On testing for a tradeoff between constitutive and induced resistance

Transcription

1 OIKOS 112: 12/11, 26 On testing for a tradeoff between constitutive and induced resistance William F. Morris, M. rian Traw and Joy ergelson Morris, W. F., Traw, M.. and ergelson, J. 26. On testing for a tradeoff between constitutive and induced resistance. / Oikos 112: 12/11. Plants possess two types of resistance against herbivores: ever-present constitutive resistance and induced resistance triggered by attack. s the production of both resistance types entails a metabolic cost, a tradeoff between them has frequently been hypothesized. Over twenty published studies have tested for the existence of this tradeoff, but this literature is marred by three methodological problems. The first problem is lack of agreement about how to measure induced resistance, a complex trait that typically involves comparison between damaged and undamaged plants. Some metrics of induced resistance confound constitutive and induced resistance, creating evidence for a tradeoff when one does not exist or obscuring real tradeoffs. On both biological and statistical grounds, we argue for the difference in mean resistance between damaged and control plants from the same family or genotype as the best metric of induced resistance. The second problem is that limited sampling (e.g. of families or of individuals within families) or errors in measuring resistance traits of individuals can generate spurious evidence for a tradeoff even when our preferred induced resistance metric is used. The third problem is that some families may show induced susceptibility (lower resistance in damaged than in undamaged plants). To provide a better test for a tradeoff, we devise a Monte Carlo procedure that accounts for sampling variation, measurement error and induced susceptibility without producing unrealistic negative resistance values, and we illustrate it with simulated data. Until the problems we describe are widely addressed and the tools we propose are widely applied, the resistance tradeoff hypothesis cannot be considered to have been adequately evaluated. Our approach also applies whenever the plasticity of a trait (measured as the difference between treatments or environments) is compared to the value of that trait in a single environment. W. F. Morris, Dept of iology, Duke Univ., ox 9338, Durham, NC , US (wfmorris@duke.edu). / M.. Traw and J. ergelson, Dept. of Ecology and Evolution, Univ. of Chicago, 111 East 57th St, Chicago, IL 6637, US. Current address for T: Dept of iological Sciences, Univ. of Pittsburgh, 176 Crawford Hall, 4249 Fifth venue, Pittsburgh, P 1526, US. y definition, resistance traits such as secondary chemicals or trichomes reduce the amount of damage individual plants or animals receive from their natural enemies. (lthough some authors measure resistance in terms of herbivore damage alone, throughout this paper we use the term resistance to refer to specific traits that are known to reduce damage.) Resistance can be classified as constitutive or induced. Constitutive resistance is always expressed, whereas induced resistance appears only after an individual has been damaged (and serves to reduce additional damage). s both types of resistance are likely to entail costs (Strauss et al. 22), a tradeoff between constitutive resistance and induced resistance has frequently been hypothesized, such that high investment in constitutive resistance is predicted to be matched by low investment in induced resistance, and vice-versa (Karban and Myers 1989, Herms and Mattson 1992, Zangerl and azzaz 1992, Karban and aldwin 1997). growing number of studies have now looked for such ccepted 3 June 25 Copyright # OIKOS 26 ISSN OIKOS 112:1 (26)

2 a tradeoff (see the meta-analysis by Koricheva et al. 24). However, three difficulties bedevil the search for tradeoffs between constitutive and induced resistance: the use of multiple measures of induced resistance, the problem of sampling variation, and the existence of induced susceptibility. Researchers have used different metrics of induced resistance when testing for a constitutive/induced resistance tradeoff (Table 1, Koricheva et al. 24), which is undesirable for two reasons. First, the use of different metrics makes it difficult to compare results across studies. Second, and more importantly, some of the metrics of induced resistance that have been used to look for tradeoffs fail to disentangle constitutive and induced resistance and so, as we explain below, can either produce false evidence of a tradeoff when one does not exist or obscure a real tradeoff. second difficulty stems from the fact that, because constitutive resistance must be measured in the absence of damage and induced resistance in the presence of damage, it is usually not possible to test for a tradeoff between the two types of resistance within individual plants (unless induced resistance is known to be nonsystemic; Zangerl and erenbaum 199). Instead, a resistance tradeoff is usually tested by comparing family or genotype means for the two types of resistance obtained from groups of replicate plants assigned to damaged and control treatments. Thus a strong test for a tradeoff requires that the family or genotype means have been estimated accurately. However two factors, measurement errors (e.g. imprecision in an assay for the concentration of a secondary compound or in trichome