The effects of group size, leaf size, and density on the performance of a leaf-mining moth

Authors


Correspondence author. E-mail: c_low@lifesci.ucsb.edu

Summary

  • 1The effects of two factors, leaf size and group size, on the performance of the Tupelo leafminer, Antispila nysaefoliella (Lepidoptera: Heliozelidae), were examined by fitting growth models to mine expansion data using nonlinear mixed-effects models.
  • 2The rate of mine expansion served as a proxy for larval performance because of its correlation with both feeding activity and growth rate and is also the means by which a larva achieves its final mine size (or total consumption).
  • 3Leaf size was used as a measure of resource availability, and was expected to reduce the impact of resource competition and enhance larval performance.
  • 4In contrast to the unidirectional effects expected for leaf size (i.e. more resources should enhance performance), the direction for the effects of group size was expected to depend on the mechanism(s) driving the effect. For example, if there is resource competition among larvae in a group, then this could increase the feeding rates of some larvae or reduce the total consumption of others. However, if leaf mining induces host plant chemical defences, then larger groups might elicit a greater defensive response by the host plant (at the leaf), and hence, be characterized by reduced feeding and growth rates.
  • 5To investigate these interactions, two growth models, the Gompertz model and a modified version of the von Bertalanffy growth equation, were fitted to time series of the sizes of individual leaf mines using nonlinear mixed-effects models. Linear and nonlinear associations of each factor (group size or leaf size) with model parameters were then evaluated using a hierarchical testing procedure by determining: (i) whether inclusion of the factor produced a better-fit model, and (ii) if it did, the form of that relationship (i.e. linear or nonlinear).
  • 6Three patterns were detected with these analyses. (i) Leaf size had a significant positive, linear relationship with mine expansion rate. (ii) Group size had a significant quadratic relationship with mine expansion rate. (iii) The effects of leaf and group size on the maximum mine size were opposite to those found with growth rate.

Introduction

Many of the traits and behaviours of organisms are shaped both by the process of selection and also by constraints and costs (Arnold 1992; Stearns 1992; Sih & Gleeson 1995). Thus, one task for researchers aiming to predict the direction of evolution is to quantify the observed natural variation in traits and then separate the contributions of different factors (e.g. Crespi 1990; Endler 1992; Kingsolver, Gomulkiewicz & Carter 2001a; Kingsolver et al. 2001b). For example, across a wide variety of insect–plant systems, both of the players involved have become ecologically and evolutionary tuned to the other, and thus, often display some degree of specialization (Price et al. 1980; Roitberg & Isman 1992; Bernays & Chapman 1994; Schoonhoven, van Loon & Dicke 2006). However, despite the expectation that selection should reduce much of the phenotypic variation in a population, a great deal of variation often remains. As a consequence, sorting through the factors that govern, or might explain, the fitness or performance of an individual organism within its environment becomes a difficult task.

Most commonly, carefully designed experiments are conducted to isolate and test the effects of the factor(s) of interest, and any remaining individual variation is then encapsulated by the error term and is considered to be ‘noise’ which is more of a problem than part of the hypothesis. However, this residual variation can be useful in fitting models to large sets of observational field data. A class of models that does exactly this are mixed-effects models where terms for both fixed and random effects are specified (Pinheiro & Bates 2000). In this study, we used mixed-effects models to analyse a large set of observational data on the feeding activity and performance of an herbivorous insect.

The goal was to evaluate the influence of two factors, group size and leaf size, on naturally occurring patterns of mine expansion rates in the Tupelo leafminer, Antispila nysaefoliella Clemens (Lepidoptera: Heliozelidae). The size of a mine is a direct measure of consumption, and we used the rate of mine expansion as a proxy for larval performance because of its positive correlation with both feeding activity and growth. Furthermore, it is the means by which a larva achieves its total consumption and mass before pupation. We chose to focus on feeding rate because we expected it to be highly sensitive to differences in resource quality, resource availability, and subsequent competitive interactions. In addition, because leaf mining is a form of herbivory, we expected that any induced defences by the host plant would be targeted directly at reducing the rate of herbivory, or the rate of mine expansion. Similarly, any stimulatory effects should also be reflected by increases in mine expansion rates.

