Mixing model for the analysis of stable isotopes: spatiotemporal
niche identification
Stable isotopic compositions of potential water source pools and plant
water provide important information on water sources and water uptake
patterns (Dawson, Mambelli, Plamboeck,
Templer, & Tu, 2002). Plants may have access to more than one water
source pool (e.g. recent rain, soil water, and groundwater) in different
proportions. Rooting depth and distribution define the depth and soil
volume from where plants potentially extract these water sources.
Therefore, water isotopic compositions of plant xylem can be viewed as a
mixture of isotopic compositions from different water sources.
Vegetation with roots distributed throughout the soil profile, for
example, garner water from different soil depths resulting in twig water
exhibiting mixed isotopic signature
(Cramer, Thorburn, & Fraser, 1999).
A typical formulation using two isotopic signatures (δ1 and δ2) to
partition the contributions (ƒ) of three sources (a, b, c) to a mixture
(m) is:
\begin{equation}
\delta_{m}^{1}=f_{a}\delta_{a}^{1}+f_{b}\delta_{b}^{1}+f_{c}\delta_{c}^{1}\nonumber \\
\end{equation}\begin{equation}
\delta_{m}^{2}=f_{a}\delta_{a}^{2}+f_{b}\delta_{b}^{2}+f_{c}\delta_{c}^{2}\nonumber \\
\end{equation}\begin{equation}
1=f_{a}+f_{b}+f_{c}\nonumber \\
\end{equation}The number of sources that can be partitioned is limited by the number
of isotopic signatures employed. For the dual isotope example above, the
mixing model is a system of three equations with three unknowns (fa, fb,
fc), for which there is a unique solution
(Phillips & Gregg, 2003). The relative
contributions of different sources to xylem water were estimated by
Bayesian mixing modelling using the Stable Isotope Analysis (SIAR)
package. Stable isotope mixing models are used extensively for studying
food webs but can also be applied to the determination of plant water
sources (Beyer, Hamutoko, Wanke, Gaj, &
Koeniger, 2018; Evaristo, Jasechko, &
McDonnell, 2015; Evaristo & McDonnell,
2017; Voltas, Lucabaugh, Chambel, &
Ferrio, 2015). We considered four different sources of water: two soil
depths (0–10 cm and 10–25 cm), soil pockets and weathered rock
(regolith) and groundwater reservoirs remaining in fractures and
fissures within the rhyolitic-rock (see Figure S2) protected from
evaporation.