An indirect approach to imply trade-off shapes: population level patterns in resistance suggest a decreasingly costly resistance mechanism in a model insect system


Mike Boots, Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK.
Tel.: +44 0114 222 0054; fax: +44 114 222 0002;


Trade-offs between life history and other traits play a key role in shaping the evolution of individuals. It is well established theoretically that the shapes of trade-off curves are as crucial to the evolutionary outcome as their strengths. However, measuring the shape of these relationships directly is often impractical. Here we use an indirect approach that examines the patterns seen within a population and then use theory to infer the shape of the trade-off curve. Using a bioassay we found that most individuals had either high susceptibility or relatively high resistance to a microparasite in a lepidopteran host population. According to general theory, this type of pattern in resistance would be most likely with a deceleratingly costly impact on fitness of increasing resistance. The implications and generality of the approach are discussed, along with the implications of the results to our understanding of the nature of innate resistance to parasites.


A central idea in life-history theory is that the evolution of particular fitness traits may be constrained by trade-offs with other life history traits (Roff, 2002). Furthermore, a key prediction of life-history theory is that the evolution of a particular trait is not just the result of the absolute strength of a trade-off but it is also critically dependent on the functional form of the trade-off relationship (Roff, 2002). The recent advent of adaptive dynamical evolutionary theory has further emphasized the importance of how costs and benefits change under different conditions (Geritz et al., 1998; Bowers & White, 2002). This adaptive evolutionary theory takes into account that trade-off relationships are unlikely to be exactly linear and that the shape of the correlation is important in determining the ultimate evolutionary outcome. In particular, the way in which the costs and benefits vary determines both the convergence stability of the evolutionary system and whether evolutionary branching will occur (Boots & Haraguchi, 1999; Bowers & White, 2002). Despite the importance of the shape of the trade-off curve there are few, if any, empirical studies that have accurately estimated its form (Roff, 2002). A detailed and rigorous measurement of these curves can therefore be seen as a key objective of evolutionary biology.

Direct estimation of these shapes is possible through, for example, a replicated set of selection experiments at different resource levels (Stearns, 1992). However, the scale of these experiments makes them impracticable in most systems. Here we take an indirect approach. We examine the patterns of variation at a population level and use these to infer the general shape of cost structures by relating the results to a theoretical model. This approach is useful because measuring phenotypic variation at the population level is relatively straightforward. If theoretical models can be constructed that predict the population level variation that would result from different cost structures, this variation can be used to infer the shape of the trade-offs. Clearly, the usefulness of this approach will depend on the quality of the theory, which will in turn be determined by the knowledge of the genetic basis of the traits concerned.

We use this indirect approach to examine the pattern of resistance to a parasite within a laboratory model insect system. We then relate this to existing general theory on the evolution of resistance (Boots & Haraguchi, 1999) that predicts the patterns of variation in resistance likely with particular shapes of trade-off curves. Boots & Haraguchi (1999) found that if the shape of the trade-off curve is (Fig. 1a) such that resistance is acceleratingly costly, then the population level pattern of resistance would be expected to be distributed around an optimal ESS resistance level that depends on the life history of the host (Fig. 1b). If costs reduce as resistance increases (Fig. 1a) in contrast, we may find maximal, minimal or dimorphic patterns in resistance, with individuals in the population having either low or high levels of resistance (Fig. 1b). Our aim is to imply the shape of the trade-off structure by quantifying the variation in the population and using theory to predict which shapes are likely to lead to the observed pattern.

Figure 1.

Trade-off curves and the pattern of variation. (a) Two potential trade-off curves, an exponential curve with the cost to fitness increasing with the level of resistance displayed by the individual and an asymptotic curve with the cost to fitness decreasing with the level of resistance. (b) The resulting pattern of variation with populations, an exponential trade-off producing a gaussian variation around an optimal evolutionarily stable strategy and an asymptotic trade-off producing bimodal variation.

Materials and methods

Plodia interpunctella (Hübner) is a well-studied phycitid lepidopteran. The larval stage is vulnerable to the granulosis virus (PiGV), a pathogen belonging to the family Baculoviridae. There is evidence of a trade-off between increased resistance and other life-history traits with resistant cohorts taking longer to develop and producing fewer viable offspring when compared to susceptible individuals (Boots & Begon, 1993). In order to assess the pattern of resistance to infection within the population, individuals were challenged at a wide variety of doses. Bioassays were carried out using a similar technique to the one described in Vail & Tebbets (1990). The virus was prepared through diluting a stock supply with sterile distilled water (SDW). Twelve doses of the virus were administered through thoroughly mixing 4 mL of diluted virus into 20 g of food. The 12 doses were 0.01, 0.03, 0.05, 0.1, 0.3, 0.5, 1, 3, 5, 10, 30 and 50 μg g−1, providing a range of viral challenges to the host. Fifty first instar larvae were placed into each diet/dose mixture and resistant individuals were counted as they emerged as adults. We carried out five replicates consisting of the 12 dose levels and one control assay (with only SDW). The larvae were maintained at 27 °C in a 16 h light: 8 h dark regime. The food was a mixture of 800 g baby food (Boots Company PLC, Nottingham, UK), 160 g brewers yeast, 200 mL glycerol, 200 mL organic honey, 1.2 g sorbic acid and 1.2 g methyl paraben.

