INTRODUCTION
Subpopulations of mainland migratory barren-ground caribou
(Rangifer tarandus groenlandicus ) are unique among the deer
family (Cervidae) because they make annual migrations between the
treeless tundra in the summer and the forested taiga in the winter and
are typically sine cyclic (Bongelli et al., 2020). Barren-ground
caribou are an age-structured, annual birth pulse species (Caughley
1977) whose natural history and ecology are consistent with the
assumptions of life table discrete population modeling (Bongelliet al . 2020, Gunn & Miller, 1986; Russell et al., 2002;
Wilson & Reeder, 2005; Government of Yukon, 2015, and COSEWIC 2016).
Ecological circumstances (e.g., the ratio of summer range to winter
range, range overlap with adjacent subpopulations, subpopulation
exchange rates, harvest removal rates, and the degree of industrial
development) can vary between subpopulations. However, Bongelli et
al., (2020) showed that 96% of the variation in nine subpopulations of
barren-ground caribou sine cycle dynamics could be explained by range
area and range productivity.
Barren-ground caribou calving period is synchronized for each
subpopulation and generally occurs over a 2-week period in June (Nagyet al., 2011; Nagy & Campbell, 2012; COSEWIC, 2016). Females
generally produce one calf annually, usually beginning at age 2+. Poor
health or nutrition may cause adult females of any age not to conceive
or produce viable calves (COSEWIC, 2016). Like all naturally occurring
species, barren-ground caribou subpopulation numbers are ultimately
regulated by density-dependent reductions in calf production and/or
survival rates (Demerec, 1957; Tanner, 1966; Caughley, 1977; McCullough,
1979; Fowler, 1981; Kie & White, 1985; Skogland, 1985; Clutton-Brocket al., 1987; Messier et al., 1988; Boyce, 1989;
McCullough, 1999; Bowyer et al., 2014).
Thomas Malthus (1798) is credited with the first formal proposition that
there are natural limitations to population growth. A continuous
mathematical formulation of this principle termed the logistic equation
was initially formulated by Verhulst (1838) and rediscovered by Pearl
and Reed (1920) and Pearl and Reed (1922). An alternative formulation of
the discrete logistic equation indicates that linear density-effects
could cause convergence on K (carrying capacity), converging cycles to
K, stable limit cycles, increasing oscillations to extinction and even
chaos depending on the population’s maximum intrinsic annual growth rate
(λmax) (May, 1976; Renshaw, 1991). We examined the
relationship between barren-ground caribou subpopulation growth rate (λ)
and K through the cycle by calculating K utilizing the discrete analog
of the Verhulst (1838) and Pearl and Reed (1920) formulation of the
logistic equation.
The maximum and minimum annual rates of population growth (or decline)
reported for barren-ground caribou varies between subpopulations, but
typically λ does not exceed 1.17 and is not less than 0.83 (Gunn, 2003).
Heard (1980) estimated the maximum stable age population growth rate for
barren-ground caribou subpopulations was λmax = 1.363,
which we confirmed using an independent life table model (Bongelli,
2019). At λmax ≤ 1.363 the logistic equation suggests
that, without lag-times, caribou subpopulations (like other deer
species) would converge on carrying capacity (May, 1976; Renshaw, 1991;
Vandermeer, 2010). Stable limit cycles are not observed until
λmax > 2.57 (May, 1976; Renshaw, 1991)
which is greater than the biologically maximum possible λ for
barren-ground caribou.
We chose the Qamanirjuaq, Bathurst, and George River subpopulations for
our comparison of barren-ground caribou cycles because they are
relatively well-known and have been frequently surveyed. We updated the
Bongelli et al. (2020) sine model for the Qamanirjuaq
subpopulation to include the most recent (2017) abundance estimate. The
updated Qamanirjuaq cycle has a period of 58 years (SE = 5.7) and an
amplitude of 218,431 (SE = 31,348). The Bathurst subpopulation sine
cycle has a period of 42 years (SE = 3.4) and an amplitude of 203,154
(SE = 23,147) (Bongelli et al., 2020). The George River
subpopulation’s sine cycle (Bongelli et al., 2020) was updated to
include the 2020 subpopulation estimate of 8,100. The updated George
River sine cycle has a period of 52 years (SE = 2.6) and an amplitude of
305,000 (SE = 26, 644).
We compared cyclic changes in population growth rates
(λt), carrying capacity (Kt), and lag
time required to reach Kt from population numbers
(Nt) for our three case studies. When the observed
λt (Nt+1/Nt) is greater
than biologically possible, the fraction of population change that is
due to extrinsic growth (i.e., immigration) was estimated, and the role
of immigration in triggering subpopulation eruption post habitat
recovery was examined. Together these summary statistics and comparisons
suggest an alternative explanation for barren-ground caribou
subpopulation dynamics from those that are strictly intrinsic and drawn
from short-term non-cyclic snapshots of the cycle. We considered the
implications of viewing barren-ground caribou as a cyclic species for
management and status determination.