## Matrix Population Modelling (MPM) Workflow

The Matrix Population Model (MPM) collection comprises 24 workflows that provide an environment for creating a stage-matrix with no density dependence. They allow users to perform several analyses on a matrix or a series of matrices. This collection allows:

- Age-specific survival analysis
- Bootstraping of observed census transitions
- Calculation and plotting the abundances over the years
- Calculation of quasi-extinction threshold
- Cohen cumulative distance
- Creation of log-log plots of variance vs. sensitivity and CV vs. elasticity in matrix elements
- Damping ratio
- Eigen analysis
- Elasticity and sensitivity of the vital rates
- Generation time (T)
- Keyfitz’s delta
- Life Table Response Experiment fixed design Place Effect
- Life Table Response Experiment Year effect in one Location or place
- Life Table Response Experiments Year effect for multiple places
- Matrix Population Model analysis v12
- Matrix Population Model construction
- Matrix Population Model construction and analysis v20
- Mean Matrix
- Net reproductive rate (Ro)
- Parametric Bootstrap or Resample a projection matrix workflow
- Simulate stochastic growth from a sequence of matrices
- Stage vectors, survival and growth rate curves (demography)
- Transient dynamics
- Variance matrix

## Who is it for?

Biology, forestry and agriculture students, scientists and biodiversity resources managers.

## What is it for?

Research and studies based on population modelling.

## How does it work?

These workflows are based mainly on the popbio and popdemo R packages.

Popbio:

http://cran.r-project.org/web/packages/popbio/index.html

http://cran.r-project.org/web/packages/popbio/popbio.pdf

http://www.jstatsoft.org/v22/i11/paper

Popdemo:

http://cran.r-project.org/web/packages/popdemo/index.html

http://cran.r-project.org/web/packages/popdemo/popdemo.pdf

http://onlinelibrary.wiley.com/doi/10.1111/j.2041-210X.2012.00222.x/abstract

## Expected results

Numerical results (.csv and .txt documents and graphs .jpg and .png)

## Links to workflow and user documentation

Pack of workflows on myExperiment

Note: This workflow for MPM Construction and Analysis utilises the above listed 24 workflows together to provide a complete environment for creating a stage-matrix with no density dependence, and then to perform several analyses on it. Each of the 24 workflows is available separately in myExperiment.

## Example of use

The graph below shows the relationship between lambda (population growth rate), calculated from projection matrices, and the time since disturbance of the vegetation in the habitat of Gentiana pneumonanthe (Marsh gentian). In the early stages after a disturbance that opens up the vegetation structure, there was ample opportunity for seedling recruitment and the populations grew rapidly, indicated by mean values of lambda higher than 1. After 7 years, the vegetation structure has closed so much by natural succession that light competition prevented most of the seeds from germinating and new seedlings could not establish. Because of this, population growth rates (lambda's) dropped to below one, and the population started to decline. The decline is slow, because

adult plants are relatively long-lived. Population extinction would occur after 40-45 years without new disturbance. Based on these results, it was clear what managers needed to do to get this rare and protected species to recover: open up the vegetation by sod removal, mowing or sheep or cattle grazing.

*Relationship between lambda (population growth rate), calculated from projection matrices, and the time since disturbance of the vegetation in the habitat of Gentiana pneumonanthe*

*(Marsh gentian).*

## News

*19 February 2015*

At the final review of the project by the EC, one of the reviewers said: *“Incredible work done with a community that is not unified. Remarkable work. It opens for new development in a near future. Hope for success. Good project. Happy that you have been financed three plus years ago.”*

Read all about the project and its results in the **Project Final Report** or read the Executive Summary only.