DISCUSSION
Caughley and Gunn (1993), Gunn (2003), Archer and Tieszen (1980), and
Payette et al. (2001) suggested that barren-ground caribou
fluctuations were mainly caused by the over-grazing of caribou when
subpopulation abundance was at high levels, followed by declines to
densities sufficiently low that the arctic/subarctic range could
recover. Bongelli et al ., (2020) provided a quantitative
demonstration that most barren-ground caribou subpopulations do not just
fluctuate, they cycle in a regular manner (sine cycles). Bongelliet al. (2020) found that approximately 96% of the variation in
the population cycles of nine sine cyclic North American barren-ground
subpopulations could be explained by a relatively simple environmental
regression model that considered only the subpopulation range size and
range productivity. Recognizing that a sine cycle provides an
unambiguous estimate of the Nt for the entire cycle, the
Verhulst (1838) equation for logistic growth was employed to show that
carrying capacity (Kt) also cycles regularly (Figure 1;
Figure 2; Figure 3). Barren-ground caribou logistic carrying capacity
(K) is best understood as a dynamic proxy variable (the units for K are
subpopulation numbers) for subpopulation range condition.
Subpopulation numbers of Qamanirjuaq, Bathurst, and George River caribou
closely tracked their respective carrying capacities (2-3 years)
throughout most of their respective cycles (Table 1; Figures 1; Figure
2; Figure 3; Figure 4). However, during the eruption phase of the cycle
all three subpopulations required about double the time to reach
Kt from intrinsic growth than during the rest of the
cycle (Table 1; Figure 4). In these three case studies, barren-ground
caribou declined when the range declined due to over-grazing, then
increased rapidly once their range had recovered. If some external
(perhaps decadal, progressive, catastrophic, or circumstantial) factor
were to impact subpopulation numbers, their range, or both there would
be a response to the trajectories of both habitat (K) and subpopulation
numbers (N). However, Bongelli et al., (2020) showed that the best
(Bayesian Information Criteria) mathematical description for
barren-ground caribou population trajectories is a sine cycle.The increase phase is symmetrical to the decline phase. Exactly half of
the cycle is spent with numbers > ½ the amplitude and
exactly half the cycle is spent with numbers < ½ the
amplitude. The regularity of barren-ground caribou population dynamics
over the history of census data collection for 9 subpopulations suggests
a simple and consistent relationship between barren-ground caribou
subpopulations and their range. Bongelli et al. (2020) suggests that
barren-ground caribou population fluctuations are not merely affected by
herbivore/range interactions; they are almost entirely determined by
this relationship. Other factors may become relevant if those factors
are unusually extreme, persistent, or occur at a sensitive time in the
cycle (e.g., immigration during eruption or high harvest rates at low
numbers). However, Bongelli et al ., (2020) suggests that
anthropogenic factors at historical levels are unlikely to have any
lasting or substantive impact on barren-ground caribou range dynamics.
In all three of our case studies, carrying capacity cycled similar to
subpopulation numbers.
We defined the eruption phase as consecutive years when annual
subpopulation growth rate (λt) is greater than 1.0 and
increasing each year, and/or λt ≥ 1.2. Sine cyclic
barren-ground caribou subpopulations are gradually increasing for half
the cycle period, and gradually declining in the other half. The
eruption phase for the Qamanirjuaq, Bathurst, and George River
subpopulations ranged from 6 to 9 years or 12-19% of the cycle (Table
1). After the eruption phase, barren-ground caribou subpopulations
continue to increase in numbers, but λt declines
progressively into the low period of the cycle (Figure 1; Figure 2;
Figure 3; Figure 4). Post-eruption, the initial decline in
λt is due to increasing densities of caribou relative to
carrying capacity. Once caribou numbers are sufficient to cause carrying
capacity to decline, the decline in λt is mainly due to
declining carrying capacity (Figure 1; Figure 2; Figure 3). The decline
in carrying capacity continues until declining caribou numbers are
insufficient to cause a continued decline in impacted forage communities
(through over-grazing and/or trampling) and habitat recovery can begin.