counts) and sampling variation (i.e. a limited number of plants per family in control and damaged treatments combined with variability in resistance traits among replicate plants due to environmental factors or uncontrolled genetic variation) collude to introduce uncertainty into estimates of family or genotype means. Unfortunately, this uncertainty biases correlation and regression analyses toward support for the conclusion that a tradeoff exists even when it does not (rett 24). third complication in testing for resistance tradeoffs is that some families or genotypes may actually become less resistant to herbivores following damage (Table 4.2 in Karban and aldwin 1997 and Nykänen and Koricheva 24). s we explain below, this so-called induced susceptibility poses challenges in designing realistic statistical tests for resistance tradeoffs. In this paper, we briefly review metrics of induced resistance that have been used to test for constitutive/ induced resistance tradeoffs, and we advocate the use of a single measure, the difference in mean resistance levels between damaged and undamaged individuals from a given family or genotype. Using this metric, we illustrate the magnitude of the spurious correlation between family means of induced and constitutive resistances produced by measurement error or sampling variation. We then propose a statistical test for a resistance tradeoff that accounts for the influence of measurement error/ sampling variation and for the possibility of induced susceptibility, and we illustrate it using simulated data. Finally, we discuss situations in which the test may be Table 1. Methods and results of studies that used statistical tests expressly to assess whether a tradeoff existed between induced and constitutive resistance. D and C represent the mean resistance in damaged and control treatments, respectively. D and D t represent damage means at times and t, and similarly for C and C t. Other tradeoff studies made qualitative (i.e. non-statistical) comparisons and are not included here (Zangerl and azzaz 1992, Zangerl and Rutledge 1996, Litvak and Monson 1998, Siemens and Mitchell-Olds 1998, Katoh and Croteau 1998, grawal et al. 1999, Havill and Raffa 1999, Ding et al. 2, Ruuhola et al. 21). Comparison Correlation between induced and constitutive resistance Entities compared Resistance trait Reference D/C vs C negative genotypes DHPPG Keinänen et al D/C vs C positive or none phenotypes resin Lombardero et al. 2 D/C * vs C negative families trichomes, glucosinolates Traw 22 D/C * vs C positive, none, and negative various various Koricheva et al. 24 D/C * vs C negative ontogenetic stages hydroxamic acids Gianoli 22 and D/C vs C D/C vs C negative phenotypes polyphenyl oxidases Stout et al D/C vs C none genotypes bioassay /mite population growth English-Loeb et al D/C vs C none species bioassay /mite population growth Thaler and Karban 1997 C/(C/D) vs C negative cultivars bioassay /herbivore feeding preference Underwood et al. 2 1/(C/D)/C vs C positive cultivars bioassay /mite population growth rody and Karban 1992 (D t /C t /D /C ) vs C positive phenotypes alkaloids Johnson et al * These studies tested for a slope less than 1 in a regression of resistance in the damage treatment against resistance in the control treatment, which asks if D/C declines as C increases. 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3 useful in looking for other tradeoffs not involving resistance traits. Which measure of induced resistance should be used to test for a tradeoff? t least three measures of induced resistance have been used specifically to look for tradeoffs between constitutive and induced resistance (Table 1): 1) the induction ratio / that is, the mean resistance in damaged plants divided by the mean resistance in control plants (Johnson et al. 1989, Stout et al. 1996, Koricheva et al. 24); 2) the ratio of the increase in resistance in damaged plants (i.e. the mean resistance in the damage treatment minus the mean resistance in the control treatment) to the mean resistance in control plants (rody and Karban 1992); and 3) the difference in mean resistance between damaged and control plants (Keinänen et al. 1999, Lombardero et al. 2, Gianoli 22, Traw 22). For completeness, we also consider the mean resistance in the damage treatment as a possible metric of induced resistance (Zangerl and erenbaum 199 computed correlations between damage resistance and control resistance, but did not use them to infer tradeoffs). In Fig. 1, we illustrate these four metrics for two genotypes that differ in their levels of constitutive resistance. For two reasons, we claim that two genotypes can be said to have equivalent levels of induced resistance only if they increase their resistance levels by the same absolute amount following damage, as in Fig. 1 and 1. First, as our goal is to assess tradeoffs between induced and constitutive resistance, it is key that we use a measure of induced resistance that accurately reflects its costs to the plant. The cost of producing additional resistance is more likely to be related to the absolute increase in resistance, rather than the proportional increase. That is, an increase in the concentration of a secondary compound from 1 to 2 mg per g of leaf tissue should be more costly to achieve than an increase from.1 to.2 mg g 1 (even though both represent the same proportional increase). Second, the benefit of