How to quantify plant tolerance to loss of biomass?

Abstract In some plant species the whole shoot is occasionally removed, as a result of specialist herbivory, grazing, mowing, or other causes. The plant can adapt to defoliation by allocating more to tolerance and less to growth and defense. Plant tolerance to defoliation (TOL1) is typically measured as the ratio between the average dry weight of a group of damaged plants and a control group of undamaged plants, both measured some time after recovery. We develop a model to clarify what TOL1 actually measures. We advocate keeping regrowth (REG2) and shoot–root ratio, both elements of TOL1, separate in the analysis. Based on a resource trade‐off, exotic Jacobaea vulgaris plants from populations in the USA (no specialist herbivory) are expected to grow faster and be less tolerant than native Dutch populations (with specialist herbivory). Indeed Dutch plants had both a significantly larger fraction biomass in roots and faster regrowth (REG2), while US plants attained the highest weight in the control without defoliation. Using key‐factor analysis, we illustrate how growth rates, regrowth, and shoot–root ratio each contribute to final biomass (plant fitness). Our proposed method gives more insight in the mechanisms that underly plant tolerance against defoliation and how tolerance contributes to fitness.

In some plant species the whole shoot is occasionally removed, as a result of specialist herbivory, grazing, mowing, or other causes. The plant can adapt to defoliation by allocating more to tolerance and less to growth and defense. Plant tolerance to defoliation (TOL1) is typically measured as the ratio between the average dry weight of a group of damaged plants and a control group of undamaged plants, both measured some time after recovery. We develop a model to clarify what TOL1 actually measures. We advocate keeping regrowth (REG2) and shoot-root ratio, both elements of TOL1, separate in the analysis. Based on a resource trade-off, exotic Jacobaea vulgaris plants from populations in the USA (no specialist herbivory) are expected to grow faster and be less tolerant than native Dutch populations (with specialist herbivory).
Indeed Dutch plants had both a significantly larger fraction biomass in roots and faster regrowth (REG2), while US plants attained the highest weight in the control without defoliation. Using key-factor analysis, we illustrate how growth rates, regrowth, and shoot-root ratio each contribute to final biomass (plant fitness). Our proposed method gives more insight in the mechanisms that underly plant tolerance against defoliation and how tolerance contributes to fitness.