First, we expected that group feeding could lead to either negative or positive effects depending on the mechanism. If herbivory alone can induce a defensive response by the host plant, then group feeding might only intensify this response and lead to a reduction in larval performance, or mine expansion rate, as a consequence (Karban & Baldwin 1997; Thaler 1999). On the other hand, group feeding may also increase mine expansion rate by increasing larval performance through host plant enhancement (Denno & Benrey 1997; Fordyce & Agrawal 2001; Fordyce 2003; Inouye & Johnson 2005) or more effective thermoregulation (Klok & Chown 1999; Bryant, Thomas & Bale 2000; Reader & Hochuli 2003).

Second, variation in feeding rates may also be due to behavioural modifications in response to resource competition. When resources are limited, individuals in a group are essentially locked in a race to consume enough or as much resources as possible to meet nutritional demands and to maximize fecundity (Awmack & Leather 2002). Thus, the larger the group, the more intense the competition may be (Faeth 1991; Connor & Beck 1993).

Finally, any detectable group size effects must also be considered within the context of leaf size, which may cause biases in leaf selection by females for oviposition either because larger leaves are easier to locate (via random chance) or they have greater nutritional content (Whitham 1978; Bultman & Faeth 1986; Damman & Feeny 1988; Connor et al. 1997; Roslin et al. 2006; Gripenberg et al. 2007). For example, if oviposition is biased towards large leaves, then individuals in large groups might be feeding and developing on leaves with more resources on average than those in small groups (Roslin et al. 2006; Gripenberg et al. 2007). Moreover, if large leaves support more larvae, then competition would, in effect, become less of a problem in general. Therefore, in order to evaluate the effects of competition alone, the density of larvae (per unit leaf area) may be the more appropriate measure for evaluating performance.

In short, using mine expansion rate as a proxy for the larval response, we ask what is the influence of group size and leaf size on larval performance? Because the effects of leaf size or group size are likely to vary between individuals and between leaves, we fit nonlinear mixed-effects models to time series of sizes of individual leaf mines using the Gompertz growth equation and a modification of the von Bertalanffy equation to answer this question. We discuss the implications of our results within the context of how selection may act simultaneously on oviposition strategies of females and the feeding strategies of larvae.

Materials and methods

study system and natural history

A. nysaefoliella is a leaf-mining moth that specializes on the leaves of black gum, Nyssa sylvatica Marsh (Cornaceae), which is a tree species that is distributed throughout the south-eastern United States. The study site is located within a deciduous forest in the northern Shenandoah Valley, Virginia (39°00·85′ N, 78°03·88′ W). Mines appear in early fall (late August to early September) and larvae feed for approximately 3 weeks. The mines of A. nysaefoliella are blotch-shaped and tend to expand radially and typically become more oblong-shaped at later instars. At the final instar, when feeding ceases, the larva positions itself at the mine periphery and forms an oval-shaped double-sided shield (c.5 mm, major diameter length) by encasing itself with silk between the upper and lower mine layers. While sandwiched inside, the larva cuts the shield away from the leaf, and then, descends into the leaf litter for pupation while remaining inside the enclosed shield. At this point, the leaf is left with an empty mine and a very distinctive ‘punch hole’ shaped by the shield that was once there. Once a larva begins forming the shield, it has finished feeding and will drop from the leaf within approximately 15–30 min. Mine density has been observed to range from 1 to 48 mines per leaf and from 0·02 to 0·8 mines per cm2 leaf area (C. Low, unpublished data 2001–06).

sampling design and data

Leaves from four similarly sized trees with a wide range of group sizes (1–48 mines per leaf) were sampled on 20 August 2004 when mines first began to appear and were approximately 1–2 mm in diameter. In the final analyses, there were 6 (1), 8 (2–4), 14 (5–10), and 15 (11–48) leaves in each group size category (in parentheses), which ranged in size from 14·9 to 85·1 cm2 and were 45·2 ± 16·2 cm2 on average (± 1 SD). Individual leaves were identified by a small piece of white labelling tape folded loosely around the petioles, and individual mines by a comparison of digital images taken of each leaf on nine dates (20 August to 13 September 4): Julian days 230, 236, 240, 243, 246, 248, 250, 252, and 254. The areas of every mine and leaf were then measured using sigmascan pro 5·0 (Systat Software Inc., San Jose, CA).

