Figure 1.
Total grizzly bear (U. arctos horribilis) mortality from hunting (solid-black line) and non-hunting sources (dashed line) in British Columbia, Canada, from 2001–2011.
A province-wide moratorium on the trophy hunt during one of two hunting seasons caused lower hunting mortality in 2001.
Figure 2.
Illustration of method for estimating the probability of overmortality in an individual Grizzly Bear (U. arctos horribilis) Population Unit (“population unit”) and period.
Blue vertical line represents the mortality limit point estimate used by government. Entire distribution (in this example a hypothetical normal distribution used for simplicity) represents the distribution of mortality limit uncertainty, or the distribution of simulated mortality limits. Red dashed line represents the known mortality for the same population unit-period. Red portion of the distribution represents the proportion of simulated mortality limits that fell below known mortality levels in the population unit-period. The percent area of the overall distribution occupied by the red portion provides a proxy for the probability that overmortality occurred. See also Video S1.
Figure 3.
Outcome uncertainty for A) total and B) female mortality in Grizzly Bear (U. arctos horribilis) Population Units (“population units”) in British Columbia, Canada, 2007–2011 (see SI for additional periods).
Black curve is a Michaelis-Menten curve fitted by maximum likelihood, assuming a negative binomial error distribution. Red dashed line indicates a 1∶1 relationship; solid red dots above this line signal population unit-level overmortality events. Dark and light grey-shaded regions encompass the 50% and 80% prediction intervals, respectively (smoothed for visual purposes). Inset histograms show the distribution of GBPU-level percent difference between known mortalities and mortality targets (conflated with limits under mortality management policy); red bars to the right of red dashed lines indicate overmortality events.
Figure 4.
Number of allocation periods (2001–2003, 2004–2006, or 2007–2011) in which female or total overmortality occurred in Grizzly Bear (U. arctos horribilis) Population Units (“population units”) of British Columbia, Canada.
Shown are 2009 population unit boundaries. Hunting is not allowed in areas denoted as “threatened”, “extirpated”, or “closed to hunting”. One additional population unit (Blackwater-West Chilcotin) has been reclassified as threatened as of 2012.
Figure 5.
Female mortality as percent of total mortality across Grizzly Bear (U. arctos horriblis) Population Units (“population units”) in British Columbia, Canada, and allocation periods (2001–2003, 2004–2006, and 2007–2011).
(A) female mortality as percent of all mortality, (B) female mortality as percent of all mortality in female overmortality events, (C) female hunting mortality as percent of all hunting mortality, and (D) female hunting mortality as a percent of all hunting mortality in female overmortality events. Vertical red lines indicate 30%, the threshold below which female mortality must remain for total mortality limits to be theoretically sustainable according to the BC government’s mortality management procedure.
Figure 6.
Total and female overmortalities of Grizzly Bear (U. arctos horribilis) Population Units (“population units”) of British Columbia, Canada, from 2007–2011 (see SI for additional periods).
A) Overmortalities detected given known hunting mortality levels and without consideration of mortality limit uncertainty. Blue indicates population units with detected overmortality whereas white indicates population units without. B–D) Simulated probability of total or female overmortality, incorporating uncertainty around mortality limits. Panel B shows simulated probability of overmortality given known mortality rates; panels C and D show what the probability of overmortality would be had hunting mortality been reduced by 50% or 100%, respectively, assuming other sources of mortality remained unchanged. Increasingly dark red indicates an increasing probability of overmortality in a given period. Grizzly bears have been extirpated from dark-grey areas. Light-grey areas indicate population units in which populations are either threatened or were closed to hunting during the study period.
Figure 7.
Illustration of our method for setting female (A and C) and total (B and D) mortality targets, with maximum probability of overmortality of 5% (A and B) or 25% (C and D) by integrating outcome uncertainty (grey distribution) and mortality limit uncertainty (red distribution), using the Stewart Grizzly Bear (U. arctos horribilis) Population Unit as an example.
Targets (dashed black lines) from this approach are set so that the resulting outcome uncertainty distribution (grey distribution) overlaps with a maximum of 5% or 25% of the mortality limit uncertainty distribution (red distribution). Red vertical lines represent mortality limits (conflated with targets in previous periods under mortality management policy) set by the government in 2007–2011. Magnitudes of recommended target reductions are shown by black double-headed arrows. E-F) Reduction in mortality targets, relative to 2007–2011 targets (conflated with limits under mortality management policy), required to maintain the probability of both female and total overmortality below E) 5% or F) 25%. Increasingly dark red indicates increasing target reductions identified.