2.7 Statistical analyses – stable isotopes
Liver is commonly used as a lipid-storage organ in vertebrates and liver lipid content can vary significantly among individuals according to variation in nutritional state and physiological condition. Lipids formed through de novo biosynthesis are isotopically lighter in δ13C values compared to proteins and the dietary sources from which they were formed (DeNiro & Epstein, 1977). If the isotopic effect of these lipids is not accounted for, they can affect assessment of consumer δ13C values. Furthermore, as the livers analyzed here were preserved in ethanol, they may have undergone some partial uncontrolled lipid extraction prior to analysis. Variation in individual lipid content can affect comparisons of δ13C values and it is therefore common to use chemical treatments to remove lipids prior to stable isotope analyses. However, the chemical treatment can affect estimated values of other stable isotopes from the same sample. Another possible solution is to use an arithmetic correction that relies on a predictable relationship between lipid content and the elemental ratio between carbon and nitrogen (C:N) in the sample (Kiljunen et al., 2006; Logan et al., 2008). Javornik et al. (2019) found small effects of ethanol storage on δ13C values in mammalian liver but reported no preservation effects on δ15N or δ34S values. Javornik et al. (2019) reported that C:N values decreased after ethanol storage but suggested that lipid-free 13C values could be reliably estimated mathematically from the C:N ratio. In our samples, liver C:N ratios varied considerably (range = 3.2-5.7, mean ± SD = 3.8 ± 0.5, n = 41). Liver C:N ratios were lower in mice captured at higher elevations (r = -0.36, n = 40, P = 0.024). As there was also a negative relationship between C:N and δ13C within samples from the same collection locality, we estimated lipid-corrected δ13C values using Equation 1a from Logan et al. (2008), resulting in a mean (± SD) isotopic shift of 1.1 ± 0.6‰. All δ13C data that we report are lipid-corrected, but liver δ15N and δ34S data are shown without correction.
Collection sites spanned ~4400 m of elevation and therefore exhibited considerable variation in vegetation cover and plant species composition. We therefore examined how stable isotopes varied within the dataset by plotting each of the stable isotopes against elevation. We then used PERMANOVA (non-parametric permutation-based equivalent of ANOVA) to examine whether stable isotope values varied among capture sites. Since we collected a single individual from site 7 (the summit of Llullaillaco), it was not included in these comparisons. Although PERMANOVA is typically used for multivariate comparisons (MANOVA), it can also be used to make robust univariate comparisons. Finally, to assess the ability of the stable isotope analysis to assign mice to capture location, and to identify mismatches that may be indicative of recent dispersal, we used canonical analysis of principal coordinates (CAP), a distance-based equivalent of discriminant function analysis (Anderson & Willis, 2003). This approach uses multivariate data (e.g., δ13C, δ15N and δ34S values) to discriminate between groups defined by elevation of capture sites. This approach also allowed us to infer the possible origin of the summit mouse from Volcán Llullaillaco (site 7). We grouped mice in bins based on their capture elevation (2000-3000 m, 3000-4000 m, 4000-5000 m, and >5000 m) and we used δ13C, δ15N and δ34S as dependent variables. We used a leave-one-out classification approach to examine relative classification success, and we then used the model to identify the elevational range that provided the best match to values from the Llullaillaco summit mouse. The ability of the CAP model to statistically discriminate between groups was estimated via permutation (n = 9999). PERMANOVA and CAP were both run in the PERMANOVA+1 add on to PRIMER 7 (Anderson et al., 2008; Clarke & Gorley, 2015).
We estimated the trophic position of P. vaccarum at each site using liver δ15N values with those of primary producers collected across a similar (but truncated) elevational range (Díaz et al., 2016). This approach (Cabana and Rasmussen 1996) allows the indirect calculation of consumer trophic position (TP): TP = λ + (δ15NConsumer − δ15NBaseline)/TDF, where λ is the trophic position of the baseline taxon, δ15NConsumer is the nitrogen isotopic value of mice at a given site, δ15NBaseline is the nitrogen isotopic value of the baseline at that site, and TDF is the mean ± SD nitrogen trophic enrichment factor (TDF) for mouse liver (here we use 4.3 ± 0.2 ‰ from Arneson and MacAvoy (2005)). We used plants as our baseline (λ =1) based on data from Díaz et al. (2016), which were collected in the same region as our study, over an elevational range of 2670-4480 m. Plant δ13C and δ15N values exhibited considerable variation across elevations (Figure 6), and we placed plants into broad elevational intervals (2000-3000 m, 3000-4000 m, 4000-5000 m, and >5000 m). We then used values from the closest elevational interval to estimate mouse trophic position at each capture site using tRophicPostion 0.8.0 (Quezada-Romegialliet al., 2018) in R 4.2.3 (López-Cortés et al. , 2007; R Core Team, 2023). Briefly, tRophicPosition uses a Bayesian approach to estimate trophic position for a population of consumers while accounting for variation in consumer and baseline isotope values. For most sites we use the onebaseline model (assuming a single baseline) but we used the twoBaselines model for mice from site 2. This is because the plants from the 3000 – 4000 m interval showed a bimodal distribution of δ13C values, which indicates the presence of plants using different photosynthetic pathways (e.g. C3, C4/CAM). Since these groups also showed evidence for a non-normal distribution of δ15N values, we used the twoBaselines full model, which also uses baseline δ13C. For all model runs we used the following parameters: chains = 3, number of adaptive iterations = 1 000, iterations = 20 000, burn-in = 1 000, thinning = 10. In case of the summit mouse from Volcán Llullaillaco we developed an individual model to calculate trophic position, astRophicPosition v 0.8.0 currently provides only population-level estimates of TP. This new model with a one baseline approach was implemented in greta (Golding, 2019) which allows the calculation of TP at the individual level. We modelled the baseline for the summit mouse as having a mean and standard deviation of δ15N values of plants >5,000 m with a normal distribution for the mean and a Cauchy distribution for the SD, with a location of plants δ15N SD a scale of 3 and truncated from 0 to infinite. In this analysis λ is 1, the TDF was modelled as having a normal distribution with a mean of 4.3 and SD of 0.2 (Arneson & MacAvoy, 2005). We calculated 10 000 samples, with a thinning of 10, 1 000 samples as warmup and 16 chains.
Due to the selective retention of heavier isotopes during the assimilation of food, consumers are typically isotopically ‘heavier’ than their food (DeNiro & Epstein, 1978; DeNiro & Epstein, 1981). These diet-tissue shifts are referred to as trophic enrichment or trophic discriminations, and are typically estimated in experimental settings. Arneson and MacAvoy (2005) provided empirical estimates for trophic discrimination factors (TDFs) in liver from groups of laboratory mice fed diets that differed in the origin of their protein and carbohydrate components. In their control diet, where carbohydrates and proteins originated from the same source, mean ± SD TDFs were 0.7 ± 0.3 ‰ for carbon (Δ13C), 4.3 ± 0.2 ‰ for nitrogen (Δ15N), and -2.1 ± 0.1 ‰ for sulfur (Δ34S). As such, we expect mouse livers to have δ13C and δ15N values that are their long-term average, in combination with δ34S values ~2 % lower than the long-term average.