Supplementary Information
Model Parameters
Inbreeding depression
The median reported number of lethal equivalents (i.e. number of single alleles
or combination of partially deleterious alleles per diploid genome which cause
death when homozygous) in a survey of 40 populations of 38 mammalian
species is 3.14, with 50% of the effects of inbreeding depression being due to
recessive lethal alleles [1], and we use this default value because specific data on
inbreeding depression in brown bears are limited. The isolated Kodiak Island
brown bear population in Alaska is relatively large (>2500 individuals) and
shows high reproductive performance despite very low levels of genetic
diversity measured at neutral markers, indicating that under some
circumstances (e.g. favourable, high-productivity habitat), brown bear
populations may be able to survive through many generations of reduced fitness
and purge strongly deleterious alleles [2]. However, low reproductive success
associated with inbreeding depression has been reported in both captive [3] and
small fragmented wild [4] European brown bear populations that are
phylogenetically close to the extinct Irish bear population, and intensive
management of threatened brown bear populations to minimise the effects of
inbreeding through processes such as translocation is a key component of
current conservation activities for the species [4-6]. Single-parameter sensitivity
analysis on the lethal equivalents parameter showed that even at half the 3.14
value, median extinction time is not likely to exceed 3000 years (Figure S4).
1
Age at first reproduction
The most common estimate of age at first reproduction for female brown bears
is between 4 and 6 years old [7-8], and a comprehensive study of over 4,700
radio-collared female brown bears [9] found the modal age of primiparity to be
4.3 years. VORTEX only accepts integer values for this parameter, and so a value
of 4 years was used. For males, age at first reproduction ranges from 3 years [10]
to 9 years [11]; the mean value of 6 years was used for this parameter. The mean
age at first reproduction for North American barren-ground brown bear
populations was calculated from eight estimates as 7.48 years, ranging between
6 and 9.6 years [12-13]; a value of 7 years was used.
Age at senescence
In many extant bear populations, human-caused mortality is a major cause of
adult mortality [8], which can result in a younger age structure in many
populations than would occur in the absence of humans [9]. As Ireland was one
of the last countries in Europe to be colonised by human settlers, around 9000
years BP [14], age at senescence in our Late Pleistocene brown bear population
must be estimated from upper survival bounds that may be rare today. We took
our estimate of age at senescence as 28 years, the age at which there is a sudden
drop in reproductive output [9].
Percentage females reproducing annually
Estimates for interbirth interval vary between 2-5 years, but 3 years is the most
commonly quoted estimate [8, 15-16]. A 3-year interbirth interval also fits with
the per capita litter production of 0.32 litters/female per year reported by ref.
[9]. However, while 3 years is the most common estimate for interbirth interval,
this parameter has been found to vary between populations occupying different
2
environments [12]; interbirth interval of Arctic barren-ground bears is 3.9 years
[12, 17].
Age-specific mortality
Data were taken from grizzly bears in Yellowstone National Park, because this
population is well-monitored and experiences a degree of protection from
poaching, and large, rigorously obtained life-history datasets are available [18].
For cubs and yearlings, only data from animals inside the park were used.
However, for adults and subadults (3-4 years old), mortality rates were not
disaggregated by location, so overall data were used [18]; adult mortality may
therefore be overestimated due to human-caused mortality being included. The
vast majority of human-caused mortality of adult bears is inflicted on males, not
females, and female mortality is accepted as far more important for bear survival
[18].
Environmental variation in mortality rate
This is estimated for cubs in Yellowstone [18] at around a quarter of the
mortality rate; the same proportion was applied to each of our mortality rates.
Population density
The lowest recorded brown bear population density is 3.8 bears/1000 km², and
the highest recorded density is 29.5 bears/1000 km² [11-12, 17, 19]. We
consider that the median of these carrying capacities (575 individuals) is most
likely to reflect real conditions in the refugium, as the maximum population
would be applicable only if the entire area constituted optimal bear habitat, an
unrealistic assumption given LGM environmental conditions, whereas the lowest
estimate may conversely be too pessimistic.
