Journal of Chemical Ecology

, Volume 34, Issue 7, pp 959–970

Impact of Herbivore-induced Plant Volatiles on Parasitoid Foraging Success: A Spatial Simulation of the Cotesia rubecula, Pieris rapae, and Brassica oleracea System

  • Molly Puente
  • Krisztian Magori
  • George G. Kennedy
  • Fred Gould
Article

DOI: 10.1007/s10886-008-9472-9

Cite this article as:
Puente, M., Magori, K., Kennedy, G.G. et al. J Chem Ecol (2008) 34: 959. doi:10.1007/s10886-008-9472-9

Abstract

Many parasitoids are known to use herbivore-induced plant volatiles as cues to locate hosts. However, data are lacking on how much of an advantage a parasitoid can gain from following these plant cues and which factors can limit the value of these cues to the parasitoid. In this study, we simulate the Cotesia rubecula–Pieris rapae–Brassica oleracea system, and ask how many more hosts can a parasitoid attack in a single day of foraging by following plant signals versus randomly foraging. We vary herbivore density, plant response time, parasitoid flight distance, and available host stages to see under which conditions parasitoids benefit from herbivore-induced plant cues. In most of the parameter combinations studied, parasitoids that responded to cues attacked more hosts than those that foraged randomly. Parasitoids following plant cues attacked up to ten times more hosts when they were able to successfully attack herbivores older than first instar; however, if parasitoids were limited to first instar hosts, those following plant cues were at a disadvantage when plants took longer than a day to respond to herbivory. At low herbivore densities, only parasitoids with a larger foraging radius could take advantage of plant cues. Although preference for herbivore-induced volatiles was not always beneficial for a parasitoid, under the most likely natural conditions, the model predicts that C. rubecula gains fitness from following plant cues.

Keywords

Tritrophic interactions Herbivore-induced plant volatiles Parasitoid behavior Signal utility Spatial simulation model 

Introduction

In numerous tritrophic systems, herbivore-induced plant volatiles elicit responses from predators and parasitoids (Dicke et al. 1990). Immediately upon being damaged by feeding, plants release preformed volatile compounds that are exposed to the air. Furthermore, the jasmonic acid and salicylic acid induction pathways enable damaged plants to synthesize and release volatiles. A number of the compounds released are common to most plants and are referred to as green leaf volatiles. However, the concentrations of specific compounds and the composition of the entire blend differ based on plant and herbivore species. These differences in volatile compound blends often allow predators and parasitoids to discriminate between species of plants (Lewis and Martin 1990; Fritzsche-Hoballah et al. 2002), species of herbivores (Lewis and Martin 1990; Blaakmeer et al. 1994; Dicke 1999), and even the age or density of herbivores (Dicke 1999; Gouinguené et al. 2003). Herbivore-induced blends of volatile compounds have the potential to provide a great deal of information to predators, but they also have the potential to provide misleading information.

The utility of herbivore-induced volatiles for agricultural biological control has been debated in the literature (Dicke et al. 1990; Bottrell et al. 1998; Degenhardt et al. 2003). Some argue that artificially enhancing volatiles in the field will arrest parasitoids in the area, leading to better control, while others argue that artificially enhanced volatiles will produce misleading signals, thus, reducing the receptiveness of parasitoids to volatiles. In a few field studies conducted in small plots, artificially enhanced volatiles have led to higher parasitism, but it is unclear whether this is due to better attraction of parasitoids from outside the plot, better retention of parasitoids within the plot, or increased efficiency of parasitoids within the plot (e.g., James and Price 2004).

Research on the quality of volatile signals has looked at the specificity of volatile production (Dicke and Takabayashi 1991; Blaakmeer et al. 1994) and the parasitoid's ability to discriminate between odors (Agelopoulos and Keller 1994; Fritzsche-Hoballah et al. 2002). However, being able to discriminate between volatiles does not mean that predators and parasitoids will respond to specific plant volatiles in the wild. Many parasitoids have the ability to learn new signals based on past experience (Lewis and Martin 1990). Additionally, there is heritable variation in parasitoids for responding to plant volatiles (Lewis and Martin 1990; Wang et al. 2004). The proximate incentives for a parasitoid to learn a response to a signal or for a population of parasitoids to evolve a response to a signal are the same; the herbivore-induced volatiles must correlate in time and space with herbivore availability. When the volatiles are not consistently correlated with herbivore presence, there is selection for parasitoids to maintain variation in this response, either through maintenance of genetic variation or evolution of phenotypic plasticity (Wang et al. 2004). In studies where the volatile signal has been uncoupled from herbivore presence, such as by saturating fields with volatiles, parasitoid response to the signals has decreased (Lewis and Martin 1990).