Within the bioassays, individuals are challenged with different average doses of the virus. In all cases the density of individuals within the individual bioassays is relatively low so that there is little intraspecific competition and since the only difference between the pots is the concentration of the virus, differences in mortality relate to deaths due to infection. This form of virus challenge replicates the situation in nature more closely than direct challenge with the virus, although it suffers from more variability in the response. It does have the advantage over direct challenge that additional components of resistance, including behavioural ones, are also examined. In addition, the laboratory resources required to carry out the different types of bioassays are such that our technique allows more doses and higher replication to take place.


In order to determine the pattern of resistance in the population, we use logit analysis, which produces equivalent results to probit plots (Crawley, 2002). The pattern of variation can then be determined directly from the shape of the logit plot using well developed methodology commonly used in pharmacological studies (Eichelbaum & Woolhouse, 1985; Vessel & Gaylor, 1995). The linearity of the probit plot is used to determine the pattern of variation, with linear plots corresponding to a normal (gaussian) pattern of variation while nonlinearities can be associated with other patterns (Penno & Vesell, 1983; Nakamura et al., 1985). Jackson et al. (1989) randomly generated data describing a range of patterns of variation, including normal, lognormal and bimodal distributions and from these data they found the corresponding shape of the probit line.

This method of analysis is rapid and powerful, but we also provide for comparison an analysis that is more common in the ecological literature. Analysis on the full data set led to nonnormal residuals from the best-fit second polynomial and non-binomial errors with logit plots. It is therefore difficult to interpret the P values because the data contravenes the requirements of both models. Outlying data points were removed carefully so that it would be possible to use the same data set for both the logit and the polynomial regression. Cook's distance plots showed which points were outliers, and models with and without these data points were compared to see if the outliers were having a significant effect on model output. Using analysis of variance to compare models, seven outliers were removed. This allowed the residuals to be normally distributed and the variance to be less inhomogeneous, so improving the polynomial regression. The same data were also shown to be binomially distributed in the logit analysis, reducing the degree of overdispersion.

The results of the five-bioassay replicates are presented in Fig. 2. Blocking analysis shows no relationship between the shape of the data and the replicated blocks (F4 = 1.028, P = 0.403). The results of the logit regression are shown in Fig. 2a. A cubic polynomial logit regression gives the best fit (T49 = −3.05, P < 0.05). The slope of this regression line is steepest at very low and very high virus concentrations, and is relatively flat at intermediate dose ranges. According to the previously discussed work of Jackson et al. (1989), this line corresponds to a bimodal pattern of resistance (Fig. 1b).

Figure 2.

(a) Logit analysis of the bioassay data. The cubic polynomial regression equation is Y = 0.172 − 3.92X − 1.38X2 − −0.928X3 (49 d.f., t value = −2.1393, P = 0.0374). The regression lines’ steepness over low and high dose ranges indicates that the pattern of variation is bimodal (Jackson et al., 1989). (b) The proportion resistant to each dose level, replicated five times. The cubic regression through this data (49 d.f., t value = −2.139, P = 0.0374) is a better fit than a quadratic regression (maximum likelihood, L. Ratio = 5.088, P = 0.0241) and is not significantly different to a quartic regression (L. Ratio = 1.372, P = 0.2415). The equation for the line is Y = 0.543 − 0.931X + 0.238X2 − 0.162X3. The shape of the slope also indicates a bimodal pattern of variation within the population (see Results).

The second form of statistical analysis also reveals a bimodal shape of variation. Figure 2b shows the proportion of individuals surviving a viral challenge over a range of doses. The cubic regression line fitted to this data explains 77% of error and maximum likelihood analysis shows that the cubic is a significantly better fit than the quadratic (L. Ratio = 5.088, P < 0.05) and is not different to the quartic (L. Ratio = 1.372, P = 0.2415). The slope of the cubic regression line can be used to determine the proportion resistant over the dose range of the experiment, assuming that individuals resistant to one dose are also resistant to all doses below it. The line slopes steeply through the low dose region of the graph, which means that there are a high number of individuals with their maximum level of resistance at low doses. Over intermediate doses, the slope levels off, signifying that the individuals resistant to these doses are also resistant to higher doses. As such there are few individuals with a level of resistance in this intermediate dose range. At high dose ranges the slope once again declines, indicating that there is another distinct proportion of the population susceptible only to these higher doses. Both methods of graphical interpretation therefore reveal a significant bimodal pattern of resistance within the population of P. interpunctella. In both analyses, jack-knifing and bootstrapping of the coefficients of the nonlinear regressions both show that the fits are robust.


