This study was conducted in the municipal nursery of the City of Montreal, province of Quebec, Canada. The site lies at 45°49′59″ N, 73°24′44″ W, at about 35 m of elevation. The mean annual precipitation is 978 mm (215 mm snow and 763 mm rain), and the mean annual temperature is 6.2°C (mean growing season temperature is 14.4°C). The mean daily maximum and minimum temperatures are 10.5°C and 0°C. Annually, there is an average of 1,958 h of sunshine, 2.8 degree-days below 10°C, and 1,099 degree-days above 10°C. Temperatures below 0°C occur between October and April (period 1971–2000; Environment Canada, climate.weather.gc.ca) and the winter season commonly extends from mid-November to the end of March (Boyer et al., 1985). Soil structure is mainly composed of a loamy clay.

We studied two tree species commonly planted in the city of Montreal: C. occidentalis L. (common hackberry) and F. pennsylvanica Marsh. (Red ash), hereafter referred to as Celtis and Fraxinus, respectively. Both species show a large variability across their geographical range, but they are generally characterized as medium-sized (Celtis reaching 15 m and Fraxinus 25 m in height), with a medium lifespan (100 years for Fraxinus and 150 years for Celtis), and are in generally considered fast growing, although they show distinctively different growth rates (Farrar, 1995). Celtis is a more resource conservative species since it has a higher foliar carbon/nitrogen ratio, lower photosynthetic capacity, and higher wood density than Fraxinus (Ramirez, 2017). Moreover, Celtis is capable of growing in very inhospitable conditions (Gucker, 2011), while Fraxinus, although showing a broad climate adaptability, prefers growing in mesic to humid sites (Gucker, 2005). The exemplars for this experiment were donated by the City of Montréal. At the seedling stage, there were no apparent differences in vigor between the species. However, after e-planting, Celtis showed signs of growth decline independent from the application of treatments. Trees at the beginning of the study (2012) were between 1.6 and 4.5 m tall for Celtis, and 2.6 to 6.1 m tall for Fraxinus. Therefore, the results presented hereafter compare both two different species and two states of vigor ( Figure 1 ). A total of 202 trees were planted in 2009 and 2010, 116 Celtis from field-grown seedlings propagated in 2004, and 86 Fraxinus seedlings propagated in 2003.

A fully factorial experiment was set up; where in addition to the control with no damage treatment, all other trees were randomly assigned to the following damage treatments: two intensities of defoliation (37%, 75%), two intensities of root reduction (37%, 75%), and one intensity of stem damage (50%) ( Table 1 , Figure 2 ). All possible combinations among these three treatments were reproduced, resulting in 18 types and levels of damage treatment. The number of replicates per treatment was 6 in Celtis and 4 in Fraxinus due to the availability of trees, and this varied slightly between treatments to ensure sufficient trees in case of mortality. Treatments were applied in July, which corresponded to the month of maximum leaf area in both 2012 and 2013. At the beginning of the dormant season in autumn 2015, a reduction pruning of the main stem was performed on all trees with the removal of the lower half of the living crown. This treatment was applied to all trees, but its effect will not be investigated in this instance as analyses specific to crown recovery and architecture have been carried out in a separate study.

For each tree, the stem discs were collected at 1.3-m height, and three large roots were cut at 5 cm from the stem base in winter 2017. These cross sections were left to air dry and subsequently sanded down to 400 grit sandpaper (Schweingruber, 1988). Tree ring widths were measured with WINDENDRO^TM (Regents Instruments, Quebec). Data quality of single tree chronologies was controlled through visual and statistical cross dating (i.e., gleichläufigkeit). Cross-dating analyses were performed with the dplr package (Bunn, 2010), and mean tree chronologies were created from the average of the three radiuses per cross section from stem and roots ( Figure 3 ). All computations were performed using R version 3.4.3 (R Core Team, 2017). Considering the short time span analyzed and the even age status of the trees, we decided to perform our calculations on both raw tree ring widths and on converted basal area increment (BAI) data, obtained with the function bai.out function in the dplr package (Bunn, 2010). This decision was to ensure the preservation of small year-to-year variability that could be potentially concealed through standardization of the chronology (Fritts, 1976).