K E Y W O R D S
herbivory, invasive plants, regrowth, shoot-root ratio

| INTRODUCTION
Specialist herbivores typically adapt to the defense chemicals of their preferred food plant (Crawley, 1983). This makes chemical defense ineffective, and the last resort of the plant is to develop tolerance, the ability to regrow after some level of defoliation (McNaughton, 1983).
Plant species that invade a new area or continent escape, for some time at least, from their specialist herbivores. Natural selection may then lead to a shift in allocation patterns; adaptation to the new environment could reduce allocation to tolerance and increase allocation to growth and defense against generalist herbivores (Bossdorf et al., 2005;Keane & Crawley, 2002;. Do plants adapt to their new environment and in what way? Reciprocal transplant experiments provide the most direct test of local adaptation. Such transplants date back to the classic work of Clausen, Keck, and Hiesey (Núñez-Farfán & Schlichting, 2001) in the first part of the 20th century and are still highly relevant today. Some modern studies (Genton, Kotanen, Cheptou, Adolphe, & Shykoff, 2005) transplanted plants over continents, following their recent range expansion. The home genotype is expected to produce most seeds or biomass, that is, attain the highest fitness. A subsequent question is which physiological adaptations allow for the success of the home genotype? To answer this question in the context of tolerance, a typical experiment has been designed (Belsky, 1986;Bustos-Segura, Fornoni, & Nunez-Farfan, 2014;Jogesh, Stanley, & Berenbaum, 2014;Scholes, Wszalek, & Paige, 2015;Strauss & Agrawal, 1999). This involves placing different genotypes into a common environment (growth room) and after some time apply complete defoliation to half the plants, Both the authors contributed equally. while leaving the other half untouched. Under the rather stringent assumption that the artificial defoliation treatment is representative of natural defoliation, one expects a native genotype to perform best in the defoliation treatment. When an exotic genotype allocates less to tolerance and more to growth, it is expected to outperform a native genotype in the control treatment. In such experiments, fitness is the number of seeds or biomass at the end of the experiment.
In analyzing these defoliation experiments, researchers have developed several measures of tolerance. The most commonly used tolerance measure is the degree to which final biomass is affected by herbivore damage, relative to the undamaged state (TOL1, Strauss & Agrawal, 1999). This tolerance measure can be compared between different genotypes but does not necessarily reflect fitness. Suppose genotype A produces 50 seeds when undamaged and 40 when damaged and genotype B produces 100 seeds when damaged and 50 when undamaged. Then in the damage treatment, genotype B has the highest fitness (50 seeds produced by B, 40 seeds by A), despite its low tolerance (TOL1 = 0.5 for B, 0.8 for A). It would be incorrect to state that A has higher tolerance and is therefore better adapted to an environment with frequent herbivory. This distinction between fitness and tolerance was already pointed out clearly by Hochwender, Marquis, and Stowe (2000).
Several studies compared tolerance of native and exotic plants. In Pastinaca sativa, tolerance to webworm herbivory increased after introduction of a specialized herbivore in Australia (Jogesh et al., 2014).
Jacobaea vulgaris genotypes from native populations (Europe) with regular defoliation by the specialist Tyria jacobaeae (Bonsall, van der Meijden, & Crawley, 2003) had higher regrowth capacity than genotypes from populations in the USA or Australia without such defoliation ; Figure 1). Contrary to this, tolerance was higher in exotic US populations of the tree Sapium sebiferum, as compared to native Chinese populations (Zou, Rogers, & Siemann, 2008).
For the subtropical shrub Chromolaena odorata, no difference in the tolerance measure was found between native populations from the south of the USA and Mexico and invasive Chinese populations (Li, Feng, & Barclay, 2012).
The greatest value of tolerance measures is, in our opinion, to clarify the mechanisms behind tolerance. Two plant strategies result in high values for TOL1. First, plants can reduce the fraction biomass lost through defoliation by storing more resources belowground, that is, a low shoot-root ratio Li et al., 2012;Stowe, Marquis, Hochwender, & Simms, 2000;van der Meijden, de Boer, & van der Veen-van Wijk, 2000). Second, fast regrowth after defoliation contributes to tolerance.
In this study, we use a simple model of exponential plant growth to illustrate how TOL1 and other tolerance measures depend on both shoot-root ratio and regrowth. Next, we advocate a new measure (REG2) for regrowth, which does not depend on shoot-root ratio. We illustrate how to compute REG2, using a small dataset of J. vulgaris that includes native and exotic genotypes. With key-factor analysis, we show how fitness (the final dry mass of plants) can be related to separate components of tolerance (REG2 and shoot-root ratio) and to other plants characters.

| A GRAPHICAL MODEL
At some time, the whole shoot is removed experimentally. The genotype that produces most seeds at the end of the experiment has the highest fitness. When the damaged plant regrows faster than the control, this is called compensation (Figure 2). Compensation may F I G U R E 1 The plant species Jacobaea vulgaris (ragwort) is frequently defoliated by its specialized herbivore Tyria jacobaeae (the cinnabar moth). After complete defoliation, the plant can recover by forming new rosettes at the stem or from root fragments. These new rosettes may flower in the subsequent year. Photograph T. Lin  ln Dry mass Time be due to increased photosynthesis, increased nutrient uptake, a different growth form, allocating the stored resources in the root back to the shoot, and switching defense pathways on or off (reviewed in Rosenthal & Kotanen, 1994). Overcompensation occurs when, after some time, the weight of damaged plant exceeds that of the control (indicated by the arrow in Figure 2, Strauss & Agrawal, 1999).
Plants can deal with biomass removal in different ways. The first strategy is simply to have a high relative growth rate (RGR) throughout, even without specific adaptations for regrowth ( Figure 3a). Even if the fast-growing genotype suffers most after a single defoliation, it will eventually catch up with a slower-growing genotype and win

