B.-J. Bårdsen et al. S1.1 S1: HISTORIC DATA (1945-1965) Data on the number of reindeer in Sweden from 1945-1965 for 38 populations (originally denoted as lappeby which is denoted as sameby in modern times). The data is a digitalized version of Table 12 in Norsk-svensk reinbeitekommisjon av 28. februar 1964 (1967). REFERENCES Norsk-svensk reinbeitekommisjon av 28. februar 1964. Innstilling fra den norsk-svenske reinbeitekommisjon av 1964. Utenriksdepartementet, Oslo, Norway, p. 267 (in Norwegian)
B.-J. Bårdsen et al. S1.2 Table S1.1. Historic time series of reindeer numbers for 38 Swedish populations (denoted as Lappby in the original report). a The combined number of reindeer for Tuorpon and Jåkkåskaska was 5415 individuals in 1945. b The combined number of reindeer for Serri and Udtja was 1637 individuals in 1945.
B.-J. Bårdsen et al. S2.1 S2: DENSITY INDEPENDENT VS. THE RICKER MODEL DETAILED INFORMATION Model selection was performed based Akaike s Information Criterion (AIC) values (e.g. Anderson et al. 2000, Burnham and Anderson 2002, Zuur et al. 2009). Specifically, we defined a set of different candidate models (i) where we rescaled and ranked models relative to the model with the lowest AIC (Δ i denotes this difference for model i). Then, we selected the simplest model with a Δ i 2. This approach was applied to data for each population and period separately. The Ricker model had an Δ i 2 for 32 out of 36 population in the historic time period (i.e. it had good support in the data for 89% of the populations), whereas the Ricker model had good support for all populations in the recent time period (Table S2.1). Additionally, we provide information on the data and model fits for each population for the 1945-1965 period (Figure S2.1). Due to our agreement with the Swedish Sami Parliament, however, we cannot publish this for the recent period. REFERENCES Anderson, D. R. et al. 2000. Null hypothesis testing: problems, prevalence, and an alternative. J. Wild. Manag. 64: 912-923. Burnham, K. P. and Anderson, D. R. 2002. Model selection and multimodel inference: a practical information-theoretic approach. Springer. Zuur, A. F. et al. 2009. Mixed effects models and extensions in ecology with R. Springer.
B.-J. Bårdsen et al. S2.2 Table S2.1. Differences in AIC values ( i ) for both periods (1945-2012 and 1995-2012) for the density independent (DI) and the Ricker (RICKER) model, respectively. i Sameby Model 1945-1965 1995-2012 Frostviken n:a DI 1.912 3.203 Frostviken n:a RICKER 0 0 Gellivare DI 0 6.048 Gellivare RICKER 0.901 0 Gran DI 0 1.114 Gran RICKER 0.423 0 Jåkkåkaska DI 1.110 0 Jåkkåkaska RICKER 0 1.203 Kaalasvuoma DI 2.897 0.551 Kaalasvuoma RICKER 0 0 Kalix DI 2.762 5.909 Kalix RICKER 0 0 Könkämä DI 5.190 0 Könkämä RICKER 0 1.934 Lainiovouma DI 5.635 0 Lainiovouma RICKER 0 1.992 Luokta-Mavas DI 2.889 0 Luokta-Mavas RICKER 0 NA Malå DI 3.615 0 Malå RICKER 0 0.990 Mausjaure DI 0 2.771 Mausjaure RICKER 1.373 0 Mellanbyn DI 1.335 0 Mellanbyn RICKER 0 0.659 Meskajaure DI 0 0 Meskajaure RICKER 0.661 1.826 Muonio DI 1.332 0 Muonio RICKER 0 0.465 Norrkaitum DI 0.595 0 Norrkaitum RICKER 0 0.472 Ran DI 0.495 3.361 Ran RICKER 0 0 Rautasvuoma DI 1.127 0 Rautasvuoma RICKER 0 1.949 Saarivuoma DI 1.090 0 Saarivuoma RICKER 0 0.969