Only 7% of all mines surveyed appeared after the second sampling date (Day 236), and only those mines that were present on the initial sampling date (day 230) were used in the analysis. In addition, of the mines that were present on day 230, only the mines of larvae that survived to the shielding stage were included because of the possible effects of parasitism or other mortality agents on feeding activity and growth. Group size was recorded as the maximum number of mines observed on a leaf, and density was calculated as group size divided by leaf area (square centimetre).

To quantify the association between larval mass and mine size, we randomly collected 30 larvae that were in the process of shielding. These larvae were placed in a freezer for 1–2 h, then placed into a drying oven at 45C for 48 h, and weighed. Their mines were measured using sigmascan pro 5·0 as described above.

nonlinear mixed-effects models

Nonlinear mixed-effects models are especially suitable for unbalanced repeated measures data because they allow for both grouping structure and random effects due to the individual variability that is independent between groups. In contrast, the more commonly used fixed-effects models such as linear regression do not account for random effects and assume that this variability is negligible or will be absorbed into the independent residual error term. Therefore, when test subjects are grouped by treatment levels but are measured multiple times and have individual variation, mixed models can produce more informative results than the comparable fixed-effects model (Pinheiro & Bates 2000). For this study, we used a nonlinear mixed-effects fitting routine because of the expected (and observed) high variability between individual mines and between leaves. In the following sections, we describe two growth models, the Gompertz equation and a modification of the von Bertalanffy equation, and the model selection procedure for determining the effects of group size, leaf size, and mine density on the rate of mine expansion.

basic model using gompertz

Let yij be the ith area measurement on the jth mine, taken at time tij (in days). Note also, that since we know which leaf contains each mine, we can also say that the jth mine is on the qth leaf. The first model assumes a Gompertz growth model for each mine, so that the measurements of mine size are described by

yij = Aj exp[–Bj exp(–Cjtij)] + ɛij(eqn 1.0)

where the ɛij are independent N(0, σ2) random variables. The Gompertz coefficients Aj, Bj, Cj, are fixed over time, but vary from mine to mine, in a manner that may depend on one of three covariates which we use as a proxy for ‘resource availability’ (i.e. group size, leaf size, mine density). Here, Aj represents the maximum size of mine j. The parameter Bj is a dimensionless parameter (related to mine size at t = 0) that regulates the initial growth rate, and Cj is a parameter with units of time−1 that determines the overall speed of the entire growth process. Thus, large values of Cj indicate faster growth rates throughout the life cycle. Large values of Bj indicate a larger ratio of final to initial size and a larger initial specific growth rate (ISGR), where ISGR = y′(0)/y(0) = BC.

The Gompertz equation appeared to capture the form of mine expansion appropriately; however, there were two basic issues with the data that presented some difficulty with obtaining reasonable fits. First, because of the very small variance in mine size at the first sampling date, the fits tended to be biased towards those very early data points. An initial step to resolve this issue was to work on a log-transformed scale so that a slight modification of model (1·0) produces

log(yij) = log{Aj exp[–Bj exp(–Cjtij)]} + ɛij(eqn 1.1)

As a baseline model, we let

Aj = α0 + α1xj + dq + aj(eqn 1.2)
Bj = β0 + β1xj + eq + bj(eqn 1.3)
Cj = γ0 + γ1xj + fq + cj(eqn 1.4)

where the α, β and γ parameters describe the ‘fixed’ relationship between a covariate xj and growth. Here, q is the index of the leaf containing mine j. aj, bj, cj dq, eq, and fq are independent normal random variables with N(0, inline image), N(0, inline image), N(0, inline image), N(0, inline image), N(0, inline image) and N(0, inline image), respectively. The quantities aj, bj and cjare the ‘random effects’ accounting for between mine variability, while dq, eq, and fq are random effects accounting for between leaf variability. α0, α1, β0, β1, γ0, γ1, σa, σb, and σc are parameters to be estimated.

Second, because the data represent different points in ontogeny between individuals even though sampling intervals were the same, the sampling dates were calibrated to the day at which every mine was equal to 0·05 cm2 through linear interpolation. This value was chosen because of the observed linear growth around this value and because there were measurements that bracketed it for all mines. These data are shown in Fig. S1.

