3 1991 front shoot analyses

3.1 Survival

This analysis uses all systems observed in 1991.

3.1.1 Data & visualization

Read in data

Select variables from the front of the system. Also filtering out rows that don’t have a leaf area record in 1990. We need to do this in order to be able to compare models from model set A (which don’t include leaf area, and so wouldn’t naturally be affected by the missing data) with models from model set B (which do include leaf area and would be affected by the missing data). In other words, removing these rows means that model set A and model set B will run using the exact same dataset, which is necessary in order for us to compare the models.

Creating the dead/alive binary and visualizing:

From this plot, we can see that several of the categories have no deaths. This is likely why the three-way interaction doesn’t run for this response variable (see below).

3.1.2 Model selection with leaf area

From this round of model selection, when lf_90 is required to be in the models that are considered, there are two models with equivalently low AICc values: one has sever, sex_90, time, lf_90, and the sever x sex_90 interaction (AICc: 382.9). The other model has only Sever, Time, and Lf_90 (AICc: 384).

3.1.3 Model selection without leaf area

## Fixed terms are "cond((Int))" and "disp((Int))"

From this round of model selection, when lf_90 is not required to be in the models that are considered, there are three models with equivalently low AICc values: one has Sever, Sex_90, Time, and the sever x sex_90 interaction (AICc: 381.2). The second has Sever and Time (AICc: 382). The third has sever, sex_90, time, lf_90, and the sever x sex_90 interaction (AICc: 382.9)–this was also one of the top two models when leaf area in 1990 was fixed.

3.1.4 Conclusion

The best model for survival of the front shoot in 1991 contains fixed effects of Sever and Time.

3.1.5 Estimated marginal means

The main effect of severing

## $emmeans
##  Sever  prob     SE  df lower.CL upper.CL
##  C     0.975 0.0115 673    0.939    0.990
##  S1    0.897 0.0289 673    0.825    0.942
##  S2    0.947 0.0187 673    0.895    0.973
##  S4    0.947 0.0187 673    0.896    0.974
## 
## Results are averaged over the levels of: Time 
## Confidence level used: 0.95 
## Intervals are back-transformed from the logit scale 
## 
## $contrasts
##  contrast odds.ratio    SE  df t.ratio p.value
##  C / S1        4.390 2.021 673  3.213  0.0075 
##  C / S2        2.160 1.062 673  1.565  0.3992 
##  C / S4        2.130 1.048 673  1.537  0.4157 
##  S1 / S2       0.492 0.184 673 -1.901  0.2284 
##  S1 / S4       0.485 0.181 673 -1.935  0.2143 
##  S2 / S4       0.986 0.407 673 -0.033  1.0000 
## 
## Results are averaged over the levels of: Time 
## P value adjustment: tukey method for comparing a family of 4 estimates 
## Tests are performed on the log odds ratio scale

S1 has a lower probability of survival than control systems.

The main effect of time

## $emmeans
##  Time  prob      SE  df lower.CL upper.CL
##  T1   0.918 0.02305 673    0.860    0.953
##  T2   0.925 0.02157 673    0.870    0.958
##  T3   0.977 0.00983 673    0.947    0.990
## 
## Results are averaged over the levels of: Sever 
## Confidence level used: 0.95 
## Intervals are back-transformed from the logit scale 
## 
## $contrasts
##  contrast odds.ratio    SE  df t.ratio p.value
##  T1 / T2       0.907 0.283 673 -0.313  0.9475 
##  T1 / T3       0.261 0.112 673 -3.119  0.0054 
##  T2 / T3       0.288 0.125 673 -2.873  0.0117 
## 
## Results are averaged over the levels of: Sever 
## P value adjustment: tukey method for comparing a family of 3 estimates 
## Tests are performed on the log odds ratio scale

Again, the CIs all overlap, but the contrasts between T1-T3 and T2-T3 are significant, indicating higher survival in the T3 systems. Also, with looking at time in isolation from the other factors, we have to keep in mind that the control systems are part of each time, so actual severing did not occur for each system at all times.

3.2 Leaf area

This analysis is the conditional leaf area–excludes the zero systems.

3.2.3 Conclusion

The simplest and best model contains fixed effects of Lf_90 and Sever.