B.-J. Bårdsen et al. S2.3 Table S2.1. Continued. i Sameby Model 1945-1965 1995-2012 Sattasjävri DI 7.122 2.839 Sattasjävri RICKER 0 0 Semisjaur-Njarg DI 2.349 0 Semisjaur-Njarg RICKER 0 NA Serri DI 2.889 0.742 Serri RICKER 0 0 Sirkas DI 0.326 0.987 Sirkas RICKER 0 0 Ståkke DI 0 3.314 Ståkke RICKER 1.694 0 Svaipa DI 0.697 1.448 Svaipa RICKER 0 0 Sörkaitum DI 2.053 2.993 Sörkaitum RICKER 0 0 Talma DI 44 0 Talma RICKER 0 NA Tuorpon DI 7.903 1.971 Tuorpon RICKER 0 0 Tärendö DI 6.388 0.199 Tärendö RICKER 0 0 Udtja DI 3.853 19.785 Udtja RICKER 0 0 Umbyen DI 3.280 17.705 Umbyen RICKER 0 0 V. Kikkejaure DI 0 0 V. Kikkejaure RICKER 22 1.650 Vapsten DI 1.944 0 Vapsten RICKER 0 0.465 Vilhelmina n:a DI 0 1.475 Vilhelmina n:a RICKER 0.731 0 Vilhelmina s:a DI 0 0.662 Vilhelmina s:a RICKER 1.317 0 Vittangi DI 0.199 0 Vittangi RICKER 0 20 Ö. Kikkejaure DI 0 0.183 Ö. Kikkejaure RICKER 0.957 0
B.-J. Bårdsen et al. S2.4 Figure S2.1. We provide predictions for the Ricker model (black line and ) and the density independent model () as well as data (1945-1965) for each population (one page per population). Please note that the parameter estimates and their statistical significance (categorizing p-values into the following categories: ns represents p > 5; * represents p 5; ** represents p 1; and *** represents p 01).
Könkämä r = 0.61*, K = 2.34***, σ = 0.15 Population growth rate (λ) 0.4 2.0 2.5 3.0
0.6 Lainiovouma r = 0.56*, K = 3.09***, σ = 0.19 Population growth rate (λ) 0.4 0.4 2.0 2.5 3.0 3.5 4.0 4.5 5.0
0.6 Saarivuoma r = 8(ns), K = 1.27***, σ = 0.16 Population growth rate (λ) 0.4 1.0 1.2 1.4 1.6 1.8 2.0
0.6 Talma r = 0.19(ns), K = 0.99**, σ = 2 Population growth rate (λ) 0.4 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Rautasvuoma r = 9(ns), K = 1.22***, σ = 0.18 0.4 Population growth rate (λ) 1.0 1.2 1.4 1.6 1.8
Kaalasvuoma r = 0.33*, K = 1.16***, σ = 0.16 Population growth rate (λ) 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Population growth rate (λ) 0.4 0.4 0.6 Norrkaitum r = 0.37(ns), K = 1.84***, σ = 2 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Mellanbyn r = 0.34(ns), K = 1.39***, σ = 0 Population growth rate (λ) 0.4 0.4 0.6 1.0 1.2 1.4 1.6 1.8
0.4 Sörkaitum r = 0.33(ns), K = 1.22***, σ = 0.14 Population growth rate (λ) 0.3 0.1 0.1 0.3 0.8 1.0 1.2 1.4 1.6
Population growth rate (λ) 0.4 Sirkas r = 3(ns), K = 0.79***, σ = 0.18 0.6 0.7 0.8 0.9 1.0 1.1 1.2
0.6 Tuorpon r = 0.53**, K = 0.55***, σ = 0.16 Population growth rate (λ) 0.4 0.4 0.3 0.4 0.5 0.6 0.7
0.6 Jåkkåkaska r = 0.31(ns), K = 0.33***, σ = 3 Population growth rate (λ) 0.4 0.4 0.3 0.4 0.5
Luokta Mavas r = 0.39*, K = 1.43***, σ = 0.13 0.4 Population growth rate (λ) 0.3 0.1 0.1 1.0 1.2 1.4 1.6 1.8
