1

Fig. 1. Location of the experiment and the structure of the experimental design with five blocks divided randomly to annual squares (marked with either black, blue or red borderline) that were further randomly divided into six monthly scarification strips.

Table 1. Starting date (day/month) of spring, summer, autumn and winter* as well as start and end date of growing season (GS**) in Sodankylä (in Tähtelä, the closest meteorological station of Finnish Meteorological Institute) during 2013–2017.
Year Spring Summer Autumn Winter Start of GS End of GS
2013 13/04 16/05 21/09 15/10 13/05 23/09
2014 11/04 29/05 13/09 10/10 19/05 20/09
2015 04/04 21/06 01/09 27/10 19/05 30/09
2016 27/03 23/05 24/08 26/10 10/05 01/10
2017 29/04 07/06 23/08 19/10 09/06 07/10
* Definitions: mean daily temperature during spring 0 – +10 °C; summer > +10 °C; autumn +10–0 °C and winter < 0 °C
** The mean daily temperature > +5 °C
Table 2. Explanatory variables (measured in the vicinity of seeding points) that have been tested in the models and their distributions. In addition to the variables mentioned in the table, seed type (Scots pine, lodgepole pine and stratified lodgepole pine), seeding month and inventory number were tested as the main important variables in the models.
Variable Minimum Maximum Mean Median
Continuous variables
Thickness of humus layer, cm 1.00 7.00 2.47 2.00
Stoniness, (depth of an iron stick in the ground) 0.00 52.00 9.49 7.00
Proportion of untouched humus or vegetation, % 0.00 50.00 0.38 0.00
Proportion of mixed humus and mineral soil, % 0.00 100.00 14.85 10.00
Proportion of exposed mineral soil, % 0.00 100.00 82.58 90.00
Categorical variables
Soil type n %
   Gravel 1174 34.55
   Sand 1926 56.68
   Silt 298 8.77
Microtopography (seeding point compared to surroundings)
   Upper 1349 39.70
   Same 1949 57.36
   Lower 100 2.94
2

Fig. 2. Predictions (with 95% confidence intervals) for the logistic mixed effects model predicting the probability of observing at least one seedling on the seeding point seeded in different months at the time of the last inventory (Model 1, Table 3). Predictions were computed for the interaction of seed type and seeding month (a), thickness of humus layer (b) and proportion of exposed mineral soil (c). Seed type abbreviations are: Scots as Scots pine, Lodgepole as lodgepole pine and Lodgepole strat. as stratified seeds of lodgepole pine.

Table 3. Parameter estimates and tests of the logistic mixed effects model (Model 1) for the observed seedling on the seeding point in the last inventory. Lodgepole denotes Lodgepole pine and strat. stratified seed. Classification efficiency (ROC) = 68.15 % (marginal model). Interaction effects are separated with : and reference category is expressed as (ref.)
Variable / parameter Estimate Std.error df t- or χ2-value p
Fixed effects
Intercept 5.573E-01 3.329E-01 2427 1.674 0.094
Month (ref. June) - - 5 69.327 < 0.001
   July –1.471E-01 2.970E-01 70 –0.495 0.622
   August –1.267E+00 3.194E-01 70 –3.967 < 0.001
   September –1.583E+00 3.285E-01 70 –4.820 < 0.001
   October –2.373E-01 2.951E-01 70 –0.804 0.424
   November 7.708E-01 2.984E-01 70 2.583 0.012
Seed type (ref. Scots pine) - - 2 1.225 0.542
   Lodgepole 5.861E-02 2.742E-01 168 0.214 0.831
   Lodgepole, strat. 2.873E-01 2.752E-01 168 1.044 0.298
Depth of humus layer, cm 1.079E-01 4.925E-02 2427 2.192 0.029
Exposed mineral soil % –1.153E-02 2.554E-03 2427 –4.517 < 0.001
Month:Seedtype - - 10 51.762 < 0.001
   July:Lodgepole 1.145E-01 3.922E-01 168 0.292 0.771
   August:Lodgeople 1.628E+00 4.093E-01 168 3.978 < 0.001
   September:Lodgepole 1.985E+00 4.149E-01 168 4.785 < 0.001
   October:Lodgepole 8.961E-01 3.920E-01 168 2.286 0.024
   November:Lodgepole –1.267E-01 3.947E-01 168 –0.321 0.749
   July:Lodgepole strat. 2.141E-01 3.928E-01 168 0.545 0.586
   August:Lodgepole strat. 1.096E+00 4.089E-01 168 2.682 0.008
   September:Lodgepole strat 1.803E+00 4.163E-01 168 4.332 < 0.001
   October:Lodgepole strat 9.972E-01 3.968E-01 168 2.513 0.013
   November:Lodgepole strat 2.112E-01 4.036E-01 168 0.523 0.602
Random effects
Block (level 1) 2.863E-03
Annual square (level 2) 0.060
Scarification strip (level 3) 0.081
Seeding square (level 4) 0.163
Dispersion parameter 0.945
3