increased resistance as measured by reduced herbivore feeding is also likely to be better predicted by the absolute level of resistance (again, we expect that a doubling from 1 to 2 mg g 1 will deter herbivores more than will a doubling from.1 to.2 mg g 1 ). ecause the induced response to damage (I) in Fig. 1 and 1 is the same for the two genotypes, there is no tradeoff between induced and constitutive resistance, and a reliable index of induced resistance should show no correlation with constitutive resistance. However, only one of the four measures of induced resistance in Fig. 1C/F shows no correlation with constitutive resistance. The mean resistance of damaged plants has Mean level of resistance trait (e.g., concentration of secondary compound) Induced resistance D=C+I (D C)/C=I/ C Genotype (low constitutive resistance) Control Damage Treatment Measure of induced resistance: Level of resistance in C damage treatment (Damage Control) E Control D/C=(C+I)/ C D C=I Constitutive resistance, C Genotype (high constitutive resistance) Control Damage Treatment the obvious fault that it includes both the resistance induced by damage and the background (i.e. constitutive) level of resistance. s a result, there is a spurious positive correlation between this measure of induced resistance and constitutive resistance (Fig. 1C), against which any negative correlation between the induced response itself and the level of constitutive resistance may be masked. Ratio-based indices (Fig. 1D, 1E) assume that proportional change in resistance is more relevant than absolute change, a view against which we have already argued. Moreover, both the induction ratio (Fig. 1E) and the ratio of the increase in resistance to the control resistance (Fig. 1D) show spurious negative correlations with constitutive resistance (Jasienski and azzaz 1999, Koricheva et al. 24). oth ratios have the mean resistance of control plants as their denominator, so that more constitutively resistant genotypes will tend to have a lower ratio even when induced resistance is equal across genotypes. Only the difference in mean D C Damage Control Damage Control Fig. 1. Four metrics of induced resistance (three of which have been used in the literature on tradeoffs between constitutive resistance and induced resistance) applied to hypothetical data for two genotypes (or family means) for which there is in fact no tradeoff. C (shaded bars) is the resistance of undamaged (i.e. control or constitutively defended) plants, D is the resistance of damaged plants, and I (open bars) is the difference in resistance between damaged and control plants. Letters in (C) /(F) correspond to genotypes in () and (). F I D 14 OIKOS 112:1 (26)

4 resistance between the damaged and control treatments (Fig. 1F) accurately reflects the absence of a tradeoff. rett (24) recently reiterated that relationships of the form Y/X vs X and of the form Y/X vs X will both show spurious correlations when X and Y are uncorrelated. Thus it may at first seem paradoxical that D/C vs C in Fig. 1 shows a spurious correlation but D/C vs C does not. The reason D/C is not spuriously correlated with C, even though it is a function of C, is that D and C are expected to be positively correlated in the absence of a resistance tradeoff. That is, if the induced response is a random variable chosen without regard to C, highly resistant genotypes in the control treatment will on average be just as much more resistant when damaged than will genotypes with low resistance in the control treatment. Therefore the difference in resistance D/C will be uncorrelated with C. The fact that the difference metric of induced resistance would not show a spurious correlation with constitutive resistance if the mean resistances in the damage and control treatments were measured with high precision has not been clearly articulated in the tradeoff literature (Zangerl and erenbaum 199, Gianoli 22, Traw 22). We conclude that the difference in mean resistance between damaged and control plants is the best metric of induced resistance to use when testing for resistance tradeoffs, both because it makes the most biologically defensible assumptions about the costs and benefits of induced resistance and because, when measured accurately, it is not expected to either mask real tradeoffs with false positive correlations (as is the mean level of resistance in damaged plants) or provide false evidence of a tradeoff when one does not exist (as do the ratiobased metrics). Note that an alternative test for tradeoffs used by Traw (22) and Gianoli (22), which regresses mean resistance in the damaged treatment against mean resistance in the control treatment and tests for a regression slope significantly less than 1, also relies on the difference metric of induced resistance, because a slope less than 1 implies that the difference between the damage and control means declines as the control mean increases. The problem of measurement error and sampling variation In the preceding discussion, we have assumed that we could measure perfectly the mean resistances of damaged and control plants in each family or genotype. Of course this is unlikely to ever be true, due to both imprecision in our measurements of resistance traits and variation among individual plants combined with limited sample sizes. oth measurement error and sampling variation will cause estimated mean resistances to vary around their