0.4 Semisjaur Njarg r = 9*, K = 1.05***, σ = 0.14 Population growth rate (λ) 0.3 0.1 0.1 0.6 0.8 1.0 1.2 1.4
Svaipa r = 8(ns), K = 0.99***, σ = 0.14 Population growth rate (λ) 0.5 0.4 0.3 0.1 0.1 0.7 0.8 0.9 1.0 1.1 1.2 1.3
0.5 Gran r = 0.13(ns), K = 1.09**, σ = 0.13 Population growth rate (λ) 0.4 0.3 0.1 0.1 0.6 0.8 1.0 1.2 1.4
Ran r = 4(ns), K = 0.85***, σ = 0.12 Population growth rate (λ) 0.4 0.3 0.1 0.1 0.8 0.9 1.0 1.1 1.2
0.4 Umbyen r = 0.37*, K = 0.57***, σ = 0.12 Population growth rate (λ) 0.3 0.1 0.1 0.3 0.50 0.55 0.60 0.65 0.70 0.75 0.80
0.5 Vapsten r = 0.34(ns), K = 0.42***, σ = 0.13 Population growth rate (λ) 0.4 0.3 0.1 0.1 0.35 0.40 0.45 0.50 0.55
0.4 Vilhelmina n:a r = 0.12(ns), K = 9***, σ = 0.13 Population growth rate (λ) 0.3 0.1 0.1 0 5 0.30 0.35
Vilhelmina s:a r = 0.10(ns), K = 4**, σ = 0.12 Population growth rate (λ) 0.3 0.1 0.1 0 5 0.30
Population growth rate (λ) 0.5 0.4 0.3 0.1 0.1 Frostviken n:a r = 0.60(ns), K = 6***, σ = 0.15 45 50 55 60 65 70
Population growth rate (λ) 0.4 0.3 0.1 0.1 Vittangi r = 0.19*, K = 3.81*, σ = 0.16 1 2 3 4 5
Gellivare r = 0.16(ns), K = 0.90***, σ = 0.13 Population growth rate (λ) 0.4 0.3 0.1 0.1 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Population growth rate (λ) 0.4 Serri r = 0.44*, K = 0.95***, σ = 0.19 0.6 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Udtja r = 3**, K = 0.41***, σ = 0.11 Population growth rate (λ) 0.3 0.1 0.1 0.1 0.3 0.4
Population growth rate (λ) Ståkke r = 9(ns), K = 3(ns), σ = 0.18 0.4 5 0.10 0.15 0 5 0.30 0.35 0.40
0.4 Ö. Kikkejaure r = 0.14(ns), K = 0.92*, σ = 0.16 Population growth rate (λ) 0.3 0.1 0.1 0.4 0.6 0.8 1.0 1.2
V. Kikkejaure r = 0.19(ns), K = 1.43**, σ = 0.17 Population growth rate (λ) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Mausjaure r = 0.10(ns), K = 1.31(ns), σ = 0.11 0.3 Population growth rate (λ) 0.1 0.1 0.5 1.0 1.5 2.0
Meskajaure r = 0.15(ns), K = 0.56***, σ = 0.12 Population growth rate (λ) 0.3 0.1 0.1 0.3 0.4 0.5 0.6 0.7
Malå r = 0.30*, K = 9***, σ = 7 Population growth rate (λ) 0.1 0.1 0.18 2 6 0.30
Population growth rate (λ) 0.4 Muonio r = 5(ns), K = 1.26***, σ = 0.16 0.6 0.8 1.0 1.2 1.4
Population growth rate (λ) 0.4 0.4 Sattasjävri r = 0.74**, K = 0.84***, σ = 0 0.6 0.7 0.8 0.9 1.0 1.1 1.2
0.4 Tärendö r = 0.72**, K = 0.82***, σ = 0.18 Population growth rate (λ) 0.6 0.7 0.8 0.9 1.0
Kalix r = 0.45*, K = 0.80***, σ = 0.11 Population growth rate (λ) 0.1 0.1 0.3 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
B.-J. Bårdsen et al. S2.1 S3: RELATIVE SUPPORT FOR THE AR(2) VS. THE AR(1) MODEL Similar to in Supplement S2, we compared the relative fit of the second-order [AR(2)] model to a first-order [AR(1)] model. The AR(2) had an Δ i 2 for all population in for both time period (i.e. it had good support in the data for all populations). In the recent time period, which was the only time period in which Δ i >2, only two had less support in the data, and in both occasions it were the AR(1) who scored above our arbitrary level set to 2 (Table S3.1).
