
Bayesian MAR(1) model
by brice.semmens, last updated 7/8/08, sharing set to public
This set of Matlab scripts conducts a first order MAR(1) model to estimate interactive effects, and covariate effects, on a time series of data from a community.It uses a Gibbs sampler to estimate parameters, and currently is set up with diffuse priors on all parameters for the model. It is pretty basic at this point, but it works.
Note on the Gamma distribution:
Going back and forth between Matlab/R/WinBUGS can be confusing, because of the different parameterizations of the gamma pdf. Here's the Matlab/BUGS forms and the R equivalents:
Matlab: X ~ g(a,b) E[X] = ab
R equivalent: X ~ g(shape=a,scale=b)
BUGS: X ~ g(a,b) E[X] = a/b
R equivalent: X ~ g(shape=a,rate=b) OR
X ~ g(shape=a,scale=1/b)

Generate stochastic population processes
by e2holmes, last updated 6/13/07, sharing set to public
These are function for generating various standard types of stochastic population processes: random walks, OrnsteinUhlenbeck, discrete Gompertz, etc. Also some random number generators needed by these are here. These matlab files need the Matlat Statistics Toolbox. 
Hierarchical linear model of MPA effects
by brice.semmens, last updated 2/5/08, sharing set to public
These are a series of Matlab routines to carry out a hierarchical linear model of fish population trajectories that includes a linear adjustment for a "reserve effect" at sites designated as MPAs. %The model is set up as follows: %FIRST LEVEL %MODEL:***** y~ intercept + abundance_index * (S_g + R_t +R_nt) + error *** %where: %S_g is the slope for a given species in a given geographic region (drawn %from a normally distributed species specific hyperparameter) %R_t is a species specific additive adjustment to the slope that is drawn %from a normally distributed hyper parameter representing the reserve effect on harvested species. Activated by a dummy variable. %R_nt is the species specific additive adjustment to the slope that is drawn from a normally distributed hyper parameter %representing the reserve effect on nonharvested species. Activated by a dummy variable. %both intercept and error terms are nuisance parameters and do not need hyperparameters. I suppose you could put in an %error hyper parameter with an informative prior just to keep the model in check. %SECOND LEVEL (hyper parameters all normally distributed) %S_g_hat  These are slopes for a given species from which S_g's are drawn %R_t_hat  This is the reserve effect for targeted species from which R_t's across targeted species are drawn %R_nt_hat  This is the reserve effect for nontarged species from which %R_nt's across nontargeted species are drawn % 
LAMBDA
by e2holmes, last updated 9/11/07, sharing set to public
LAMBDA is a MatLab toolkit designed to do MAR1 based data analysis on longterm datasets and is based on the methods described in Ives et al. 2003, Ecological Monographs 73:301330. LAMBDA is designed to allow the user to step through the entire modeling process, from importing the data, to obtaining descriptive statistics of the dataset, to, finally, performing a MAR1 regression model and obtaining output parameters. A MAR1 process is a Multivariate, AutoRegressive first (1st) order process. Essentially, it is a means of estimating interactions between multiple variates from time series data, using matrix algebra. A MAR1 model is a stochastic, nonmechanistic model that uses time series data on species numbers and covariates to deduce interpopulation interactions and the effects of covariates (e.g., physical variables) on populations.Where does it come from?
LAMBDA is a product of the Mathematical Biology program at the Northwest Fisheries Science Center in Seattle, WA, and was developed with support by NOAA/NMFS and the National Research Council. It is opensource software released under the GNU GPL license, meaning you are free to use and modify it in (almost) any way you see fit. LAMBDA was developed by Steven Viscido while on a National Research Council postdoctoral associateship with Elizabeth Holmes.Credits
LAMBDA is based on the techniques outlined in the paper Ives et al. 2003, Ecological Monographs 73:301330. The code for the actual MAR1 regression was based on the "MARbasic.m" MatLab script written by Tony Ives (available at the Ecological Archives). The parameter search code was based on an unpublished script written by Tony Ives. All other code was written by Steven Viscido.Executable version
Download the LAMBDA executable along the installation instructions from the links below.LAMBDA_MCR_pkg.exe 0.9.2 Warning: This is a 138 MB file!
The executable version of LAMBDA does not require MatLab. Its system requirements are Windows XP/2000, 256 MB of RAM, and 150 MB of Hard Drive Space.
If Installation hangs
This is a bug on MatLab's side. To work around it, you will need to install vcredist_x86.exe (32 bit systems) or vcredist_x64.exe (64 bit system) first and then repeat the LAMBDA installation. But read the If_Installation_Hangs.txt readme file if this happens to you. This bug affects about 20% of computers, randomly it would seem.Matlab Source Code
This is not needed if you are using the executable version. Current source code version is LAMBDA_0.9.2Beta.zip. The source code can be downloaded below. Requirements for running LAMBDA from the source code are MatLab version 7.0.1 (R14) w/service Pack 1, or later
 MatLab's Statistics and Optimization toolboxes
 At least 256 MB of RAM on your system
 5 MB of Hard Drive space for the LAMBDA installation

Null model methods
by brice.semmens, last updated 1/7/08, sharing set to public
These files give code for ecological null model analyses.