GIS for Environmental Decision Making - Chapter 7 ppt

117
CHAPTER 7
GIS and Predictive Modelling: A Comparison of
Methods for Forest Management and Decision-Making

A. Felicísimo and A. Gómez-Muñoz

7.1 INTRODUCTION
GIS can be a useful tool for spatial or land-use planning, but only if several
conditions are fulfilled. The key conditions are related to 1) the quality of basic
spatial information, and 2) the statistical methods applied to the spatial nature of the
data. Appropriate information and methods allow the generation of robust models
that guarantee objective and methodologically sound decisions.
In this study we apply several multivariate statistical methods and test their
usefulness to provide robust solutions in forestry planning using GIS. We must
emphasize that in our Iberian study area, where forests have progressively
decreased in extent over centuries, the main aims of forestry planning are the
reduction of forest fragmentation, biodiversity conservation, and restoration of
degraded biotopes.
The research develops a set of likelihood or suitability models for the presence
of tree species that are widely distributed over a study area of 41,000 km
2
. The
utility of suitability models has been demonstrated in some previous studies
1
, but
they are still not as widely employed as might be expected.
A suitability model is a raster map in which each pixel is assigned a value
reflecting suitability for a given use (e.g., presence of a tree species). Suitability
models can be generated through diverse techniques, such as logistic regression or
non-parametric CART (classification and regression trees) and MARS (multiple

adaptive regression splines)
2-4
. All of these techniques require a vegetation map
(dependent variable) and a set of environmental variables (climate, topography,
geology, etc.) which potentially influence the vegetation distribution. The
foundation of the method is to establish relationships between the environmental
variables and the spatial distribution of the vegetation. Typically, each vegetation
type will respond in a different way as a consequence of its contrasting
environmental requirements.
Suitability is commonly expressed on a 0-1 scale (incompatible-ideal). The
precise value depends on a set of physical and biological factors that favor or limit
the growth of each type of vegetation. Once the distribution of suitability values
across a region is known, decisions on land use and management can be made on
the basis of objective criteria.
© 2008 by Taylor & Francis Group, LLC
118 GIS for environmental decision-making

The set of suitability values for a region can be considered as the potential
distribution model if presented as a map: the area defined as ‘suitable’ in a model
should reflect the potential area for the vegetation type under consideration. Such
a model also represents the relationships between presence/absence of each forest
type and the values of the potentially influential environmental variables in a given
region. Usually, current forest distributions are significantly smaller than the
potential spatial extents because they have been systematically logged. Potential
distribution models allow the recognition and delineation of such former
distribution areas in order to direct current and future management plans, provide
valuable data for restoration initiatives and highlight areas where such actions
should be considered a priority.
7.2 OBJECTIVES
The main objectives of the study were to 1) use several different statistical

methods to generate maps of potential distributions and suitability for each of three
species of Quercus (oak) in the study area, and 2) identify the most appropriate
method and assess its advantages and limitations. In order to fulfill these
objectives, we developed a workflow that included sampling strategies, GIS
implementation of statistical models and validation of results.
7.3 STUDY AREA
The study area was Extremadura, one of the 17 Autonomous Communities of
Spain, covering 41,680 km
2
, and located in the west of the Iberian Peninsula
(Figure 7.1). It has a Mediterranean climate, somewhat softened by the relative
proximity to the sea and the passage of frontal systems from the Atlantic.
The study subjects, which partially cover this area, were three species of the
genus Quercus that grow in forests or ‘dehesas’. Dehesas are artificial ecotypes
derived from original forest clearings (Figure 7.2). Continuous forest cover
disappeared centuries ago and currently only scattered patches remain over a large
potential area. In some places deforestation was complete and not even the most
open dehesas remain. Trees from the genus Quercus are the dominant constituents
of forests in the area, the most important species (and those considered in the
analysis) being Quercus rotundifolia Lam. (holm oak, 12,680 km
2
, synonym:
Quercus ilex L. ssp. ballota (Desf.) Samp.), Quercus suber L. (cork oak, 2,130
km
2
) and Quercus pyrenaica Wild. (Pyrenean oak, 950 km
2
). With some
exceptions, Pyrenean oak appears most commonly in forests, while cork and holm
oaks preferentially occur in dehesas.