Range recovery is slow initially, prolonging the time when caribou are
at low numbers and keeping the rate of caribou recovery sufficiently low
that increase is difficult to detect given the variance inherent to
standard survey methods. The surge of habitat recovery preceded the
surge in caribou numbers by 2-4 years in all three subpopulations.
Population growth rates continued to track K throughout the eruption
phase for the Qamanirjuaq subpopulation (Figure 1). The Qamanirjuaq
subpopulation appeared to be limited by carrying capacity throughout
eruption phase (i.e., λt <1.2). The maximum
and minimum rates of population growth and decline identified for the
Qamanirjuaq subpopulation (λmax = 1.196;
λmin = 0.837), align with previously reported (Gunn,
2003) maximum and minimum rates of population growth and decline for
barren-ground caribou generally (λmax = 1.17;
λmin = 0.830). The Qamanirjuaq subpopulation increased
more slowly and declined more slowly than the Bathurst and George River
subpopulations. For the Qamanirjuaq subpopulation our estimates of
logistic Kt from sine curve Nt indicated
that subpopulation recovery cannot occur faster than habitat
regeneration occurs. Once range recovery is well under way, Qamanirjuaq
caribou have the potential to double in about 4 years with no
immigration under natural conditions. Conversely, the maximum observed
rate of decline suggests the half-life of the subpopulation during the
cycle period of maximum decline was a little over 3 years. Our results
suggest that at any given time in the cycle, the number of caribou in
the Qamanirjuaq subpopulation is typically only a few years away from
the current carrying capacity of its range (Figure 4).
Both the Bathurst and George River subpopulations increased at rates
exceeding the maximum possible intrinsic rates of increase (i.e.,
λt >1.363) during the eruption phase of
their cycle (Figure 2; Figure 3; Table 1). Population growth rates
greater than the maximum plausible rate of increase (> 1.2)
during the eruption phase were observed for 9 of 42 years during the
Bathurst cycle, and 9 of 52 years for the George River cycle. Observed
population growth rates were greater than the intrinsic (or plausible)
maximum for the Bathurst and George River subpopulations during the
eruption phase, indicating that immigration was contributing to the
eruptive increase from low numbers (Figure 5; Figure 6)
The Qamanirjuaq subpopulation did not experience detectable levels of
immigration during any part of its cycle. The George River subpopulation
experienced the highest observed subpopulation growth rates (λ = 2.85),
the greatest percentage of immigration driven increase (89.2%) and the
shortest lag time values (0.765 years) during its eruption period
(Figure 5; Figure 6; Figure 7). Immigration during the Bathurst eruption
was initially intermediate (~39%), then increased to
~57%, and then gradually declined to about 20% (Figure
6). Net immigration was observed only during the eruption phase for the
Bathurst and George River subpopulations. Immigration may be important
in initiating and sustaining the eruption phase of barren-ground caribou
when immigrants are available from adjacent subpopulations that share
the winter range. Our method of calculating immigration assumes net
immigration in a given year is a permanent transfer of individuals from
an adjacent subpopulation
There were no significant differences between subpopulation cycle mean
lag times (p = 0.249) or subpopulation cycle mean annual growth rates (p
= 0.249) when the eruption years were excluded from the cycle samples
(Table 3; Table 4). When the eruption years were included in the
subpopulation cycle samples, the George River subpopulation had a
significantly shorter mean lag time than the Qamanirjuaq (p = 0.018),
but there were no significant differences between subpopulation annual
growth rates (p = 0.958) (Table 3). When only the eruption years were
considered, the George River subpopulation mean lag time was shorter
than the Qamanirjuaq mean lag time (p = 0.013) and the George River
subpopulation mean annual growth rate was larger than the Qamanirjuaq
mean annual growth rate (p < 0.001) (Table 3; Table 4). There
was no significant difference between the Bathurst mean lag times or the
Bathurst mean annual population growth rates when compared to either the
George River or the Qamanirjuaq subpopulations (Tables 3; Table 4). The
only differences between subpopulation mean lag times and mean annual
growth rates were those due to immigration during the eruption phase.
