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 \delta^{15}N and \delta^{15}C baselines. Default is FALSE meaning the model will use uninformed priors, however, the supplied data.frame needs values for both \delta^{15}N and \delta^{15}C baseline (c1, c2, n1, and n2).

lambda

numerical value, 1 or 2, that controls whether one or two lambdas are used. See details for equations and when to use 1 or 2. Defaults to 1.

Details

We will use the following equations derived from Post 2002 and Heuvel et al. (2024) doi:10.1139/cjfas-2024-0028:

  1. \alpha = (\delta^{13} C_c - \delta ^{13}C_2) / (\delta ^{13}C_1 - \delta ^{13}C_2)

  2. \alpha = \alpha_r \times (\alpha_{max} - \alpha_{min}) + \alpha_{min}

  3. \delta^{13}C = c_1 \times \alpha_c + c_2 \times (1 - \alpha_c)

  4. \delta^{15}N = \Delta N \times (tp - \lambda_1) + n_1 \times \alpha_c + n_2 \times (1 - \alpha_c)

  5. \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, \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).

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

brms::brms()

Examples

two_source_model_arc()


[Package trps version 0.1.0 Index]