Appendix G. Results of the proportional hazards regression for root survivorship data (species and root branching order effects).
TABLE G1. Results of the proportional hazards regression for root survivorship data (species and root branching order effects). The analysis was used to assess the effects of three covariates (species, root order and species * root order interaction) on root life span. The analysis was performed for all root cohorts produced between 19th February 1999, until 30th September 2001, equivalent to a duration of 1006 days (144 weeks). A method of partial likelihood estimates the β coefficient associated with each covariate in the model. All species effects are comparisons with Quercus margaretta and all root order effects are comparisons with the first root order. A negative parameter indicates that increasing values of the covariate are associated with a decreasing risk of mortality relative to Q. margaretta and/or to the first root order, and vice versa for positive parameter values. A chi-square statistic was used to test the null hypothesis that each b coefficient is equal to zero. Also reported is the risk ratio, defined as eβ. A risk ratio >1 indicates increasing risk for that variable, <1 decreasing, and =1 no difference in mortality risk. Bold numbers indicate values significantly different than 1 at 95% confidence. The risk ratio is interpreted as the ratio of the hazard of a given species versus Q. margaretta (e.g., β < 1 indicates lower mortality risk of roots of each given species), vs. the first root order (e.g., β < 1 indicates lower mortality risk of roots of each given root order), and the interaction of species by root order. The significant interaction term suggests greater/lower (>1/ <1) divergence of risk between root orders for Q. margaretta as compared to each one of the other species. All significant eβvalues are bolded for clarity.
In this analysis the risk of mortality was interpreted with two variables: the β parameter of each covariate and the risk ratio (eβ). Both coefficients predict the risk of mortality of any species relative to Q. margaretta (species effect) and any root order relative to first order roots (root order effect). Similar to findings using univariate survival analysis, the risk of mortality relative to Q. margaretta was lower in Q. laevis and Q. incana (β < 0 and eβ < 1), but higher in P. palustris (β > 0 and eβ > 1), whereas the risk of mortality relative to first order roots was lower in mycorrhizal and third+fourth order roots but greater in second order roots. Inspection of the species*root order covariate coefficients indicate that comparative mortality risks of the different root orders varied among species. For instance, the divergence in mortality risks between mycorrhizal and first order non-mycorrhizal roots was greater in Q. incana (eβ= 2.4) and P. palustris (eβ= 1.3), to a lesser extent, relative to Q. margaretta, but lower in Q. laevis (eβ = 0.37). Albeit exhibiting shorter lifespans (Table 6), second order roots had slightly greater risk of mortality than first order roots. This comparative risk (first vs. second order roots) was greater in Q. laevis (eβ = 1.7), lower in P. palustris (eβ = 0.78) and similar in Q. incana (eβ~ 1). On the other hand, third order roots were less likely to die than first order roots, but the difference in risks was lower in Q. incana relative to Q. margaretta (eβ = 0.52) and similar in the other species.
Variable | Parameter estimate |
Wald chi square |
Confidence interval (95%) |
|||||
Lower |
Upper |
|||||||
Species (Pp) |
1 |
0.5019 |
0.0673 |
548.99 |
<0.0001 |
1.652 |
1.448 |
1.885 |
Species (Qi) |
1 |
-0.7519 |
0.1241 |
548.99 |
<0.0001 |
0.471 |
0.370 |
0.588 |
Species (Ql) |
1 |
-1.0531 |
0.1410 |
548.99 |
<0.0001 |
0.349 |
0.265 |
0.449 |
Order (2) |
1 |
0.2689 |
0.0705 |
126.13 |
<0.0001 |
1.309 |
1.140 |
1.502 |
Order (3-4) |
1 |
-0.5877 |
0.1609 |
126.13 |
<0.0001 |
0.556 |
0.405 |
0.738 |
Order (myc) |
1 |
-0.1930 |
0.0980 |
126.13 |
<0.0001 |
0.824 |
0.680 |
0.999 |
Species (Pp)* order (2) |
1 |
-0.2540 |
0.0811 |
119.36 |
<0.0001 |
0.776 |
0.662 |
0.909 |
Species (Pp)* order (3-4) |
1 |
0.2527 |
0.1781 |
119.36 |
<0.0001 |
1.288 |
0.908 |
1.825 |
Species (Pp)* order (myc) |
1 |
0.2881 |
0.1050 |
119.36 |
<0.0001 |
1.334 |
1.086 |
1.639 |
Species (Qi)* order (2) |
1 |
-0.1930 |
0.1483 |
119.36 |
<0.0001 |
0.824 |
0.617 |
1.102 |
Species (Qi)* order (3-4) |
1 |
-0.6625 |
0.3477 |
119.36 |
<0.0001 |
0.516 |
0.229 |
0.942 |
Species (Qi)* order (myc) |
1 |
0.8711 |
0.1595 |
119.36 |
<0.0001 |
2.390 |
1.748 |
3.267 |
Species (Ql)* order (2) |
1 |
0.5267 |
0.1566 |
119.36 |
<0.0001 |
1.693 |
1.246 |
2.301 |
Species (Ql)* order (3-4) |
1 |
-0.1426 |
0.3541 |
119.36 |
<0.0001 |
0.867 |
0.433 |
1.611 |
Species (Ql)* order (myc) |
1 |
-1.0028 |
0.2597 |
119.36 |
<0.0001 |
0.367 |
0.221 |
0.610 |
Species identifiers: Quercus laevis (Ql), Q. incana (Qi), Q. margaretta (Qm), Pinus palustris (Pp)
Root order identifiers: Second order (2), Third and fourth orders (3–4), mycorrhizal (myc)