Some work has been done to document the lag time between herbivore damage and production of volatiles that elicit parasitoid responses (Mattiacci et al. 2001). Relating this time course to parasitoid efficiency at host finding, however, has not been thoroughly investigated. Mattiacci et al. (2001) found that Cotesia glomerata responded to Brussels sprout plants only after herbivores had been feeding for at least 3 days, but they stopped responding to plants if the herbivores had been removed for more than 1 day. Additionally, Agelopoulos and Keller (1994) found that induced cabbage plants where the herbivores had been removed were just as attractive to C. rubecula 22 h after herbivore removal as immediately after removal. This seems to indicate that the plant's lag time for commencing volatile production is longer than the lag time needed to cease volatile production, but that both lag times are expected to be of biological importance. This leads to the question addressed in this study: how long can a plant's lag time be without reducing the relevance of the volatiles as signals to the parasitoid?

While it has been shown that herbivore-induced volatile emission can result in attraction of parasitoids to plants within a wind tunnel type of environment (Agelopoulos and Keller 1994) and that induced plants can arrest predators and parasitoids (Agelopoulos and Keller 1994), we have no record of the distances over which these induced cues may act in the field. Designing field experiments to test attraction to induced plants is a difficult task. Identifying the point at which an insect switches from random movement to directed flight as well as identifying which environmental cues out of the complex volatile environment triggered the change is a challenge that has yet to be successfully tackled in the field.

While not a replacement for field studies, computer simulation models can be used to predict how parasitoids should respond to a complex environment (e.g., Dunning et al. 1995). This allows simultaneous testing of more variables than is possible in a laboratory setting while affording more control over parameters than is possible in most field experiments. By artificially establishing diverse patterns of environmental parameters, we can identify which combinations of plant, herbivore, and parasitoid behaviors are predicted to have the strongest impact on parasitoid foraging success. This information can then be used in designing more efficient field studies.

In this paper, we use the tritrophic system of Cotesia rubecula, Pieris rapae, and Brassica oleracea to ask how the temporal and spatial patterns of herbivore-induced plant volatiles impact parasitoid foraging success. The extensive work on volatile signals in this system, as well as the extensive life history data available for these three species, renders this an ideal tritrophic system for detailed simulation analysis. P. rapae, the cabbage white butterfly, is a cosmopolitan herbivore that feeds primarily on Brassicaceae (Kaiser and Cardé 1992). While these plants generally share similar chemical defensive profiles (Kaiser and Cardé 1992; Geervliet et al. 1994), there is also variation in form and distribution of the plants, and it has been shown that P. rapae prefers certain host types over others, even within the species B. oleracea (Jones and Ives 1979). C. rubecula is a specialist parasitoid that can attack all stages of P. rapae caterpillars, but this parasitoid's larvae suffer greater mortality when attacking older hosts (Nealis 1990; van Driesche et al. 2003). This species has been shown repeatedly to be responsive to herbivore-induced plant volatiles with positive experience reinforcing this response (Kaiser and Cardé 1992; Blaakmeer et al. 1994; Geervliet et al. 1994). The larval parasitoid C. rubecula will respond to plant volatiles multiple times after caterpillars have left (Nealis 1990), so they could be negatively affected by asynchronous signals in the field.

Methods and Materials

Plants

We modeled a rectangular, contiguous, grid-like field of Brassica oleracea plants with the center of each plant located 1 m from its nearest neighbors. For the analyses, the field was fixed at a 20 × 20 size (a total of 400 plants). Individual Brassica plants were assumed to be induced by the feeding of Pieris larvae to produce volatiles that attract parasitoids. Plants were assumed to start effective volatile production following the onset of herbivore feeding (induction delay, ranging from 1 to 5 days). Plants continued to emit volatiles throughout herbivore feeding, and stopped the emission of volatiles (relaxation delay, ranging from 1 to 5 days) after the cessation of herbivore feeding (due to death or pupation of all herbivore larvae on the plant). Therefore, some plants in the field without herbivores did emit volatiles and potentially misguide parasitoids that were attracted to the volatiles.