3.2.4 Estimated marginal means

the main effect of sever

## $emmeans
##  Sever emmean   SE  df lower.CL upper.CL
##  C        633 18.0 156      598      669
##  S1       326 21.6 222      284      369
##  S2       491 19.1 186      453      528
##  S4       556 18.5 166      519      592
## 
## Degrees-of-freedom method: satterthwaite 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast estimate   SE  df t.ratio p.value
##  C - S1      307.1 26.2 415 11.716  <.0001 
##  C - S2      142.7 24.3 412  5.862  <.0001 
##  C - S4       77.5 23.8 412  3.253  0.0067 
##  S1 - S2    -164.4 27.1 419 -6.072  <.0001 
##  S1 - S4    -229.5 26.7 423 -8.599  <.0001 
##  S2 - S4     -65.2 24.7 413 -2.633  0.0434 
## 
## Degrees-of-freedom method: satterthwaite 
## P value adjustment: tukey method for comparing a family of 4 estimates

Control systems have the most leaf area, then S4, then S2, then S1. All contrasts are significant.

the main effect of leaf area

This analysis uses data from all systems (e.g. dead systems would have a leaf area of 0 and be included) so it is the product of survival and growth.

3.2.6 Model selection with leaf area

From this round of model selection, when Lf_90 is required to be in the models that are considered, there are four models within two AICc units: (1) Lf_90, Sever, Sex_90, Time, and the Sever x Sex_90 interaction (AICc: 6738.5); (2) Lf_90, Sever, Sex_90, Time, the Sever x Sex_90 interaction, and the Sex_90 x Time interaction (AICc 6738.8); (3) Lf_90, Sever, Sex_90, Time, the Sever x Sex_90 interaction, and the Sever x Time interaction (AICc 6740.1); (4) Lf_90, Sever, Sex_90, Time, and all three two-way interactions (AICc 6740.2)

3.2.8 Conclusion

The simplest and best model contains fixed effects of Lf_90, Sever, Sex_90, Time, and the Sever x Sex_90 interaction.

3.2.9 Estimated marginal means

the sex x sever interaction

## $emmeans
## Sever = C:
##  Sex_90 emmean   SE  df lower.CL upper.CL
##  S         676 26.0 343      625      727
##  V         597 24.4 317      549      645
## 
## Sever = S1:
##  Sex_90 emmean   SE  df lower.CL upper.CL
##  S         325 29.9 359      266      384
##  V         327 30.7 375      267      388
## 
## Sever = S2:
##  Sex_90 emmean   SE  df lower.CL upper.CL
##  S         511 27.2 356      458      565
##  V         471 26.2 339      420      523
## 
## Sever = S4:
##  Sex_90 emmean   SE  df lower.CL upper.CL
##  S         568 26.7 344      516      621
##  V         545 25.1 324      496      595
## 
## Results are averaged over the levels of: Time 
## Degrees-of-freedom method: satterthwaite 
## Confidence level used: 0.95 
## 
## $contrasts
## Sever = C:
##  contrast estimate   SE  df t.ratio p.value
##  S - V       79.17 35.8 415  2.214  0.0273 
## 
## Sever = S1:
##  contrast estimate   SE  df t.ratio p.value
##  S - V       -2.01 42.8 424 -0.047  0.9625 
## 
## Sever = S2:
##  contrast estimate   SE  df t.ratio p.value
##  S - V       39.76 37.5 420  1.059  0.2903 
## 
## Sever = S4:
##  contrast estimate   SE  df t.ratio p.value
##  S - V       23.08 36.6 418  0.631  0.5281 
## 
## Results are averaged over the levels of: Time 
## Degrees-of-freedom method: satterthwaite

Sexual systems have more leaf area in the control treatment. In all other severing treatments, sexual and vegetative systems have approximately the same amount of leaf area.

the main effect of sex

## $emmeans
##  Sex_90 emmean   SE    df lower.CL upper.CL
##  S         520 16.1 106.1      488      552
##  V         485 15.7  99.1      454      516
## 
## Results are averaged over the levels of: Sever, Time 
## Degrees-of-freedom method: satterthwaite 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast estimate   SE  df t.ratio p.value
##  S - V          35 22.4 429 1.561   0.1192 
## 
## Results are averaged over the levels of: Sever, Time 
## Degrees-of-freedom method: satterthwaite

Sexual systems have more leaf area overall, but this is not significant.