It is to be noted that Celtis showed a replanting shock reaction in 2009, while Fraxinus showed a smaller growth decline due to replanting, which occurred in 2009 and 2010. Overall, it should be observed that controls for Celtis showed a declining growth rate, while Fraxinus showed a vigorous growth trend. Therefore, the effect of the treatments should be related to the actual growth trends of the two species, and the results presented are relative to these growth trends.

Overall, both stem and root growth of Celtis were less affected by the various levels and combinations of damage treatments than Fraxinus, showing few significant growth differences when compared to the control; in some cases, the stem damage treatment stimulated growth ( Table S.1 and Figures 4A, C ). On the contrary, stem and root growth of Fraxinus were, in general, significantly negatively affected by most damage treatments, both alone and in combination, especially the combinations of defoliation and root damage (at both high and low intensities) where it had the lowest stem growth ( Table S1 and Figures 4B, D ). Fraxinus root growth was consistently reduced by all damage treatments. Only following SD and low DF-SD treatments, Fraxinus did show a nonsignificant decrease in growth compared to the control.

The results calculated by the GBM models indicating the effect of the three damage treatments in the years after they were applied are shown in Figure 5 . Defoliation had the strongest impact on both Celtis and Fraxinus stem growth in the 2 years after the damage treatments. However, in the subsequent years, root reduction had the strongest impact. Stem damage had only a minor effect on stem growth ( Figures 5A, B ), but it had a stronger impact on root growth for both Celtis and Fraxinus throughout the years ( Figures 5C, D ). Celtis root growth was more strongly impacted by defoliation than by root reduction in the 2 years after the damage treatments and vice versa in the later years, while the impact of defoliation and root reduction on Fraxinus root growth was similar in all years.

The marginal effects of each treatment level on the decomposition of stems ( Figure 6D ) and root growth ( Figures 6E–H ) for both species in the first year (2012) and last year (2015) are shown in Figure 6 . The variable with the highest relative influence is also the one accounting for the greatest differences in growth; when a variable is more influential, the fitted growth shows a positive or negative trend depending on the effect of the damage treatment (i.e., from 0 = control, low = 37% damage, and high = 75% damage, see Table 1 ). The mean annual growth for each treatment can be calculated by summing the GBM fitted results in Figure 6 for the respective treatment level.

High defoliation in Celtis showed the lowest contribution to growth rates in 2012, while low defoliation and no defoliation damage treatments had similar contribution rates ( Figure 6A ). On the contrary, in 2015, root reduction played the biggest part in differentiating growth rates, which was indirectly proportional to its intensity ( Figure 6B ). Similar patterns can be observed for Celtis root growth; however, in 2015, the differences between the damage treatment levels are more evident ( Figures 6E, F ). Interestingly, in this case, low defoliation shows higher growth than the null and high damage treatments, while root reduction contribution is still decreasing with increasing intensity of damage treatments ( Figure 6F ).

The decomposition of Fraxinus growth shows a more even distribution among the damage treatments. Interestingly, the low intensity DF and RR damage treatments show a more similar effect than their control counterparts for stem growth ( Figures 6C, D, H ). The trend of the DF contribution to growth drastically changes in 2015, showing a higher contribution to growth from high DF than the null and low intensity damage treatments ( Figures 6D, H ), while high intensity RR shows the lowest contribution to the growth of roots ( Figure 6E ). For both species, in most cases, the SD treatment has either an equal or a higher contribution than the no stem damage.