Population Dynamics of Herbivores

Population dynamics of Pieris rapae infesting a field were simulated by using an age-structured model based on field-collected life table data. The model tracked up to 20 Pieris larvae per plant. The model assumed that all damage-induced plants produced the same concentrations of volatiles, regardless of how many larvae were infesting the plant. However, it has been found that C. rubecula is more responsive to plants that host more larvae (Kaiser and Cardé 1992; Kaiser et al. 1994; Geervliet et al. 1998), so being able to follow multiple larvae opened up the possibility in the future of simulating a change in volatile strength due to the herbivore load on a particular plant.

Life table data for P. rapae immature stages were gathered from several sources (Harcourt 1966a; Dempster 1967; Parker 1970; Jones et al. 1987). Overall preadult mortality ranged from 69.1 to 95.9%. If the data provided by Harcourt (1966a) which included no egg parasitism were ignored, the average preadult mortality was 91.6% ± 3.0% SD (N = 7); this is surprisingly consistent considering the variety of host plants and geographic regions these data were collected from. We chose to use the life table from Dempster (1967) because it was consistent with the majority of published life tables and covered the herbivore's lifespan in more detail. The daily herbivore mortality rates used in the reported simulations are given in Table 1. Individual larval death was a stochastic process; for each simulated larva on each day, a random number between 0 and 1 was selected by the computer, and if the number was less than the probability of mortality, the larva was “killed”. In a large field, this process should produce roughly the same overall mortality rate as in found in Table 1.

Table 1 Life table for Pieris rapae

Stage

Day

Mortality

Mortality (Deterministic)

Egg

1

0.024

0

2

0.024

0

3

0.024

0

4

0.024

0

5

0.024

0

1st instar

6

0.187

0.187

7

0.187

0.187

8

0.187

0.187

2nd instar

9

0.087

0.087

10

0.087

0.087

11

0.087

0.087

3rd instar

12

0.084

0.084

13

0.084

0.084

14

0.084

0.084

4th instar

15

0.137

0.137

16

0.137

0.137

17

0.137

0.137

5th instar

18

0.233

0.233

19

0.233

0.233

20

0.233

0.233

Pupae

21

0.007

0

22

0.007

0

23

0.007

0

24

0.007

0

25

0.007

0

26

0.007

0

27

0.007

0

28

0.007

0

All adult female P. rapae were stored in a single cohort regardless of the day they eclosed. Richards (1940) found that adult P. rapae populations usually had a 1:1 sex ratio; therefore, half of all final stage pupae were assumed to be males and were excluded from the adult cohort upon eclosion. Adult female P. rapae live for about 3 weeks, so for each daily time step, the number of adults was reduced by the number of new adults present 21 days prior to that time step. No other adult mortality is considered.

P. rapae eggs are disproportionately aggregated at the edges of fields (Harcourt 1966b). This is primarily due to the movement patterns of adult butterflies, which have been studied extensively (e.g., Jones 1977; Root and Kareiva 1984). In natural populations, individual butterflies were observed to fly in a roughly straight path (Jones 1977; Root and Kareiva 1984).We based our herbivore distribution on an algorithm developed by Jones (1977) to recreate the movement patterns of ovipositing P. rapae females. In the model, each adult was given a starting position and a directional bias at random. The adult either remained at her current location or moved to an adjoining plant; the direction the adult moved was determined by using the probability of a butterfly turning from an initial directional flight bias (Root and Kareiva 1984) (see Fig. 1). Following movement, the probability that the adult would oviposit was 0.23, the median probability found by Jones (1977). Field observations found that butterflies crossed patch boundaries without stopping (e.g., Root and Kareiva 1984). In order to reflect this and maintain the same field densities, adults that reached the edges of the simulated field are ‘mirrored’ to the opposite side of the field. Adults continued to follow this algorithm until they had laid a set number of new eggs. To prevent butterflies remaining indefinitely in a field that had reached its capacity of eggs and larvae, when butterflies encounter ten successive plants that are fully occupied, they leave the model field.
Fig. 1

