A spatial, climate-determined risk rating for Scleroderris disease of ...

1400 Can. J. For. Res. Vol. 28, 1998
Table 2. Diagnostics from four logistic regression analyses.
Diagnostics
Backward
stepwise selection
(11 variables)
al. (1996) generated mathematical climate surfaces for the province
using the thin-plate smoothing-spline techniques of Hutchinson
(1991). These monthly surfaces were created as a function of
latitude, longitude, and elevation to capture both spatial and temporal
variations in lapse rates. Errors associated with the surfaces
are approximately ±0.5°C for temperature related variables, and
10–20 mm for precipitation.
These surfaces enable us to append climate variables to
georeferenced (latitude, longitude, elevation) historical field survey
data. Also, the climate variables can be mapped by coupling the
mathematical surfaces to a digital elevation model (a regular grid
of latitude, longitude, and elevation representing the topography on
an area; see Moore et al. 1991). A digital elevation model for Ontario
has been developed based on the National Topographic Series
1 : 250 000 digital topographic data resolved at a 1-km grid. Mathematical
surfaces were developed for long-term mean monthly averages
of minimum temperature, maximum temperature, and
precipitation. Secondary climate variables, that are likely to reflect
processes determining distributions of organisms, were derived
from these primary surfaces (see Mackey et al. 1996 for further details
on climate modelling).
Analysis
We used logistic regression analysis to examine the probability
of occurrence of Scleroderris disease as a function of aspects of
temperature and precipitation. For each sample location where
Scleroderris disease was confirmed as present or absent, we attached
an estimate of each of the climate variables listed in
Table 1. The severity of the disease was not considered as all plantations
are at risk after the disease becomes established. We ran
several different models. First, we used all climate variables in a
backward stepwise selection procedure to identify the best possible
predictability that could be derived from these explanatory variables
using a criterion of α = 0.05 to remove a variable. Then we
selected two variables (the mean temperature of the coldest quarter
and the precipitation of the coldest quarter) that we anticipated
would explain variance in the probability of occurrence based on
our experience and on previously published work on the ecology
of the disease. We compared these two models using concordance
(an index of classification accuracy). We were attempting to identify
the most parsimonious model without incurring a large loss in
our ability to predict (based on classification). We then ran models
for each of the two selected climate variables separately and compared
the concordance with the two-variable model to evaluate the
usefulness of these variables on their own. Once we identified our
XTMPCLDQ
PRPCLDQ
XTMPCLDQ
(mean temperature
in coldest quarter)
–2log L (intercept only) 1534.2 1534.2 1534.2 1534.2
–2log L (intercept + covariates) 821.0 1089.9 1294.0 1520.9
Chi-square for covariates 713.2 444.3 240.3 13.3
df (model) 11 2 1 1
P (model) 0.0001 0.0001 0.0001 0.0003
Concordance (%) 91.4 84.4 74.0 57.6
Best probability 0.46 0.40 0.34 0.40
Sensitivity 85.6 76.8 60.8 56.7
Specificity 83.6 77.9 66.6 64.1
False negatives 22.3 30.1 45.1 48.6
False positives 10.4 16.6 28.3 31.2
PRPCLDQ
(precipitation in
coldest quarter)
Note: There were 1139 observations in the data set: 457 observations of presence and 682 observations of absence. See Table 1
for a description of the climate variables.
final model we examined the model in more detail by randomly
splitting the original data in half, running the model with half of
the data and generating a classification table from the other half of
the data. We repeated this procedure 10 times and summarized the
results. This procedure examines the ability of the model to predict
the occurrence of the species for locations that are not included in
the model and is therefore a more rigorous test of classification accuracy.
This test also indicates how dependent these results are on
the individual observations that are included in the model. Lastly,
we used the regression equation from the final model to predict the
probability of occurrence over the entire area of Ontario using the
gridded estimates of climate. We compared this map of probability
of occurrence to the original map of the observed locations of the
disease.
The results show a good match between the observed distribution
of Scleroderris disease (Fig. 1a) and the map of
probability of occurrence (Fig. 1b). We have not made predictions
for the most northern parts of Ontario because of
the relative scarcity of appropriate hosts in that area and because
we have no data that samples that environmental
space. Disease distribution was found to be closely related to
certain climatic variables. Using a backward stepwise procedure,
11 of the 23 climate variables were retained in the logistic
regression model (Table 1). The overall concordance
was 91.4%, an extremely high value, with a sensitivity (the
occurrence of an event (presence) when it was predicted) of
85.6% and specificity (the absence of an event when it was
predicted to be absent) of 83.6% (Table 2). This model has a
very good fit but is not very interpretable because there are
11 explanatory variables in the model. Also, more explanatory
variables result in a model that is increasingly dependent
on a particular set of observations.
On the basis of our knowledge of the ecology of the fungus,
two variables, mean temperature of the coldest quarter
and precipitation in the coldest quarter, were tested separately.
This model with only two variables was also a good
fit with a concordance of 84.4%, sensitivity of 76.8%, and
specificity of 77.9% (Table 2). This indicates that most of
the 11 explanatory variables in the first model do not
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