true values. In this section, we address the issue of how measurement error and sampling variation affect tests for tradeoffs that use the difference metric of induced resistance. Imagine two families with identical true mean constitutive resistance and identical true mean induced resistance. We randomly assign replicate individuals of both families to damage and control treatments and estimate mean resistances in all four genotype/treatment combinations. For simplicity, assume that the estimated mean values for both families in the damage treatment happen to equal exactly the true mean, but that in the control treatment, our sample happens to overestimate the mean resistance for the first family and underestimate it for the second family. When we now estimate induced resistance by subtracting the estimated control mean from the estimated damage mean, our estimate for the first family will be an underestimate of the true induced resistance, while the estimate for the second family will be an overestimate. This combination of an underestimated induced resistance with an overestimated constitutive resistance and vice versa will cause the estimated correlation between the induced and constitutive resistances to be negative, even though the true correlation is zero. The approach of regressing the mean resistance of damaged plants against the mean resistance of control plants and testing for a slope less than 1 (Gianoli 22, Traw 22) was proposed as a way of sidestepping spurious relationships created by the fact that control resistance is used to measure both constitutive resistance and the induced resistance increment. However, this approach is subjected to a bias of a different sort. Standard (i.e. model I) linear regression assumes that the independent variable is measured without error. Errors in the estimate of mean resistance of control plants due to measurement imprecision or sampling variation will cause the slope of a linear regression to be biased towards zero (Snedecor and Cochran 198, pp. 171/172), but this is precisely the direction in which the tradeoff hypothesis predicts that the slope should lie. We performed Monte Carlo simulations to gauge how sample size and degree of variation among replicate plants (due to measurement error, uncontrolled environmental or genetic factors, or both) would affect the likelihood of obtaining spurious evidence of a resistance tradeoff. Specifically, we simulated data for all combinations of 2, 4 or 8 families, 4, 8, 16 or 32 plants per family per treatment, and levels of measurement error/ sampling variation (as measured by the coefficient of variation (standard deviation }/ mean) among replicate plants within families and treatments) ranging from to 1 in units of.1. These parameter values lie within the ranges seen in actual resistance tradeoff studies (Table 1). OIKOS 112:1 (26) 15

5 For each run of the simulation, we first drew a true constitutive resistance level for each family from a lognormal distribution (which is bounded below by zero, thus avoiding negative constitutive resistances). We then drew a true induced resistance for each family from a separate lognormal distribution (the means and variances of these lognormal distributions were chosen to reflect actual resistance traits). s the constitutive and induced resistances were drawn independently from separate distributions, there was on average no correlation between them; the simulated data do not contain a tradeoff. We added the true induced resistances to the true constitutive resistances to obtain the true family mean resistances for the damaged treatment. Then, to mimic the sampling/ measurement process, we drew from a lognormal distribution a resistance measure for each of the required number of replicate plants for each family/ treatment combination, with the appropriate true mean and coefficient of variation among replicate plants. We used each sample data set to compute the among-family correlation between induced resistance (mean of damage treatment minus mean of control treatment) and constitutive resistance (mean of control treatment), as well as the slope of a linear regression of damage means against control means. We repeated this entire procedure 5 times for each combination of number of families, number of plants per family per treatment, and coefficient of variation among replicate plants, and we took the 5th percentile of the resulting distributions of correlation coefficients and regression slopes to represent the minimum values of these tradeoff measures that were likely to arise purely by chance where there was in fact no tradeoff. When an induced resistance experiment involves relatively few families and few replicate plants per family per treatment, and when the degree of variability among replicate plants is high, quite strong negative correlations between estimates of induced and constitutive resistance can arise by chance when no tradeoff exists (Fig. 2). For example, with only 2 families and 4 plants per family per treatment, and a coefficient of variation of 1 among replicate plants, there is a 5% probability of observing a spurious correlation as or more negative than /.7. Measurement error/sampling variation also affects the slope of a regression of family mean resistance in the damaged treatment against family mean resistance in the control treatment; slopes substantially less than 1 can arise by chance in the