Ecological Archives E096-136-A4

Ecological Archives E096-136-A4

Susanne Wurst, Nina Kaiser, Susann Nitzsche, Josephine Haase, Harald Auge, Matthias C. Rillig, and Jeff R. Powell. 2015. Tree diversity modifies distance-dependent effects on seedling emergence but not plant–soil feedbacks of temperate trees. Ecology 96:1529–1539. http://dx.doi.org/10.1890/14-1166.1

Appendix D. Description of the model selection procedure and model output for the full and minimum adequate models.

Model selection procedure

Starting with the full model, containing the four fixed-effect terms and all possible interactions and fit using maximum likelihood, we systematically removed terms from the model until we no longer observed improvements in AICc scores, the result being the minimum adequate model. Our systematic approach was to sequentially remove terms within each level of interactions (four-, three-, then two-way interactions), then remove main effects that did not appear in higher level interactions, starting with those terms having estimated (standardized) coefficients close to zero. In cases where the minimum adequate model contained an interaction term, we generated subsets of the data from one of the factors of the interaction and compared models including and excluding the other term.

Effects Tables

Definitions of random effects:

block: one of two blocks each containing plots (randomized complete block design)
plot: identity of field plot from which soil inoculum was collected
field_plant: identity of the tree adjacent to where soil inoculum was collected
pot: identity of the pot containing plants on which measurements were made

Definitions of fixed effects:

diversity: number of tree species (plot-level manipulation; high = five/six species, low = one species)
position: distance between focal tree in field and collection point of soil inoculum (field_plant-level manipulation; close = 15cm, far = 50cm)
gh_plant: species of tree grown in pot containing soil inoculum (pot-level manipulation; Fagus = Fagus sylvatica, Quercus = Quercus petraea)
HvA: relationship between tree species adjacent to the location of inoculum collection and the tree species in pot containing said inoculum (pot-level manipulation; away = heterospecific inoculum, home = conspecific inoculum)

Response 1 of 6: number of seedlings emerging within inoculated pots

> summary(emergeMAM)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial ( logit )
Formula: cbind(success, fail) ~ diversity + position + gh_plant + HvA +      diversity:position + (1 | block/Plot/field_plant)
   Data: emerge.data

     AIC      BIC   logLik deviance df.resid 
   317.4    340.5   -149.7    299.4       87 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.23311 -0.69987  0.05638  0.54940  1.97903 

Random effects:
 Groups                   Name        Variance  Std.Dev.
 field_plant:(Plot:block) (Intercept) 0.0004635 0.02153 
 Plot:block               (Intercept) 0.0000000 0.00000 
 block                    (Intercept) 0.0000000 0.00000 
Number of obs: 96, groups: field_plant:(Plot:block), 36; Plot:block, 10; block, 2

Fixed effects:
                         Estimate Std. Error z value Pr(>|z|)    
(Intercept)               -1.1285     0.1888  -5.979 2.25e-09 ***
diversitylow              -0.3385     0.2206  -1.535   0.1249    
positionfar               -0.0966     0.2198  -0.439   0.6603    
gh_plantQuercus            2.5091     0.1593  15.748  < 2e-16 ***
HvAhome                   -0.3487     0.1575  -2.214   0.0268 *  
diversitylow:positionfar   0.7454     0.3128   2.383   0.0172 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


> summary(emergeFULL)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial ( logit )
Formula: cbind(success, fail) ~ diversity * position * gh_plant * HvA +      (1 | block/Plot/field_plant)
   Data: emerge.data

     AIC      BIC   logLik deviance df.resid 
   332.2    380.9   -147.1    294.2       77 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.5880 -0.5945  0.1362  0.6354  2.0702 

Random effects:
 Groups                   Name        Variance Std.Dev.
 field_plant:(Plot:block) (Intercept) 0        0       
 Plot:block               (Intercept) 0        0       
 block                    (Intercept) 0        0       
Number of obs: 96, groups: field_plant:(Plot:block), 36; Plot:block, 10; block, 2