© 2008 by Taylor & Francis Group, LLC
Predictive modelling of tree species 119

Figure 7.1 Location of Extremadura in the Iberian Peninsula.












Figure 7.2 Dehesas are artificial ecotypes comparable to savannas: a Mediterranean (seasonal) grassland
containing scattered trees of the genus Quercus.



© 2008 by Taylor & Francis Group, LLC
120 GIS for environmental decision-making

7.4 DATA
A set of raster maps was compiled to reflect the spatial distribution of
dependent and independent (predictive) variables.
7.4.1 Quercus Distributions

Current Quercus species distribution maps were taken from the Forestry Map of
Spain (scale 1:50,000), produced by the Spanish General Directorate for Nature
Conservation during the period 1986-96. We used the digital version of the map to
identify the main vegetation classes and the current spatial distributions (Figure

7.3).


























Figure 7.3 Current distribution of Quercus species in the study area (black represents Pyrenean oak, Q.
pyrenaica; dark gray, cork oak, Q. suber; and pale gray, holm oak, Q. rotundifolia).

© 2008 by Taylor & Francis Group, LLC
Predictive modelling of tree species 121

7.4.2 Predictive Variables

Raster maps were generated to represent the following independent variables:

• Elevation. A digital elevation model (DEM) was constructed using
Delaunay triangulation of spot height and contour data from the 1:50,000
scale topographic map of the Army Geographical Service, followed by
transformation to a regular 100 m resolution grid.
• Slope angle was calculated from the DEM by applying Sobel's algorithm
5
.
• Potential insolation. A measure was derived following the method
proposed by Fernández Cepedal and Felicísimo
6
. This used the DEM to
assess the extent of topographical shading given the position of the sun at
different standard date periods
7
. The result was an estimate of the time
that each point on the terrain surface was directly illuminated by solar
radiation. The temporal resolution was 20 minutes and the spatial
resolution 100 m.
• Temperature maps of the annual maxima and minima were interpolated
from data for 140 meteorological monitoring points (National Institute of
Meteorology, Spain) using the thin-plate spline method
8,9
with a spatial

resolution of 500 m.
• Quarterly rainfall maps were interpolated from data for 276
meteorological monitoring points (National Institute of Meteorology,
Spain) using the thin-plate spline method with a 500 m spatial resolution.

These variables were selected because of their potential influence on the
distribution of the vegetation and the availability of sufficient data to generate GIS
digital layers. Lack of data eliminated other variables (e.g., soils) commonly used
in ecological modelling.
7.5 METHODS
7.5.1 Statistical Methods

The methods used in predictive modelling are usually of two main types: global
parametric and local non-parametric. Global parametric models adopt an approach
where each entered predictor has a universal relationship with the response
variable. An advantage of global parametric models, such as linear and logistic
regression, is that they are easy and quick to compute, and their integration with a
GIS is straightforward. As an example of such a model we used logistic multiple
regression (LMR). This is widely employed in predictive modelling
10
, but has
several important limitations. For instance, ecologists frequently assume a
© 2008 by Taylor & Francis Group, LLC
122 GIS for environmental decision-making

response function which is unimodal and symmetric, yet this is often not
justified
11,12
.
An alternative hypothesis when modelling organism or community distributions

is to assume that the response is related to predictor variables in a non-linear and
local manner. Local non-parametric models are appropriate for such an approach
since they use a strategy of local variable selection and reduction, and are flexible
enough to allow non-linear relationships. Two examples of this type of model are
CART (classification and regression trees) and MARS (multiple adaptive
regression splines).
All three types of model used in this study were calculated from stratified
random samples of pixels with an approximately even representation of points
where each Quercus species was present or absent. Each random sample covered
about 10-20% of the total area for each species. One sample was used to generate
the models, and a second to test the reliability of the predictions.
7.5.1.1 Logistic Multiple Regression
Logistic multiple regression (LMR) has been used to generate likelihood
models for forecasting in a variety of fields. It requires a dichotomous
(presence/absence) dependent variable and the predicted probability of presence
takes the form shown in Equation 7.1:

P(i) = 1 / 1+exp[-(b
0
+ b
1
· x
1
+ b
2
· x
2
+…+ b
n
· x

n
)] (7.1)

where P(i) is the probability of presence (e.g., for a tree species), x
1
x
n
represent
the values of the independent variables, and b
1
b
n
the coefficients. The predicted
values from the regression are probabilities which range from 0 to 1 and can be
interpreted as measures of potential suitability
13
. Several studies have combined
LMR with GIS tools to present such probabilities in cartographic form. For
instance, Guisan et al.
14
used LMR in the ArcInfo GIS to generate a distribution
model for the plant Carex curvula in the Swiss Alps. A similar study on aquatic
vegetation was conducted by Van de Rijt et al.
15
using the GRASS GIS. In this
study LMR was performed using a forward conditional stepwise method in SPSS
®

11.5
16

and the results were then imported back into the ArcInfo
®
GIS
17
for
mapping.
7.5.1.2 Classification and Regression Trees
CART is a rule-based method that generates a binary tree through ‘binary
recursive partitioning’, a process that splits a node based on yes/no answers about
the values of the predictors
2
. Each split is based on a single variable, and while
some variables can be used several times in a model, others may not be used at all.
The rule generated at each step minimizes the variability within each of the two
resulting subsets. Applying CART often results in a complex tree of subsets based
© 2008 by Taylor & Francis Group, LLC
Predictive modelling of tree species 123

on a node purity criterion and subsequently this is usually ‘pruned back’ to avoid
over-fitting via cross-validation.
The main drawback of CART models when used to predict organism
distributions is that the generated models can be extremely complex and difficult to
interpret. For example, work on Australian forests by Moore et al.
18
produced a
tree with 510 nodes from just 10 predictors. In this study, the optimal tree
generated from the Quercus rotundifolia data set had 4889 terminal nodes.
Although the complexity of such a tree does not diminish its predictive power, it
makes it almost impossible to interpret, which in many studies is a key
requirement. Moreover, implementation of such an analysis within a GIS is

difficult. Nevertheless, as part of this study we developed a method to translate the
large CART reports (text files) to AML (Arc Macro Language) files that could be
run with the ArcInfo GIS. Such files can be large (e.g., the text file containing the
CART decision rules for constructing the Q. rotundifolia suitability map was 1.8
Mb in size) and execution times may be long (about 55 hours for the Q.
rotundifolia model).
7.5.1.3 Multivariate Adaptive Regression Splines
MARS is a relatively novel technique that combines classical linear regression,
mathematical construction of splines and binary recursive partitioning to produce a
local model where relationships between response and predictors can be either
linear or non-linear
3
. To do this, MARS approximates the underlying function
through a set of adaptive piecewise linear regressions termed ‘basis functions’. For
example, the first four basis functions from the Q. pyrenaica model are:

BF1 = MAX (0, PT4 - 3431)
BF2 = MAX (0, 3431 - PT4 )
BF3 = MAX (0, MDE50 - 1181)
BF4 = MAX (0, 1181 - MDE50)

where PT4 is the mean rainfall for the period October-December (l/m
2
* 10) and
MDE50 is elevation (m).
Changes in the slope of these basis functions occur at points called ‘knots’ (the
values 3431 or 1181 in the above examples). Regression lines are allowed to bend
at the knots, which mark the end of one region of data and the beginning of another
with different functional behavior. Like the subdivisions in CART, knots are
established in a forward/backward stepwise way. A model which clearly overfits is

produced first and then those knots that contribute least to efficiency are discarded
in a backwards-pruning step to avoid overfitting. The best model is selected via
cross-validation, a process that applies a penalty to each term (i.e., a knot) added to
the model in order to keep complexity as low as possible.
© 2008 by Taylor & Francis Group, LLC
124 GIS for environmental decision-making

