Table 1. Summary of δ13C and δ15N values for each fecal sample. Mean δ13C = -17.78 ± 0.87‰; Mean δ15N = 11.58 ± 1.08‰.
Sample ID δ13C (‰) δ15N (‰)
HW-20240911-GN-F1-FEC-SIA -18.35 10.84
HW-20240822-GN-F1-FEC-SIA -17.78 10.54
HW-20240822-GN-F4-FEC-SIA -17.87 11.53
HW-20240822-GN-F5-FEC-SIA -17.93 11.06
HW-20240823-GN-F1-FEC-SIA -17.57 11.56
HW-20240823-CC-F2-FEC-SIA -16.43 10.64
HW-20240912-GN-F1-FEC-SIA -18.39 10.42
HW-20240712-GN-F2-FEC-SIA -19.11 11.51
HW-20240821-GN-F1-FEC-SIA -16.47 11.53
HW-20240821-GN-F2-FEC-SIA -16.86 11.40
HW-20240821-GN-F3-FEC-SIA -17.74 14.29
HW-20240717-GN-F1-FEC-SIA -19.22 12.18
HW-20240815-GN-F1-FEC-SIA -17.37 13.05

Analyses and Modelling

  1. Check the effects of lipid extraction on 13C and 15N isotopes within fecal samples.

Show t-test details (lipid extraction and δ13C) 
 
    Paired t-test

data:  wide$LE and wide$NLE
t = 8.4323, df = 12, p-value = 2.185e-06
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
 1.070203 1.815951
sample estimates:
mean difference 
       1.443077
Show t-test details (Lipid extraction and δ15N) 
 
    Paired t-test

data:  wide$LE and wide$NLE
t = 8.4323, df = 12, p-value = 2.185e-06
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
 1.070203 1.815951
sample estimates:
mean difference 
       1.443077



Lipid extraction helps correct artificially depleted fecal ¹³C values. However, δ¹⁵N appears affected by lipid extraction as well, perhaps some mechanism is unintentionally extracting nitrogen-containing compounds. Therefore, we will use LE values for 13C and NLE values for 15N.



  1. Check if our humpback whale fecal values (δ13C and δ15N) vary significantly between months (The data set violated at least one ANOVA assumption of normality and equal variance with both N and C values, so Kruskal-Wallis test was used)
Table 2. Kruskal–Wallis tests by month for δ13C (LE) and δ15N (NLE).
Analyte Kruskal–Wallis χ² df p-value
δ13C (‰) 10.04 2 0.007
δ15N (‰) 4.05 2 0.132

Month appears to affect our lipid-extracted δ13C values. However, we have extremely uneven group size (N=10 august, N= 2 July, N=2, September) and low statistical power. Same is the case with the NLE δ15N values. Therefore, cannot rely on statistical inference in this case. There is not enough power to say isotopic signature of feces changed significantly between months.



  1. We have so few isotopic prey values from our study zone, so we can apply a baseline shift correction to a larger 2023 Strait of Georgia (SOG) dataset. Pacific Krill act as an isotopic baseline in both the SOG and our study zone, Juan de Fuca (JdF). Using the shift in 13C and 15N between both sites, we can apply an adjustion to prey collected from the SOG in 2023, to represent what isotopic prey signatures would be seen in JdF 2024.

Our time and location adjust values for krill, juvenile herring, and adult herring are:

##   d13C_mean_adj d13C_sd_adj d15N_mean_adj d15N_sd_adj
## 1       -17.755     1.37188         8.945    1.354668
##   d13C_mean_adj d13C_sd_adj d15N_mean_adj d15N_sd_adj
## 1       -14.755    1.077986        13.105    0.464679
##   d13C_mean_adj d13C_sd_adj d15N_mean_adj d15N_sd_adj
## 1       -16.395    1.146278        12.185   0.3852617



  1. Now that we have three sources (with k independent tracers, you can uniquely solve for k + 1 sources), lets generate a Bayesian stable isotope mixing model (SIMM) using lipid-extracted δ13C values and non-lipid extracted δ15N values.

## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 26
##    Unobserved stochastic nodes: 31
##    Total graph size: 152
## 
## Initializing model

## 
## Summary for 1
##                    mean    sd
## deviance         82.632 4.591
## Krill             0.754 0.081
## Adult Herring     0.094 0.054
## Juvenile Herring  0.152 0.085
## sd[d13C]          0.950 0.452
## sd[d15N]          1.058 0.479
## 
## Summary for 1
##                    2.5%    25%    50%    75%  97.5%
## deviance         76.333 79.366 81.789 84.875 94.037
## Krill             0.580  0.704  0.758  0.811  0.898
## Adult Herring     0.018  0.052  0.085  0.127  0.219
## Juvenile Herring  0.026  0.085  0.141  0.205  0.343
## sd[d13C]          0.266  0.637  0.882  1.196  1.981
## sd[d15N]          0.326  0.727  0.997  1.314  2.183

## Most popular orderings are as follows:
##                                          Probability
## Krill > Juvenile Herring > Adult Herring      0.6664
## Krill > Adult Herring > Juvenile Herring      0.3311
## Juvenile Herring > Krill > Adult Herring      0.0025



  1. Sensitivity analysis of our SIMM. Check how sensitive the model outputs are to the fecal correction factors. Also check sensitivity to more informative priors. The SIMMR package describes process of adding informative priors.

This is the extent of SIA fecal analyses available to us. Trophic position cannot be determined since feces is not an assimilated tissue. Nitrogen isnt affect by lipid content, so this works well.