Fixed effects:
                                                 Estimate Std. Error z value Pr(>|z|)    
(Intercept)                                      -1.09861    0.29814  -3.685 0.000229 ***
diversitylow                                     -0.28768    0.43938  -0.655 0.512632    
positionfar                                      -0.28768    0.43938  -0.655 0.512633    
gh_plantQuercus                                   2.11021    0.41727   5.057 4.26e-07 ***
HvAhome                                          -0.51083    0.45704  -1.118 0.263707    
diversitylow:positionfar                          0.98083    0.61010   1.608 0.107911    
diversitylow:gh_plantQuercus                      0.37469    0.60595   0.618 0.536338    
positionfar:gh_plantQuercus                       0.77001    0.62418   1.234 0.217342    
diversitylow:HvAhome                              0.02532    0.67623   0.037 0.970134    
positionfar:HvAhome                               0.40319    0.65144   0.619 0.535963    
gh_plantQuercus:HvAhome                           0.99315    0.63674   1.560 0.118820    
diversitylow:positionfar:gh_plantQuercus         -0.84697    0.88813  -0.954 0.340257    
diversitylow:positionfar:HvAhome                 -0.41412    0.91703  -0.452 0.651562    
diversitylow:gh_plantQuercus:HvAhome             -0.98722    0.90332  -1.093 0.274448    
positionfar:gh_plantQuercus:HvAhome              -1.53215    0.90089  -1.701 0.088999 .  
diversitylow:positionfar:gh_plantQuercus:HvAhome  1.49743    1.27067   1.178 0.238613    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Response 2 of 6: number days prior to seedling emergence within inoculated pots

> summary(timeMAM)
Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: logdays ~ gh_plant + (1 | block/Plot/field_plant/pot)
   Data: emerge.time.data

     AIC      BIC   logLik deviance df.resid 
   147.7    176.7    -66.8    133.7      459 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.2523 -0.6717  0.0591  0.6234  3.1930 

Random effects:
 Groups                         Name        Variance Std.Dev.
 pot:(field_plant:(Plot:block)) (Intercept) 0.000    0.0000  
 field_plant:(Plot:block)       (Intercept) 0.000    0.0000  
 Plot:block                     (Intercept) 0.000    0.0000  
 block                          (Intercept) 0.000    0.0000  
 Residual                                   0.078    0.2793  
Number of obs: 466, groups: pot:(field_plant:(Plot:block)), 94; field_plant:(Plot:block), 36; Plot:block, 10; block, 2

Fixed effects:
                Estimate Std. Error t value
(Intercept)      0.71029    0.02765   25.68
gh_plantQuercus  0.47732    0.03129   15.26



> summary(timeFULL)
Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: logdays ~ diversity * position * gh_plant * HvA + (1 | block/Plot/field_plant/pot)
   Data: emerge.time.data

     AIC      BIC   logLik deviance df.resid 
   168.6    255.6    -63.3    126.6      445 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.1385 -0.6696  0.0297  0.6314  3.1248 

Random effects:
 Groups                         Name        Variance  Std.Dev. 
 pot:(field_plant:(Plot:block)) (Intercept) 0.000e+00 0.000e+00
 field_plant:(Plot:block)       (Intercept) 0.000e+00 0.000e+00
 Plot:block                     (Intercept) 0.000e+00 0.000e+00
 block                          (Intercept) 1.422e-18 1.193e-09
 Residual                                   7.682e-02 2.772e-01
Number of obs: 466, groups: pot:(field_plant:(Plot:block)), 94; field_plant:(Plot:block), 36; Plot:block, 10; block, 2

Fixed effects:
                                                 Estimate Std. Error t value
(Intercept)                                       0.73632    0.07156  10.289
diversitylow                                     -0.07119    0.10735  -0.663
positionfar                                      -0.10356    0.10735  -0.965
gh_plantQuercus                                   0.44057    0.08287   5.316
HvAhome                                          -0.07317    0.11315  -0.647
diversitylow:positionfar                          0.17438    0.14753   1.182
diversitylow:gh_plantQuercus                      0.06426    0.12238   0.525
positionfar:gh_plantQuercus                       0.13344    0.12181   1.095
diversitylow:HvAhome                              0.03500    0.16973   0.206
positionfar:HvAhome                               0.25313    0.16183   1.564
gh_plantQuercus:HvAhome                           0.10041    0.12696   0.791
diversitylow:positionfar:gh_plantQuercus         -0.14724    0.16830  -0.875
diversitylow:positionfar:HvAhome                 -0.19924    0.22699  -0.878
diversitylow:gh_plantQuercus:HvAhome             -0.06434    0.18921  -0.340
positionfar:gh_plantQuercus:HvAhome              -0.34007    0.18138  -1.875
diversitylow:positionfar:gh_plantQuercus:HvAhome  0.24940    0.25518   0.977

