Browse exercises

This page gives you an option to browse through the exercises presented in the book LITTER DECOMPOSITION: A GUIDE TO CARBON AND NUTRIENT TURNOVER by Björn Berg and Ryszard Laskowski (Advances in Ecological Research 38, Elsevier, 2006). It comprises a few simple exercises that can be solved with basic calculations as well as some more advanced problems for which some knowledge in statistics is necessary. For each exercise there is a direct link to the solution, and data can be downloaded as an MS-Excel file containing data for all exercises. This will save your time for problem solving rather then typing the data to the computer.

In those cases where some statistics has been used, we have included printouts from a statistical package (Statgraphics) with additional comments (in italics) helping to understand the results of tests performed.

Exercise I: Foliar litter fall

Presentation of the problem

You measure foliar litter fall in a mature Austrian pine forest. The canopy is not really closed and you have placed 15 litter traps with 0.25 m² surface randomly over an area of ca 50´50 m. The litter traps are placed in the field on August 15. You decide to empty the traps three times in the first year, the first time after the litter fall peak in late October, the 2^nd time in late May and the 3^rd time on August 15. As you will note two litter traps were found disturbed, one in the 2^nd and one in the 3^rd sampling.

After samplings, the foliar litter is sorted out from other litter, dried at 85°C, weighed and after ca one month after the last sampling you have the following table with foliar litter mass given as grams per trap.

Table I.I. Amount of litter (g dry mass) recorded in particular traps, 1 through 15, on the three sampling occasions. 

The task is to calculate the annual foliar litter fall and give the results as kg/ha.

Exercise II: Comparing foliar litter fall of different tree species

Presentation of the problem

The stand described above in the Exercise I was in fact one of stands in a block experiment. You have four stands of Austrian pine and four stands of Sitka spruce, each stand measuring 50´50 m. All stands, which are paired, are located within a limited area that is less than 1000´1000 m. The climate is the same and the soil conditions are similar all over this area. You have measured foliar litter fall for one year using 15 replicate litter traps in each stand like in the Exercise I.

Table II.I. Litter fall measured at the eight stands used in the experiment. The results are given in kg dry matter per hectare with standard deviation in parenthesis.

The task is to determine whether there is any significant difference in litter fall between the two tree species.

Exercise III: Foliar litter fall in a climatic transect after climate change

Presentation of the problem

We have seen (chapter 2) that the foliar litter fall of mature Norway spruce stands is well related to the climate index actual evapotranspiration (AET) (R² = 0.787) for a boreal to temperate area ranging from ca 66°30’N to ca 55°45’N corresponding to an AET interval from 370 to 626 mm. The equation relating litter fall to AET is:

Litter fall =  22.24´AET - 8283.5

In a given forest stand with the AET value of 405 mm the annual foliar litter fall today is 724 kg/ha. A new climate prediction suggests that there will be a full climate change in ca year 2050. This boreal system (in Fennoscandia) is energy limited (Berg and Meentemeyer, 2002) and we can estimate that a climate change will give an increase in AET of ca 27%, corresponding to an increase in annual average temperature of ca 4°C and an increase in precipitation of ca 40%. 

The task is to estimate foliar litter fall at that stand in the year 2050 for a mature Norway spruce forest. We make the assumption that nutrient availability does not become limiting for tree growth in the new climate.  

Exercise IV: Calculating litter mass loss

Problem presentation

You have prepared a set of litter bags, incubated them, have made a sampling and want to determine litter mass loss. When you prepared the litter bags you dried them in the air at room temperature for four weeks. To make an exact determination of the moisture content you took 20 samples of the air-dried litter and dried them at 85°C for 24 hours. That determination gave a moisture level of 6.04% and a standard error of 0.17. Thus, the litterbags were prepared with litter containing 6.04% water and the registered litter weight thus also includes that moisture.

The litterbags were then incubated in the field, and you have made a sampling of 20 bags, cleaned their contents, dried the leaves at 85°C and weighed them. Finally, when ready to calculate the mass loss, you have the following data listed (Table IV.I).

Table IV.I. Litter mass in litter bags before and after incubation (air-dried mass).

The task. To calculate litter mass loss for all samples as well as for the average mass loss.

Exercise V: Calculating annual litter mass loss during decomposition

Presentation of the problem

The data used for this example originate from a study on decomposition of white pine needle litter. The litter bags were incubated for 5 years and collected a few times a year with 20 replicates (Table V.I).

Table V.I. Average accumulated mass loss and the remaining mass for consecutive samplings.

The task is to calculate annual mass loss rates for consecutive years of decomposition.

