Supplementary Material for Soria-Díazet al. “Top-down and bottom-up control on cougar and its prey in a central Mexican Natural Reserve”. European Journal of Wildlife Research. Corresponding autor:

Fig. S1 Per-capita changes in abundance (pca) calculated over 12 seasons (Wet & Dry) for the four species considered in this study. Each species’pca is calculated as the natural logarithm of the ratio of the Relative Abundance Index (RAI) in the next season (t+1) compared to the RAI in the current season (t), pcai,t = ln(RAIi,t+1/RAIi,t). Panels show pca for (A) Cougar, P. concolor, (B) White-tailed deer, O. virginianus, (C) Coati, N. narica and (D) Armadillo, D. novemcinctus.

Table S1 Comparisons for different candidate models describing within and between species interactions in the SNNR food web.Key: K = number of estimated parameters; AICc = Akaike Information Criteria corrected for small sample sizes; AICc = change in AICc compared to the most parsimonious model; AICc Weight = Akaike weights; Cum. Weight = cumulative Akaike weights. An intercept term was fitted to all models, but is not presented in the Model column for brevity. AIC comparison and results carried out using the ‘AICcmodavg’ package in R (Mazerolle 2016).Parameter names P = cougar (P. concolor) RAI, V = white tailed deer (O. virginianus) RAI, C =coati (N. narica) RAI, A = armadillo (D. novemcinctus) RAI, pcais: seasonal per-capita changes in abundance of cougar and their main prey and NDVI is the Normalized Difference Vegetation Index.

Response variable / Model / K / AICc / AICc / AICc Weight / Cum. Weight / Log Likelihood
pcaP / ln(P) + ln(V) / 4 / 27.96 / 0.00 / 0.42 / 0.42 / -6.65
ln(P) + ln(C) + ln(A) / 5 / 29.04 / 1.07 / 0.24 / 0.66 / 0.48
ln(P) / 3 / 29.18 / 1.22 / 0.23 / 0.89 / -9.88
ln(P) + ln(C) / 4 / 30.80 / 2.84 / 0.10 / 0.99 / -8.07
ln(A) / 3 / 35.10 / 7.14 / 0.01 / 1.00 / -12.15
ln(V) / 3 / 39.31 / 11.35 / 0.00 / 1.00 / -14.94
ln(C) / 3 / 40.43 / 12.47 / 0.00 / 1.00 / -15.50
ln(C) + ln(V) / 4 / 43.86 / 15.89 / 0.00 / 1.00 / -14.59
ln(P) + ln(C) + ln(A) + ln(V) / 6 / 52.22 / 24.26 / 0.00 / 1.00 / 0.89
ln(C) + ln(A) + ln(V) / 5 / 53.93 / 25.97 / 0.00 / 1.00 / -11.96
pcaV / ln(P) / 3 / 28.45 / 0 / 0.81 / 0.81 / -9.51
ln(P) + ln(V) / 4 / 33.02 / 4.57 / 0.08 / 0.89 / -9.18
ln(P) + NDVI / 4 / 33.49 / 5.04 / 0.06 / 0.95 / -9.41
ln(V) / 3 / 34.80 / 6.35 / 0.03 / 0.99 / -12.69
NDVI / 3 / 36.90 / 8.45 / 0.01 / 1.00 / -13.74
ln(P) + ln(V) + NDVI / 5 / 39.71 / 11.26 / 0.00 / 1.00 / -8.86
ln(V) + NDVI / 4 / 39.82 / 11.37 / 0.00 / 1.00 / -12.58
pcaC / ln(C) / 3 / 23.77 / 0 / 0.42 / 0.42 / -7.17
NDVI / 3 / 24.31 / 0.54 / 0.32 / 0.73 / -7.44
ln(P) / 3 / 26.16 / 2.39 / 0.13 / 0.86 / -8.37
ln(A) + NDVI / 4 / 26.97 / 3.19 / 0.08 / 0.94 / -6.15
ln(P) + ln(C) / 4 / 29.01 / 5.24 / 0.03 / 0.97 / -7.17
ln(P) + NDVI / 4 / 29.43 / 5.66 / 0.02 / 1.00 / -7.38
ln(P) + ln(C) + NDVI / 5 / 34.16 / 10.38 / 0.00 / 1.00 / -6.08
pcaA / ln(P) / 3 / 8.68 / 0.00 / 0.57 / 0.57 / 1.06
ln(A) / 3 / 10.01 / 1.33 / 0.30 / 0.87 / 0.39
ln(P) + ln(A) / 4 / 13.06 / 4.37 / 0.06 / 0.93 / 2.47
ln(P) + ln(A) + NDVI / 4 / 15.06 / 6.38 / 0.02 / 0.96 / 1.47
ln(P) + NDVI / 3 / 15.85 / 7.17 / 0.02 / 0.97 / -2.53
ln(A) + NDVI / 4 / 15.88 / 7.20 / 0.02 / 0.99 / 1.06
ln(A)+ ln(C) + ln(V) / 4 / 16.76 / 8.08 / 0.01 / 1.00 / 0.62

Table S2 Statistical model fit to seasonal time-series data for the SNNR food web. This model describes cougar pca similarly well to the most parsimonious model selected by AICc (AICc= 1.07). Parameter names: α = intercept, P = cougar (P. concolor) RAI, V = white tailed deer (O. virginianus) RAI, C =coati (N. narica) RAI, A = armadillo (D. novemcinctus) RAI, pcais: seasonal per-capita changes in abundance. All models represent the best from the set of candidate models, selected by AICc.

Model/Parameterfitted / ParameterEstimates
(± S.E.) / AICc / R2 / F-stat / p-value
pca(P)=α+ln(P)+ln(C)+ln(A) / 29.04 / 0.95 / 32.71 / 0.001
α / 3.06 ± 0.82 / 0.013
ln(P) / -3.05 ± 0.35 / <0.001
ln(C) / 1.67 ± 0.28 / 0.002
ln(A) / 2.82 ± 0.67 / 0.008

Fig S2 Percentage seasonal error rate on seasonal time interval across the study period (Wet and Dry; 2005-2009) for all species of the SNNR food web. This was determined following the methodology used by Hamel et al. (2013), for each species, the error rate for each of the longer season intervals as the percentage of days-sites for which a species was classified as present (photograph), based on 2005 D (Dry) reference level but absent based on the longer interval.

References:

Hamel S, Killengreen ST, Henden JA, Eide NE, Roed-Eriksen L, Ims RA, Yoccoz NG (2013) Towardsgoodpracticeguidance in using camera-traps in ecology: influence of samplingdesignonvalidity of ecologicalinferences. MethodsEcolEvol4:105-113 doi: 10.1111/j.2041-210x.2012.00262

Mazerolle, MJ. (2016). AICcmodavg: Model selection and multimodel inference based on (Q)AIC(c). R package version 2.0-4.

R Core Team (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.

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