3
Scenario
settings
Species
description
Reproductive
system
Scenario name
Number of iterations
Number of years
Lethal equivalents *
% due to recessive alleles
EV concordance of reproduction
and survival
Number of catastrophe types
Reproductive system
Female age at first reproduction *
Male age at first reproduction
Reproductive
rates
Mortality rates
Mate
monopolization
Initial
population size
Carrying
capacity
Maximum age of reproduction
Max number of broods / year
Max progeny per brood
% sex ratio at birth (M)
% adult females breeding *
Average Bear
Model
1000
10,000
3.14
50
Barren-Ground
Bear Model
1000
10,000
3.14
50
Yes
0
polygynous [refs
11, 20]
4
Yes
0
polygynous [refs
11, 20]
7
6
28
1
4 [ref 15]
50 [refs 21-22]
6
28
1
4 [ref 15]
50 [refs 21-22]
33
100
7 [ref 15]
55 [ref 15]
32 [ref 15]
6 [ref 15]
50.5
26.8
18.6
18.6
6
0.2546*mortality
50.5
26.8
26.8
26.8
21.2
21.2
21.2
0.2546*mortality
25.5
100
7 [ref 15]
55 [ref 15]
32 [ref 15]
6 [ref 15]
50.5
26.8
18.6
18.6
6
6
6
6
0.2546*mortality
50.5
26.8
26.8
26.8
21.2
21.2
21.2
0.2546*mortality
49 [ref 11]
49 [ref 11]
575
575
58
575
575
58
Distribution: 1 brood
Probability: 1 offspring (%)
P: 2 offspring (%)
P: 3 offspring (%)
P: 4 offspring (%)
Female mortality: 0-1
F mortality: 1-2
F mortality: 2-3
F mortality: 3-4
F mortality: adult *
EV in female mortality
Male mortality rate (%): 0-1
M mortality: 1-2
M mortality: 2-3
M mortality: 3-4
M mortality: 4-5
M mortality: 5-6
M mortality: 6+
EV in male mortality (%)
% males successfully siring
offspring
SA Range, or Justification
for Exclusion from SA
Low importance
Adequate
Varied as low as 1
Low importance
Low importance
Not necessary
Good data available
3-7
Not as important; only
important for genetic
diversity
Low importance
Good data available
Good data available
Good data available
20-50%
Good data available
Good data available
Good data available
Good data available
Good data available
Low importance
Low importance
Low importance
Low importance
2.5-19%
Good data available
Low importance
Low importance
Low importance
Low importance
Low importance
Low importance
Low importance
Good data available
Low relative importance
Initial population size *
111-865
Carrying capacity *
EV in carrying capacity
111-865
Low importance
Table S1. Values used for each parameter in the two historical population viability
models and sensitivity analyses. The main differences between the models (highlighted
in blue) are female age at first reproduction and interbirth interval. F = female; M =
male; P = probability; EV = environmental variation. Parameters on which the sensitivity
of model outcomes was tested are indicated with asterisks.
4
Comparison between PVA Models
Mills et al. [23] investigated the outputs of four different PVA models, and
demonstrated how the conclusions of a PVA can vary substantially between
different models. In a declining population such as that of the bears we are
modeling, and in a situation such as ours that models environmental
stochasticity but no density dependence, VORTEX is the most pessimistic model,
in that in “average N at year 48” and “proportion of the replicates extinct from
500 runs”, VORTEX gives the lowest N and the highest proportion extinct. In an
approximately linearly declining population, both N and proportion extinct at a
particular time are linearly related to extinction time. Therefore we can estimate
that other models with methods comparable to our VORTEX scenarios (GAPPS
and INMAT) would have estimated extinction time for the Irish bear population
at approximately 1.5 and 2.1 times longer respectively than our extinction time
estimates. Given that neither of these alternative extinction times comes close to
the duration of the LGM (approximately 10,000 years), we remain convinced of
our conclusion that bears are unlikely to have persisted through the LGM in
Ireland.
