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 217

and the professional judgment of polar bear expert S. Amstrup
(Tables D1a and D1b). Because BN models combine expert
judgment and interpretation with quantitative and qualita-
tive empirical information, inputs from multiple experts are
sometimes used to structure and parameterize a “final” model.
Because the model presented was parameterized with the judg-
ment of only one polar bear expert, it should be viewed as a
first-generation version. Accordingly, it will be refined through
formally developed processes (see section 4) at a future time.

2.6.2. Node C3: Distribution response. Distribution re-
fers here to the functional response of polar bears (namely,
movement and spatial redistribution of bears) to changing
conditions:

· same as now, polar bear distribution equivalent to that
at year 0;
· reduced but resident, bears would still occur in the
area but their spatial distribution would be more lim-
ited than at year 0;
· transient visitors, changing conditions would season-
ally limit distribution of polar bears;
· extirpated, complete or effective year-round dearth of
polar bears in the area.

2.6. Output States of the Bayesian Network Model

The final outcomes of BN model runs were statements of
relative probabilities that the population in each ecoregion
would be larger than now, same as now, smaller than now,
rare, or extinct. Responses of polar bears to projected habitat
changes and other potential stressors could affect polar bear
distribution or polar bear numbers independently in some
cases, or they could affect both distribution and numbers si-
multaneously. Principal results of the BN model are levels of
relative probabilities for the potential states at output nodes.
In the polar bear BN population stressor model, outcomes of
greatest interest were (1) those related to listing factors used
by the FWS, (2) the distribution responses, (3) numerical
responses, and (4) the overall population response.
We defined our output nodes (shown in Plate 3) in such a
way that their possible states could be assessed empirically
through future field observations. Potential states at the three
principal output nodes are described below.

2.6.3. Node D1: Overall population outcome. Overall
population outcome refers to the collective influence of both
numerical response (node C4) and distribution response
(node C3). It incorporates the full suite of effects from all
anthropogenic stressors, natural disturbances, and environ-
mental conditions on the expected occurrence and levels of
polar bear populations in the ecoregion. Overall population
outcome states were defined as follows:

· larger, polar bear populations have a numerical re-
sponse greater than at present (year 0) and a distribu-
tion response at least the same as at present;
· same as now, polar bear populations numerically and
distributionally indistinguishable from present;
· smaller, polar bears at a reduced density and dis-
tributed the same as at present or density same as at
present but occur as transient visitors;
· rare, polar bears are numerically difficult to detect and
have a distribution response same as at present, or oc-
cur as small numbers of transient visitors;
· extinct, polar bears are numerically absent or distribu-
tionally extirpated.

2.6.1. Node C4: Numerical response. This node represents
the anticipated numerical response of polar bears in an eco-
region based upon the sum total of the identified factors
which are likely to have affected numbers of polar bears in
each ecoregion:

· increased density, polar bear density detectable as
significantly greater than that at year 0, where density
can be expressed in terms of number of polar bears
per unit area of optimal habitat (thus expressing “eco-
logical density”) or of total (optimal plus suboptimal)
habitat (thus expressing “crude density”);
· same as now, equivalent to the density at year 0;
· reduced density, polar bear density less than that at year
0 but greater than one half of the density at year 0;
· rare, polar bear density less than half of that at year 0;
· absent, polar bears are not demonstrably present.

Here, the “extinct” state refers to conditions of (1) com-
plete absence of the species (N=0) from an ecoregion; or (2)
numbers and distributions below a “quasi-extinction” level,
that refers to a nonzero population level at or below which
the population is near extinction [ Ginzburg et al. , 1982; Ot-
way et al. , 2004]; or (3) functional extinction, that refers to
being so scarce as to be near extinction and contributing
negligibly to ecosystem processes [ Sekercioglu et al. , 2004;
McConkey and Drake , 2006].

Plate 3. (Opposite) Full Bayesian network population stressor model developed to forecast polar bear population outcomes in the 21st
century. Values shown in the bottom of nodes B, N, and C represent expected values +/- 1 standard deviation which are automatically
calculated and displayed by the Netica® modeling shell for continuous nodes with defined state values, based on Gaussian distributions.