As described in Ives et al. 2003, the Multivariate Autoregressive Model, also known as the MAR(1) model, is a discrete-time model for a multispecies stochastic community subject to environmental noise. It is a Markov process. Given multispecies time series (log) abundance data without observation error, parameter estimation of this model parameters can be quickly done via Conditional Least Squares.
Arguments
- comm.mat
Data frame with log-scale abundance for each time step following burn-in. We expect one column per species and one row per time-step.
- covariate
Matrix of covariates (ex. precipitation per time step) with each column representing a variable and each row representing a time step. Defaults to "NULL" when no matrix is supplied.
Value
Resulting data frame includes:
A, vector of length p (p = number of species) containing the estimates of the intrinsic rate of natural increase of each species.
B, a matrix of p x p estimates where the diagonal elements represent the intra-specific, density-dependent effects. The elements \(b_{ij}\) gives the effect of the abundance of species j on per capita growth rate of species i.
sigma, a matrix of p x p, represents environmental noise variance-covariance matrix.
C, a vector of estimated coefficients for every covariate representing the effects of every covariate on every species.
E, vector representing stochastic environmental variability.
Yhat, \(\hat{Y}\) estimator of predicted abundance.
R2, \(R^2\), proportion of explained variation in the log scale population abundance for each species.
R2_D, conditional \(R^2\), proportion of variation in the change in one unit of time of the log scale population abundance explained by the model for each species.
AIC, Akaike information criterion.
BIC, Bayesian information criterion.
lnlike, maximized log likelihood of the MAR(1) model.