Supplementary/additional Online Information for
Divergence of the Potential Invasion Range of Emerald Ash Borer and its Host
Distribution in North America under Climate Change
Liang Liang and Songlin Fei
Liang Liang
Corresponding author
Department of Geography
University of Kentucky
817 Patterson Office Tower,
Lexington, KY 40506, USA
E-mail address: liang.liang@uky.edu
Phone: 1-859-257-7058
Fax: 1-859-323-1969
Songlin Fei
Department of Forestry and Natural Resources
Purdue University
221E Pfendler Bldg., 715 West State St.
West Lafayette, IN 47907, USA
E-mail address: sfei@purdue.edu
Phone: 1-765-496-2199
Supplementary Note on Climatic Suitability Multi-threshold Determination
A multi-threshold approach was used to delineate climatic suitability classes from
continuous climatic suitability spectrum based on the sum of sensitivity and specificity
(SSS) index (Fei et al. 2012). Sensitivity here refers to the ratio of correctly predicted
presences to their total number, and specificity indicates the ratio of correctly predicted
absences to their total number (Jiménez-Valverde and Lobo 2007). The sum of these two
measures provides an overall accuracy estimate for binary (presence/absence)
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predictions. Testing thresholds between 0 and 1 with 0.01 intervals were then applied to
the continuous EAB climatic suitability predictions in its native range. For each specific
threshold, suitability values were designated as absence if smaller than the threshold or
presence otherwise. The series of binary results from using different testing thresholds
were compared to the native range to calculate the SSS index values. A central threshold
was identified when the SSS value was maximized, which corresponded with potentially
the most accurate binary prediction. Identifying the central threshold is useful for
dichotomous mapping of generally suitable and unsuitable climates.
However, the distinction between suitable and unsuitable climates is often not clear-cut
as there are transitional zones where neither term might strictly apply. To address this
uncertainty, on both sides of a central threshold, we searched for a lower boundary and an
upper boundary in order to define a threshold window instead of a cut-off point
(Appendix Fig. 3). These boundary thresholds were delineated at the “turning points”
where the SSS values deviate significantly from the “plateau” which is characterized by
relatively gentle variations. To assist detecting the turning points, we calculated moving
standard deviations for consecutive SSS values. A three-period moving standard
deviation line was fitted on the SSS values against testing thresholds. Turning points
were then determined when the moving standard deviation values significantly departed
from a relatively low and stable level (corresponding to the “plateau”).
As shown in Appendix Fig. 3, SSS value first increases then decreases with the
increment of testing threshold, showing a parabolic curve shape. A central threshold
(0.27) was found when SSS reached its maximum, where the increment value changes
sign (from + to -). Points with abrupt changes on the moving average lines correspond
with the boundary thresholds (0.09 and 0.45). The magnitude of SSS change within the
delineated threshold window is quite small, between -0.01 and 0.01. A suitability ratio
between the lower boundary threshold and the central threshold indicates that the climate
is likely to be suitable, yet may not be favorable. When the ratio falls below the lower
boundary threshold, the climate is likely unsuitable, while a ratio that is beyond the upper
boundary threshold indicates that the corresponding climate is very favorable or highly
suitable. Accordingly, we defined the suitability levels as below: unsuitable (<0.09), low
suitability (0.09~0.27), medium suitability (0.27~0.45), and high suitability (>0.45). The
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multi-threshold delineation of EAB climate suitability zones and implied risk levels
allowed evaluating the impact of climate change on EAB invasion in a more
management-friendly context.
References
Jiménez-Valverde A, Lobo J (2007) Threshold criteria for conversion of probability of
species presence to either-or presence-absence. Acta Oecologica 31 (3):361-369
Fei S, Liang L, Paillet FL, Steiner KC, Fang J, Shen Z, Wang Z, Hebard FV (2012)
Modelling chestnut biogeography for American chestnut restoration. Divers and
Distrib 18 (8):754-768
Appendix Tables
Appendix Table 1 Area under the receiver operating characteristic (ROC) curve (AUC)
values for Maxent model predictions. The Average AUC was calculated from the AUC
values from 10 replicate model runs for respective climate regimes.
Climate
1980-2000
2020 (A2a)
2020 (B2a)
2050 (A2a)
2050 (B2a)
Average AUC
0.817
0.819
0.819
0.816
0.820
σ
0.003
0.003
0.003
0.002
0.002
Appendix Table 2 Summary of environmental variables used in the Maxent models.
Relative importance of each variable is quantified using mean percentage contribution
estimates. The environmental ranges (with lower and upper limits) of variables defining
suitable climate for EAB were delineated using the central threshold (Cf. Appendix Fig.
2).
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Climate variables* Mean % contribution Lower limit (ºC) Upper limit (ºC)
Tmax
14.5
22.0
33.0
Tmin
13.0
-38.0
0.5
Trange
20.5
27.5
61.0**
Tmin (June)
52.0
7.0
19.0
*Tmax, maximum temperature of the warmest month; Tmin, minimum temperature of
the coldest month; Trange, annual temperature range; Tmin (June), minimum June
temperature.
** Taiwan showed an outlying temperature range (14.5-15.5 ºC).
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Appendix Figures
Appendix Fig. 1 Response curves of climatic suitability against environmental variables
respectively. Mean response (red) and +/- 1 standard deviation intervals (blue) are
shown. Environmental variables (°C) are: Tmax, maximum temperature of the warmest
month; Tmin, minimum temperature of the coldest month; Trange, annual temperature
range; and Tmin (June), minimum June temperature. An outlying spike of Trange on the
low end is seen, corresponding to the smaller annual temperature variation in Taiwan.
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Appendix Fig. 2 Emerald ash borer (EAB, Agrilus planipennis Fairmaire) infested areas
as of September 5, 2013 (USDA APHIS) and the distribution of green ash (Fraxinus
pennsylvanica), white ash (F. americana), black ash (F. nigra) and blue ash (F.
quadrangulata), respectively. The underlying background provides state and province
boundaries in the U.S. and Canada.
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Appendix Fig. 3 Sum of sensitivity and specificity (SSS, left y-axis) and the moving
standard deviation of SSS values between consecutive points (right y-axis) against testing
thresholds (0.01~0.60 presented, at intervals of 0.01). Locations of identified central and
boundary thresholds are marked with lines.
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