable (McCullagh
and Nelder 1989). Generalized linear models (GLM) comprise a
number of model families e.g. binomial, Poisson, etc. (Guisan
and Zimmermann 2000). However, assuming a specific
theoretical distribution for the data used in this study seems to
be difficult. Differing collecting procedures (i.e. different ways
to the next tree and rock patch) rules out the model of the data
as a Poisson process. Therefore we used the simplest “first aid”
transformation (square root transformation) that allows coping
with count data. For each of the four field data sets (total
species richness, species richness for lichens on trees, on rocks
and on soil) we performed a stepwise dropping of our 29
explanatory variables — allowing both backward and forward
selection to build the models. We assumed that the relatively
high number of explanatory variables, often intercorrelated,
would be handled adequately by this stepwise methodology.
Among the variables remaining in the final models, 1st level
variables are used as single and as quadratic terms, whereas 2nd
level variables were square-root transformed. The complete
final models and their explanatory variables are listed below:
° Richness total - variance nir + variance _nir” + ratio2 + ratio2? +
sqrt(forest) ^ sqrt(grass light)
. . . . m
° Richness trees — varlance_nir + varıance_nır"
° Richness rocks ~ variance nir + variance nir + skewness +
skewness” + sqrt(grass_light)
o Richness soil ~ ratiol + ratiol* + skewness + skewness’ +
sqrt(rock&gravel&soil) [1]
The 96 sampling plots are divided into a calibration data set of
48 randomly sampled relevés and a reference data set consisting
of the remaining 48. With this calibration data set the model
was built and prediction values were calculated for the 48
sampling plots of the reference data. This was carried out 100
times. The means of the 100 runs are shown in table 2.
848
2.4 Validation
Several statistic measures were applied to evaluate the predicted
species richness against the measured species richness of the
sampling plots. Correlation of the fitted values with the
calibration data values was chosen as a measure for the model
quality (r model in table 2). The predictive power of the model
is estimated by the correlation of predicted data values with the
reference data values (r reference in table 2).
In the present study, the 95% quantile of the absolute errors, the
bias (difference between the mean values and the mean fitted
values), mean of absolute errors MAE (predicted species
richness compared to reference species richness) and the G-
value are applied as accuracy measures. The G-value (G) is a
measure of accuracy in the case of a quantitative response and
gives an indication of how effective a prediction might be,
relative to that which could have been derived from using the
sample mean alone. G is given by the equation 2:
n
S Eo Tan
i=l
Ri ke l
i=l
G=1-
[2]
Where Z(Xi) is the measured value at a sampling plot 1, Z(xi) is
the estimated value, and is the overall mean of the measured
sampling plots. A value of | indicates a perfect prediction,
while a value of 0 describes no significant agreement, and
negative values indicate that the predictions are less reliable
than if one had used the sample mean instead (Schloeder et al.
2001).
2.5 Application of models
[n order to extrapolate the predicted species richness of the
sampling plots to the entire area of the six LUUs the model had
to be applied accordingly. Lichen species richness for each
pixel of the six test sites was calculated implementing the
explanatory variables for the final models in a moving window
approach (in our case a moving circle). The sum of values
within a 56 m radius circle was calculated for each pixel of the
selected explanatory variable (see fig. 4) using GIS operations.
Then pixel-wise calculation of species richness for all lichens,
lichens on trees, on rocks and on soil was performed using the
four corresponding model equations (with their coefficients) as
given in the section model development. The results are maps
of predicted number of lichen species for each pixel in the
entire six LUUS (see fig. 5).
3. RESULTS
The best results of the models and the combination of
explanatory variables retained in each model are given in table
2. The quality of the models (r model) ranges between 0.59 for
lichens on soil and 0.79 for lichens on trees. Predictive power,
with a correlation coefficient (r reference) ranging between 0.48
and 0.79 and G ranging between 0.63 and 0.37, are obtained. In
general, species richness is slightly underestimated for sampling
plots with high species richness and overestimated for sampling
plots with low species richness. A total of 29 variables
correlated with the number of lichen species but only seven
were used for the final models.
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