two_source_model_arc {trps} | R Documentation |
Bayesian model - Two Source Trophic Position with \alpha_r
and carbon mixing model
Description
Estimate trophic position using a two source model with \alpha_r
derived from
Post 2002 and Heuvel et al. (2024) doi:10.1139/cjfas-2024-0028 using a Bayesian framework.
Usage
two_source_model_arc(bp = FALSE, lambda = NULL)
Arguments
bp |
logical value that controls whether informed priors are
supplied to the model for both |
lambda |
numerical value, |
Details
We will use the following equations derived from Post 2002 and Heuvel et al. (2024) doi:10.1139/cjfas-2024-0028:
-
\alpha = (\delta^{13} C_c - \delta ^{13}C_2) / (\delta ^{13}C_1 - \delta ^{13}C_2)
-
\alpha = \alpha_r \times (\alpha_{max} - \alpha_{min}) + \alpha_{min}
-
\delta^{13}C = c_1 \times \alpha_c + c_2 \times (1 - \alpha_c)
-
\delta^{15}N = \Delta N \times (tp - \lambda_1) + n_1 \times \alpha_c + n_2 \times (1 - \alpha_c)
-
\delta^{15}N = \Delta N \times (tp - (\lambda_1 \times \alpha_c + \lambda_2 \times (1 - \alpha_c))) + n_1 \times \alpha_c + n_2 \times (1 - \alpha_c)
For equation 1)
This equation is a carbon source mixing model with
\delta^{13}C_c
is the isotopic value for consumer,
\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)
\alpha
is being corrected using equations in
Heuvel et al. (2024) doi:10.1139/cjfas-2024-0028.
with \alpha_r
being the corrected value (bound by 0 and 1),
\alpha_{min}
is the minimum \alpha
value calculated
using add_alpha()
and \alpha_{max}
being the maximum \alpha
value calculated using add_alpha()
.
For equation 3)
This equation is a carbon source mixing model with \delta^{13}
C being
estimated using c_1
, c_2
and \alpha_c
calculated in equation 1.
For equation 4) and 5)
\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
,
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
).
Value
returns model structure for two source model to be used in a
brms()
call.
See Also
Examples
two_source_model_arc()