absence of a tradeoff (Fig. 2). lso notice that even when replicate plants within families do not vary (CV/), negative correlations and slopes less than 1 will often arise by chance, especially when there are relatively few families, simply because the families chosen for an experiment poorly reflect the lack of a tradeoff in the larger population. Fifth percentile of correlation coefficients Fifth percentile of regression slopes etter tests for resistance tradeoffs Given the results in Fig. 2, how can we use experimental data from damage and control treatments to assess resistance tradeoffs while minimizing the potentially misleading effects of measurement error and sampling variation? In this section, we propose two solutions. ( third solution, the use of ayesian hierarchical models (Carlin and Louis 2), is beyond the scope of this paper.) The first solution is to modify the standard tradeoff experiment to include twice as many plants per family in the control treatment as in the damage treatment. One could then use the damaged plants and half of the control plants (randomly chosen) to compute the difference metric of induced resistance and the other half of the control plants to estimate constitutive resistance for each family, and then compute the among-family correlation between induced and constitutive resistance. ecause the sampling/measurement errors of the two control groups should be independent, overestimation of constitutive resistance will not always be accompanied by underestimation of induced resistance, and vice versa, so the expected correlation would be zero in the absence of a tradeoff. The obvious downside of this solution is that it increases the number of replicate plants per family by 5%, at potentially substantial cost given that the numbers of families Coefficient of variation among replicate plants within family x treatment combinations 2 families 4 families 8 families Fig. 2. Minimum values (5th percentiles) of the correlation coefficient (difference between means of damage and control treatments vs. mean of control treatment) and regression slope (damage means vs control means) likely to arise by chance when there is no tradeoff between induced and constitutive resistance, for different levels of experiment size and measurement error/ sampling variation (as represented by the coefficient of variation among replicate plants). Within each panel, lines from bottom to top correspond to 4, 8, 16 or 32 plants per family per treatment. 16 OIKOS 112:1 (26)

6 should still be kept as large as possible to adequately sample the entire population. second solution is to perform a randomization test using the experimental data. For motivation, we briefly describe a simple randomization test, but we then go on to explain why induced susceptibility poses difficulties for this simple test. simple randomization test would be performed as follows: 1) draw with replacement sets of n plants from the damage and control treatment for each family (where n is the number of plants per family per treatment in the original experiment; this step accounts for sampling variation in the estimation of family means); 2) compute the constitutive resistance (i.e. mean resistance of plants in the control treatment) and induced resistance (i.e. mean resistance of plants in the damage treatment minus mean resistance of plants in the control treatment) for each family; 3) randomly reassign induced resistances among families to break any association between constitutive and induced resistance; 4) compute and store the among-family correlation between the estimated constitutive resistances and the re-assigned induced resistances; 5) repeat the preceding steps many times and make a histogram of the resulting correlation coefficients; the lower 5th percentile of this distribution is the most negative correlation likely to arise by chance when there is no tradeoff. Unfortunately, this simple approach will be precluded in most cases by the biological constraint that most resistance traits (e.g. concentration of secondary compounds, leaf toughness, trichome density) cannot take negative values. If a family shows induced susceptibility (i.e. lower mean resistance in the damage treatment than in the control treatment), its difference measure of induced resistance will be negative. Randomly assigning an induced resistance of /X to a family whose constitutive resistance is smaller than X would produce the biologically unrealistic outcome of negative resistance in the damage treatment. If we allowed the randomization procedure to generate negative values for resistance traits, we would then be using simulated data sets that could never be observed in the real world to judge the likelihood that the observed correlation between the two resistance types arose by chance. Even if none of the induced resistances estimated from the original data are negative, step 1 of the procedure described above can produce lower mean resistance in the damage treatment than in the control treatment, and therefore the possibility of negative resistance values when induced resistances are reassigned among families. To avoid negative resistance values, we devised the following Monte Carlo procedure as an alternative to the simple procedure described above (MTL code to perform the Monte Carlo procedure is available from the first author): 1) compute the (grand) mean and variance of the family mean resistances in the control treatment; these estimate the true population mean and among-family variance of constitutive resistance. 