The basic model can be augmented or simplified by adding or removing linear dependencies from any of the fixed effect or random effect expressions that contribute to each coefficient. Using Aj as an example for mine jon a particular leaf, in general we require that the coefficients can be written in the form

image(eqn 1.5)

where inline image is the jth row of a model matrix for the ‘fixed effects’ and inline image and inline image are rows of model matrices describing the dependence of Aj on the random effects at the leaf and mine levels, respectively. α is the vector of fixed effect parameters for Aj; aj and dq are the vectors of random effects for jth mine on the qth leaf, respectively, with aj having multivariate normal distribution MVN(0, ψa) and dq having a MVN(0, ψd) distribution where covariance matrices ψa and ψd will usually have some parameters that have to be estimated. Models of this sort fall within the nlme class of Pinheiro & Bates (2000) and can be estimated using the likelihood-based methods using these authors’nlme package in r.

modification of von bertalanffy

In order to investigate whether our results from the Gompertz fit may have been artefacts of the model (eqn 1·1), we also fitted a modification of the von Bertalanffy growth equation where there is a single growth rate parameter (Kj) to be estimated rather than the two in Gompertz (Bj and Cj). In this model, log-transformed measurements of mine area are assumed to follow the von Bertalanffy equation and are described by

log(yij) = Lj exp(–Kjtij) + Mj[1 – exp(–Kjtij)] + ɛij(eqn 2.0)

where yij is the ith area measurement on the jth mine (which we again know to be on the qth leaf), taken at time tij, and the ɛij are independent random variables with N (0, σ2) – as described for the basic model. Similarly, Lj, Mj, and Kj are coefficients that are fixed over time but can vary between mines according to any one of the covariates (leaf size, group size, or mine density). Thus, we let

Lj = λ0 + λ1xj + lj + nq(eqn 2.1)
Mj = µ0 + µ1xj + mj + oq(eqn 2.2)
Kj = κ0 + κ1xj + kj + pq(eqn 2.3)

where q is again the index of the leaf containing mine j. lj, mj, kj, nq, oq, and pq are independent random variables with N(0,inline image), N(0,inline image), N(0,inline image), N(0,inline image), N(0,inline image), and N(0,inline image), respectively, and have similar interpretations to the random effects for model (1·1). λ0, λ1, µ0, µ1, κ0, κ1, σl, σm, and σk are now the fixed parameters to be estimated. As described for the basic model, xj denotes the measurement of the covariate for the jth mine (on the qth leaf).

model selection

The fitting routine consisted of a series of 10 submodels, which are defined in Table 1. Model m0 was a simple nonlinear least squares fit of the Gompertz model (eqn 1·1) or the modified von Bertalanffy model (eqn 2·0), which allowed us to examine the data structure, initial starting values, and basic fits. In models m1 and m2, all parameters were free to vary; however, m2 included a covariate. The residual error terms were found to be positively biased for large values of mine size; and in order to meet the assumption of constant variance, the fitted values generated from m0 were used to weight the nlme fitting procedure for models m3–m9 using the power variance function (varpower) in r. In these models, random effects are expressed for a single parameter only.

Table 1.  The 10 sub-models used in the fitting routine for eqn 1·1. For each model, the fixed-effects and random-effects components are described for the Gompertz parameters, Aj, Bj, and Cj, and covariates, group size (x) and leaf size (z), for individual mine j on leaf q. Equation 2·0 can be similarly defined for the parameters Mj, Lj, and Kj with the fixed-effects components, µj, λj, and κj and random-effects components, mj, lj, and kj (with kj for m3–m9). All models include the error term ɛij
ModelAjBjCj
FixedRandomFixedRandomFixedRandom
m0α0 β0 γ0 
m1α0dq+ajβ0eq+bjγ0 
m2α01xj2zjdq+ajβ01xj2zjeq+bjγ01xj2zjfq+cj
m3α0 β0eq+bjγ0fq+cj
m4α01xj β01xjeq+bjγ01xj 
m5α02zj β02zjeq+bjγ02zj 
For a single covariate analysis, m5 is:
 