B.-J. Bårdsen et al. S2.2 Table S3.1. Differences in AIC values ( i ) for both time periods (1945-2012 and 195-2012) for the AR(1) and AR(2) model, respectively. Sameby Model i 1945-1965 1995-2012 Frostviken n:a AR(1) 0 0 Frostviken n:a AR(2) 1.176 1.887 Gellivare AR(1) 0 0 Gellivare AR(2) 1.984 1.998 Gran AR(1) 0 0 Gran AR(2) 1.890 1.092 Jåkkåkaska AR(1) 0 0 Jåkkåkaska AR(2) 1.766 1.842 Kaalasvuoma AR(1) 0 0 Kaalasvuoma AR(2) 1.612 1.308 Kalix AR(1) 0 0 Kalix AR(2) 1.832 1.989 Könkämä AR(1) 1.891 0 Könkämä AR(2) 0 0.707 Lainiovouma AR(1) 85 0 Lainiovouma AR(2) 0 1.933 Luokta-Mavas AR(1) 0.459 0 Luokta-Mavas AR(2) 0 0.625 Malå AR(1) 0 0 Malå AR(2) 0.996 1.954 Mausjaure AR(1) 2.075 0 Mausjaure AR(2) 0 1.761 Mellanbyn AR(1) 0 0 Mellanbyn AR(2) 1.992 1.853 Meskajaure AR(1) 0 1.674 Meskajaure AR(2) 1.681 0 Muonio AR(1) 0 0 Muonio AR(2) 1.850 1.818 Norrkaitum AR(1) 0 0 Norrkaitum AR(2) 1.951 1.862 Ran AR(1) 0 0 Ran AR(2) 1.449 1.954 Rautasvuoma AR(1) 0 0 Rautasvuoma AR(2) 2.000 1.875 Saarivuoma AR(1) 84 0 Saarivuoma AR(2) 0 1.315
B.-J. Bårdsen et al. S2.3 Table S3.1. Continued. i Sameby Model 1945-1965 1995-2012 Sattasjävri AR(1) 2.539 0 Sattasjävri AR(2) 0 2.000 Semisjaur-Njarg AR(1) 0 0 Semisjaur-Njarg AR(2) 1.459 1.506 Serri AR(1) 0 0 Serri AR(2) 1.801 1.164 Sirkas AR(1) 0 0 Sirkas AR(2) 1.811 1.772 Ståkke AR(1) 0.829 0.149 Ståkke AR(2) 0 0 Svaipa AR(1) 0 0 Svaipa AR(2) 1.976 1.470 Sörkaitum AR(1) 0 0 Sörkaitum AR(2) 1.771 0.681 Talma AR(1) 0 0 Talma AR(2) 1.992 1.948 Tuorpon AR(1) 0 0 Tuorpon AR(2) 1.920 1.736 Tärendö AR(1) 1.884 0 Tärendö AR(2) 0 1.973 Udtja AR(1) 0 0 Udtja AR(2) 1.912 1.747 Umbyen AR(1) 0 0 Umbyen AR(2) 51 1.960 V. Kikkejaure AR(1) 0.376 0 V. Kikkejaure AR(2) 0 1.470 Vapsten AR(1) 0 0.576 Vapsten AR(2) 1.611 0 Vilhelmina n:a AR(1) 0 0 Vilhelmina n:a AR(2) 1.628 1.756 Vilhelmina s:a AR(1) 0 0 Vilhelmina s:a AR(2) 1.205 1.892 Vittangi AR(1) 0 0 Vittangi AR(2) 1.768 1.351 Ö. Kikkejaure AR(1) 0.491 0 Ö. Kikkejaure AR(2) 0 0.672
B.-J. Bårdsen et al. S4.1 S4: SIMPLE ANALYSES OF AVERAGE VALUES We applied Analysis of Variance (ANOVA), using the lm function in R, to estimate the extent in which the average parameter estimates from the two population models (i.e. r, K, σ R, 1-β 1, β 2 and σ TS ; see main text for details) differed between the two periods (1945-1965 vs. 1995-2012). ESTIMATES FROM THE RICKER MODELS Neither the estimated intrinsic growth rates (r) nor the ecological carrying capacity (K) differed significantly between the two periods (Tables S4.1; Figure S4.1). This means that the population dynamics, as assessed by the Ricker models, did not differ in time. Nonetheless, it was evidence that the Ricker model was appropriate in explaining population dynamics as both r and K was significantly different from zero (the latter only when back-transformed: Figure S4.1 vs. Table S4.1) for both periods. ESTIMATES FROM THE TIME SERIES MODELS Both direct (1-β 1 ) and delayed (β 2 ) density dependence differed significantly between the two time periods