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.