In 2017, the final DBH and the total root area cover showed a nonsignificant difference between the damaged trees and the controls in most cases ( Figures 7A, B ). DBH in Fraxinus trees was significantly lower than control in low DF/high RR, low DF/high RR/SD, and high DF/high RR treatments. Celtis showed no significant differences in DBH but showed a higher growth of roots in the trees with low DF/low RR, low DF/high RR, high DF/low RR, and high DF/high RR/SD than in the control. There was an increase in production of finer roots with increasing intensity of the damage treatments, particularly for the low RR/SD treatment in Celtis, and high RR in Fraxinus ( Figure 7C ).

The correlations between DBH and total larger root diameter in 2017 were strong for both species (r ² = 0.7 for Celtis and r ² = 0.5 for Fraxinus for both treatments). Damage treatments did not have a significant (P > 0.5) effect on Fraxinus correlations, while the damage treatment combination of low DF/high RR significantly and positively affected Celtis abundance of roots ( Figure 8 ).

Multiple damages did not have a simple cumulative effect on growth contrary to our first hypothesis. In most cases, they led to a less negative effect on tree growth than expected. In fact, the maximum damage treatment (DF 75%, RR 75%, and SD) did not have the most negative effect on stem and root growth for either species. Above- and below-ground woody production was decreased by all damage treatments for Fraxinus trees, but this decrease was relatively independent of treatment intensity and similar in all 18 damage treatments. In contrast, Celtis, which was experiencing a growth decline when damage treatments were applied, showed only a slight both positive and negative growth responses to treatments.

Interestingly, the effect of increasing intensity or number of damage treatments applied did not show a linear cumulative pattern. The effects of low or high intensity damage to only roots or the foliage did not affect the overall tree growth differently compared to the combined root and foliage damage treatments. Similar results can be found in urban oak where compensatory pruning was administrated following root loss to reduce water demand and crown dieback (Watson, 1998). Paired treatments did not decrease growth further; rather, it was similar to the reduction caused by a single treatment of defoliation or root reduction (Watson, 1998). This may indicate a synergistic effect of the damage treatments, inducing physiological responses that protect the trees from the second type of damage (Rennenberg et al., 2006; Bansal et al., 2013). It may also indicate that, in response to any significant stress, trees rapidly stop their growth to reallocate resources (i.e., mainly C from their photosynthesis or reserve pools) to cope with maintenance respiration, tissue reconstruction, or new tissue production (Körner, 2003; Muller et al., 2011; Körner, 2015).

The different types, intensities, and combinations of damage treatments affected Celtis less than Fraxinus, 2 years after the last application, contrary to our second hypothesis. Moreover, trees treated with stem damage showed a greater stem growth compared to the control ( Figures 4 and 7 ). This increased growth could be explained by a reaction to the injury and consequent compensatory growth to maintain tree viability, especially in trees already showing a decline in growth. Also, following stem damage like girdling, carbohydrates tend to accumulate in the upper parts of the tree (Winkler and Oberhuber, 2017), allowing above-ground compartments to be insensitive to or even to benefit from such treatment. Similarly, the low defoliation treatment in combination with stem damage had a boosting effect on both stem and root growth ( Figures 4 and 7 ). In fact, the inclusion of stem damage with other damage treatments tended to reduce the negative effects of these other treatments, presumably due to the triggering of compensatory growth as has been shown in earlier studies (Mcnaughton, 1983; Gill, 1992; Watson, 1998). However, the small growth response of Celtis to any combination of treatments should take into account the low growth trend shown by this species following replanting ( Figure 1A ), and the additional stresses did not worsen the already observed decline. This would reinforce the hypothesis that under stress or with tissue damage, this species expresses a particularly high control of resource allocation to its C sinks to maintain its carbon balance (Hoch, 2015). Indeed, under stress, Celtis seems to be able to minimize growth and avoid mortality, sustaining “minimum growth levels” for several years. Such strategy may allow for the preservation of scarce resources and provide the capability of dealing with stress and associated secondary metabolism (Muller et al., 2011; Hartmann and Trumbore, 2016).