Spatial bias for Pieris rapae butterflies. Assuming a butterfly begins on a plant in the center square and has a bias to the right, the probability that a butterfly will travel to each square is shown by the P value in that square

We wanted herbivore populations to reflect natural population sizes, so we set the initial adult population size to 1, included adult movement dynamics, and set the number of eggs to 1, 2, 5, 10, 15, or 20 eggs/butterfly/day. After five runs, the daily average of eggs, larvae, and adults for each of the oviposition rates were calculated for 100 days trials. We then compared the average simulated values to reported field densities, correcting for field size. The density of eggs observed in Parker (1970) was higher than any values we obtained, but the densities observed in Jones et al. (1987) were approximated relatively well by either 15 or 20 eggs/butterfly/day, especially in the second and third generations. The first instar densities observed by van Driesche (1988) in kale were closely approximated by 10 eggs/butterfly/day (see Fig. 2), while the first instar densities observed by van Driesche and Bellows (1988) in collards were approximated by the second generation of simulations for 15 or 20 eggs/butterfly/day (an offset of about 30 days) (see Fig. 2). The number of adults in the field observed by van Driesche (1988) was similar to the results of 10 eggs/butterfly/day. Therefore, for the remainder of the experiments, we assumed 10 eggs/butterfly/day as “low herbivore density” and 20 eggs/butterfly/day as “high herbivore density”.
Fig. 2

Comparison of simulated herbivore population dynamics with published field data. The larger black symbols are counts of first instars obtained from published studies by van Driesche (1988) and van Driesche and Bellows (1988), adjusted to match the size of our simulated field (400 plants). The numbers in the legend refer to the maximum number of eggs each female butterfly could lay per day

Parasitoid Behavior and Parasitism

In essence, the model assesses the fitness of a single parasitoid entering an herbivore-infested field that has had no prior parasitism. Therefore, the parasitism behavior of individual adult Cotesia was modeled in detail but its population dynamics were not included. The range of host stages suitable for parasitoid development has been shown to be an important biological parameter for many parasitoids, including the closely related species, C. glomerata and C. rubecula. The parasitoid C. glomerata is unable to attack P. rapae larvae older than the third instar because the hosts are able to encapsulate the parasitoid larvae at that stage, so there is higher parasitism on host plants that slow the growth of P. rapae larvae (Benrey and Denno 1997). Similarly, C. rubecula face higher risks of damage from counterattacks by larvae older than the second instar (Nealis 1990). It has been shown that C. glomerata cannot identify the stage of an herbivore based on plant volatile cues (Mattiacci and Dicke 1995) and, therefore, may be attracted to plants with unsuitable larval stages. In the model, parasitoids are only able to successfully attack larvae of the host up to a model-specified instar (host stage). Since, in the model, plants that harbor larvae too old to be attacked by parasitoids still emit volatiles, parasitoids that follow signals might be further misled. We varied model parameter values to consider cases where parasitoids could attack first instars only, first and second instars only, or all five instars.

Because we are specifically interested in how herbivore-induced plant volatiles impact parasitoid foraging success, we chose to focus on how underlying host distributions, timing of plant volatiles responses, and parasitoid sensitivity to odor impact parasitoid efficiency. Numerous environmental factors that influence parasitoid foraging efficiency such as wind speed (Keller 1990), light intensity, or previous experience (Keller 1990; Kaiser and Cardé 1992; Geervliet et al. 1998) can also be important, but they are beyond the scope of this paper. We assumed the following constants for both randomly foraging and selectively foraging parasitoids. Sato and Ohsaki (2004) observed that for the closely related C. glomerata searching for Pieris larvae, the time spent searching one leaf was 73.5 ± 11.9 s, so this was used as the time spent in fruitless search if the parasitoid arrived on a plant with no host. There is some evidence that C. glomerata avoids superparasitizing already parasitized larvae (Fatouros et al. 2005), so a parasitized larva was considered “nonhost” but was still capable of inducing a plant to produce volatiles. We assumed a parasitoid would be equally likely to find a host early or late in that search time interval; so on average, a parasitoid would spend half as much time searching if it encountered a host on that plant. Although there are circumstances that would prevent parasitoids from discovering available hosts (e.g., plant architecture), we assumed that if a viable host was available, the parasitoid would find it. The time it took for a parasitoid to successfully sting a host was 13.1 ± 3.9 s (Sato and Ohsaki 2004). The recorded flight speed for C. rubecula was 0.33 m/s (Kaiser et al. 1994).

