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

H₂

Clipping for two consecutive years

D-D set to 0.5 by definition

D-G₂ were taken from CLP2, because the production of G₂ growing points mainly depends on the ability of the grand-grand-mother segment to produce new offspring (Rydgren et al. 2001).

7. Clipping

H₃

The first year following two consecutive years of clipping

Non-zero transitions were taken from CLP2, except D-G₂ that was taken from CLP1, because G₂ 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’ G₂ growing points were produced from segments clipped twice).

8. Clipping and combination of Gap formation and Clipping

H₄

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-G₂ 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 G₂-G₀, G₂-S₂...S₈ that were taken from REM2, since they represent the recovery of G_2.

11. Combination of Gap formation and Clipping

H₂/REM1

Clipping and gap formation for two consecutive years

D-D set to 0.5 by definition

D-G₂ 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

H₃/REM2

The first year following two consecutive years of clipping and gap formation

Non-zero transitions were taken from CLP2, except D-G₂ that was taken from REM2, because the opening of the bryophyte carpet was most important for this transition