Most (89%) of the initial George River eruption increase was due to
immigration, while none of the Qamanirjuaq eruption increase was due to
immigration (Figure 6). The Bathurst eruption was aided by up to
~50% immigration (Figure 6), but even that contribution
was insufficient to cause mean lag times and mean annual subpopulation
growth rates during the eruption to be statistically (p ≤ 0.05)
different from the no-immigration Qamanirjuaq eruption phase or high
immigration George River phase (Table 3; Table 4).
There are no life history limits to the rates at which a subpopulation
might decline except those imposed by extirpation. The George River
subpopulation had the highest observed λmax values but
also the highest observed rates of decline (λmin).
Bathurst subpopulation maximum rates of increase and decline were
intermediate to the George River and Qamanirjuaq subpopulation
λmax and λmin values. Optimal foraging
theory suggests that individuals will shift their habitat to maximize
energy intake (Stephens and Krebs, 1986). We suggest that as carry
capacity continually declines, individuals may emigrate from their home
range to an adjacent range if greater availability and quality of forage
species are available there. Migration to the best range conditions
would increase the rate of subpopulation decline in the contributing
subpopulation and increase the rate of growth in the adjacent
(receiving) subpopulation.
Bathurst and George River eruption patterns suggest that eruption is
predicated on habitat recovery but can be accelerated by immigration
from adjacent subpopulations. In both cases immigration peaked early in
the eruption phase, and then declined as the subpopulation increased.
Although substantial net immigration may occur during the eruption
phase, these results are most consistent with the view that
barren-ground caribou subpopulations may be demographically closed for
management purposes. Although immigration may be a factor in triggering
the eruption phase, the role of immigration is quickly subordinated by
the intrinsic capacity for Nt to quickly close on
Kt. Immigration appears to play only a brief and
transitory role in barren-ground caribou cycles relative to intrinsic
subpopulation growth rates. The main determinant of barren-ground
caribou subpopulation numbers and trend is range carrying capacity for
all but a few years of the eruption cycle.
George River caribou have one of the largest total ranges and the
largest winter ranges of all barren-ground caribou subpopulations
(Bongelli et al., 2020; Schmelzer & Otto, 2003). Schmelzer &
Otto (2003) found that George River caribou summer range habitat quickly
deteriorated during the mid-1980s which corresponds to a period of
significant population growth. During this time, George River caribou
experienced what Schmelzer & Otto (2003) termed winter range drift.
Schmelzer & Otto (2003) suggest that winter range forage allowed George
River caribou to delay the effects of density-dependent population
decline due to summer forage limitations by expanding their use of the
winter range. The ability of George River caribou to shift winter range
to provide a compensatory source of forage, delays the density-dependent
feedback of range deterioration allowing them to maintain greater
numbers, ultimately increasing over-grazing of the summer range before
the inevitable decline occurs. Schmelzer & Otto (2003) suggest that the
demographic benefits of winter range drift are limited by the cost of
lengthier migration to the traditional calving grounds.
Radio collar telemetry data indicated partial overlap between the George
River and Leaf River subpopulations during the 1990s and early 2000s
(Taillon et al., 2016) which corresponds to a period of growth
and peak abundance in the George River subpopulation. However there has
been no overlap identified between the two subpopulations since
approximately 2006 (Taillon et al., 2016). We speculate that the
eruption period of subpopulation growth throughout the 1960s for George
River caribou was augmented by immigrants from the adjacent Leaf River
subpopulation which was estimated to be at or near its peak during that
time (Bongelli et al., 2020). Leaf River caribou are currently
declining (CARMA, 2016), so it is unlikely that immigration from the
Leaf River subpopulation will contribute substantially (or at all) to
the recovery of the George River subpopulation from its current period
of low densities. Asynchrony with the Leaf River subpopulation may delay
the recovery of the George River subpopulation.