Response 3 of 6: seedling biomass accumulation (mg per day) within inoculated pots

> summary(biomassMAM)
Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: biomass_mgperday ~ gh_plant + HvA + gh_plant:HvA + (1 | block/Plot/field_plant)
   Data: biomass.data

     AIC      BIC   logLik deviance df.resid 
   -99.9    -79.9     57.9   -115.9       82 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.8122 -0.7037  0.1052  0.5950  2.6655 

Random effects:
 Groups                   Name        Variance Std.Dev.
 field_plant:(Plot:block) (Intercept) 0.00000  0.0000  
 Plot:block               (Intercept) 0.00000  0.0000  
 block                    (Intercept) 0.00000  0.0000  
 Residual                             0.01615  0.1271  
Number of obs: 90, groups: field_plant:(Plot:block), 36; Plot:block, 10; block, 2

Fixed effects:
                        Estimate Std. Error t value
(Intercept)              0.27851    0.02774  10.041
gh_plantQuercus          0.19383    0.03798   5.104
HvAhome                  0.07346    0.03878   1.895
gh_plantQuercus:HvAhome -0.18837    0.05366  -3.511



> summary(biomassFULL)
Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: biomass_mgperday ~ diversity * position * gh_plant * HvA + (1 |      block/Plot/field_plant)
   Data: biomass.data

     AIC      BIC   logLik deviance df.resid 
   -85.5    -35.5     62.7   -125.5       70 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.4232 -0.5639  0.1703  0.6728  2.3668 

Random effects:
 Groups                   Name        Variance Std.Dev.
 field_plant:(Plot:block) (Intercept) 0.00000  0.0000  
 Plot:block               (Intercept) 0.00000  0.0000  
 block                    (Intercept) 0.00000  0.0000  
 Residual                             0.01452  0.1205  
Number of obs: 90, groups: field_plant:(Plot:block), 36; Plot:block, 10; block, 2

Fixed effects:
                                                 Estimate Std. Error t value
(Intercept)                                       0.24416    0.04919   4.963
diversitylow                                     -0.02046    0.07778  -0.263
positionfar                                       0.05598    0.07296   0.767
gh_plantQuercus                                   0.28178    0.06957   4.051
HvAhome                                           0.10816    0.07296   1.482
diversitylow:positionfar                          0.05170    0.10664   0.485
diversitylow:gh_plantQuercus                     -0.08773    0.10435  -0.841
positionfar:gh_plantQuercus                      -0.13272    0.10081  -1.317
diversitylow:HvAhome                              0.04032    0.10664   0.378
positionfar:HvAhome                              -0.07325    0.10550  -0.694
gh_plantQuercus:HvAhome                          -0.28459    0.10081  -2.823
diversitylow:positionfar:gh_plantQuercus          0.10375    0.14509   0.715
diversitylow:positionfar:HvAhome                 -0.06101    0.14839  -0.411
diversitylow:gh_plantQuercus:HvAhome              0.09241    0.14675   0.630
positionfar:gh_plantQuercus:HvAhome               0.22638    0.14426   1.569
diversitylow:positionfar:gh_plantQuercus:HvAhome -0.26186    0.20460  -1.280

Response 4 of 6: mildew cover of Quercus leaves

> summary(mildewMAM)
Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: mildew ~ HvA + (1 | block/Plot/field_plant)
   Data: data1

     AIC      BIC   logLik deviance df.resid 
   449.6    460.7   -218.8    437.6       41 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.7383 -0.7665 -0.1087  0.8521  2.1636 

Random effects:
 Groups                   Name        Variance Std.Dev.
 field_plant:(Plot:block) (Intercept)   0       0.00   
 Plot:block               (Intercept)   0       0.00   
 block                    (Intercept)   0       0.00   
 Residual                             647      25.44   
Number of obs: 47, groups: field_plant:(Plot:block), 24; Plot:block, 8; block, 2

Fixed effects:
            Estimate Std. Error t value
(Intercept)   26.306      5.192   5.067
HvAhome       20.039      7.422   2.700



> summary(mildewFULL)
Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: mildew ~ position * diversity * HvA + (1 | block/Plot/field_plant)
   Data: data1