image
 
image
eq+bj
image
 
m6 α01xj2zj  β01xj2zjeq+bj γ01xj2zj 
m7
image
 
image
eq+bj
image
 
m8
image
 
image
eq+bj
image
 
m9
image
 
image
eq+bj
image
 

Parameters were estimated in models m1 to m9 using maximum likelihood. The importance of each factor on the model fit was evaluated using generalized likelihood-ratio tests, which tested the more complex model against the simpler model (e.g. m4 vs. m3, and m5 vs. m4). The inclusion of a covariate (density), set of covariates (group size + leaf size), or the linear or quadratic term in the fixed-effects factor was determined by a significance value P ≤ 0·05 and by minimization of the Akaike information criterion (AIC) (Akaike 1974; Pinheiro & Bates 2000). These statistics would indicate whether the change in the log-likelihood value was significantly greater (or not) in the more complex model, and hence, whether the additional term should be included.

Results

mine size and larval mass

From the data on the 30 randomly chosen larvae that were in the process of shielding, we estimated that a shielding larva consumes an average of 2·48 ± 0·56 cm2 of leaf tissue, weighs 0·472 ± 0·22 mg (dry weight), and measures 3·18 ± 0·07 mm in length (mean ± 1 SD) by the time of shielding. The dry weight (mg) of a larva can be predicted by mine size according to the regression model: dry weight = 0·12 + 0·14 × mine area (F1,27 = 8·16, R2 = 0·232, P = 0·008). Therefore, in the absence of actual measurements of larval mass, mine size is an accurate proxy for larval size.

group size and leaf size

The results of the generalized likelihood-ratio tests comparing model fits for both Gompertz (eqn 1·1) and von Bertalanffy (eqn 2·0) models indicate that model m7 was the best model, where model parameters varied according to a positive linear association with leaf size and a quadratic association with group size (Table 2). Results from the Gompertz fit showed that both the parameters Bj and rate Cj peaked at approximately 25–26 mines (Fig. 1). In contrast, the maximum size (Aj) appears to ‘trade off’ with growth rate, where the fastest growing mines result in becoming the smallest (Figs 1–2). The quadratic relationship between parameter values and group size alone (m5; with random effects specified for parameter Bj ) is shown in Fig. 2a.

Table 2.  Results of generalized likelihood-ratio tests comparing models of group size + leaf size for fits of eqns 1·1 and 2·0
Modeld.f.Equation 1·1Equation 2·0
AICBIClogLikTestL.RatioPAICBIClogLikTestL.RatioP
m3 7378·60405·94–182·30   378·60405·94–182·30   
m410357·40396·45–168·70m3 vs. m427·202< 0·0001357·40396·45–168·70m3 vs. m427·201< 0·0001
m510350·50389·56–165·25m3 vs. m534·097< 0·0001350·50389·55–165·25m3 vs. m534·100< 0·0001
m613353·59404·36–163·80m3 vs. m637·008< 0·0001353·59404·36–163·80m3 vs. m637·007< 0·0001
m410357·40396·45–168·70   357·40396·45–168·70   
m613353·59404·36–163·80m4 vs. m6 9·8050·020353·59404·36–163·80m4 vs. m6 9·8060·020
m510350·50389·56–165·25   350·50389·55–165·25   
m613353·59404·36–163·80m5 vs. m6 2·9110·406353·59404·36–163·80m5 vs. m6 2·9070·406
m613353·59404·36–163·80   353·59404·36–163·80   
m716351·37413·86–159·69m6 vs. m7 8·2200·042351·37413·86–159·69m6 vs. m7 8·2200·042
m816358·97421·46–163·49m6 vs. m8 0·6190·892358·97421·46–163·49m6 vs. m8 0·6180·892
m919355·94430·15–158·97m7 vs. m9 1·4270·699355·94430·14–158·97m7 vs. m9 1·4290·699
Figure 1.

Estimated parameter values for the fixed effects of group size at three leaf sizes (in cm2) representing the full range of sizes in the data set. These are results from m7, eqn 1·1. Aj is the maximum size at shielding, Bj is proportional to the initial (size)-specific growth rate, and Cj represents the speed of the overall growth process. See text for more detail and explanation.

Figure 2.