Parasitoids were given 3,600 s (i.e., 1 h) of total foraging time per day. The exact amount of time they spend foraging in the field is unknown, but 1 h per day was considered a low but feasible estimate given that most parasitoids only forage during the brightest hours of daylight and must divide time between foraging for food and foraging for hosts (Bartlett 1964). A greater period of time for foraging per day often resulted in all volatile-emitting plants being visited in our small field and produced artifactual results. A parasitoid started its foraging in a field location randomly selected by the simulation model and immediately searched the plant it was on. If no viable host were present, the giving-up time was discounted from the total foraging time and the parasitoid moved to the next plant. If a viable host were present, the host was marked as parasitized, the handling time was discounted from the total foraging time, and half the giving-up time was discounted from the total foraging time to account for search time. After successfully parasitizing a host, parasitoids had a 0.67 probability of leaving a plant. Otherwise they remained to continue searching (Tenhumberg et al. 2001) with a new giving-up time discounted from the foraging time. For many other systems, a more complicated algorithm for calculating giving-up time would be more appropriate; however, because P. rapae is not a gregarious host, this method of resetting the giving-up time following each successful oviposition is a close approximation of what occurs in nature (Vos et al. 1998). In wind tunnel experiments, the presence and concentration of host odors did not affect C. rubecula's flight speed or direction of travel, but did impact a parasitoid's “willingness” to take off and whether a parasitoid completed a flight away from the initial location (Keller 1990; Kaiser et al. 1994). Therefore, we used a 0.67 flight probability for both randomly and selectively foraging parasitoids.

The spatial aspects of parasitoid foraging are poorly understood, so we had to make many assumptions in this part of the model. The following assumptions we believe to be reasonable:
  • Plant volatiles are diluted over space, so the closer an emitting plant is to a parasitoid the more likely it is to be detected.

  • Parasitoids use volatiles to detect a potential host plant, even if they are not herbivore-induced plant volatiles, so a randomly foraging parasitoid is also more likely to detect plants that are closest to it (Nordlund et al. 1988).

  • Parasitoids decide which plant they will fly to before they leave the plant they are on (Keller 1990).

We used two different shapes of dispersal for the weighting: linear and exponential. According to Elkinton et al. (1987), over short distances, volatiles such as pheromone plumes spread out in a linear fashion, therefore, one dispersal shape was “linear”. We assumed that the strength of signal had a value of one at the distance of 1 m and zero at a distance of 6 m and decreased linearly from the highest to lowest value (Table 2, Linear Diffusion). This created a bias where a parasitoid was five times as likely to go to a plant 1 m away compared to a plant 5 m away. The other dispersal shape we assumed was an exponential diffusion. In diffusion models, where plumes are not as well delineated, dilution of volatile concentrations happen at a rate relative to the inverse of the radius squared (Murlis et al. 2000). This created a bias in the model where a parasitoid was 25 times as likely to go to a plant 1 m away compared to a plant 5 m away (Table 2, Exponential Diffusion). Although it is likely that the actual spatial dynamics of detection distances is not either of these two options, we felt this would be adequate for looking at the sensitivity of the model to a parasitoid's odor detection bias.

Table 2 Volatile distance biases

Distance

Linear

Exponential

Expected

Bias

Expected

Relative

Bias

1

1

5

1

25

25

2

0.8

4

0.25

6.25

6

3

0.6

3

0.11

2.78

3

4

0.4

2

0.06

1.56

2

5

0.2

1

0.04

1

1

The plant the parasitoid would fly to was randomly selected from the weighted list of possible destination plants. Parasitoids were prevented from immediately returning to the plant they came from. In the case of parasitoids that responded to herbivore-induced volatiles, only induced plants (emitting volatiles) were added to the weighted list of possible destination plants. If none of the plants on the weighted list of possible destination plants was signaling, then the weighted list was remade with the random movement algorithm, and the parasitoid was moved to a random non-induced plant.