     AIC      BIC   logLik deviance df.resid 
   455.5    477.7   -215.7    431.5       35 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.43694 -0.72671 -0.04831  0.69252  2.27551 

Random effects:
 Groups                   Name        Variance Std.Dev.
 field_plant:(Plot:block) (Intercept)   0.0     0.00   
 Plot:block               (Intercept)   0.0     0.00   
 block                    (Intercept)   0.0     0.00   
 Residual                             568.3    23.84   
Number of obs: 47, groups: field_plant:(Plot:block), 24; Plot:block, 8; block, 2

Fixed effects:
                                 Estimate Std. Error t value
(Intercept)                        22.263      9.732   2.288
positionfar                         5.993     13.764   0.435
diversitylow                       -1.272     13.764  -0.092
HvAhome                            40.622     13.764   2.951
positionfar:diversitylow            6.728     19.465   0.346
positionfar:HvAhome               -25.807     19.465  -1.326
diversitylow:HvAhome              -30.277     19.465  -1.556
positionfar:diversitylow:HvAhome   30.186     27.869   1.083

Response 5 of 6: frequency of roots infected by Cylindrocarpon

> summary(cylindMAM)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial ( logit )
Formula: cbind(Cylindrocarpon, 2 * rootfrags - Cylindrocarpon) ~ diversity +      gh_plant + diversity:gh_plant + (1 | block/Plot/field_plant) + 
     (1 | pot)
   Data: fungi.data
Control: glmerControl(optimizer = "bobyqa")

     AIC      BIC   logLik deviance df.resid 
   547.5    567.2   -265.7    531.5       79 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.65626 -0.38262  0.03608  0.41801  1.45564 

Random effects:
 Groups                   Name        Variance Std.Dev.
 pot                      (Intercept) 0.2094   0.4576  
 field_plant:(Plot:block) (Intercept) 0.0000   0.0000  
 Plot:block               (Intercept) 0.0000   0.0000  
 block                    (Intercept) 0.0000   0.0000  
Number of obs: 87, groups: pot, 87; field_plant:(Plot:block), 35; Plot:block, 10; block, 2

Fixed effects:
                             Estimate Std. Error z value Pr(>|z|)    
(Intercept)                  -0.57543    0.12681  -4.538 5.69e-06 ***
diversitylow                 -0.26547    0.17864  -1.486   0.1373    
gh_plantQuercus               0.09609    0.17242   0.557   0.5773    
diversitylow:gh_plantQuercus  0.60945    0.24483   2.489   0.0128 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1



> summary(cylindFULL)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial ( logit )
Formula: cbind(Cylindrocarpon, 2 * rootfrags - Cylindrocarpon) ~ position *      diversity * gh_plant * HvA + (1 | block/Plot/field_plant) + 
     (1 | pot)
   Data: fungi.data
Control: glmerControl(optimizer = "bobyqa")

     AIC      BIC   logLik deviance df.resid 
   567.5    616.8   -263.7    527.5       67 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.60833 -0.39100 -0.02165  0.49155  1.33683 

Random effects:
 Groups                   Name        Variance Std.Dev.
 pot                      (Intercept) 0.1949   0.4415  
 field_plant:(Plot:block) (Intercept) 0.0000   0.0000  
 Plot:block               (Intercept) 0.0000   0.0000  
 block                    (Intercept) 0.0000   0.0000  
Number of obs: 87, groups: pot, 87; field_plant:(Plot:block), 35; Plot:block, 10; block, 2

Fixed effects:
                                                 Estimate Std. Error z value Pr(>|z|)  
(Intercept)                                      -0.62204    0.24718  -2.517   0.0118 *
positionfar                                       0.09798    0.34905   0.281   0.7789  
diversitylow                                     -0.06350    0.40339  -0.157   0.8749  
gh_plantQuercus                                   0.03094    0.33587   0.092   0.9266  
HvAhome                                           0.14104    0.34991   0.403   0.6869  
positionfar:diversitylow                         -0.29768    0.52623  -0.566   0.5716  
positionfar:gh_plantQuercus                       0.27656    0.47309   0.585   0.5588  
diversitylow:gh_plantQuercus                      0.42646    0.51484   0.828   0.4075  
positionfar:HvAhome                              -0.28870    0.49543  -0.583   0.5601  
diversitylow:HvAhome                             -0.29419    0.52661  -0.559   0.5764  
gh_plantQuercus:HvAhome                          -0.18813    0.47934  -0.392   0.6947  
positionfar:diversitylow:gh_plantQuercus         -0.13086    0.69294  -0.189   0.8502  
positionfar:diversitylow:HvAhome                  0.45310    0.71218   0.636   0.5246  
positionfar:gh_plantQuercus:HvAhome               0.06841    0.67441   0.101   0.9192  
diversitylow:gh_plantQuercus:HvAhome              0.52409    0.70351   0.745   0.4563  
positionfar:diversitylow:gh_plantQuercus:HvAhome -0.07593    0.96798  -0.078   0.9375  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Response 6 of 6: frequency of roots colonised by ectomycorrhizal fungi