Fig. 3. Predictions (with 95% confidence intervals) for the logistic mixed effects model predicting the probability of observing a seedling on the seeding point in different inventories (Model 2, Table 4). Predictions were computed for the interaction of seeding month and seed type (a), the interaction of the number of inventory (time series) and seeding month (b), the interaction of the number of inventory and seed type (c), the interaction of the number of inventory and the soil type of seeding point (d) and the interaction of the number of inventory and the proportion of exposed mineral soil (e). Seed type abbreviations: see Fig. 2.

Table 4. Parameter estimates and tests of the logistic mixed effects model (Model 2) with autoregressive (AR(1)) error term for the probability of at least one seedling on the seeding point at the certain point and time of inventory. Lodgepole denotes Lodgepole pine and strat. stratified seed. Classification efficiency (ROC) = 70.25 % (marginal model). Interaction effects are separated with : and reference category is expressed as (ref.).
Variable / parameter Estimate Std.error df t- or χ2-value p
Fixed effects
Intercept 1.910E+00 3.524E-01 19641 5.421 0.000
Month (ref. June) - - 5 307.592 < 0.001
   July –1.701E-01 2.938E-01 70 –0.579 0.564
   August –2.283E+00 2.883E-01 70 –7.919 0.000
   September –4.274E+00 3.238E-01 70 –13.200 0.000
   October –6.333E-01 3.004E-01 70 –2.108 0.039
   November 8.189E-01 3.339E-01 70 2.453 0.017
Seed type (ref. Scots pine) - - 2 72.124 < 0.001
   Lodgepole –2.102E+00 2.525E-01 168 –8.326 0.000
   Lodgepole, strat. –8.372E-01 2.603E-01 168 –3.216 0.002
Soil type (ref. Gravel) - - 2 18.364 < 0.001
   Sand –4.712E-02 1.240E-01 2426 –0.380 0.704
   Silt 9.441E-01 2.405E-01 2426 3.926 0.000
Inventory –4.079E-02 3.553E-02 19641 –1.148 0.251
Exposed mineral soil % 2.985E-03 3.142E-03 19641 0.950 0.342
Month:Seedtype - - 10 118.994 < 0.001
   July:Lodgepole 9.186E-02 3.092E-01 168 0.297 0.767
   August:Lodgeople 1.195E+00 3.134E-01 168 3.814 0.000
   September:Lodgepole 3.072E+00 3.429E-01 168 8.959 0.000
   October:Lodgepole 1.883E+00 3.256E-01 168 5.782 0.000
   November:Lodgepole 8.297E-01 3.364E-01 168 2.466 0.015
   July:Lodgepole strat. 2.940E-02 3.151E-01 168 0.093 0.926
   August:Lodgepole strat. 6.514E-01 3.161E-01 168 2.061 0.041
   September:Lodgepole strat 2.297E+00 3.454E-01 168 6.650 0.000
   October:Lodgepole strat 1.414E+00 3.350E-01 168 4.221 0.000
   November:Lodgepole strat 5.755E-01 3.494E-01 168 1.647 0.102
Month:Inventory - - 5 224.052 < 0.001
   July:Inventory –2.612E-03 1.947E-02 19641 –0.134 0.893
   August:Inventory 1.219E-01 2.027E-02 19641 6.015 0.000
   September:Inventory 2.393E-01 2.289E-02 19641 10.452 0.000
   October:Inventory –6.174E-02 2.457E-02 19641 –2.513 0.012
   November:Inventory –1.084E-01 2.763E-02 19641 –3.923 0.000
Seedtype:Inventory - - 2 140.230 < 0.001
   Lodgepole:Inventory 1.976E-01 1.670E-02 19641 11.827 0.000
   Lodgepole_strat:Inventory 1.171E-01 1.711E-02 19641 6.845 0.000
Soiltype:Inventory - - 2 39.274 < 0.001
   Sand:Inventory –8.518E-03 1.474E-02 19641 –0.578 0.563
   Silt:Inventory –1.819E-01 2.975E-02 19641 –6.113 0.000
Inventory:Exposed mineral soil, % –1.819E-03 3.751E-04 19641 –4.850 0.000
Random effects, AR(1)
Block (level 1) 4.345E-18
Annual square (level 2) 0.052
Scarification strip (level 3) 0.089
Seeding square (level 4) 0.105
Seeding point (level 5) 1.962E-06
Dispersion parameter 0.993
Phi 0.831