Fitted values from model m5 for group size (a) and m4 for leaf size (b) plotted for the Gompertz model (eqn 1·1). Each curve in (a) is associated with different numbers of mines per leaf, and in (b), different leaf sizes (in cm2).

The fit of the modified von Bertalanffy using model m7 produced similar results where Mj and Kj followed the qualitative patterns of Aj and Cj of the Gompertz model, respectively (Table 2). The initial log-size (Lj) also appears to correspond to those of Bj in Gompertz, where, for example, large Bj corresponds with a small initial log-size, Lj. However, in comparison to eqn (1·1), only the fixed effects associated with the maximum size (Mj) are statistically significant.

The addition of the quadratic term for leaf size in model m8 had no effect (Table 2). Fitting the Gompertz model produced a linearly decreasing association of the maximum size (Aj), decreasing scaled ISGR (decreasing values of Bj), and increasing overall growth rate (increasing values of Cj) with leaf size (Fig. 2b). These results were matched by those of the modified von Bertalanffy fit (eqn 2·0) using Mj, Lj, and Kj, respectively (Table 2) (Coefficient values and collinearity statistics can be found in Tables S1-1, S1-2).

density

Results from model analyses using density were not qualitatively different from those of group size alone (m5; Table 3, S2-1, S2-2). There was a positive correlation between group size and leaf size (Pearson correlation, r = 0·478, n = 47, P = 0·001), but the differences in leaf size did not sufficiently offset the increases in group size for a constant density across group sizes (Fig. 3). A regression analysis revealed that density could be strongly predicted by group size (density = 0·067 + 0·015 × group.size; F1,45 = 164·4, R2 = 0·79, P < 0·001), but not by leaf size (density = 0·166 + 0·001 × leaf.size; F1,45 = 0·579, R2 = 0·013, P =0·451; Fig. 3). Therefore, the effects of density alone cannot be differentiated from those related to group size.

Table 3.  Results of generalized likelihood-ratio tests comparing models of mine density for fits of eqns 1·1 and 2·0
ModeldfEquation 1·1Equation 2·0
AICBIClogLikTestL.RatioPAICBIClogLikTestL.RatioP
m3 7417·31444·73–201·66   417·32444·73–201·66   
m410398·74437·91–189·37m3 vs. m424·570< 0·0001398·75437·91–189·37m3 vs. m424·567< 0·0001
m513387·68438·59–180·84m4 vs. m541·633< 0·0001387·69438·60–180·84m4 vs. m517·063  0·007
Figure 3.

Scatterplots of larval density (per cm2) by group size (a) and by leaf size (b).

Discussion

This study generated two basic findings. First, the results indicate that the performance of A. nysaefoliella, measured by rates of mine expansion, increases linearly with leaf size, but is hump-shaped with respect to group size and density. In general, these results are consistent with the patterns, as well as, the potential mechanisms reported by studies investigating the effects of the stimulatory effects of aggregative feeding, dose-dependent induction of defensive responses of the host plant, and the consequences of resource limitation on larval performance (Fordyce 2003; Reader & Hochuli 2003; Inouye & Johnson 2005; Coley, Bateman & Kursar 2006). Second, we found that although individuals in the smallest and the largest groups had the slowest growth rates, they were predicted by our models to have the largest mine sizes – suggesting a trade-off between rapid feeding and final consumption, or analogously, rapid growth and final size.

This trade-off may seem somewhat contrary to the goal of maximizing fecundity because larvae that feed quickly should continue to feed, rather than stopping short. However, this may not be a paradox if we consider that insects must reach some critical threshold in mass before pupation can occur. Therefore, if an insect can feed more efficiently on high quality resources, then it can afford to feed less, grow faster, and achieve a sufficient amount of nutrients for pupation in less time (Clancy & Price 1987). In a high-risk environment, these insects will have a considerable advantage over those that are feeding more slowly on low-quality resources. However, without the costs associated with slow feeding or slow growth, then perhaps, insects should indeed feed for as long as possible to maximize mass for greater fecundity (Stearns & Koella 1986; Awmack & Leather 2002). Variation in both social and ecological conditions sets the stage for the evolution of alternative life history strategies (Stearns 1989; Stearns 1992). The results of this study and their implications are discussed within this context here.