as both estimates were more negative in the past as compared to recent time (Tables S4.2; Figure S4.2). In the past, both 1-β 1 and β 2 were significantly negative, implying that populations were regulated through a combination of direct and delayed density dependence (Table S4.2 and Figure S4.2). In present time, however, both estimates were significantly more positive and seemed to be no different from zero (Figure S4.2). MODEL FIT: UNEXPLAINED VARAINCE For both population modelling approaches, the unexplained variance (σ R and σ TS ), were significantly higher in the past (1945-1965) compared to recent (1995-2012) time (Table S4.1-2; Figure S4.3). This means the models explained the processes in the data poorer in the past, which may be due to a number of reasons. This could, for example, mean that the quality of data was poorer in the past (more observation errors) or it could mean that the impact of climate or other external factors were more pronounced in the past as compared to the present.
B.-J. Bårdsen et al. S4.2 Table S4.1. Estimates from linear models relating the estimated (a) intrinsic growth (r), ecological carrying capacity (K) and the unexplained variance (σ R ) from the Ricker model to time period (a factor variable with two levels: 1945-1965 and 115-2012). Parameter Ricker model estimates Estimate SE t P (a) Intrinsic growth, r Intercept 0.316 32 9.772 <01 Time Period (1995-2012) -31 47-0.670 0.505 (F = 0.49; df = 1,67; P = 0.51; R 2 < 1) (b) Carrying capacity, log e (K ) Intercept -14 0.135-1.594 0.116 Time Period (1995-2012) 0.171 0.195 0.880 0.382 (F = 0.74; df = 1,67; P = 0.38; R 2 = 1) (c) Sigma, σ R Intercept 0.154 06 25.058 <01 Time Period (1995-2012) -60 09-6.703 <01 (F = 44.94; df = 1,67; P < 0.38; R 2 = 0.40) Table S4.2. Estimates from linear models relating the estimated (a) first- and second-order autoregressive (AR) coefficients (i.e. 1-β 1, and β 2) and the unexplained variance (σ TS2 ) from the time series model to period (a factor variable with two levels: 1945-1965 and 115-2012). Parameter Autoregressive (AR) model estimates Estimate SE t P (a) The first-order AR coefficient [AR(1)], 1-β 1 Intercept -0.183 51-3.603 01 Time Period (1995-2012) 50 73 3.444 01 (F = 11.86; df = 1,72; P < 1; R 2 = 0.14) (a) The second-order AR coefficient [AR(2)], β 2 Intercept -0.150 31-4.794 <01 Time Period (1995-2012) 0.120 45 2.667 09 (F = 7.12; df = 1,72; P < 1; R 2 = 9) (c) Sigma 2 2, σ TS Intercept 24 02 15.060 <01 Time Period (1995-2012) -15 02-6.419 <01 (F = 41.20; df = 1,72; P < 1; R 2 = 0.36)
B.-J. Bårdsen et al. S4.3 Ricker model Average effect size SE 0.4 0.6 0.8 1.0 1945-1965 1995-2012 r Parameter K Figure S4.1. Estimates (± 1 standard error, SE; from the models presented in Table S4.1-2): i.e. the average of the estimated parameters from the Ricker models fitted to each population and period (1945-1965 and 1995-2012) separately. Please note that the estimated carrying capacity were back-transformed from log e - to normal-scale.