As in the CART analysis, we transformed the MARS text report files into AML
and then generated the suitability models using the ArcInfo GIS.
7.5.2 Model Evaluation
The predictive capacity of a model can be evaluated as a function of the
percentages of correct classifications, both for presences and absences (sensitivity
and specificity parameters). The sensitivity and specificity of the model depend on
the threshold or cut-off, which is set so as to classify each point according to its
likelihood value.
To assess model performance we used the area under the Receiver Operating
Characteristic (ROC) curve, particularly a measure commonly termed AUC
19
. The
ROC curve is a plot of the relationship between sensitivity and specificity across all
cut-off points of the model. We developed a method to construct the ROC curves
by importing the databases associated with sample points into the SPSS statistical
package. The ROC curve is recommended for comparing two-class classifiers, as it
does not merely summarize performance at a single arbitrarily selected decision
threshold, but across all possible decision thresholds
20,21
. AUC is a synthesized
overall measure of model accuracy where 1 indicates a perfect fit and a value of 0.5
indicates that the model is performing no better than chance. AUC is also
equivalent to the normalized Mann-Whitney two-sample statistic, which makes it

comparable to the Wilcoxon statistic.
7.6 RESULTS
7.6.1 Suitability Models
All the LMR equations, MARS basis functions and CART classification rules
were translated into ArcInfo GIS syntax. ArcInfo was subsequently used to
generate the spatial suitability models, whose goodness-of-fit was evaluated by
AUC values. Table 7.1 compares the overall results for different tree species and
statistical methods, with bold text highlighting the best fitting models for each
species. The AUC values indicate that the LMR models provided the poorest
goodness-of-fit for each species, while the CART ones were the best performers.
However, there were some differences between tree species with a relatively
narrow range of AUC values for Q. pyrenaica (i.e., all the methods produce a good
fit) and a much greater one in the Q. rotundifolia case. This may be related to
differences in the current extent of the species (see Section 7.3) with Q.
rotundifolia being the most common and therefore having potentially more
complex environmental relationships. It is also worth noting that greater
complexity (number of terminal nodes) in the CART models does not guarantee
better results. This is an interesting finding that could assist in the practicalities of
implementing such models within a GIS framework.

© 2008 by Taylor & Francis Group, LLC
Predictive modelling of tree species 125

Table 7.1 Summary statistics for the suitability models
Quercus Species Method
Terminal
Nodes AUC
Confidence
Interval (95%)
Q. pyrenaica, Pyrenean oak

LMR Not Applicable 0.924 Not Available
Sample Size MARS Not Applicable 0.972 0.970-0.974
18,880 positive cases CART 56 0.970 0.968-0.972
18,590 negative cases CART 102 0.974 0.972-0.976
CART 204 0.979 0.977-0.981
CART 817 0.974 0.972-0.976
Q. suber, cork oak RLM Not Applicable 0.790 Not Available
Sample Size MARS Not Applicable 0.802 0.799-0.805
42,040 positive cases CART 525 0.971 0.970-0.972
41,979 negative cases CART 1016 0.975 0.974-0.977
CART 2355 0.975 0.973-0.976
Q. rotundifolia, holm oak RLM Not Applicable 0.627 Not Available
Sample Size MARS Not Applicable 0.767 0.764-0.770
50,394 positive cases CART 1343 0.889 0.887-0.891
50,690 negative cases CART 2347 0.894 0.892-0.896
CART 4889 0.895 0.893-0.897