5
Supplementary Procedures
Sensitivity Analysis
This was conducted on key parameters that were either data-deficient or had a
wide range of values in the literature, in order to assess the effect of parameter
value choice on our conclusions about brown bear survival. Parameters
investigated were adult female mortality rate, initial population size (K),
interbirth interval, and female age at first reproduction. These parameters were
explored both as single-parameter variations on the general model, and together
using a Latin hypercube (LHC) sampling design. The single-parameter variation
gives information on the shape of the relationship between parameter value and
time to extinction. The LHC sampling brings out the most important
parameter(s) and shows whether model relationships hold when combinations
of parameter values within the range of uncertainty are tested. If there are
strong interactions between parameters, or if a parameter is considerably less
influential than others, a weak or non-existent relationship will be apparent.
However the most important use of LHC is by testing how often (i.e. what
proportion of) parameter combinations within plausible limits would cause the
conclusions of modelling work to change. Parameters were varied in randomlychosen integer steps between high and low values as follows: adult female
mortality rate between 3-19%; interbirth interval (i.e. 1 / % of females breeding
annually 20-50%) between 2-5 years; female age at first reproduction between
3-7 years; initial population size between 111-865. Fifty LHC sample scenarios
were made; each scenario was run 1000 times, for 10,000 years.
6
a) female mortality rate
b) % females breeding each year
%B
Female mortality
7000
6000
6000
Time to extinction
5000
5000
4000
4000
3000
3000
2000
2000
1000
1000
0
0
2
7
12
17
10
22
c) female age at first reproduction
Female min reproductive age
20
30
40
50
60
d) initial population size
K
3500
2500
3000
2000
2500
1500
2000
1500
1000
1000
500
500
0
0
0
2
4
6
8
0
200
400
600
800
1000
Figure S1. Sensitivity analyses based on single-parameter variations, showing
median and 95% confidence intervals.
7
a) female mortality rate
b) % females breeding each year
6000
6000
5000
5000
y = 1.1927x2 - 26.882x + 4.0282
R² = 0.2545
4000
y = 17.245x2 - 479.25x + 3480.6
R² = 0.2871
4000
3000
3000
Median time to extinction
2000
2000
1000
1000
0
0
0
0
5
10
15
20
40
60
-1000
c) female age at first reproduction
d) initial population size
6000
6000
5000
5000
4000
4000
y = -94.92x2 + 1038.2x - 2184.2
R² = 0.0365
3000
20
y = 0.0021x2 - 1.9978x + 866.25
R² = 0.0126
3000
2000
2000
1000
1000
0
0
0
2
4
6
8
0
200
400
600
800
1000
Figure S2. Sensitivity analyses based on 50 Latin hypercube samples of the same
parameter space as the single-parameter variations shown in Figure S1. Circles
show median extinction time of 1000 model runs; lines of best fit were generated
by fitting quadratic models to these median values.
8
Frequency of LHC SA results
25
20
15
10
5
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000
3200
3400
3600
3800
4000
4200
4400
4600
4800
5000
0
Median time to extinction
Figure S3. Distribution of median extinction times based on Latin hypercube
sampling of parameter space.
LE
7000
6000
5000
4000
3000
2000
1000
0
0
1
2
3
4
Figure S4. Sensitivity analyses on variation of lethal equivalents alone, showing
median and 95% confidence intervals.
9
In the absence of variation in other parameters (Figure S1), it is clear that small
increases in % mortality of female bears will dramatically reduce the time that
bears can persist during the LGM. By contrast, the time to extinction varies more
linearly with respect to the other three parameters. When the likely effect of
parameter variations is taken into account together in the LHC sampling
sensitivity analysis, female mortality is seen to have a large impact, as does the %
of females breeding each year, which also showed a large range in the singleparameter tests. Only 1/50 LHC samples returned an expected extinction time of
>3000 years.
10
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13