two_source_priors_params_arc {trps} | R Documentation |
Adjust Bayesian priors - Two Source Trophic Position with \alpha_r
and carbon mixing model
Description
Adjust priors for 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
Usage
two_source_priors_params_arc(
a = NULL,
b = NULL,
n1 = NULL,
n1_sigma = NULL,
n2 = NULL,
n2_sigma = NULL,
c1 = NULL,
c1_sigma = NULL,
c2 = NULL,
c2_sigma = NULL,
dn = NULL,
dn_sigma = NULL,
tp_lb = NULL,
tp_ub = NULL,
sigma_lb = NULL,
sigma_ub = NULL,
bp = FALSE
)
Arguments
a |
( |
b |
( |
n1 |
mean ( |
n1_sigma |
variance ( |
n2 |
mean ( |
n2_sigma |
variance ( |
c1 |
mean ( |
c1_sigma |
variance ( |
c2 |
mean ( |
c2_sigma |
variance ( |
dn |
mean ( |
dn_sigma |
variance ( |
tp_lb |
lower bound for priors for trophic position. Defaults to |
tp_ub |
upper bound for priors for trophic position. Defaults to |
sigma_lb |
lower bound for priors for |
sigma_ub |
upper bound for priors for |
bp |
logical value that controls whether informed baseline priors are
supplied to the model for |
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_r + c_2 \times (1 - \alpha_r)
-
\delta^{15}N = \Delta N \times (tp - \lambda_1) + n_1 \times \alpha_r + n_2 \times (1 - \alpha_r)
-
\delta^{15}N = \Delta N \times (tp - (\lambda_1 \times \alpha_r + \lambda_2 \times (1 - \alpha_r))) + n_1 \times \alpha_r + n_2 \times (1 - \alpha_r)
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_r
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
).
This function allows the user to adjust the priors for the following variables in the equation above:
The random exponent (
\alpha
;a
) and shape parameters (\beta
;b
) for\alpha_r
. This prior assumes a beta distribution.The mean (
n2
;\mu
) and variance (n2_sigma
;\sigma
) of the second\delta^{15}
N for a given baseline. This prior assumes a normal distributions.The mean (
c1
;\mu
) and variance (c1_sigma
;\sigma
) of the second\delta^{13}
C for a given baseline. This prior assumes a normal distributions.The mean (
c2
;\mu
) and variance (c2_sigma
;\sigma
) of the second\delta^{13}
C for a given baseline. This prior assumes a normal distributions.The mean (
dn
;\mu
) and variance (dn_sigma
;\sigma
) of\Delta
N (i.e, trophic enrichment factor). This prior assumes a normal distributions.The lower (
tp_lb
) and upper (tp_ub
) bounds for priors for trophic position. This prior assumes a uniform distributions.The lower (
sigma_lb
) and upper (sigma_ub
) bounds for variance (\sigma
). This prior assumes a uniform distributions.
Value
stanvars
object to be used with brms()
call.
See Also
two_source_priors_arc()
, two_source_model_arc()
, and brms::brms()
Examples
two_source_priors_params_ar()