Another feature of the CART model output became apparent when the results
were converted into suitability maps. As is illustrated in Figure 7.4a the CART
maps show abrupt transitions between areas of high and low suitability (darker and
lighter shading respectively) which reflects the reliance on binary rules. In
addition, due to the influence of climate variables, the suitability models frequently
replicate the shapes of isopleths, which makes them visually less convincing.
Although the backward pruning process in CART reduces the number of terminal
nodes and makes the final model less complex, it does not eliminate such effects.
These features are not present in the MARS-based maps (Figures 7.4b-7.4d) which
show more smoothed and continuous distributions of suitability values. For this
reason, we decided to use the MARS model output to generate a potential
vegetation distribution.
© 2008 by Taylor & Francis Group, LLC

126 GIS for environmental decision-making

Figure 7.4 Suitability models: a) CART model for Q. rotundifolia, b) MARS model for Q. pyrenaica, c)
MARS model for Q. suber, d) MARS model for Q. rotundifolia. Darker shading indicates higher
suitability.
7.6.2 Potential Vegetation Model
Suitability models for the three tree species were combined to generate a
potential vegetation distribution map that could be used to inform land management
and decision-making. This map was generated through a decision rule that took
into account both suitability values as well as proximity to the current presence of
forests. We defined a function where, for each cell, the suitability value for each
species was corrected by the inverse of the distance to the closest cell where the
species currently grows. This correction can be considered as a coarse indicator of
© 2008 by Taylor & Francis Group, LLC
Predictive modelling of tree species 127

colonization likelihood. The result of these calculations was a model showing, for
each cell, the type of forest with the highest potential value after considering
colonization processes. Figure 7.5 shows the result, highlighting relatively
clustered regions for Q. pyrenaica amidst more dispersed distributions for the other
two Quercus species.

Figure 7.5 Potential distribution model of Quercus species in Extremadura; Q. pyrenaica (black), Q.
suber (dark gray), Q. rotundifolia (pale gray).
7.7 CONCLUDING DISCUSSION
Suitability maps represent a useful tool for environmental management as they
synthesize a wide range of knowledge which is difficult to integrate in any other
way. Until recently, most potential vegetation maps were developed by largely
subjective methods, usually by an ‘expert’. In contrast, the approach used in this
study is based on robust statistical or GIS operations, and objective cartographical
© 2008 by Taylor & Francis Group, LLC

128 GIS for environmental decision-making

information. There is an explicit procedure to produce the final result and the
entire workflow of information is transparent and repeatable.
The models used are based on real data (data driven) and in our experience
these methods give good results in mountainous areas because the limiting factors
are mainly physical: elevation, potential insolation, slope, etc. Data on such
variables are generally available (e.g., elevation) or can be derived with sufficient
accuracy (e.g., potential insolation). However, the choice of statistical methods to
employ can be very important.
Our results (see also Muñoz and Felicísimo
4
) show that spatial distributions can
be better defined if we accept that they may follow non-linear patterns. LMR has
been widely used in predictive modelling to successfully predict organism/
community distributions despite drawbacks such as an inability to deal with skewed
or multi-modal responses, but we have also provided evidence that CART and
MARS are very effective methods in the most difficult cases.
The analysis presented in this chapter has used various procedures to link
statistical tools and GIS, but it is clear that there is still a need for better integration
of such capabilities in most common commercial GIS. Transferring the potential
vegetation model into practical forestry action would also require further
information, especially on soil properties and economic factors. Dealing with such
implementation issues is beyond the scope of this chapter, but it is evident that the
generated maps and statistics represent data of obvious utility. Combining such
model-based maps with current land-use information and management data could
help provide decision support tools that would be extremely useful in many aspects
of spatial or environmental planning.
7.8 ACKNOWLEDGMENTS
This study was conducted as part of Project 2PR01C023 co-funded by the Junta

de Extremadura and FEDER (Fondo Europeo de Desarrollo Regional).
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