the main effect of sever

## $emmeans
##  Sever emmean   SE  df lower.CL upper.CL
##  C        636 17.8 161      601      672
##  S1       326 21.5 227      284      368
##  S2       491 19.0 191      454      529
##  S4       557 18.4 171      521      593
## 
## Results are averaged over the levels of: Sex_90, Time 
## Degrees-of-freedom method: satterthwaite 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast estimate   SE  df t.ratio p.value
##  C - S1      310.2 26.1 416 11.872  <.0001 
##  C - S2      145.0 24.2 413  5.987  <.0001 
##  C - S4       79.5 23.7 413  3.352  0.0048 
##  S1 - S2    -165.2 26.9 420 -6.135  <.0001 
##  S1 - S4    -230.7 26.6 424 -8.680  <.0001 
##  S2 - S4     -65.5 24.6 414 -2.661  0.0402 
## 
## Results are averaged over the levels of: Sex_90, Time 
## Degrees-of-freedom method: satterthwaite 
## P value adjustment: tukey method for comparing a family of 4 estimates

Control systems have the most leaf area. S1 systems have the least leaf area. S2 and S4 systems are intermediate and not different from each other.

the main effect of time

## $emmeans
##  Time emmean   SE  df lower.CL upper.CL
##  T1      504 18.1 156      468      540
##  T2      493 16.4 122      461      526
##  T3      511 16.8 128      478      544
## 
## Results are averaged over the levels of: Sex_90, Sever 
## Degrees-of-freedom method: satterthwaite 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast estimate   SE  df t.ratio p.value
##  T1 - T2     10.89 22.6 417  0.482  0.8797 
##  T1 - T3     -6.88 23.2 421 -0.297  0.9525 
##  T2 - T3    -17.77 21.3 421 -0.836  0.6811 
## 
## Results are averaged over the levels of: Sex_90, Sever 
## Degrees-of-freedom method: satterthwaite 
## P value adjustment: tukey method for comparing a family of 3 estimates

T1 and T2 have the same amount of leaf area. T3 has significantly more leaf area than T2, but not T1.

the main effect of leaf area

plots for MS

## Cannot use mode = "kenward-roger" because *pbkrtest* package is not installed
## Cannot use mode = "kenward-roger" because *pbkrtest* package is not installed
## NOTE: Results may be misleading due to involvement in interactions
## Cannot use mode = "kenward-roger" because *pbkrtest* package is not installed
## NOTE: Results may be misleading due to involvement in interactions
## Cannot use mode = "kenward-roger" because *pbkrtest* package is not installed
## Cannot use mode = "kenward-roger" because *pbkrtest* package is not installed

3.3 Branching

For these analyses, we filtered the dataset to only plants that are alive (1 or more branches) and created a binary variable for whether plants have 1 branch, or more than 1 branch.

3.3.2 Model selection with leaf area

From this round of model selection, when Lf_90 is required to be in the models that are considered, there are two models within 2 AICc units: (1) Lf_90, Sever, Time, and Sever x Time (AICc 595); (2) Lf_90, Sever, Sex, Time, and Sever x Time (AICc 596.4).

3.3.4 Conclusion

The best and simplest model has main effects of Sever, Time, and Leaf area in 1990, and the Sever x Time interaction.

3.3.5 Estimated marginal means

Below are the relevant visualizations of the best model:

the sever x time interaction

## $emmeans
## Sever = C:
##  Time   prob     SE  df lower.CL upper.CL
##  T1   0.1016 0.0419 606   0.0439    0.218
##  T2   0.2183 0.0605 606   0.1222    0.359
##  T3   0.1636 0.0528 606   0.0840    0.294
## 
## Sever = S1:
##  Time   prob     SE  df lower.CL upper.CL
##  T1   0.5734 0.0868 606   0.4010    0.730
##  T2   0.2444 0.0694 606   0.1339    0.403
##  T3   0.1505 0.0510 606   0.0749    0.280
## 
## Sever = S2:
##  Time   prob     SE  df lower.CL upper.CL
##  T1   0.2294 0.0690 606   0.1215    0.391
##  T2   0.1635 0.0553 606   0.0811    0.302
##  T3   0.1642 0.0524 606   0.0849    0.294
## 
## Sever = S4:
##  Time   prob     SE  df lower.CL upper.CL
##  T1   0.1075 0.0463 606   0.0447    0.237
##  T2   0.1404 0.0491 606   0.0684    0.266
##  T3   0.0486 0.0256 606   0.0169    0.132
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the logit scale 
## 
## $contrasts
## Sever = C:
##  contrast odds.ratio    SE  df t.ratio p.value
##  T1 / T2       0.405 0.220 606 -1.662  0.2209 
##  T1 / T3       0.578 0.324 606 -0.977  0.5916 
##  T2 / T3       1.428 0.693 606  0.733  0.7440 
## 
## Sever = S1:
##  contrast odds.ratio    SE  df t.ratio p.value
##  T1 / T2       4.156 2.042 606  2.899  0.0108 
##  T1 / T3       7.584 3.883 606  3.957  0.0002 
##  T2 / T3       1.825 0.928 606  1.182  0.4642 
## 
## Sever = S2:
##  contrast odds.ratio    SE  df t.ratio p.value
##  T1 / T2       1.523 0.807 606  0.795  0.7064 
##  T1 / T3       1.515 0.778 606  0.809  0.6973 
##  T2 / T3       0.995 0.513 606 -0.010  0.9999 
## 
## Sever = S4:
##  contrast odds.ratio    SE  df t.ratio p.value
##  T1 / T2       0.738 0.441 606 -0.509  0.8672 
##  T1 / T3       2.361 1.652 606  1.228  0.4372 
##  T2 / T3       3.199 2.057 606  1.809  0.1674 
## 
## P value adjustment: tukey method for comparing a family of 3 estimates 
## Tests are performed on the log odds ratio scale