Another possibility to dependency on immigration from the Leaf River
subpopulation for eruptive recovery of the George River subpopulation is
that some George River caribou have temporarily foregone the annual
migration because the summer range was severely over-grazed. As the
George River summer range regenerates, the numbers counted (calving
ground census) on the summer range could be augmented by a return to
annual migration pattern. Still another possibility is that George River
caribou may become more aggregated on the calving ground as it
increases, and the appearance of immigration during the eruption phase
may be due to disaggregation at low densities (resulting in
under-estimation) when they are at low numbers. The data available to us
were insufficient to limit or discriminate between these or other
possibilities for George River caribou recovery scenarios. We do believe
that the eruption phase is imminent for the George River caribou, and
suggest researchers monitor not only the numerical increase but also
determine how the George River subpopulation recovers in the current
cycle to guide future management when subpopulation is once again at the
low point of its cycle.
Bathurst caribou are intermediate with respect to total range area and
the proportion of the total range that is summer range (Bongelliet al., 2020). Like the George River subpopulation, Bathurst
caribou can be found further south in the winter range when cycle
numbers are high, possibly extending the period of decline to minimum
numbers and thus increasing over-grazing damage to the summer range.
Bathurst caribou differ from Qamanirjuaq and George River caribou in
that their winter range overlaps with two other barren-ground caribou
subpopulations (Bluenose East, and Beverly). The most recent (2021)
population abundance estimates for Bathurst and Bluenose-East caribou
are 6,240 and 23,200 respectively (Government of Northwest Territories,
2021). The most recent (2018) Beverly population abundance estimate is
103,400 (BQCMB, 2021). The 2021 Bathurst calving ground aerial photo
survey and aerial reconnaissance survey found high levels of overlap
between Bathurst, Beverly, and Bluenose-East caribou on the calving
ground (Government of Northwest Territories, 2021). More recent 2022
telemetry data documents immigration from the Bathurst herd to the
Beverly herd. Bathurst spring composition counts appear to contain
annually variable fractions of Bluenose-East, and Beverly caribou.
Immigration from these adjacent subpopulations could trigger and sustain
the eruption phase of the Bathurst subpopulation once its habitat had
sufficiently recovered.
Bongelli et al. (2020) found that the sine cycle fit for the
Bathurst subpopulation was well-supported, but not as definitive as it
was for other more demographically segregated subpopulations.
Immigration from adjacent subpopulations sufficient to trigger an
eruption would be expected to vary from cycle to cycle depending on the
degree of synchrony/asynchrony and the degree of overlap with adjacent
subpopulations. Predicting precisely when the Bathurst subpopulation
will erupt may be more difficult than predicting the eruption phase for
a subpopulation that is more demographically segregated and thus mainly
driven by intrinsic subpopulation processes (e.g., Qamanirjuaq).
Some subpopulations (e.g., Qamanirjuaq) appear to cycle entirely due to
density dependent intrinsic rates of birth and death. Other
subpopulations appear to be demographically distinct yet exhibit a
dramatic eruption phase that requires substantial immigration or
repatriation (e.g., George River). Some subpopulations have overlapping
summer and winter ranges with adjacent subpopulations, and
inter-subpopulation exchange between these subpopulations is well
documented (e.g., Bathurst). Yet all three subpopulations exhibit stable
sine cyclic population dynamics rather than converge on some stable
equilibrium density or experience periodic extirpation (Bongelli et al.
2020).