2) Compute the mean and variance across all families of the difference in family mean resistance in damage vs control treatments; these estimate the true population mean and among-family variance of induced resistance. 3) Draw a population-level mean and variance for constitutive resistance from their respective sampling distributions, and then from a lognormal distribution with this mean and variance draw a constitutive resistance value for each family, equal to the number of families in the original experiment. Use of the lognormal distribution ensures that all constitutive resistances are non-negative. The smallest of these values (call it C min ) represents the largest absolute value of induced susceptibility that will avoid negative resistances when induced resistance values are randomly assigned among families. 4) Next, draw a population-level mean Ī and variance V for induced resistance from their respective sampling distributions, and then draw an induced resistance I for each family as I/L{/Ī/C min,v}/ C min, where L{a,b} represents a random number drawn from a lognormal distribution with mean a and variance b. The resulting values of I will follow a shifted lognormal distribution with mean, variance, and minimum value of Ī; V, and /C min, respectively. We have thus preserved the estimated among-family mean and variance of induced resistance while allowing for the maximum level of induced susceptibility consistent with the requirement that all resistance measures be non-negative. ecause constitutive and induced resistances are drawn independently in steps 3 and 4, there is no tradeoff. dd the induced resistance (which may be negative) to the constitutive resistance for each family to get the expected resistance in the damage treatment. 5) Now draw resistances for the replicate plants in a family from two lognormal distributions, one for the control and one for the damage treatment. The coefficient of variation for these distributions is estimated by the variability among replicate plants within treatments in the experimental data (here we average the coefficients of variation for damage and control treatments, but one could allow them to differ if there is reason to believe that one treatment will be more variable than the other). This step mimics real variation among replicate plants and/or measurement error. 6) Finally, compute for all families the mean resistance from the control and damage samples, the OIKOS 112:1 (26) 17

7 difference measure of induced resistance, and the correlation between constitutive and induced resistance. Repeat this entire procedure many times and identify the lower 5th percentile of the resulting distribution of correlation coefficients as the most negative correlation likely to arise by chance when there is no tradeoff. To illustrate these tests, we produced simulated data with a constitutive/induced resistance tradeoff using the parameters in Table 2 (Fig. 3). Note that some of the simulated families show induced susceptibility. The means of replicate plants (Fig. 3) show a more negative correlation between (estimated) constitutive and induced resistance than do the true family resistances in Fig. 3, due to the spurious influence of sampling variation. Similarly, the slope of a least squares linear regression of damage vs control means is biased toward zero by sampling variation (compare Fig. 3C and 3D). We applied the Monte Carlo procedure described above to produce the distribution of estimated correlations between induced and constitutive resistance for 1 random data sets shown in Fig. 4. Note that the range of correlations that can arise by chance is fairly wide. The mean correlation coefficient is negative, reflecting the spurious correlation generated by sampling variation. In fact, with 5 families and the family means and variances, sample sizes, and level of sampling variation in Table 2, there is a 5% probability that a correlation coefficient of /.36 or lower will arise by chance in the absence of a tradeoff. However, only one of the 1 random data sets produced a correlation as low or lower than the observed value of /.63. s the probability that this value would arise by chance is thus approximately 1 4, the test successfully detects the tradeoff. Table 2. Parameters used to simulate data with a tradeoff between constitutive and induced resistance. Parameter Value Number of families 5 Expected correlation between log constitutive /.5 resistance and log induced resistance mong-family mean constitutive resistance 1 mong-family variance in constitutive resistance 5 mong-family mean induced resistance 25 mong-family variance in induced resistance 5 Minimum induced resistance /25 Number of replicate plants per family per 8 treatment Coefficient of variation in resistance among.3 replicate plants within family/treatment groups Distribution of family mean constitutive and Lognormal induced resistance, and of resistance of replicate plants within family/treatment groups Induced resistance Induced resistance Constitutive resistance Constitutive resistance Discussion Resistance (control) The use of different measures of induced resistance, the inevitability of measurement errors and sampling variation, and the possibility of induced susceptibility have all Resistance (damage) Resistance (damage) Resistance (control) Fig. 3. Simulated data (Table 2) used to illustrate the Monte Carlo test for a tradeoff between constitutive and induced resistance. () True family means show a tradeoff between induced and constitutive resistance. () Means computed from one randomly chosen set of 8 replicate damage and 8 control plants per family. (C, D) The same values from (, ) plotted as damage vs control means. least squares regression line (solid) has a slope substantially less than the slope of the 1:1 line (dashed), but the least squares regression slope is biased toward zero by sampling variation (compare the slopes of the regression lines in (C) and (D)). lso note that the correlation coefficient r is more negative in () than in (). Number of replicates Correlation coefficient Fig. 4. Distribution of the correlation between constitutive and induced resistance in 1 Monte Carlo data sets based on the simulated data in Fig. 3. See text for details on the Monte Carlo procedure. Dashed line indicates the position the lower 5th percentile of the distribution, and the solid line indicates the observed correlation. C D 18 OIKOS 112:1 (26)

8 complicated the testing of a hypothesized tradeoff between constitutive and inducible resistance traits in plants. In particular, use of ratio-based indices of induced resistance (Fig. 1D, 1E) and measurement error/sampling variation (Fig. 2) tend to produce evidence for tradeoffs when they do not exist. We have argued that the difference measure of induced resistance (Fig. 1F) avoids spurious correlations between constitutive and induced resistance that other measures would produce even if resistance traits could be measured precisely and replicate plants did not vary, and we have proposed a statistical test that allows for both measurement error/sampling variation and induced susceptibility. Monte Carlo tests allow for the fact that most resistance traits (e.g. trichome density, secondary chemical concentration) cannot be negative, and so their distributions may not be normal (as, for example, linear regression models assume). Here, we have both simulated data and performed Monte Carlo tests assuming that resistance traits are lognormally distributed, but our procedure can easily be modified to use any other probability distribution that better fits a particular experimental data set. We constructed our Monte Carlo test so that no family could show induced susceptibility greater in absolute value than the lowest constitutive resistance of any family. This constraint is consistent with the absence of a tradeoff. Even though families with higher constitutive resistance could show a greater decrease in resistance following damage than less constitutively resistant families without producing negative resistance values, such a pattern would indicate that higher constitutive resistance comes at a cost of greater induced susceptibility, i.e. that there is a resistance tradeoff. Given the complications we have raised here, we conclude that to this date, the experimental tests of a tradeoff between induced and constitutive resistance have been incomplete. Some of the negative correlations in Table 1 may have resulted simply from the choice of metric for induced resistance, or from the spurious effects of measurement errors or sampling variation. re-analysis of the apparent tradeoff reported by Traw (22) will be reported elsewhere. However, the positive correlations in Table 1 cannot result from the use of an inappropriate measure of induced resistance. Instead, they may reflect positive correlations between both resistance traits and the overall amount of resource a plant can acquire (van Noordwijk and de Jong 1986), a realistic possibility that confounds the search for tradeoffs between any two traits. lthough our focus here has been on understanding patterns in plant defense, the statistical approach we advocate can be applied in testing for tradeoffs involving the plasticity of any trait (especially those that have only non-negative values). In particular, whenever plasticity measured as the difference in a trait between two environments is compared to the value of that trait in one environment, the potential effects of measurement error or sampling variation (Fig. 2) need to be considered. For example, in global change studies, researchers sometimes correlate the difference in growth between elevated and ambient CO 2 conditions to growth under ambient CO 2 (Norby et al. 21, Yin 22). Due to an increased interest in trait plasticity in other fields of ecology, the solutions we discuss here are likely to be widely applicable. cknowledgements / This research was supported by NSF grant DE-8796 to WFM, a grant from the Dropkin Foundation to MT, and NIH grant GM 6254 to J. The authors thank. grawal for comments. References grawal,.., Gorski, P. M. and Tallamy, D. W Polymorphism in plant defense against herbivory: constitutive and induced resistance in Cucumis sativum. / J. Chem. Ecol. 25: 2285/234. rett, M. T. 24. When is a correlation between nonindependent variables spurious? / Oikos 15: 647/656. rody,. and Karban, R Lack of a tradeoff between constitutive and induced defenses among varieties of cotton. / Oikos 65: 31/36. Carlin,. P. and Louis, T.. 2. ayes and empirical ayes methods for data analysis, 2nd ed. / Chapman and Hall. Ding, H., Lamb, R. J. and mes, N. 2. 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