Resistance towards a granulosis virus in P. interpunctella has previously been shown to carry a cost (Boots & Begon, 1993). The aim of this study was to infer the shape of this trade-off curve by examining the population level variation in resistance and asking what trade-off shapes are theoretically expected to lead to this pattern. An extensive bioassay indicated that there was a dimorphic pattern of resistance, with most individuals possessing either a low or high level of resistance and very few with an intermediate level (Fig. 2). This pattern is possibly caused at least in part by the shape of the underlying resistance cost structure. According to general evolution of resistance theory (Boots & Haraguchi, 1999), a bimodal pattern of resistance relates to trade-off where resistance becomes deceleratingly costly (Fig. 1a).

The concept of trade-offs existing between different components of life history is a fundamental aspect of evolutionary ecology, yet the exact nature of such trade-off relationships is very difficult to find empirically (Stearns, 1992). This paper, in conjunction with previous theory (Boots & Haraguchi, 1999), suggests that the shape of the resistance trade-off curve can be inferred from patterns of variation in resistance within a population that is easily estimated by standard bioassay techniques and simple logit regression analysis. Theory predicts that particular patterns of resistance within a species are generated by specific trade-off curve shapes and that these are fundamentally determined by the mechanism of resistance (Boots & Haraguchi, 1999). Another advantage of estimating the cost structure of resistance using these methods therefore is that we can also gain insights into the mechanisms of resistance within the host. Relatively little is known about the underlying resistance mechanisms that invertebrates use in response to viruses. Many of the mechanisms that have been suggested from the simple thickening of mechanical barriers such as the gut wall or the sloughing of infected gut wall cells (Washburn et al., 1998) might be expected to become acceleratingly costly (Boots & Haraguchi, 1999) and would therefore not fit the pattern suggested here. One mechanism that may fit is the humoural and cellular responses where costs associated with phenyloxidase may be increasingly mitigated by the recruitment of haeomocytes leading to a decreasingly costly response. The costs associated with phenoloxidase activity are the production of toxic quinones and oxygen species, which may damage the host's own tissues (Nappi et al., 1995; Slepneva et al., 1999). However, these costs can be minimized by the haemocyte capsule, which might be a means by which such toxins are directly targeted at the infected cell (Russo et al., 1996). As more haemocytes capsules are formed, more toxins should become targeted at the infected cell, and away from healthy tissues. Such limitation of damage from quinones and oxygen species may mean that the relative costs of increasing phenoloxidase production would decrease, and so the fitness trade-off curve may match the asymptotic one found in this study (Fig. 1a). It should be emphasized that this argument is somewhat speculative in this system, but the ability to link mechanisms that underlie costs to the shapes of trade-offs that they may produce may prove useful in many systems where these mechanisms are better understood. Encapsulation of virus particles by haemocytes has also been suggested as a resistance mechanism in insects (Washburn et al., 1996) including our system (Begon et al., 1993). Understanding the implications of this and other mechanisms for the shape of the resistance cost relationship is likely to be helped by detailed within host models of the immune interaction.

The indirect nature of these concepts means the methodology requires careful application and interpretation. In the laboratory system used in this paper, the expression of host resistance is a quantitative trait rather than a product of a qualitative gene-for-gene interaction. If resistance was a qualitative trait, any within-population variation may be a product of the ratios of corresponding host and pathogen genes, rather than phenotypic variation resulting from the shape of the trade-off curve. Another important qualification is in the interpretation of the variation found, which could possibly result from nonlinear relationships between pathogen dose and infection generated through transmission and virulence thresholds of the virus rather than host resistance.

For clarity, this work has focused on trade-offs with resistance to parasites. However, the approach taken in this paper may represent a method for studying the shape of the trade-off curves in a wider context. The approach of using theory to predict patterns that arise from particular cost structures and then examining the patterns directly at the level of the population potentially has wide applicability. Indeed, recent general theory (Bowers & White, 2002) suggests that the curvature of trade-off functions, interpreted in terms of accelerating or decelerating costs, is crucial to the evolutionary outcome in a wide range of situations. Measuring trade-off curves directly will always be difficult, but tightly controlled examinations of population level variation may help us understand fundamental selective pressures.


MM was funded by a NERC studentship, MB by a NERC fellowship. Dr Patrick Vail (USDA-Fresno) supplied the virus and Dr Steve Hubbard (University of Dundee) donated the P. interpunctella. Comments from Jens Rolfe and the anonymous referees improved the manuscript.