Exercise VI:  Describing accumulated litter mass loss dynamics by functions

Problem presentation

A decomposition experiment has been made using two different litter species, one being lodgepole pine needle litter and the other grey alder leaf litter. The litterbags of the two litter species were incubated in parallel in the same stand and samplings were made at the same time and with the same intervals with 25 replicate bags in each sampling. Table VI.I reports average accumulated mass loss for each time interval with accompanying standard errors (SE), and Table VI.II gives initial chemical composition of both litters which may be helpful in interpreting the results of the Exercise.

Table VI.I. Accumulated mass loss (%) with standard errors (SE) for the two species being compared.

Table VI.II. The initial chemical composition (mg/g) of nutrients in the two litter species.

The task is to determine which function describes the accumulated mass loss best and to determine whether the decomposition patterns differ among the litter species studied. You should compare the three functions you learned from the book, namely the one-compartment exponential, the two-compartment exponential and the asymptotic function.

Exercise VII: Regulating factors for litter decomposition rates

Problem presentation

The data given in Table VII.I present results of an experiment with litter decomposition rates on one Scots pine stand using needle litter with five different nutrient levels. Ih needles originate from a very nutrient poor Scots pine forest, N0 from a Scots pine forest on relatively rich soil – although still N is limiting for the microorganisms. N1, N2 and N3 are denominations for litter originating from stands fertilized with 40, 80 and 120 kg N as ammonium nitrate per hectare and year. The litter bags were incubated in parallel with all five litter types in the same design in the same stand for 4 years and sampled at the same dates. Besides litter mass loss, the litter was also analyzed for concentrations of N, P and lignin.

The task: To determine possible regulating factors for the decomposition rate of Scots pine needle litter, using needles from trees fertilized with different concentrations of N.

Ih litter

N0 litter

N1 litter

N2 litter

N3 litter

Exercise VIII. Nitrogen dynamics – concentrations and amounts

Problem presentation

The data set below originates from decomposing local Scots pine needle litter in a boreal Scots pine monoculture stand, covering ca 3 ha. Bags were incubated on 20 spots, randomly distributed all over the stand. At each sampling 20 replicate litter bags were collected. Litter mass loss was determined and nitrogen concentration was measured on combined samples from each sampling (Table VIII.I).

Table VIII.I. Litter mass loss and N concentration during decomposition of Scots pine needle litter.

The task in this exercise is to calculate and plot the changes in absolute amount and in concentrations of N with time for decomposing Scots pine needle litter using the data set below.

Exercise IX: Increase rate in litter N concentration

Problem presentation

The data set to be used in this exercise is that in Table VIII, which originates from decomposing local Scots pine needle litter in a boreal Scots pine monoculture stand, covering ca 3 ha. Bags were incubated on 20 spots, randomly distributed all over the stand. At each sampling 20 replicate litter bags were collected. Litter mass loss was determined and nitrogen concentration was measured on combined samples from each sampling.

The task in this exercise is to calculate the increase rate in litter N concentration. 

Exercise X: Differences in increase rates for nitrogen concentrations

Problem presentation

Two litter types have been incubated in the same stand during the same time period and using the same incubation and sampling design. The data originate from decomposing green and brown local Scots pine needle litter incubated in a boreal Scots pine monoculture (Table X.I). 20 replicate litter bags were taken of each litter type at each sampling.

Table X.I. Accumulated mass loss and corresponding N concentration in decomposing green and brown Scots pine needles.

The task in this exercise is to calculate the increase rate in litter N concentration in the two litter types and to determine whether the slopes (NCIR) are significantly different.

Exercise XI: Calculating the sequestered fraction of litter N

Problem presentation

During a 4-year experiment you have collected the following data (Table XI.I) for the decomposition of Scots pine needle litter. The experiment was performed in a Scots pine monoculture covering 3 hectares and there were 20 litter bag replicates in each sampling. For each sampling date you have the accumulated litter mass loss and N concentration in the litter.

Table XI.I. Accumulated mass loss and N concentrations in decomposing Sots pine needle litter.

The task is to calculate the fraction of the original amount of N that will be stored in the recalcitrant part of the litter. 

Exercise XII: Nitrogen stored in litter at the limit value

Problem presentation

This exercise connects to exercise XI, in which you calculated the fraction of remaining nitrogen in a foliar litter that had reached the limit value or the humus stage. In that exercise you started with accumulated mass-loss values and N concentrations. In the present case we have simplified the task somewhat as we give the calculated limit values and N concentrations at the limit value. You thus obtain the data set reported in Table XII.I.

Table XII.I. Initial N concentrations in 7 different litter species and related estimated asymptotic decomposition limit values and N concentrations at the limit value.

The task is to calculate the (i) amount of N that is stored in the remains of what initially was 1.0 gram litter, and (ii) fraction of initial litter N that is stored in the recalcitrant remains.