> summary(ectoMAM)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial ( logit )
Formula: cbind(colonized_r, roots) ~ gh_plant + (1 | block/Plot/field_plant) +      (1 | pot)
   Data: ecto.data
Control: glmerControl(optimizer = "bobyqa")

     AIC      BIC   logLik deviance df.resid 
   459.7    474.5   -223.9    447.7       81 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-1.79634 -0.45695 -0.05195  0.42210  1.15264 

Random effects:
 Groups                   Name        Variance Std.Dev.
 pot                      (Intercept) 0.2065   0.4544  
 field_plant:(Plot:block) (Intercept) 0.1594   0.3993  
 Plot:block               (Intercept) 0.0000   0.0000  
 block                    (Intercept) 0.0000   0.0000  
Number of obs: 87, groups: pot, 87; field_plant:(Plot:block), 35; Plot:block, 10; block, 2

Fixed effects:
                Estimate Std. Error z value Pr(>|z|)    
(Intercept)      -2.9141     0.1519  -19.19  < 2e-16 ***
gh_plantQuercus   1.2258     0.1710    7.17 7.52e-13 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1



> summary(ectoFULL)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial ( logit )
Formula: cbind(colonized_r, roots) ~ diversity * position * HvA * gh_plant +      (1 | block/Plot/field_plant) + (1 | pot)
   Data: ecto.data
Control: glmerControl(optimizer = "bobyqa")

     AIC      BIC   logLik deviance df.resid 
   472.3    521.6   -216.1    432.3       67 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-1.86888 -0.49485 -0.03061  0.37020  1.88902 

Random effects:
 Groups                   Name        Variance  Std.Dev. 
 pot                      (Intercept) 1.338e-01 3.658e-01
 field_plant:(Plot:block) (Intercept) 1.508e-01 3.883e-01
 Plot:block               (Intercept) 4.324e-16 2.079e-08
 block                    (Intercept) 0.000e+00 0.000e+00
Number of obs: 87, groups: pot, 87; field_plant:(Plot:block), 35; Plot:block, 10; block, 2

Fixed effects:
                                                 Estimate Std. Error z value Pr(>|z|)    
(Intercept)                                       -3.2065     0.4308  -7.442 9.89e-14 ***
diversitylow                                       0.1430     0.6894   0.207  0.83567    
positionfar                                        0.8485     0.4775   1.777  0.07556 .  
HvAhome                                            0.1118     0.5721   0.195  0.84501    
gh_plantQuercus                                    1.3159     0.5094   2.583  0.00978 ** 
diversitylow:positionfar                          -0.4408     0.7548  -0.584  0.55923    
diversitylow:HvAhome                               0.4465     0.8459   0.528  0.59762    
positionfar:HvAhome                               -0.6990     0.6756  -1.035  0.30087    
diversitylow:gh_plantQuercus                       0.1368     0.7884   0.173  0.86227    
positionfar:gh_plantQuercus                       -1.1002     0.5802  -1.896  0.05794 .  
HvAhome:gh_plantQuercus                            0.2189     0.6870   0.319  0.75007    
diversitylow:positionfar:HvAhome                  -0.7743     1.0104  -0.766  0.44347    
diversitylow:positionfar:gh_plantQuercus           0.6540     0.8781   0.745  0.45643    
diversitylow:HvAhome:gh_plantQuercus              -0.3831     1.0556  -0.363  0.71670    
positionfar:HvAhome:gh_plantQuercus                0.7676     0.8115   0.946  0.34419    
diversitylow:positionfar:HvAhome:gh_plantQuercus   0.3019     1.2044   0.251  0.80210    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

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