leaf quality and female decisions

The potential number of larvae on any leaf is determined first by the number of eggs that are deposited either by a single female or collectively by many females that visit a particular leaf. Because of this, and selection for females to choose leaves that are good for her offspring, the number of larvae on a leaf could reflect female preferences for certain leaves or locations in the tree and should match patterns of larval performance (e.g. Damman & Feeny 1988; Pilson & Rausher 1988; Thompson & Pellmyr 1991; Heisswolf, Obermaier & Poethke 2005; Bergstrom, Janz & Nylin 2006; Roslin et al. 2006). In this study, we found that larvae on leaves with initial group sizes that were very small or very large tended to develop (or feed) at slower rates than those at intermediate group sizes or densities. Therefore, if the number of larvae reflects female preference for leaves that enhance larval performance, then female decisions would explain only the linear increase of feeding rates at group sizes below the optimum, but not the decline at group sizes greater than the optimum. These latter effects might be, instead, due to the general (negative) effects of overcrowding or dose-dependent anti-herbivore responses of the host plant. For sessile phytophagous insects, either of these effects can be especially costly because of their intimate and non-negotiable existence with their host leaf. Thus, the nonlinear relationship of group size or density with larval performance may be driven by the benefits of increasing resource quality at one end of the density spectrum and the costs of high-density living at the other.

The linear increase of mine expansion rates with leaf size suggests that larger leaves are of better quality or are somehow more suitable. Even on small leaves, leaves are not consumed entirely and a large proportion is left uneaten (Low 2007). Therefore, one possible explanation is that large leaves are generally found in areas of greater light availability, and there may be associated differences in temperature and humidity which can affect both metabolic rates and activity levels of the larvae (Alonso 1997; Kreuger & Potter 2001; Bryant, Thomas & Bale 2002; Levesque, Fortin & Mauffette 2002). Second, leaves that are larger may have more efficient photon capture and yield higher rates of photosynthesis (Poorter & Evans 1998; Reich, Ellsworth & Walters 1998). Leaves in areas of greater light availability typically have more rapid rates of cell elongation during leaf expansion and are associated with higher nutritional quality (see Kursar et al. 2006). In the end, whether the mechanism affecting larval performance is direct or indirect, larger leaves are associated with faster growth or feeding activity; and if faster feeding is beneficial, then females should bias their oviposition towards larger leaves.

trade-offs and larval strategies

We know from many experimental studies that aggregative feeding by herbivorous insects can have both positive and negative effects on herbivore fitness by facilitating feeding (Reader & Hochuli 2003), enhancing host plant suitability (Fordyce 2003), or by inducing the anti-herbivore responses of the host plant (Karban & Baldwin 1997; Tollrian & Harvell 1999). However, in nature, it may also be the case that these anticipated effects on fitness might never be realized – not only because of the interplay and balance of multiple ecological factors, but also because of alternative strategies that larvae can use, which have evolved in response to a highly variable environment.

The models and analyses presented here elucidated some possible strategies that insect larvae, and possibly, other animals or plants could take under variable social and environmental conditions to achieve similar values in fitness. One trade-off that has received considerable attention is the ‘slow-growth high-mortality’ hypothesis where insect larvae are expected to be more at risk to parasitism if they remain as larvae, thereby exposed, for longer periods of time (Benrey & Denno 1997; Cornelissen & Stiling 2006). However, our results suggest that despite the potential increased risk associated with slower feeding, it may lead to greater or equivalent levels of fecundity for those that survive. In addition, when the risk of parasitism is low (e.g. small groups are less detectable, Low 2008), then feeding for a longer length of time may not have substantial fitness costs even when an individual is feeding on a low quality resource. In conclusion, we suggest that selection can act on specific growth parameters to: (i) adjust initial development times or maximum growth rates to affect survival, or (ii) adjust final sizes to affect fecundity. Ultimately, it will be the product of both components of fitness that will determine what strategies and traits will persist.

Acknowledgements

We wish to thank the University of Virginia's Blandy Experimental Farm for providing funding, logistical support, and other resources to C. L., and Stonebridge Farm for access to their property. John Endler, Al Uy, Tom Starmer, and Steve Ellner provided helpful comments on the manuscript.

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