Model Verification

Predictions of the present model cannot be immediately tested against lack of empirical data. However, it was possible to assess whether there were errors in the coding of this simulation model by comparing predictions of this stochastic model to predictions of a simpler stage-specific model described in Puente et al. (2008, preceding article) that modeled the same phenomena in a nonspatial, deterministic manner.

The maximum number of hosts a parasitoid could attack in the deterministic model is limited by the time it has to forage rather than the number of hosts in the field, Therefore, by comparing the results of our stochastic model with the deterministic model run with the same parameters, we could identify the minimum field size that led to time-limited, rather than space-limited, foraging. For all parameter combinations explored, randomly foraging parasitoids were able to exhaust their time in fields with greater than 70 plants. Parasitoids foraging with signals needed larger fields to exhaust their time budget. Except for unrealistic parameters, a field size of 400 plants was sufficient for the signal-foraging parasitoids.

Additionally, we were also able to use results from the deterministic comparison to identify how many runs were necessary to account for the stochastic variation caused by herbivore oviposition and mortality. We calculated the mean and standard error of the number of hosts attacked for both signal-following and randomly foraging parasitoids for a number of successive runs with extreme values of parameters (induction and relaxation delays, viable host stage, etc.), and determined how many runs were necessary for the standard error to fall within 5% and 10% of the mean. Under most circumstances, the standard error was within 10% of the mean after fewer than five runs, and 20 runs were sufficient to reach a standard error within 5% of the mean for both number of hosts attacked for signal-following parasitoids and number of hosts attacked for randomly foraging parasitoids. This indicated that for most parameters 20 runs are sufficient. A summary of the variables and constants used in this simulation can be found in Table 3.

Table 3 Parameters used in the model

Parameter

Values

(Oldest viable) Host stage

1, 2, 5

Induction delay (in days)

1, 3, 5

Relaxation delay (in days)

1, 3, 5

Occupation rate (in eggs/plants/field)a

0.1–0.9

Herbivore density (in eggs/butterfly/day)

Low (10), high (20)

Total foraging time (Tt) (in seconds)

3,600

Flight speed (a) (in meters/second)

0.33

Handling time (b) (in seconds/host)

13.1

Giving-up time (c) (in seconds/plant)

73.5

Foraging style

Random, signal following

Distance biasb

Linear, exponential

aOccupation rate was used solely in validating the model; for actual runs, herbivore density values were used

bDistance bias is more thoroughly explained in Table 2

Results

We examined time series of the mean number of herbivores attacked by parasitoids randomly foraging and by parasitoids following signals, for both linear and exponential distance biases, for the 54 combinations of parameters we considered. In all parameter combinations, the mean number of hosts attacked by randomly foraging parasitoids with linear biases was within one standard deviation of the mean number of hosts attacked by randomly foraging parasitoids with exponential dispersal of volatile compounds. Averaging over all parameter combinations, parasitoids that randomly foraged visited about eight more plants per day than parasitoids following signals, regardless of the type of volatile dispersal. By looking at the difference in mean number of larvae attacked for each 5-day-sampling interval for parasitoids following signals versus parasitoids randomly foraging, each of the combinations of induction delays, relaxation delays, herbivore densities, and viable host stages could be classified as one of four patterns:
  1. A.

    (6 of 54) Following signals was on average disadvantageous, but individual runs could be advantageous due to large variances,

     
  2. B.

    (12 of 54) Following signals was not significantly different from random foraging for any time interval sampled,

     
  3. C.

    (5 of 54) Following signals was advantageous for at least one host generation, as long as the parasitoid flight bias was linear,

     
  4. D.

    (31 of 54) Following signals was advantageous for at least one host generation, regardless of parasitoid flight bias.

     
In pattern A, parasitoids following signals generally attacked as many hosts as parasitoids not following signals through the first two generations of herbivores, but fell much lower in the third generation (Fig. 3a). Of the 54 parameter combinations, six combinations fell into this pattern. In the most extreme loss of efficiency, parasitoids that followed signals attacked 40% fewer hosts than randomly foraging parasitoids, under the conditions of a 3-day induction, 1-day relaxation, low herbivore density, only first instars as viable hosts, and linear distance bias. In these simulations, the variance of hosts attacked in the third generation of herbivores was quite large such that the mean for parasitoids randomly searching was well within a single standard deviation of the parasitoids following signals. This first pattern was seen only when the induction delay was greater than one and the oldest viable hosts were either first or second instars.
Fig. 3

