jSDM-package

joint species distribution models

jSDM is an R package for fitting joint species distribution models (JSDM) in a hierarchical Bayesian framework.

The Gibbs sampler is written in 'C++'. It uses 'Rcpp', 'Armadillo' and 'GSL' to maximize computation efficiency.

Package:	jSDM
Type:	Package
Version:	0.2.1
Date:	2019-01-11
License:	GPL-3
LazyLoad:	yes
package

Details

The package includes the following functions to fit various species distribution models :

function	data-type
jSDM_binomial_logit	presence-absence
jSDM_binomial_probit	presence-absence
jSDM_binomial_probit_sp_constrained	presence-absence
jSDM_binomial_probit_long_format	presence-absence
jSDM_poisson_log	abundance

• jSDM_binomial_probit :

  Ecological process:

$$y_{ij} \sim \mathcal{B}ernoulli(\theta_{ij})y_ij ~ Bernoulli(\theta_ij),$$

where

if n_latent=0 and site_effect="none"	probit $(\theta_ij) = X_i \beta_j$
if n_latent\>0 and site_effect="none"	probit $(\theta_ij) = X_i \beta_j + W_i \lambda_j$
if n_latent=0 and site_effect="fixed"	probit $(\theta_ij) = X_i \beta_j + \alpha_i$ and $\alpha_i ~ N(0,V_\alpha)$
if n_latent\>0 and site_effect="fixed"	probit $(\theta_ij) = X_i \beta_j + W_i \lambda_j + \alpha_i$
if n_latent=0 and site_effect="random"	probit $(\theta_ij) = X_i \beta_j + \alpha_i$
if n_latent\>0 and site_effect="random"	probit $(\theta_ij) = X_i \beta_j + W_i \lambda_j + \alpha_i$ and $\alpha_i ~ N(0,V_\alpha)$

• jSDM_binomial_probit_sp_constrained :

  This function allows to fit the same models than the function jSDM_binomial_probit except for models not including latent variables, indeed n_latent must be greater than zero in this function. At first, the function fit a JSDM with the constrained species arbitrarily chosen as the first ones in the presence-absence data-set. Then, the function evaluates the convergence of MCMC $\lambda$ chains using the Gelman-Rubin convergence diagnostic ($\hat{R}$). It identifies the species ($\hat{j}_l$) having the higher $\hat{R}$ for $\lambda_{\hat{j}_l}$. These species drive the structure of the latent axis $l$. The $\lambda$ corresponding to this species are constrained to be positive and placed on the diagonal of the $\Lambda$ matrix for fitting a second model. This usually improves the convergence of the latent variables and factor loadings. The function returns the parameter posterior distributions for this second model.

• jSDM_binomial_logit :

  Ecological process :

$$y_{ij} \sim \mathcal{B}inomial(\theta_{ij},t_i)y_ij ~ Binomial(\theta_ij,t_i),$$

where

if n_latent=0 and site_effect="none"	logit $(\theta_ij) = X_i \beta_j$
if n_latent\>0 and site_effect="none"	logit $(\theta_ij) = X_i \beta_j + W_i \lambda_j$
if n_latent=0 and site_effect="fixed"	logit $(\theta_ij) = X_i \beta_j + \alpha_i$
if n_latent\>0 and site_effect="fixed"	logit $(\theta_ij) = X_i \beta_j + W_i \lambda_j + \alpha_i$
if n_latent=0 and site_effect="random"	logit $(\theta_ij) = X_i \beta_j + \alpha_i$ and $\alpha_i ~ N(0,V_\alpha)$
if n_latent\>0 and site_effect="random"	logit $(\theta_ij) = X_i \beta_j + W_i \lambda_j + \alpha_i$ and $\alpha_i ~ N(0,V_\alpha)$

• jSDM_poisson_log :

  Ecological process :

$$y_{ij} \sim \mathcal{P}oisson(\theta_{ij})y_ij ~ Poisson(\theta_ij),$$

where

if n_latent=0 and site_effect="none"	log $(\theta_ij) = X_i \beta_j$
if n_latent\>0 and site_effect="none"	log $(\theta_ij) = X_i \beta_j + W_i \lambda_j$
if n_latent=0 and site_effect="fixed"	log $(\theta_ij) = X_i \beta_j + \alpha_i$
if n_latent\>0 and site_effect="fixed"	log $(\theta_ij) = X_i \beta_j + W_i \lambda_j + \alpha_i$
if n_latent=0 and site_effect="random"	log $(\theta_ij) = X_i \beta_j + \alpha_i$ and $\alpha_i ~ N(0,V_\alpha)$
if n_latent\>0 and site_effect="random"	log $(\theta_ij) = X_i \beta_j + W_i \lambda_j + \alpha_i$ and $\alpha_i ~ N(0,V_\alpha)$

• jSDM_binomial_probit_long_format :

  Ecological process:

$$y_n \sim \mathcal{B}ernoulli(\theta_n)y_n ~ Bernoulli(\theta_n)$$

such as $species_n=j$ and $site_n=i$, where

if n_latent=0 and site_effect="none"	probit $(\theta_n) = D_n \gamma + X_n \beta_j$
if n_latent\>0 and site_effect="none"	probit $(\theta_n) = D_n \gamma + X_n \beta_j + W_i \lambda_j$
if n_latent=0 and site_effect="fixed"	probit $(\theta_n) = D_n \gamma + X_n \beta_j + \alpha_i$ and $\alpha_i ~ N(0,V_\alpha)$
if n_latent\>0 and site_effect="fixed"	probit $(\theta_n) = D_n \gamma + X_n \beta_j + W_i \lambda_j + \alpha_i$
if n_latent=0 and site_effect="random"	probit $(\theta_n) = D_n \gamma + X_n \beta_j + \alpha_i$
if n_latent\>0 and site_effect="random"	probit $(\theta_n) = D_n \gamma + X_n \beta_j + W_i \lambda_j + \alpha_i$ and $\alpha_i ~ N(0,V_\alpha)$

References

Chib, S. and Greenberg, E. (1998) Analysis of multivariate probit models. Biometrika, 85, 347-361.

Warton, D. I.; Blanchet, F. G.; O'Hara, R. B.; O'Hara, R. B.; Ovaskainen, O.; Taskinen, S.; Walker, S. C. and Hui, F. K. C. (2015) So Many Variables: Joint Modeling in Community Ecology. Trends in Ecology & Evolution, 30, 766-779.

Ovaskainen, O., Tikhonov, G., Norberg, A., Blanchet, F. G., Duan, L., Dunson, D., Roslin, T. and Abrego, N. (2017) How to make more out of community data? A conceptual framework and its implementation as models and software. Ecology Letters, 20, 561-576.

Author(s)

Ghislain Vieilledent ghislain.vieilledent@cirad.fr

Jeanne Clément jeanne.clement16@laposte.net

Frédéric Gosselin frederic.gosselin@inrae.fr