B.-J. Bårdsen et al. S4.4 AR(2) model Average effect size SE -0-0.10 0 5 0.10 1945-1965 1995-2012 1 1 2 Parameter Figure S4.2. Estimates (± 1 standard error, SE; from the models presented in Table S4.1-2): i.e. the average of the estimated parameters from the autoregressive time series models fitted to each population and period (1945-1965 and 1995-2012) separately.
B.-J. Bårdsen et al. S4.5 Figure S4.3. Estimates (± 1 standard error, SE; from the models presented in Table S4.1-2): i.e. the average degree of model uncertainty from the Ricker (σ R ) and the autoregressive models (σ TS 2 ) fitted to each population and period (1945-1965 and 1995-2012) separately.
B.-J. Bårdsen et al. S5.1 S5: ANCOVA DETAILED INFORMATION In addition to the effects of the key parameter, we selected one models and used if for inference among a set of a priori defined candidate models 1. These models included latitude, longitude and potential interactions (Table S5.1-2), and the model selection approach in these analyses were similar to the one described in Supplement S2 except that we selected the simplest candidate model with a Δ i 1.5. ESTIMATES FROM THE RICKER MODELS We selected and used the same model for inference for both the intrinsic growth (r) and the carrying capacity (K). In both cases, estimates from the present (1995-2012) was predicted based on estimates from the past (1945-1965), which represented the key parameter included in all candidate models, in addition to the main effect of both latitude and longitude (Table S5.1). We selected and used the simplest model, which only included the key parameter, for inference in the analyses of model precision (Table S5.1). ESTIMATES FROM THE TIME SERIES MODELS The estimates of direct density dependence (1-β 1 ) based on present data was predicted based on their past estimates in addition to the main effect of both latitude and longitude (Table S5.2). The estimates of delayed density dependence (β 2 ) based on present data was, however, only predicted based on the estimates from the past (Table S5.2). We selected the most complex model structure in the analyses of model precisions as both latitude and longitude as well as the interaction between its past estimate and latitude was included in this model (Table S5.2). 1 In these analyses, we predicted the present estimates based on their initial values (i.e. the estimates based on data from the past).
B.-J. Bårdsen et al. S5.2 Table S5.1. Differences in AIC values ( i ) for each candidate ANCOVA model (i) used in the analyses of present (1995-2012) estimates from the Ricker population models (Table 1 in the main text provides estimates for the selected models shown in underlined and bold text). Initial value reflects the estimates from the past (1945-1965). Model Initial Longitude, Latitude, Ricker population model ( i ) IV X IV Y X Y df (i ) value (IV) E-W (X) S-N (Y) r log e (K ) σ R 1 x x x x x x 8 8.359 5.684 8.056 2 x x x x x 7 4.993 4.813 5.374 3 x x x x 6 2.298 2.290 4.910 4 x x x x x 7 4.872 4.541 6.131 5 x x x x 6 2.417 2.987 3.545 6 x x x x 6 2.534 1.568 3.958 7 x x x 5 0 0 2.307 8 x x 4 5.988 8.676 1.708 9 x 3 3.521 7.624 0 10 x x 4 1.741 6.307 2.263 11 x x x 5 4.043 8.823 3.191 12 x x x 5 8.605 5.643 3.373
B.-J. Bårdsen et al. S5.3 Table S5.2. Differences in AIC values ( i ) for each candidate ANCOVA model (i) used in the analyses of present (1995-2012) estimates from the autoregressive models (Table 2 in the main text provides estimates for the selected models shown in underlined and bold text). Initial value reflects the estimates from the past (1945-1965). Model Initial Longitude, Latitude, Autoregressive (AR) model ( IV X IV Y X Y df i ) 2 (i ) value (IV) W-E (X) S-N (Y) AR(1) AR(2) σ TS 1 x x x x x x 8 4.730 13.357 0.553 2 x x x x x 7 2.239 183 0.525 3 x x x x 6 20 7.889 2.068 4 x x x x x 7 1.519 10.524 1.376 5 x x x x 6 1.693 7.503 0 6 x x x x 6 2.943 7.027 1.416 7 x x x 5 0 5.131 0.334 8 x x 4 5.054 2.527 1.437 9 x 3 2.520 0 1.503 10 x x 4 00 2.430 3.525 11 x x x 5 0.763 4.606 2.861 12 x x x 5 7.200 4.270 2.512
B.-J. Bårdsen et al. S6.1 S6: SPATIAL COVARIANCE We used univariate data in an assessment of spatial covariance of the estimates from the Ricker and autoregressive models, respectively (i.e. one estimate per population/site and period). These analyses provided no evidence of the presence of any spatial autocorrelation neither for the estimates from the Ricker models (Fig. S6.1) nor the autoregressive models (Fig. S6.2).