Fraxinus, which recovered well from replanting ( Figure 1B ), reacted more negatively to all treatments but for a shorter period of time compared to Celtis ( Figures 1 and 4 ). The trees reacting to treatments, which combined similar levels of defoliation and root reduction, did not fare better than those following a single damage treatment. Growth showed a similar reduction when affected by single damage treatments compared to multiple damage treatments. Only trees undergoing stem damage, or stem damage paired with low defoliation, were not significantly different from the control. Roots showed a significant growth reduction with all damage treatments regardless of the type, intensity, or combination of damage, except in the trees that experienced only stem damage. This result refutes the hypothesis that damage to both above- and below-ground parts can minimize the negative impact on growth by balancing relative activity occurring both above- and below-ground. One should rather acknowledge that trees need to deal with each stress independently perhaps even simultaneously (see next section below). Hence, there is no benefit, nor apparent disadvantage, in trying to compensate for above- or below-ground damage by a similar reduction above- or below-ground.

In answer to our third question, the three main damage treatments influence on growth shifted in importance and intensity in the years following their application. For stem growth, defoliation had a strong effect right after the damage treatment, while root reduction showed the highest negative effect in the long term ( Figures 5 and 6 ). Stem damage was the factor with the lowest influence on stem growth, while it had a relatively strong effect on root growth. On the contrary, all damage treatments had equal weight in the contribution to root growth, and their effects remained constant in the years following the treatments. Fraxinus roots were the most affected by stem damage in the first year after treatment and equally affected by all three treatments thereafter. Celtis roots were affected most by defoliation in the first 2 years after damage treatment, while root reduction drove the differences in growth afterward.

In some cases, defoliation may reduce tree growth, or, on the contrary, photosynthetic up-regulation reactions may compensate for the loss of foliage resulting in a smaller impact on growth (Pinkard and Beadle, 1998; Vanderklein and Reich, 1999; Eyles et al., 2009; Li et al., 2016). In our study, Celtis stem growth rate had little response to defoliation, since growth of this species was actually already affected by other unknown factors. Nevertheless, there are numerous examples showing the lack of effect of low intensity defoliation on tree growth. For example, trees can compensate for a 25% or more defoliation treatment, showing no changes in concentration of nonstructural carbohydrates (Körner, 2003; Boege, 2005; Würth et al., 2005). A crown removal of 50% in Eucalyptus species showed no significant reduction in height and diameter increments over a 2-year period (Alcorn et al., 2008; Alcorn et al., 2013), indicating the great capability of trees to maintain above-ground growth rate from their reserve pools despite loss of foliage. On the contrary, Fraxinus stem growth responded to defoliation, by showing reduced growth rate initially, but recovering in the second year after the treatment, and remaining consistent in the following years ( Figure S1 ). This compensation response after defoliation has already been reported and associated with the enhancement of photosynthetic efficiency after leaf loss and movement of resources to storage (Pinkard and Beadle, 1998; Quentin et al., 2012; Liu et al., 2019). The null and low root reduction and defoliation treatments showed a similar contribution to Fraxinus stem growth, while 75% of treatments showed the lowest contribution in the first 2 years after the treatment ( Figure 6 , Figure S1 ). Interestingly, in 2014 and 2015, high defoliation had a higher contribution to growth than the treatments of lower intensities.

In all cases, null and low root removal treatments showed similar growth contribution. Therefore, to maintain growth, low root removal might have a positive effect on remaining root activities, due to compensatory mechanisms enhancing water and nitrogen utilization efficiency (Blake, 1983; Ferree et al., 1999). However, this enhancement seemed to be insufficient or absent under higher root removal. Similarly, studies of root removal treatments on Cunninghamia lanceolata have also indicated multiple compensatory responses associated with root pruning, although above-ground biomass production was significantly negatively associated with increasing root removal (Dong et al., 2016). Trees treated with root removal exhibited higher water use efficiency, both right after the treatment and in the long term, along with an increase in fine root production. Root pruning at the 25% level seemed to be the most effective treatment to enhance photosynthetic nitrogen-use efficiency and stem dry mass accumulation (Dong et al., 2016).