| A MATHEMATICAL MODEL
With exponential growth, it is convenient to plot the weight of the plant on a log scale ( Figure 1). The slope corresponds to the RGR (in gram per gram per time unit, all parameters are summarized in Table 1). Plants start to grow at t = 0 are completely defoliated at t = 1 and then regrow until the experiment is finished, and seeds or biomass are measured, at t = 2. We assume exponential growth at a constant rate and, for simplicity, that the time interval between t = 0 and t = 1 equals that between t = 1 and t = 2. Uncut control plants have subscript c. Damaged plant have subscript d. Before defoliation weight of all plants is multiplied by a factor λ 1 between t = 0 and t = 1.
The weight of control plants is multiplied by a factor λ c,2 between t = 1 and t = 2. Damaged plants grow with a factor λ d,2 in that same period.
We then have for the control plants: At defoliation, a fraction h is removed and a fraction 1 − h, the biomass in the root, remains. The weight of the defoliated plants at t = 1 is then a fraction 1 − h of the control plants just before defoliation occurs. The plants subsequently regrow until t = 2 with a factor λ d,2 .
In equation In Figure 2, plant weight is plotted on a log scale, so that the slope of the line for one time unit (i.e., the RGR) before the defoliation is ln(W c,1 ) − ln(W 0 ). In the second period, control plants have a RGR of ln(W c,2 ) − ln(W c,1 ) and when exponential growth continues at the same rate, this equals the RGR in the first period. The RGR for damaged plants in the second period is ln(W d,2 ) − ln(W d,1 ).

| REG1
An intuitive way to define regrowth (REG) is to compare the RGR in the first period and in the second period after damage. The higher F I G U R E 3 Four different strategies to cope with defoliation. Plants begin to grow at t = 0 are completely defoliated at t = 1 and then regrow until t = 2. Two genotypes A and B are depicted, solid and broken lines. In all cases, the strategy depicted by the solid line wins (highest dry mass at t = 2), but for different reasons. (a) Strategy A wins because of its higher RGR. (b) Genotype A wins because its greater storage in roots reduces the fraction biomass lost. (c) Genotype A wins because has higher regrowth. (d) Of course many combinations are possible. In this case, genotype A has fast growth and a high shoot/root ratio. Consequently, it grows faster but suffers more from removal of the whole shoot. At time 2, type A wins, but with earlier harvest, it would not have enough time to catch up and would lose continue at exactly the same rate as before, they would reach a final weight that is a fraction 1 − h of the weight of the undamaged controls. In that case (Figure 2b), REG2 is zero. If the RGR of the damaged plants is slower than RGR of the control plants in the second period, then REG2 is negative. If RGR of damaged plants is larger that of controls, then REG2 is positive and there is compensation ( Figure 2); with enough time the weight of the damaged plants will exceed that of the control (overcompensation).

| TOLERANCE MEASURES USED
Following Strauss and Agrawal (1999) tolerance is typically measured as the ratio (see also  with an undamaged control) and when it has low shoot-root ratio so that the fraction biomass removed is low.
All tolerance measures depend in slightly different ways from both regrowth, the fraction biomass in roots or even the RGR. This problem can be avoided by calculating REG2 and the fraction biomass in roots separately. This is illustrated in the next paragraph. (2) (4) REG2 = ln W d,2 (1 − h)W c,2 . were germinated (Lin, 2015). In Dutch populations, the specialist Tyria jacobaea regularly defoliates plants (Bonsall et al., 2003), while this herbivore is absent in the US populations. It is expected that native Dutch genotypes invest in tolerance and perform best in a defoliation treatment. The US genotypes may invest more in growth and would then grow best in the control treatment without defoliation. Four well-grown seedlings from each mother plant were selected and randomly assigned to four groups. For each group, there were 1 seedling × 3 motherplants × 11 populations = 33 plants. The first group was harvested before potting, and dry mass of seedlings was measured. The remaining groups were allowed to grow in 1-L pots with 20% potting soil (Slingerland potting soil, in the third group, while the last group was undamaged. These two groups were allowed to grow for another 4 weeks before all plants were harvested. The data in Table 2 are always the averages of three plants from the same population. These results can be summarized as follows. In the selective regime of defoliation the Dutch plants attained the highest dry mass; W d,2 = 1.807 g for the Dutch and 1.386 g for the US plants (Table 2).
Without damage, the US control plants tended to grow faster than the Dutch plants, the final dry weight at t = 2 was 41% higher (result not shown), even though the RGRs were not significantly different between Dutch and US plants in neither period 1 nor period 2 ( Table 2).
The results are consistent with our hypothesis that Dutch plants invest relatively more in tolerance and US plants in growth. Plants from Dutch populations had a significant higher fraction from their biomass in roots than plants from North America ( T A B L E 2 Averages of growth parameters from five Dutch a and six US b populations of Jacobaea vulgaris that were allowed to grow in period 1, then defoliated and were allowed to regrow in period 2 on total fitness to estimate their relative effect, c i = a + β i ln (W d,2 ). This procedure is called key-factor analysis and Royama (1996) discussed this specific method. The value of β gives the relative importance of a factor for the variation in the logarithm of some multiplicative factor.
This multiplicative factor is usually survival, but in this case, it is fitness, including both growth and biomass lost. The five values of β i sum to 1, so that it is possible to compare the relative effects of different stages on ln(W d,2 ).
Using the data from  period ( Figure 4). We used linear regression (function lm) in the statistics program R, which generates standard errors and significance values. The procedure illustrates that we can distinguish be effects of growth, regrowth (REG2) and fraction biomass in roots on final dry weight (fitness).