B.-J. Bårdsen et al. S6.2 Correlation 95% CI -1.0-0.5 0.5 1.0 (A) Carrying capacity (K) 1945-1965 1995-2012 0 5000 10000 15000 20000 Correlation 95% CI -1.0-0.5 0.5 1.0 (B) Intrinsic growth (r) 0 5000 10000 15000 20000 Distance (m) Figure S6.1. Spline correlograms for parameters from the Ricker models: (A) the ecologic carrying capacity (K); and (B) the intrinsic growth rate (r). Both sub-plots shows correlations as a function of distance (m).
B.-J. Bårdsen et al. S6.3 Correlation 95% CI -1.0-0.5 0.5 1.0 (A) Direct regulation (1 1 ) 1945-1965 1995-2012 0 5000 10000 15000 20000 Correlation 95% CI -1.0-0.5 0.5 1.0 (B) Delayed regulation ( 2 ) 0 5000 10000 15000 20000 Distance (m) Figure S6.2. Spline correlograms for parameters from the second-order autoregressive models: (A) AR(1) coefficients (1-β 1 ) in which measure evidence of direct regulation; and (B) AR(2) coefficients (β 2 ) in which measure evidence of delayed regulation population. Both sub-plots shows correlations as a function of distance (m).
B.-J. Bårdsen et al. S7.1 S7: DESCRIPTIVE STATISTICS FROM THE SWEDISH SAAMI PARLIAMENT In this supplement, we present temporal trends based on national-level official statistics from the Swedish Sami Parliament on the number of: 1) family groups for two common predators (www.sametinget.se/statistik/rovdjur); 2) reindeer owners and group leaders (www.sametinget.se/statistik/ren%c3%a4gare); 3) slaughtered calves (https://www.sametinget.se/statistik/renslakt); and 4) the number of reindeer (www.sametinget.se/statistik/renhjorden; all data assessed 01-Apr- 2016). In the slaughtering statistics we focused on the calves as most of the animals slaughtered are calves. In 2011/2012 (the last year in the overall analyses), 72%, or 41334 out of 57675 animals in total, of the slaughtered animals were calves (www.sametinget.se/statistik/renslakt). Technical details, available in Swedish, are available at www.sametinget.se/statistik/definitioner. All figures presented shows raw data as points and trend lines based on statistical models fitted to the data (for the counts we log e -transformed the data and then back-transformed the data when we produced the plots). These trend lines was based on Generalized Additive Models (GAMs) fitted to the data using the gam-function in the mgcv library (Wood 2012) in R where we used cubic regression splines to model potential non-linear effects of continuous variables. We used a gamma (γ) of 1.4 in order to increase the cost to each the effective degree of freedom to avoid over-fitting (Wood 2006). One of the advantages of GAM is that the degree of complexity or smoothness, represented by the effective degrees of freedom (edf), within the limits set by k, which were set to 6, can be selected objectively (Wood 2006). Finally the trend lines in the plots was produced using the predict.gam-function in the mgcv library. For predators, the number of wolverine in Swedish Sápmi has increased over time while the number of lynx had decreased even though the latter trend was only marginally significant (Figure S7.1). The number of reindeer owners increased from ca. 2000 to 2010, and after that it decreased even though the number of herders is still larger than what it was before 2008 (Fig. S7.2A). The number of group leaders, i.e. the leader for each reindeer husbandry enterprise, increased during the whole period (Fig. S7.2). The number of slaughtered calves increased from 1995 until c. 2007 (Fig. S7.3A). After 2007, this number decreased (Fig. A7.3A). More or less the same pattern was apparent for the number of slaughtered calves per female even though this relationship was not significant (Fig. S7.3B). Reindeer numbers generally decreased from 1995 to 2000, and then increased from 2000 to 2005 after which it has either stabilized (total numbers and females) or shown a marginal decrease (males and calves; Fig. S7.4). The number of males per female has decreased from >0.18 in 1995 to <0.12 in 2015 (Fig. S7.5). Finally, meat production (from the calves only) per female increased from 1995 to around 2005 even though this effect was not statistically significant (Fig. S7.6), whereas the average slaughter mass for the calves showed a curved trend in time (Fig. S7.7: the predictions from the fitted model varied from ca. 20.5 kg in 1997 and 2016 to ca. 21.3 kg around 2005). REFERENCES Wood, S. N. 2006. Generalized additive models: an introduction with R. Chapman & Hall/CRC. Wood, S. N. 2012. mgcv: GAMs with GCV/AIC/REML smoothness estimation and GAMMs by PQL. R package version 1-7-22.
