I am trying to calculate the litter decomposition rate (k) however I have found a few different explanations of how to do it and am getting quite different results from each.
The first technique is from Makkonen et al. (2012) where you calculate as follows:
k = -ln(Mt/M0)/t
Where Mt = final litter mass and M0 = initial litter mass and t = time in years.
This method gives me a number which looks to be in the right ballpark (i.e. it's positive and a decimal below 1 e.g. between 0.7 and 0.2)
The second method however is from Harmon et al. where you use the same equation but graph it as follows "The single negative exponential model can be fit to the data by least-squares linear regression of the natural logarithm of mean percent mass remaining over time". In this case the slope of the line is k. However when I plot the natural logarithm of my percent mass remaining over time I get a negative k value. Similarly, Austin and Vivanco (2006) say to plot the natural log of organic matter remaining/initial organic matter which gives me the same negative k value as the last method, but they have different intercepts.
Why am I getting different results with each method and which should I go with? Am I getting different results because I am doing something wrong? Is it preferable to calculate k, or obtain it graphically?
Any feedback would be greatly appreciated, thank you.
Place 10 ml of 1 N NaOH solution containing vial in a conical flask having material for decomposition. Takeout the vial and pour in 100 ml conical flak and add methyl red indicator. Titrate the contents with 1 N HCl. From the titre value you can calculate decomposition rate as mg of carbon di-oxide per day for a weight of decomposed material placed initially.
Hi.
I hope the following information is useful.
Krishna, M.P., Mohan, M. Litter decomposition in forest ecosystems: a review. Energ. Ecol. Environ. 2, 236–249 (2017). https://doi.org/10.1007/s40974-017-0064-9.
Also, read the following document.
Hi everyone, thanks for your answers. I have read the chapter by Karberg already, so what I was really hoping for was some clarification as to why I am obtaining different results using these different methods outlined above (since they are all slight variations on the same equation/technique), and why I might be getting negative values using the graphical methods. Is it normal to get a negative value when calculated graphically and you just remove the negative from the value to account for the negative in the equation?
Freza Butler,
Have you tried Olsen (1963), mentioned in Jha (2010), published in the Indian Forester, vol 136 no 4: 433-450. It may help you compare your results further.
Dear Freja
Your question is good and you likely refer to the equation ascribed to Olson (1963)
This model, was first proposed by Jenny et al. (1949), and later elaborated by Olson.
The equation gives a ’first-order kinetics’ and a basic condition for applying this equation is that the process runs at the same rate (constant fractional rate), irrespective of the amount of material left at any given point in time, and that one component (‘unified chemical composition’) is considered as active in the process.
The formula is often used in this form
ln(Mt / M0) = -k t
M0 is the initial mass of organic matter or carbon, Mt is the mass of organic matter or carbon, t, is time (e.g. year or day) and kS is the constant for decay rate. The equation also implies that all substrate is used up, decaying at the same rate.
You asked about positive or negative sign on the k value that you calculate. Although it may seem strange – no problem. The numerical value is the same. Let us say that Mo above is the initial amount, for example in a decomposition experiment and Mt is the remaining amount at time t. This mean that the amount decreases and you get a minus sign.
I once talked with Jerry Olson and quoting him ‘this is probably the most common question that I get – the one about plus or minus and it is of no consequence.’
Anyway, there is a lot of further things to comment on as regards k. For example the litter substrate is almost never decomposing at a constant rate and not ‘completely’.
I have developed this in a chapter in my book – please write a mail to my address [email protected] and I will be happy to send you an e-copy (for free).
Best regards
Björn Berg
Very good question. There are three basic reasons why you will get different values depending on which method you use: issues with your experimental methods, random measurement error and model misspecification.
Experimental methods tend to play a big role, especially differences in moisture content. If you compare a dry intact sample to a relatively moist decayed sample, its mass can appear to increase over time, resulting in a negative value for any decay rate parameter. It's also possible that mass increases because decomposers add biomass during certain intervals, but I am not sure if I have every seen this in any of my own experiments or observations.
Random measurement error can also generate differences for different decay formulae. If your balance is not very precise, the your measurements will deviate randomly from their true mass. In this situation, comparing analytical methods (the first formula that you cite) to statistical approaches like regression, can cause discrepancies. In a nutshell, measurement error tends to decrease the slope and increase the intercept of a regression, which can change your parameter estimates compared to simple conversions.
Finally, most biological samples probably do not decay the same way as radioactive isotopes (i.e. negative exponential decay). Let's say that your samples are a composite of many substances each with a different decay rate. In the aggregate, your samples may lose mass according to a log-uniform decay process. If you try to analyze mass loss as if it were negative exponential, you can get some misleading results.
For a good explanation of different decay models see:
Manzoni, Stefano, et al. "Analytical models of soil and litter decomposition: solutions for mass loss and time-dependent decay rates." Soil Biology and Biochemistry 50 (2012): 66-76.
For a handy R tool to choose a good model see:
Cornwell, W. K., & Weedon, J. T. (2014). Decomposition trajectories of diverse litter types: a model selection analysis. Methods in Ecology and Evolution, 5(2), 173-182.
For a paper of mine that addresses many of these issues see:
Oberle, B., Lee, M. R., Myers, J. A., Osazuwa‐Peters, O. L., Spasojevic, M. J., Walton, M. L., ... & Zanne, A. E. (2020). Accurate forest projections require long‐term wood decay experiments because plant trait effects change through time. Global Change Biology, 26(2), 864-875.
The decomposition rate was calculated using a first-order exponential decay function (Olson 1963; Silver and Miya 2001;Wieder and Lang 1982
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