| Time lag period
The plant will not regrow immediately but with some time lag. In this paper, growth was calculated over a period of 4 weeks, starting immediately after defoliation. We could also have waited with growth measurements until the first new leaf unfolded. We did not record this lag time, which could well be different between genotypes. Differences in growth rate of the damaged plants λ d could therefore be due to a different time lag or to a difference in RGR once plants start growing again. It is recommended to keep these two parameters apart.
The commonly used tolerance measure TOL1 was higher for the Dutch than for the US populations, with the highest significance in Slow regrowth as a survival strategy is shown by the clonal species Solidago missouriensis. After massive herbivory different clones took between 1 and 10 years to reappear, recolonizing their habitat within a single season (Morrow & Olfelt, 2003). In this species, a long time lag for recovery is apparently a successful strategy to avoid the herbivore.
REG2 and shoot-root ratio could change in different directions, and then, it makes even more sense to keep them separate in the analysis.
Different changes in shoot-root ratio and REG2 will not become clear if only TOL1 is considered.

| Costs of tolerance
As noted by Strauss and Agrawal (1999), an intuitive way to test for cost of tolerance is plot dry mass of undamaged plants W c,2 (on x) against fitness of damaged plants W d,2 (see also Hochwender et al., 2000). For the J. vulgaris data in Table 1, this gives no significant negative (r = −.12, p = .72) relationship. It seems reasonable that plants that make no investment in tolerance will suffer the greatest reduction in their growth rate (REG2 smallest). Plants with high RGR in the (6) W d,2 = W 0 λ 8 1 (1 − h)λ 4 d,2 .
F I G U R E 4 In a key-factor analysis plant fitness (log dry weight of the damaged plants at the end of the experiment) is regressed on its five different components (Equation 6). The three components with the strongest relation with fitness (highest slope) are shown: triangles = RGR control in the second period (0.112), open squares = regrowth measure REG2 (0.790), circles fraction biomass in roots (0.378). The slopes for initial weight (−0.0971) and RGR in the first period (−0.1831) are not shown. The five slopes (Equation 6) add up to one, so that each slope shows its relative effect on variation in fitness control are the ones that invest least in regrowth. One would then expect a negative correlation between RGR c,1 (or RGR c,2 ) and REG2.
Neither the correlation between RGR c,1 and REG2 (r = −.39, p = .22) nor that between RGR c,2 and REG2 (r = −.17, p = .61) was significant for the Jacobaea data. Root storage draws resources away from primary production, and one expects this to be costly. This can be tested by plotting the fraction dry weight in the roots (1 − h) against the RGR of control plants. A negative relation existed in the J. vulgaris data between 1 − h and RGR c,2 (r = −.55, p = .07), but this correlation was almost zero for 1 − h and RGR c,1 (r = .05, p = .87). It has been emphasized (Strauss & Agrawal, 1999) that fitness variation among families and genotype may exist and makes detection of costs problematic.
The existence of trade-offs between growth, defense, and tolerance is the basis for our expectations about the performance of native and exotic plants in the defoliation experiment. Therefore, these tradeoffs and the mechanisms underlying tolerance require further detailed study.