B.-J. Bårdsen et al. S7.2 edf 1.00, P 1, R adj 2 0.90 edf 3.03, P 7, R adj 2 0.39 Number of predators ( N pred ) 40 60 80 120 160 Lynx Wolwerine 1995 2000 2005 2010 2015 Time (year) Figure S7.1. The number of predator family groups (consisting of adults that breeds; denoted as Föryngring in the original data set) in Swedish Sápmi over the years from 1999 (equaling the season 1994/1995) to 2015 (equaling the season 2014/2015). We only used data on lynx and wolverine even though the number of wolves (Canis lupus) was available (no wolf family groups were preset except for 2014 and 2015 when 1 and 2 groups were present). Trends (± standard errors) are from Generalized Additive Models (GAMs) fitted to the data, GAM output includes the effective degrees of freedom (edf) that denotes the degree of smoothness and its statistical significance (P), whereas the adjusted R 2 for the GAM denotes how well the model explains the variability in the response.
B.-J. Bårdsen et al. S7.3 A) Number of group leaders (N leaders ) 900 950 1000 B) edf 2.69, P 1, R adj 2 0.88 1995 2000 2005 2010 2015 Time (year) Figure S7.2. Temporal trends in A) the number of reindeer owners and B) the number of group leaders in Sweden (time denotes season as in Fig. S7.1). See legends in Fig. S7.1 for details about the fitted model (line).
B.-J. Bårdsen et al. S7.4 Number of slaughtered calves [ N)] 25000 35000 45000 A) edf 2.13, P 1, R adj 2 0.42 1 Calf harvest per female [ N cal N fem ] 0.16 0 4 8 B) edf 1.72, P 7, R adj 2 5 1995 2000 2005 2010 2015 Time (year) Figure S7.3. Temporal trends in A) the number of slaughtered calves and the B) number of slaughtered calves per female in Sweden (time denotes season as in Fig. S7.1). See legends in Fig. S7.1 for details about the fitted models.
B.-J. Bårdsen et al. S7.5 A) edf 4.56, P 1, R adj 2 0.86 edf 4.38, P 1, R adj 2 0.91 Number of reindeer [ N)] 160000 200000 240000 Female Total edf 4.28, P 1, R adj 2 0.77 B) edf 4.62, P 1, R adj 2 0.85 Number of reindeer [ N)] 20000 40000 60000 Male Calf 1995 2000 2005 2010 2015 Time (year) Figure S7.4. Temporal trends in the number of A) reindeer and females, and the B) calves and males in Sweden. See legends in Fig. S7.1 for details about the fitted models.
B.-J. Bårdsen et al. S7.6 1 Males per female [ N mal N fem ] 0.12 0.14 0.16 0.18 edf 4.69, P 1, R adj 2 0.91 1995 2000 2005 2010 2015 Time (year) Figure S7.5. Temporal trends in the number of males per female in Sweden. See legends in Fig. S7.1 for details about the fitted models.
B.-J. Bårdsen et al. S7.7 Figure S7.6. Temporal trends in meat production for the calf-segment (kg) per female in Sweden. See legends in Fig. S7.1 for details about the fitted models.
B.-J. Bårdsen et al. S7.8 Figure S7.7. Temporal trends in the average slaughter body mass (kg) for the calves in Sweden. See legends in Fig. S7.1 for details about the fitted models.