BioCro 0.93

Markov chain Monte Carlo for C4 photosynthesis parameters

Usage

MCMCEc4photo(obsDat, niter = 30000, iCa = 380, iOa = 210, iVcmax = 60, iVpmax = 120, iVpr = 80, iJmax = 400, thresh = 0.01, scale = 1)

Arguments

obsDat
observed assimilation data, which should be a data frame or matrix. The first column should be observed net assimilation rate (\mu mol m^{-2} s^{-1}). The second column should be the observed quantum flux (\mu mol m^{-2} s^{-1}). The third column should be observed temperature of the leaf (Celsius). The fourth column should be the observed relative humidity in proportion (e.g. 0.7).
niter
number of iterations to run the chain for (default = 30000).
iCa
CO2 atmospheric concentration (ppm or \mubar).
iOa
O2 atmospheric concentration (mbar).
iVcmax
initial value for Vcmax (default = 60).
iVpmax
initial value for Vpmax (default = 120).
iVpr
initial value for Vpr (default = 80).
iJmax
initial value for Jmax (default = 400).
thresh
this is a threshold that determines the ``convergence'' of the initial burn-in period. The convergence of the whole chain can be evaluated by running the model with different starting values for Vcmax and alpha. The chain should convergence, but for this, runs with similar thresholds should be compared. This threshold reflects the fact that for any given data the model will not be able to simulate it perfectly so it represents a compromise between computability and fit.
scale
This scale parameter controls the size of the standard deviations which generate the moves in the chain. Decrease it to increase the acceptance rate and viceversa.

Value

a list structure with components

Description

This function attempts to implement Markov chain Monte Carlo methods for models with no likelihoods. In this case it is done for the von Caemmerer C4 photosynthesis model. The method implemented is based on a paper by Marjoram et al. (2003). The method is described in Miguez (2007). The chain is constructed using a Gaussian random walk. This is definitely a beta version of this function and more testing and improvements are needed. The value of this function is in the possibility of examining the empirical posterior distribution (i.e. vectors) of the Vcmax and alpha parameters. Notice that you will get different results each time you run it.

References

P. Marjoram, J. Molitor, V. Plagnol, S. Tavare, Markov chain monte carlo without likelihoods, PNAS 100 (26) (2003) 15324--15328.

Miguez (2007) Miscanthus x giganteus production: meta-analysis, field study and mathematical modeling. PhD Thesis. University of Illinois at Urbana-Champaign.

Examples

## <strong>Not run</strong>: 
# ## This is an example for the MCMCEc4photo
# ## evaluating the convergence of the chain
# ## Notice that if a parameter does not seem
# ## to converge this does not mean that the method
# ## doesn't work. Careful examination is needed
# ## in order to evaluate the validity of the results
# data(obsNaid)
# res1 <- MCMCEc4photo(obsNaid,100000,thresh=0.007)
# res1
# 
# ## Run it a few more times
# ## and test the stability of the method
# res2 <- MCMCEc4photo(obsNaid,100000,thresh=0.007)
# res3 <- MCMCEc4photo(obsNaid,100000,thresh=0.007)
# 
# ## Now plot it
# plot(res1,res2,res3)
# plot(res1,res2,res3,type='density')
# ## <strong>End(Not run)</strong>