*2.4. Statistical Analyses*

To account for statistical non-independence caused by having several samples at the same carcass site, the variable "site" was added as a random effect in a generalized linear mixed model (GLMM) framework [37]. We used a model selection procedure based on the Akaike information criterion corrected for small sample sizes [38] to identify which variables were best at explaining the variation in the concentration of a particular nutrient. The full model included the concentration of a nutrient as the dependent variable, and "distance" (distance from the center of the carcass) and "season" (season of kill) as explanatory variables. The minimum adequate model (MAM, hereafter) for each analysis was chosen based on the AICc value, Akaike weight and the number of parameters [38]. If the variable "distance" was not included in the MAM, we assumed that the effect of the carcass was not detectable on that parameter.

Shapiro–Wilk normality tests and Q–Q plots were used to check for normality. Response variables were transformed to improve normality, when not normally distributed. For soil nutrient concentrations, we square root-transformed nitrogen, calcium and magnesium, cube root-transformed phosphorus and sodium and log-transformed (natural logarithm) all other parameters. For vegetation samples, we square root-transformed calcium and magnesium, cube root-transformed sodium and log-transformed all other parameters.

The analyses were conducted separately for soil and for each of the two plant species using R 2.6.1 software [39], where the model selection was done with the R package MuMIn version 1.43.17 [40] and the linear mixed models were run with the add-on package lme4 [41]. The mixed models were fitted with maximum likelihood for the calculation of the AICc values, while the parameter estimates and their standard errors were from models fitted with restricted maximum likelihood [37].

#### **3. Results**

The variable "distance" was not included in the MAM for either soil or vegetation nutrients (data on model selection shown in Table 1 for soil, and in Tables 2 and 3 for *V*. *myrtillus*, and *A*. *flexuosa*, respectively). This indicated that the effect of the carcasses on soil and vegetation nutrient concentrations could not be detected (Figures 2–4).

**Table 1.** Set of linear mixed effect models with concentration (g/100 g) of minerals in soil in southeastern Norway in 2004 as the dependent variable and winter vs. summer (Season) and distance from the center of the carcass (Distance) as the explanatory variables. (a) C/N ratio; (b) nitrogen, N; (c) ammonium, NH4+; (d) nitrate, NO3−; (e) phosphorus, P; (f) phosphate, PO4−; (g) calcium, Ca; (h) potassium, K; (i) magnesium, Mg; (j) sodium, Na. The plus sign (+) indicates that the factor was included in the model.


<sup>a</sup> The explanatory variable "Distance" was square root-transformed. The models were ranked by the AICc—corrected Akaike information criterion (AIC). The minimum adequate model is on the top of each list; <sup>b</sup> K, number of parameters;

<sup>c</sup> Δ AICc, difference in Akaike values between the first and the actual model; <sup>d</sup> ωi, Akaike weights.





**Figure 2.** Response values in soil with increasing distance (0, 0.5, 2 and 20 m) from lynx-killed roe deer carcasses in southeastern Norway. (**a**) C/N ratio; (**b**) nitrogen, N; (**c**) ammonium, NH4+; (**d**) nitrate, NO3−; (**e**) phosphorus, P; (**f**) phosphate, PO4−; (**g**) calcium, Ca; (**h**) potassium, K; (**i**) magnesium, Mg; (**j**) sodium, Na. All values are in percentage mass; the boxplots show the median (black line within the box) and quartiles (the boundaries of the box). Whiskers above and below the box indicate the 10 th and 90 th percentiles. Points above and below the whiskers indicate outliers outside the 10 th and 90 th percentiles.

**Figure 3.** Response values in *Vaccinium myrtillus* with increasing distance (0, 0.5, 2 and 20 m) from lynx-killed roe deer carcasses in south-eastern Norway. (**a**) C:N ratio; (**b**) Nitrogen, N; (**c**) Phosphorus, P; (**d**) Calcium, Ca; (**e**) Potassium, K; (**f**) Magnesium, Mg; (**g**) Sodium, Na. All values are in percentage mass. For additional information, see Figure 2.

**Figure 4.** Response values in *Avenella flexuosa* with increasing distance (0, 0.5, 2 and 20 m) from lynx-killed roe deer carcasses in south-eastern Norway. (**a**) C:N ratio; (**b**) Nitrogen, N; (**c**) Phosphorus, P; (**d**) Calcium, Ca; (**e**) Potassium, K; (**f**) Magnesium, Mg; (**g**) Sodium, Na. All values are in percentage mass. For additional information, see Figure 2.
