A Bayesian Network Modeling Approach to Forecasting the 21st Century Worldwide Status of Polar Bears - Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications - page 214

status according to the Endangered Species Act [ U.S. Fish
and Wildlife Service , 2007]. We included summary nodes
for factor A, habitat threats; factor B, overutilization; factor
C, disease and predation; and factor E, other natural or man-
made factors. We did not include factor D, inadequacy of
existing regulatory mechanisms, because our model focused
on ecosystem effects; however, regulatory aspects could be
seamlessly added at a future time.

outputs. We ensured that input conditions matched the cur-
rent understanding of polar bear ecology and parameterized
the conditional probability tables to assure that node struc-
tures were specified in accordance with available polar bear
data or expert understanding of data. We checked the valid-
ity of the model parameterization by testing whether the BN
model responded to particular input conditions in ways that
paralleled responses of polar bear populations to conditions
that have been observed.
When the model is run, it calculates posterior probabilities
of outcomes by applying standard Bayesian learning to the
values assigned to each input variable. The relative influ-
ence of each input node, in terms of inherent model sensi-
tivity structure, is determined by the values assigned in the
conditional probability tables that underlie each summary or
output node in the network. One input variable can be given
greater influence than another if the result of a change in
the first variable is thought to have a greater influence on
the outcome states of the summary or output node than the
second, and if the conditional probabilities are assigned ac-
cordingly. For example, it may be thought that the temporal
absence of sea ice from the continental shelf is more impor-
tant to the availability of foraging habitat than is the distance
to which the ice retreats while it is absent. If data or pro-
jections suggest both measurements change in parallel, then
temporal absence would have the greater final influence. If,
however, data or projections show there is a greater change
in distance than in time of absence, then distance may have
the greatest contribution to posterior (outcome) probabilities
even though its weight in the conditional probability table
might be lower than temporal absence.
We used three different methods to arrive at final model
structure: (1) sensitivity analyses of subparts of the model,
(2) solving the model backward by specifying outcome
states and evaluating if the most likely input states that were
returned were plausible according to what we know about
polar bears now, and (3) running the model (and subparts)
forward to ascertain if the summary and output nodes re-
sponded as expected given the states of the input nodes. Our
goals were to ensure that input conditions matched the cur-
rent understanding of polar bear ecology and that the model
responded to particular input conditions in ways that paral-
leled observed responses of polar bear populations.
As fully specified, the BN model consisted of 38 nodes, 44
links, and 1667 conditional probability values specified by
the modelers (Plate 3 and Appendices A and B). The model
was solved for each combination of four ecoregions, six time
periods, and three future GCM scenarios (ensemble mean,
maximum, and minimum).
The input data to run each combination were specified by
summarizing the respective GCM-derived habitat variables

2.5. Parameterizing the Bayesian Network Model

We averaged the sea ice parameters for each GCM over
decadal periods to generate metrics that were less sensitive
to the intrinsic variability of GCM projections that occurs
at annual timescales. The BN model was applied to each
of the four ecoregions at six decadal time periods: 1985-
1995, 1996-2006, 2020-2029, 2045-2054, 2070-2079, and
2090-2099. For convenience, we hereinafter refer to these
six time periods, in relation to the present, as years − 10, 0,
25, 50, 75, and 95. Analyses included observed habitat con-
ditions from the satellite passive microwave data for years
− 10 and 0 and future habitat conditions projected by GCM
ice projections for future years. To capture the full range of
uncertainty in GCM outputs, we solved the BN model using
sea ice parameters from the (1) GCM multimodel (ensem-
ble) means, (2) GCM that projected the minimum ice extent,
and (3) GCM that projected the maximum ice extent, for
each ecoregion in each time period. Inputs other than sea ice
features included various categories of anthropogenic stres-
sors [ Barrett , 1981] such as harvest, pollution, oil and gas
development, shipping, and direct bear-human interactions.
Inputs also included other environmental factors that could
affect polar bear populations such as availability of primary
and alternate prey and foraging areas and occurrence of par-
asites, disease, and predation [ Ramsay and Stirling , 1984].
Whereas the ice habitat factors were entered into the BN
model as ranges of values (e.g., ice retreat of 0-200 or 200-
800 km beyond current measures), other potential stressors
were included as ordinal or qualitative categories (Tables
D1a and D1b).
Because we were interested in forecasting changes from cur-
rent conditions, states of each node were expressed categori-
cally as “compared to now.” That is, an outcome state could
represent a condition similar to present, better than present, or
worse than present. Here, now or year “0” means the 1996-
2006 period when referring to observations and 2000-2009
when referring to sea ice model projections. Before the BN
model was run, we specified the states for each input node
that seemed most plausible (Tables D1a and D1b).
States of environmental correlates were established under
each combination of time step, ecoregion, and GCM model