Approximating a Markov chain

Description

Given a vegetation data frame considerd a time series with releves as rows and species as columns transition matrices are derived vor each time step based on some simple assumptions. These are averaged and a model series is derived trough scalar products. Time steps are given in a separate vector t. Missing steps are properly processed.

Usage

1
2
3
4
5
6
7
fitmarkov(veg, t, adjust = FALSE, ...)
rfitmarkov(veg, t, adjust)

## Default S3 method:
fitmarkov(veg, t, adjust = FALSE, ...)
## S3 method for class 'fitmarkov'
plot(x,...)

Arguments

veg

This is a vegetation data frame, releves are rows, species columns

t

The time step scale of length according with rows in x

x

An object of class "fitmarkov"

adjust

A logical vector adjusting the sum of species scores to 1.0. Default is adjust=FALSE

...

Vector colors of any length for line colors, vector widths for line widths. See example below.

Details

This method yields a possible solution for fitting a Markov series. The true process may be very different.

Value

An output list of class "fitmarkov" with at least the following intems:

fitted.data

The fitted time series'

raw.data

The input time series'

transition.matrix

The mean transition matrix'

t.measured

The time steps upon input where time steps may be missing'

t.modeled

The time steps upon output, no missing steps'

Note

The aim of this method is to provide a smooth curve based on input data. Because this relies on incomplete information, it is just one out of many solutions.

Author(s)

Otto Wildi

References

Orloci, L., Anand, M. & He, X. 1993. Markov chain: a realistic model for temporal coenosere? Biom. Praxim 33: 7-26.

Lippe, E., De Smitt, J.T. & Glenn-Lewin, D.C. 1985. Markov models and succession: a test from a heathland in the Netherlands. Journal of Ecology 73: 775-791.

Wildi, O. 2013. Data Analysis in Vegetation Ecology. 2nd ed. Wiley-Blackwell, Chichester.

Examples

1
2
3
4
# data frame ltim is Lippe's data (see references)
# ltim just contains the time scale of the same
o.fm<- fitmarkov(lveg,ltim$Year)
plot(o.fm)

Want to suggest features or report bugs for rdrr.io? Use the GitHub issue tracker.