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Bayesian model - Two Source Trophic Position

Source: R/two_source_model.R
two_source_model.Rd

Trophic position using a two source model derived from Post 2002 using a Bayesian framework.

Usage

two_source_model(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 \(\lambda\)s are used. See details for equations and when to use 1 or 2. Defaults to 1.

Value

returns model structure for two source model to be used in a brms() call.

Details

We will use the following equations from Post 2002 and Vander Zanden and Vadeboncoeur (2002):

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

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

  3. $$\delta^{15}N = \Delta N \times (tp - (\lambda_1 \times \alpha + \lambda_2 \times (1 - \alpha))) + n_1 \times \alpha + n_2 \times (1 - \alpha)$$

For equation 1)

is a carbon use model derived from Vander Zanden and Vadeboncoeur (2002)-9658%282002%29083%5B2152%3AFAIOBA%5D2.0.CO%3B2),\(\delta^{13}C_c\) 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 \(\lambda_2\)).

See also

brms::brms()

Examples

two_source_model()
#> d13c ~ alpha * (c1 - c2) + c2 
#> alpha ~ 1
#> d15n ~ dn * (tp - l1) + n1 * alpha + n2 * (1 - alpha) 
#> alpha ~ 1
#> tp ~ 1
#> dn ~ 1