Examples of how signals can impact the number of hosts attacked. a Detrimental signals (Pattern A); shown here is the case where induction delay is 3 days, relaxation delay is 3 days, herbivore density is low, and viable host stage is first instars only. b Signals no better or worse (Pattern B); shown here is the case where induction delay is 5 days, relaxation delay is 5 days, herbivore density is high, and viable host stage is first instars only. c Signals beneficial as long as the parasitoid distance bias is linear (Pattern C); shown here is the case where induction delay is 1 day, relaxation delay is 1 day, herbivore density is low, and viable host stages are second and first instars. d Signals beneficial (Pattern D); shown here is the case where induction delay is 1 day, relaxation delay is 1 day, herbivore density is high, and all instars are viable host stages. For each example, four cases were plotted: parasitoids randomly foraging where plants produce volatiles with an exponential diffusion (random exponential), parasitoids randomly foraging where plants produce volatiles with a linear diffusion (random linear), parasitoids following volatile plant cues where plants produce volatiles with an exponential diffusion (signal exponential), and parasitoids following volatile plant cues where plants produce volatiles with a linear diffusion (signal linear). For all four graphs, vertical bars are ±1 SD

In pattern B, parasitoids that followed signals generally attacked as many hosts as parasitoids not following signals throughout the year (Fig. 3b). Over a season, this could result in average of up to 40% more hosts attacked or 20% fewer hosts attacked, but for any day sampled, the means for number of hosts attacked if the parasitoids followed signals were well within one standard deviation of the means for number attacked if the parasitoids foraged randomly. Of the 54 combinations we tested, 12 combinations fell into this pattern. In all such cases, the oldest susceptible host stage was either first or second instars, and in almost all of these cases, the induction delay was 5 days; the only exception being two cases where the induction delay was 3 days and only first instars were attacked. In all of these cases, the signals were produced after the inducing host had matured beyond the viable attack stages; therefore, it is not surprising that the resulting host attack rates for parasitoids following signals should not be significantly different from randomly foraging parasitoids.

In pattern C, there was an effect of volatile dispersion on parasitoid success in the first generation of herbivores (Fig. 3c). When volatiles were assumed to have a linear dispersal pattern, parasitoids that followed volatiles attacked between 50% to 200% more hosts than randomly foraging parasitoids. For these same conditions, when volatiles were assumed to have an exponential dispersal pattern, the difference between the signal foraging parasitoids and the randomly foraging parasitoids ranged from attacking 10% fewer hosts to attacking 25% more hosts than randomly foraging parasitoids. Pattern C occurred in five of the 54 combinations, all of which had first and second instars as viable hosts and an induction delay of either 1 or 3 days. Because this advantage was apparent only in the first generation of the herbivores when they are rare in the field, it is likely that a linear dispersal of the volatiles that allowed parasitoids to detect plants from greater distances also allowed them to encounter more patches of viable hosts, and a well synchronized induction then led to their remaining in the patch of viable hosts. Randomly foraging parasitoids with linear volatile dispersion patterns were just as likely to leave a patch of viable hosts as they were to enter a patch, thus giving parasitoids following signals the advantage. Signal foraging parasitoids with exponential volatiles dispersion patterns were less likely to encounter a patch because they did not stray far from a patch they had already exploited.

The remaining 31 parameter combinations (57.5% of all combinations) fell into pattern D, where parasitoids that followed signals attacked more hosts than randomly foraging parasitoids in at least one generation of herbivores, regardless of parasitoid distance bias (Fig. 3d). The advantage occurred primarily in the first herbivore generation but sometimes extended into the second generation. By the third generation, there were sufficiently dense populations of hosts that parasitoids were reaching their saturation point regardless of their foraging strategy. This can be seen by the small standard deviations from day 80 onward. If all five instars were viable hosts, parasitoids benefited from following signals for all herbivore generations regardless of the volatile dispersal patterns. When only first instars were viable hosts, pattern D occurred only when the induction delay was 1 day. When second instars were the oldest viable hosts, if the host density was high and the induction delay was 1 or 3 days, pattern D occurred, but when host densities were low, pattern C occurred.