The λt versus lag time phase plane suggests a gradation
of barren-ground caribou demographic performance rather than
subpopulation specific clusters (Figure, 7). Extremes of eruption
periods between mostly immigration (George River) and entirely intrinsic
(Qamanirjuaq) were significantly different, but the intermediate
immigration eruption subpopulation (Bathurst) was not significantly
different from either extreme (Table 2; Figure 7). In all three of our
ecologically distinct case studies, Nt closely followed
Kt in symmetrical sine cycles. In these three
subpopulations, range condition closely moderates caribou numbers except
for the eruption phase. Post-eruption phase, range condition is almost
immediately reduced by grazing. The
Nt→Kt lag time is shortest during the
decline portion of the cycle and greatest during the eruption phase that
initiates the increase portion of the cycle (Figure 1; Figure 2; Figure
3). The regularity and symmetry of both the increase and decline phases
of these cycles suggests that barren-ground caribou cycles are both
stable and resilient. Short of extensive range management practices to
enhance range productivity and/or availability there is little else
managers can do to prevent or mitigate cyclical caribou declines or to
speed up recovery.
Our relatively simple view of barren-ground population dynamics has
strong quantitative support and is relevant to both wildlife
co-management and species status designation. These case studies of the
Qamanirjuaq, Bathurst, and George River barren-ground caribou
subpopulations identify both similarities and differences in the
ecological circumstances of barren-ground caribou subpopulations. The
biggest similarity and the central demographic characteristic of these
subpopulations is that they are sine cyclic and Ntclosely follows Kt. We suggest that barren-ground
caribou subpopulations will cycle indefinitely as a demographic result
of herbivore-range dynamics in contiguous tundra/taiga habitat.
Barren-ground caribou subpopulations are genetically indistinguishable,
but most of them can be regarded as demographically closed for
management purposes. Immigration appears to play a role in the
initiation and acceleration of the eruption period in some
subpopulations, but not all of them. Synchrony and asynchrony with
adjacent subpopulations can affect the timing of the eruption phase but
cannot independently initiate the eventual recovery of subpopulations
until the range has recovered.
Precautionary harvest management at low numbers prior to the eruption
phase will likely shorten the recovery time from low numbers. Once
habitat has recovered the need for harvest management measures will
diminish then disappear because it will become logistically impossible
to stop barren-ground caribou from increasing to the point that they
over-graze their range. Over-grazing begins and rapidly increases well
before subpopulation numbers peak (Figure 1; Figure 2; Figure 3). Given
the fundamental importance of the range to barren-ground caribou,
wildlife co-managers could consider a “No Net Loss” policy requiring
viable habitat replacement and/or critical habitat protection measures
(e.g., calving, and calving migrations routes) for commercial
developments on caribou range that cause harmful alteration, disruption,
or destruction of caribou habitat. The utility of precautionary
up-listing the conservation status of barren-ground caribou during the
portion of their cycle when they are declining and at low numbers is
unclear and appears inconsistent with their natural history. Species
status determination could employ fidelity to an historical cycle as an
alternative to generation-based designation criteria for cyclic species.
The underlying assumption of these findings is that the census estimates
for these subpopulations of barren-ground caribou were accurate. Our
results are empirical, not simulation model results. We are describing
the demographic consequences of Bongelli et al. (2020) finding that the
Qamanirjuaq, Bathurst, and George River (and most barren-ground caribou
subpopulations) are sine cyclic. Our paper is fundamentally descriptive,
not theoretical. Population growth rate (λt), carrying
capacity (Kt), and lag time
(Nt→Kt) are highly correlated (Table 5)
because of how these variables are calculated. The axes of Figure 7 are
population growth rate (λt) and lag time
(Nt→Kt), and obviously we find that
shorter lag times are associated with higher population growth rates for
all three subpopulations. It is also apparent that there is a geometric
relationship between (λt) and
(Nt→Kt). We use these axes to define a
phase plane useful in determining if there are subpopulation eruption
clusters. The apparent geometric relationship between population growth
rate and lag time is due to autocorrelation. The linear correlation
measures between (λt), (Kt), and lag
time (Nt→Kt) (Table 7) are highly
significant but imperfect because the relationship between these two
variables is geometric not linear; and because immigration rates between
these subpopulations during the eruption phase were different.
Population growth rate (λt), carrying capacity
(Kt), and lag time
(Nt→Kt) are descriptive summary
statistics that derive from the sine cycles of the three subpopulations
considered.