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of polar bears (e.g., availability of alternative regions) and
for biotic and environmental interactions (as expressed in
the conditional probability tables; see Appendix B). The
spread of probabilities among the BN outcome states, reflect
the combinations of uncertainties in states across all other
variables, as reflected in each of their conditional probability
tables (Appendix B). This spread carries important informa-
tion for the decision maker who needs to weigh alternative
outcomes in a risk assessment (see below).
Finally, uncertainty in model predictions entails address-
ing model credibility, acceptability, and appropriateness of
the model structure. We made every effort to ensure that the
model structure was appropriate and credible and that the in-
puts (Tables D1a and D1b) and conditional probability tables
(Appendix B) were parameterized according to best avail-
able knowledge of polar bears and their environment. We
explored the logic and structure of our BN model through
sensitivity analyses, running the model backward from par-
ticular states to ensure it returned the appropriate starting
point, and performing particular “what if” experiments (e.g.,
by fixing values in some nodes and watching how values at
other nodes respond). We are as confident as we can be at
this point of development that our BN model is performing
in a plausible manner and providing outcomes that can be
useful in qualitatively forecasting the potential future status
of polar bears.
Although this manuscript and the model it describes have
been peer reviewed by additional polar bear experts, the
model structure and parameterizations were based upon the
judgments of only one expert. Therefore, additional criteria
of model validation must be addressed through subsequent
peer review of the model parameters and structure [
Mar-
cot
et al.
, 1983;
Marcot
, 1990, 2006;
Marcot
et al.
, 2006].
This requirement means the model presented here should be
viewed as a first-generation alpha level model [
Marcot
et
al.
, 2006]. The next development steps have been described
in detail by
Marcot
et al.
[2006] and include peer review of
the alpha model by other subject matter experts and con-
sideration of their judgments regarding model parameteriza-
tion; reconciliation of the peer reviews by the initial expert;
updating the model to a beta level that incorporates the re-
views; and testing the beta model for accuracy with exist-
ing data (e.g., determining if it matches historic or current
known conditions). Additional updating of the model can
include incorporation of new data or analyses if available.
Throughout this process, sensitivity testing is used to verify
model performance and structure. This framework has been
used successfully for developing a number of BN models
of rare species of plants and animals [
Marcot
et al.
, 2001,
2006;
Raphael
et al.
, 2001;
Marcot
, 2006]. Model variants
that may have emerged in this process would represent the
range of expert judgments and experiences (possibly veri-
fied with new data), and this range could be important infor-
mation for decision making.
Because these additional steps in development have not
yet been completed, it is important to view probabilities
of outcome states of our first-generation model in terms
of their general direction and overall magnitudes rather
than focusing on the exact numerical probabilities of the
outcomes. When predictions result in high probability of
one population outcome state and low or zero probabili-
ties of all other states, there is low overall uncertainty of
predicted results. When projected probabilities of various
states are more equally distributed, however, careful con-
sideration should be given to large probabilities represent-
ing particular outcomes even if those probabilities are not
the largest. Consistency of pattern among scenarios (e.g.,
different GCM runs) also is important to note. If the most
probable outcome has a much higher probability than all
of the other states and if the pattern across time frames and
GCM models is consistent, confidence in that outcome pat-
tern is high. If, on the other hand, probabilities are more
uniformly spread among different states and if the pattern
varies among scenarios, importance of the numerically most
probable outcome should be tempered in view of the com-
peting outcomes. This approach takes advantage of the in-
formation available from the model while recognizing that
it is still in development. It also conforms to the concept of
viewing the model as a tool describing relative probabilis-
tic relationships among major levels of population response
under multiple stressors.
4.2. Bayesian Network Model Outcomes
In the BN model, for each scenario run, the spread of
population outcome probabilities (or at least nonzero possi-
bilities) represented how individual uncertainties propagate
and compound across multiple stressors. Beyond year 50,
“extinct” was the most probable overall outcome state for all
polar bear ecoregions, except the AE (Plate 4 and Table 2).
For the decade of 2020-2029, outcomes were intermediate
between the present (year 0) and the foreseeable future (year
50) time frames. We projected that polar bear numbers in
the AE and PBCE could remain the same as now through the
earlier decade, becoming smaller by mid century. In the SIE
and PBDE, polar bears appeared to be headed toward ex-
tinction soon. however, probabilities they may persist in the
PBDE and SIE were much higher at year 25 than at mid cen-
tury (Plate 4). Although our BN model suggests polar bears
are most likely to be absent from the PBDE and SIE by mid
century, there is much uncertainty regarding when, between
now and then, they might disappear from these ecoregions.
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