Appendix A. Overview of the different matrices used in the calculation of the different scenarios and how they were parameterized.
Matrix description (treatment) |
Matrix abbreviation |
Explanation |
Parameterization (a_{ij}) |
1. Unmanipulated |
REF |
Reference data |
Field data 1990, ..., 2002; giving 12 transition periods (matrices). |
2. Gap formation |
REM1 |
The first one-year period after removal of 50% of the population |
Experimental field data 1993–1994 |
3. Gap formation |
REM2 |
The second one-year period after removal of 50% of the population |
Experimental field data 1994–1995 |
4. Clipping |
CLP1 |
The first one-year period after clipping of all growing points |
Experimental field data 1993–1994 |
5. Clipping |
CLP2 |
The second one-year period after clipping of all growing points |
Experimental field data 1994–1995 |
6. Clipping |
H_{2} |
Clipping for two consecutive years |
D-D set to 0.5 by definition D-G_{2} were taken from CLP2, because the production of G_{2} growing points mainly depends on the ability of the grand-grand-mother segment to produce new offspring (Rydgren et al. 2001). |
7. Clipping |
H_{3} |
The first year following two consecutive years of clipping |
Non-zero transitions were taken from CLP2, except D-G_{2} that was taken from CLP1, because G_{2} production appears most strongly affected by growth conditions during development (Økland 1995) and because we assumed that the potential for regeneration of the previous year’s grand-grand-mother segment had by then become exhausted (i.e., that no ‘extra’ G_{2} growing points were produced from segments clipped twice). |
8. Clipping and combination of Gap formation and Clipping |
H_{4} |
The second year following two consecutive years of clipping |
Non-zero transitions were taken from the corresponding REF matrix |
9. Combination of Gap formation and Clipping |
CLP1/REM1 |
Clipping and gap formation for one year |
All transitions were taken from the CLP1 except D-G_{2} that was taken from REM1, since the Gap formation disturbance provoked a stronger burst of germination from the diaspore bank the first year after disturbance than the Clipped treatment (Rydgren et al. 2001). |
10. Combination of Gap formation and Clipping |
CLP2/REM2 |
The first year after one year with clipping and gap formation |
All transitions were taken from CLP2 except G_{2}-G_{0}, G_{2}-S_{2}...S_{8} that were taken from REM2, since they represent the recovery of G_{2.} |
11. Combination of Gap formation and Clipping |
H_{2}/REM1 |
Clipping and gap formation for two consecutive years |
D-D set to 0.5 by definition D-G_{2} taken from CLP2, likely underestimates the real transition probability for this treatment because it did not fully account for the opening of the bryophyte carpet brought about by disturbance. |
12. Combination of Gap formation and Clipping |
H_{3}/REM2 |
The first year following two consecutive years of clipping and gap formation |
Non-zero transitions were taken from CLP2, except D-G_{2} that was taken from REM2, because the opening of the bryophyte carpet was most important for this transition |
Notes: For each matrix type there exists 12 matrices for every one-year transition from 1990 to 2002.
LITERATURE CITED
Økland, R. H. 1995. Population biology of the clonal moss Hylocomium splendens in Norwegian boreal spruce forests. I. Demography. Journal of Ecology 83:697–712.
Rydgren, K., H. de Kroon, R. H. Økland, and J. van Groenendael. 2001. Effects of fine-scale disturbances on the demography and population dynamics of the clonal moss Hylocomium splendens. Journal of Ecology 89:395–405.