RESULTS
Sine cycle subpopulation growth rates for the Qamanirjuaq subpopulation (λt) varied from a maximum of 1.196 in the increase phase to 0.837 in the decline phase (Table 1; Figure 1). All the sine cycle λ values for the Qamanirjuaq subpopulation were within the maximum plausible rate of increase (i.e., < 1.2). However, calculated sine cyclic estimates of the maximum and minimum rates of annual subpopulation growth were sometimes greater than the maximum biologically possible intrinsic rate of increase (λmax = 1.363) during the eruption phase for both the Bathurst (λmax = 1.47; λmin = 0.68) and George River (λmax = 2.85; λmin = 0.35) subpopulations (Table 1; Figure 2; Figure 3).
Barren-ground caribou subpopulation numbers (Nt) closely tracked carrying capacity (Kt) for all three subpopulations (Table 1; Figure 1; Figure 2; Figure 3; Figure 4). Mean cycle lag times (years for Nt →Kt) at observed λt (Nt+1/Nt) for the Qamanirjuaq, Bathurst, and George River subpopulations were 2.898 (SE = 0.008), 2.661 (SE = 0.103), and 2.430 (SE = 0.121) respectively (Table 2; Figure 4). Kruskal-Wallis pairwise comparison of the observed mean Nt →Kt lag times of each subpopulation over one complete cycle demonstrated that the mean lag time (intrinsic + immigration) for the George River subpopulation was significantly different from the Qamanirjuaq (p = 0.018), but not significantly different from the Bathurst (p = 0.838) subpopulation (Table 3). The difference in mean lag times between the Qamanirjuaq and Bathurst subpopulation was also not significant (p = 0.414) (Table 3). When the period of eruption years was excluded from the comparison of mean lag time values (i.e., only intrinsic lag times included) there were no significant differences in the projected lag time values between any of the three subpopulations (p = 0.249) (Table 3). When pairwise comparisons were restricted to only the eruption period the mean lag time for the George River subpopulation was significantly different from the Qamanirjuaq (p = 0.013) but not significantly different from the Bathurst (p = 0.690). The difference in mean lag time between the Qamanirjuaq and Bathurst subpopulations was also not significant (p = 0.221) (Table 3).
Kruskal-Wallis pairwise comparison of mean population growth rates resulted in no significant difference between subpopulations for one complete cycle (p = 0.958) or for one complete cycle excluding eruption years (p = 0.249) (Table 4). When only eruption years were considered separately, the mean population growth rate for the George River subpopulation was significantly different than mean population growth rate for the Qamanirjuaq (p = 0.001) but not significantly different from the Bathurst mean population growth rate (p = 0.427). The difference in mean population growth rate between the Qamanirjuaq and Bathurst subpopulations was also not significant (p = 0.070) (Table 4).
Subpopulation annual growth rates during the eruption phase of the sine cycle sometimes exceeded the biologically possible and biologically plausible intrinsic growth rates for barren-ground caribou in both the Bathurst and George River subpopulations (Figure 5). However, the Qamanirjuaq subpopulation growth rates were entirely within the plausible intrinsic value (λplausible = 1.2) (Figure 5). The additional annual increase observed in the George River and Bathurst eruption phase was attributed to extrinsic growth (i.e., immigration) (Figure 6). Immigration rates for the Bathurst subpopulation initially increased, peaked, and then declined (Figure. 6). Immigration rates for the George River subpopulation were highest initially then declined throughout the eruption phase (Figure 6).
K-means cluster analysis identified three distinct clusters of lag time values and population growth rate values for the eruption years of each subpopulation cycle. Clusters were characterized as: 1) short N→K time lags and high lambda values, 2) intermediate N→K time lags and intermediate lambda values, and 3) long N→K time lags and low lambda values (Figure 7). Cluster 1 was exclusively associated with the George River subpopulation (Figure 7). Cluster 2 was mainly comprised of Bathurst records but also contained George River and Qamanirjuaq records. Cluster 3 was predominantly associated with the Qamanirjuaq subpopulation.
Population growth rate, carrying capacity, and lag time were all correlated (p≤0.05) for each of the three subpopulations (Table 5).