Projects found

This program allows one to walk through the steps required to conduct a population viability analysis, or PVA, using a population time time series. The model outputs probabilities of extinction as a function of time steps into the future, and importantly, gives confidence intervals for these probabilities.

This tool has two major advantages over traditional PVA techniques:

1) It uses a state-space Kalman filter that allows for both process and non-process error.

So what's the big deal? --Functionally it filters the data, and allows a more accurate fit for population parameters of interest.2) It uses a Bayesian sampling-importance-resampling algorithm to fully address uncertainty in the parameter estimates given the data.Rather than developing a single function that describes the probability of population extinction through time, we can use the uncertainty in parameter estimates to develop 'probabilities of probabilities', or, the uncertainty surrounding the probability of extinction through time.

We use a multivariate state-space model and a time series of yearly migration dates for sockeye salmon to estimate the heritability coef from the classic breeder's equation.

The 2 files below are the dataset and the R script.

This is the DEVELOPMENT site for the MARSS.  For the current MARSS  release go to CRAN or download straight from the R GUI using "Install Packages" menu.

MARSS fits mulitvariate autoregressive state-space (MARSS) models with Gaussian errors to multivariate time series data.  A MARSS model is:

x(t) = B x(t-1) + u + v(t), v(t)~MVN(0,Q)

y(t) = Z x(t) + a + w(t), w(t)~MVN(0,R)

Project news (Jan 27, 2012): MARSS 2.8 uploaded to CRAN.  2.3+ implements the algorithm for a fully unconstrained MARSS model with fixed and shared elements in all parameters.  See changes.pdf for the fixes since 2.5.  MARSS 2.9 is in the works which will allow more typical specification of covariates. I'm also working on MARSS 3.0, which implements the general EM algorithm with linear constraints on the parameter matrices. MARSS 2.8 is implementing a constrained version of the more general algorithm in the EMDerivation paper.  The change for 3.0 requires changing the 'wrappers' so user can specify the linear constraints.  The actual algorithm code (MARSSkem.r) is unchanged.

Developers: Eli Holmes, Eric Ward and Kellie Wills

Current known issues:

• lap-p models not working with method=kem since kemcheck is blocking.  Need to review EM algorithm per constraint that B subblock corresponding to diag(Q)=0 must be diagonal.    Use method="BFGS" as a work around. 
• moving average models not tested.
• The likelihood for the covariate "trick" where you want covariate to affect process only and do that by setting R=zero is wrong.  There shouldn't be a likelihood of the covariate added in, but will be since Q=1.I added a note to manual for 2.8 saying you need to subtract off that extra LL.
  
• For cross-platform compatibility with MacOS, I think all of the source files need a hard return / empty line as the last line.

A series of modules for estimation of PVA parameters from time series data. Uses kalman filters, REML, and slope methods.

This is some matlab labs for teaching basic concepts about stochastic population trajectories and estimation for those trajectories.