two_source_priors_params_arc: Adjust Bayesian priors - Two Source Trophic Position with...
In trps: Bayesian Trophic Position Models using 'stan'

View source: R/two_source_priors_params_arc.R

two_source_priors_params_arc

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) \Sexpr[results=rd]{tools:::Rd_expr_doi("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`	(`\alpha`) exponent of the random variable for beta distribution. Defaults to `1`. See beta distribution for more information.
`b`	(`\beta`) shape parameter for beta distribution. Defaults to `1`. See beta distribution for more information.
`n1`	mean (`\mu`) prior for first `\delta^{15}`N baseline. Defaults to `8.0`.
`n1_sigma`	variance (`\sigma`)for first `\delta^{15}`N baseline. Defaults to `1`.
`n2`	mean (`\mu`) prior for second `\delta^{15}`N baseline. Defaults to `9.5`.
`n2_sigma`	variance (`\sigma`) for second `\delta^{15}`N baseline. Defaults to `1`.
`c1`	mean (`\mu`) prior for first `\delta^{13}`C baseline. Defaults to `-21`.
`c1_sigma`	variance (`\sigma`)for first `\delta^{13}`C baseline. Defaults to `1`.
`c2`	mean (`\mu`) prior for second `\delta^{13}`C baseline. Defaults to `-26`.
`c2_sigma`	variance (`\sigma`) for second `\delta^{13}`C baseline. Defaults to `1`.
`dn`	mean (`\mu`) prior value for `\Delta`N. Defaults to `3.4`.
`dn_sigma`	variance (`\sigma`) for `\delta^{15}`N. Defaults to `0.25`.
`tp_lb`	lower bound for priors for trophic position. Defaults to `2`.
`tp_ub`	upper bound for priors for trophic position. Defaults to `10`.
`sigma_lb`	lower bound for priors for `\sigma`. Defaults to `0`.
`sigma_ub`	upper bound for priors for `\sigma`. Defaults to `10`.
`bp`	logical value that controls whether informed baseline priors are supplied to the model for `\delta^{15}`N baselines. Default is `FALSE` meaning the model will use uninformed priors, however, the supplied `data.frame` needs values for both `\delta^{15}`N baseline (`n1` and `n2`)

Details

We will use the following equations derived from Post 2002 and Heuvel et al. (2024) \Sexpr[results=rd]{tools:::Rd_expr_doi("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) \Sexpr[results=rd]{tools:::Rd_expr_doi("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, \DeltaN 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 \DeltaN (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.