For T1 (in red on the raw data plot on the left), S1 systems are significantly more likely to branch than all other systems. In the emmeans plot on the right, we can see that the green bar for S1 at T1 is distinct from the other three severing treatment. The chances of branching do not vary across other times of severing.

the main effect of time

## $emmeans
##  Time  prob     SE  df lower.CL upper.CL
##  T1   0.214 0.0404 606   0.1448    0.304
##  T2   0.188 0.0350 606   0.1288    0.266
##  T3   0.120 0.0273 606   0.0759    0.185
## 
## Results are averaged over the levels of: Sever 
## Confidence level used: 0.95 
## Intervals are back-transformed from the logit scale 
## 
## $contrasts
##  contrast odds.ratio    SE  df t.ratio p.value
##  T1 / T2        1.17 0.319 606 0.585   0.8281 
##  T1 / T3        1.99 0.591 606 2.318   0.0541 
##  T2 / T3        1.70 0.462 606 1.941   0.1281 
## 
## Results are averaged over the levels of: Sever 
## P value adjustment: tukey method for comparing a family of 3 estimates 
## Tests are performed on the log odds ratio scale

Likelihood of branching generally decreases from T1 to T2 to T3, but only the contrast between T1 and T3 is marginally significant; all others are non-significant.

the main effect of sever

## $emmeans
##  Sever  prob     SE  df lower.CL upper.CL
##  C     0.155 0.0341 606   0.0992    0.234
##  S1    0.298 0.0502 606   0.2100    0.405
##  S2    0.184 0.0380 606   0.1206    0.270
##  S4    0.091 0.0255 606   0.0518    0.155
## 
## Results are averaged over the levels of: Time 
## Confidence level used: 0.95 
## Intervals are back-transformed from the logit scale 
## 
## $contrasts
##  contrast odds.ratio    SE  df t.ratio p.value
##  C / S1        0.431 0.128 606 -2.823  0.0253 
##  C / S2        0.814 0.246 606 -0.679  0.9051 
##  C / S4        1.833 0.625 606  1.777  0.2856 
##  S1 / S2       1.889 0.552 606  2.176  0.1312 
##  S1 / S4       4.250 1.436 606  4.280  0.0001 
##  S2 / S4       2.250 0.763 606  2.392  0.0796 
## 
## Results are averaged over the levels of: Time 
## P value adjustment: tukey method for comparing a family of 4 estimates 
## Tests are performed on the log odds ratio scale

When pooling across the timing of severing, systems severed at S1 are more likely to branch than conrol or S4 systems. S1 and S2 actually aren’t significantly different.

the main effect of leaf area

3.4 Sexual status

These analyses use systems that were alive in 1991; e.g., they had 1 or more branches. We are analyzing whether a system was sexual (had one or more sexual branches) or not (all branches were vegetative).

3.4.2 Model selection with leaf area

From this round of model selection, when Lf_90 is required to be in the models that are considered, there are two models within 2 AICc units: (1) Lf_90 and Sex_90 (AICc 761.7); (2) Lf_90, Sex_90, and Time (AICc 763.3).

3.4.4 Conclusion

The simplest model with the lowest AICc has main effects of Lf_90 and Sex_90.