Trophic position using a two source model derived from Post 2002 using a Bayesian framework.
Arguments
- bp
logical value that controls whether informed priors are supplied to the model for both \(\delta^{15}\)N and \(\delta^{15}\)C baselines. Default is
FALSE
meaning the model will use uninformed priors, however, the supplieddata.frame
needs values for both \(\delta^{15}\)N and \(\delta^{15}\)C baseline (c1
,c2
,n1
, andn2
).- lambda
numerical value,
1
or2
, that controls whether one or two \(\lambda\)s are used. See details for equations and when to use1
or2
. Defaults to1
.
Details
We will use the following equations from Post 2002:
$$\delta^{13}C_c = \alpha \times (\delta ^{13}C_1 - \delta ^{13}C_2) + \delta ^{13}C_2$$
$$\delta^{15}N = \Delta N \times (tp - \lambda_1) + n_1 \times \alpha + n_2 \times (1 - \alpha)$$
$$\delta^{15}N = \Delta N \times (tp - (\lambda_1 \times \alpha + \lambda_2 \times (1 - \alpha))) + n_1 \times \alpha + n_2 \times (1 - \alpha)$$
For equation 1)
where \(\delta^{13}C_c\) is the isotopic value for consumer, \(\alpha\) is the ratio between baselines and consumer \(\delta^{13}C\), \(\delta^{13}C_1\) is the mean isotopic value for baseline 1, and \(\delta^{13}C_2\) is the mean isotopic value for baseline 2
For equation 2) and 3)
\(\delta^{15}\)N are values from the consumer,
\(n_1\) is \(\delta^{15}\)N values of baseline 1, \(n_2\) is
\(\delta^{15}\)N values of baseline 2,
\(\Delta\)N is the trophic discrimination factor for N (i.e., mean of 3.4
),
tp is trophic position, and \(\lambda_1\) and/or
\(\lambda_2\) are the trophic levels of
baselines which are often a primary consumer (e.g., 2
or 2.5
).
The data supplied to brms()
when using baselines at the same trophic level
(lambda
argument set to 1
) needs to have the following variables, d15n
,
c1
, c2
, n1
, n2
, l1
(\(\lambda_1\)) which is usually 2
.
If using baselines at different trophic levels (lambda
argument set to 2
)
the data frame needs to have l1
and l2
with a numerical value for
each trophic level (e.g.,2
and 2.5
; \(\lambda_1\) and \(\lambda_2\)).