Surprisingly, the negative effects of the damage treatments were less pronounced than expected, showing no dramatic reduction when compared to the control, both above- and below-ground. Fine root production found near the stump increased in some of the damaged Celtis trees, especially those with the low root damage treatment. However, Fraxinus did not show any significant increase in fine root production in relation to the various damage treatments. The correlations between DBH and root production also show only minor differences among the damage treatments, and only the low DF/high RR showed a significant reduction for Celtis, probably due to a shift in resource allocation to a higher production of small roots and structural roots. The lack of significant differences between DBH and the larger root area produced in 2017 suggests that although these two species have different strategies when reacting to damage treatments and different growth rates and vitality, they both show that the impacts of damage treatments are not cumulative on tree growth.

Nonetheless, these results should be considered in light of the very different growth patterns of Celtis and Fraxinus in the growing conditions of this experiment, regardless of the treatments applied. Where Celtis showed low annual increments, Fraxinus showed high annual increments and a larger root system (Gucker, 2005; Gucker, 2011). Whereas Celtis control trees had reached an average of 8 cm DBH in 2017, Fraxinus reached a DBH of 11 cm, showing a 37.5% larger stem ( Figure 7 ). Greater differences were found at the root level where Fraxinus grew 167% more roots than Celtis, although Celtis had a higher production of fine roots (on average 5% vs. 30%–40% of area covered by fine roots). In the event of a damage treatment, Fraxinus tended to keep the entire crown alive while sacrificing stem growth for a short period of time, whereas Celtis tended to sacrifice crown development and overall growth in order to maintain minimal stem and root increment ( Figure 3 ). It is also interesting to notice how the correlation between roots produced and diameter growth did not drastically differ between the species and the treated groups ( Figure 8 ), suggesting the capacity of both species to reach an equilibrium in above- and below-ground production, only 3 to 4 years after application of damage treatments. The only group showing a significantly higher root production was Celtis low DF/low RR. As discussed above, this is also evidence of a root-oriented compensatory mechanisms in Celtis, which stimulates root growth when low root removal is applied (Fare, 2014; Dong et al., 2016).

Furthermore, these species-specific differences need to be accounted for to understand any reaction to stress treatments. Overall, Celtis showed a system that focuses on the survival of the individual, possibly through a laborious and high-C demanding compartmentation and repair. One consequence is a long-term reduction or cessation of growth, to reduce structural growth sink and save C to cope with this stress response. The considerably low growth rates, probably associated with the shock of replanting, are consistent with trees that are capable of naturally growing in ravines and very rocky, unfavorable soils (Gucker, 2011). Celtis has been rated as the most damage-resistant species following hurricane damage (Xi and Peet, 2008), and a successful species in the rehabilitation of mining sites (Ashby et al., 1984). On the contrary, Fraxinus shows a high capacity for resource acquisition, compartmentalization after wounds, and growth recovery. This possibly explains its wide distribution across North America, ranging from southeastern Alberta, through central Montana to southeastern Texas, Florida, and up the east coast to Halifax (Kindscher and Holah, 1998). Although this species shows good climate adaptability, it is most often described in association with riparian areas, floodplains, and swamps, but is also found in areas that experience drought.

Finally, increasing stress does not imply a greater reduction in woody mass production. Although differences in their tolerance to damage were evident, neither species showed mortality with increasing stress. This indicates their suitability as urban trees. However, although this experiment shows the high capacity for adaptability of both Celtis and Fraxinus, it should be noted that physical damage still increases the occurrence of fungal and pathogenic infections, and vulnerability to insects, and therefore, injury should be avoided whenever possible (Clair-Maczulajtys et al., 1999). These conclusions do not take into account the emerald ash borer, which is posing a serious threat to Fraxinus health and vitality, and call into question the recommendation of planting Fraxinus in the urban setting (Klooster et al., 2018).