A summary of all simulations can be found in Supplementary Table 1, where results are reported as “relative advantage” to the parasitoid from following volatiles (i.e., the number of hosts attacked by parasitoids following signals minus the number attacked by parasitoids randomly foraging divided by the number attacked by randomly foraging parasitoids.). The overall patterns of when parasitoids benefited from following signals was the same if we looked at relative advantage or absolute number of hosts attacked; however, by looking at relative advantage, the gains from the beginning of the season were more pronounced compared to the gains at the end of the season. This is a more biologically relevant measure, as a fitness gain for a parasitoid early in the season would account for a larger overall gain in fitness if we had followed the long-term population dynamics of the parasitoid population.

Although relaxation delay did not impact qualitatively which pattern a simulation fell into, the relaxation delay did impact the overall gain in expected fitness over a season. For example, in the case where all five instars were viable hosts, induction delay was 5 days and host density was high; if the relaxation delay was 1 day, the parasitoids that followed signals could attack on average 130% more hosts compared to randomly foraging parasitoids; if the relaxation delay was 3 days, this gain was reduced to 92% more hosts; and if the relaxation delay was 5 days, this gain was reduced to 78% more hosts.

Discussion

For the majority of parameter combinations (57.5% with exponential shape of dispersal and 66.6% with linear shapes of dispersal), the following of herbivore-induced plant volatiles was a beneficial strategy for parasitoids, but the degree of benefit varied depending on values of a number of parameters. While this result indicates that herbivore-induced plant volatile cues can be a robust indicator for parasitoids in many types of environments, we note that the most likely environment, (where host attacks are limited to first or second instars, and relaxation and induction delay vary between 1 and 3 days), is where there is a transition between the volatile cues being useful all of the time (pattern D) and only in certain volatile dispersal conditions (pattern C). We found that induction delay had an important impact on the utility of volatile signals. Plants with patterns A and B, where plants with induced volatiles were irrelevant or possibly detrimental to the parasitoids, tended to have an induction delay of 3 or 5 days. Relaxation delay was also important for determining the magnitude of effect of following signals could have on parasitoids. These results differ slightly from our deterministic model (Puente et al. 2008, preceding article), where relaxation delay was more important than induction delay in determining relevance. The difference between results of the two models is due to the fact that the deterministic model assesses attack rate when the plant population has reached an equilibrium frequency of individuals in each of the four states. In the stochastic spatial model, the impact of following signals is assessed throughout the season while frequencies of plants in each state are changing and herbivore density is changing.

Both models show that understanding the molecular mechanism responsible for inducing signals will be important for engineering volatile producing plants that optimize parasitoid foraging efficiency. Future work in the P. rapae system can test our prediction by examining how the natural variation among cultivars in volatile induction and cessation impacts parasitoid behavior and attack rates. We predict that C. rubecula should have a preference for varieties of B. oleracea that can begin volatile production within a day of onset of herbivory and can cease volatile production within a day of the end of herbivore attack.

Our model shows that how parasitoids perceive volatiles in space can be important for determining whether or not it gains an advantage by following signals. Volatiles are considered important cues for “long-distance” foraging (Geervliet et al. 1998), but what constitutes “long-distance” has not been described quantitatively in the literature. If this means that parasitoids can detect signals 1 m away, that would be comparable to our exponential volatile dispersion where parasitoids were 25 times more likely to visit a plant one meter away compared to a plant 5 m away; in this case, parasitoids gained nothing from following signals in several cases. However, if parasitoids can detect and respond to signals from five times that distance, as in our linear bias example, signals more often had at least some positive impact on parasitoid foraging success. While this differentiation (pattern C) only occurred in five cases, these cases all occurred in simulations where second instars were the oldest viable host stage, which is biologically relevant for C. rubecula. In all of these cases, herbivore density was low, which would be the desirable state for an agricultural setting. Because of the potential likelihood of these parameter conditions occurring in nature, understanding how volatile plumes disperse in space and how parasitoids perceive these volatiles in space could be important for knowing whether breeding for inducing plants will be a successful endeavor.

Finally, as with our deterministic model, the current model shows the importance of herbivore density to the relevance of volatile cues. In the first herbivore generation, when the number of herbivores was at its lowest (Fig. 2), signals had the greatest impact (Fig. 3c,d). In the third generation, when herbivores were at their highest densities, volatile signals were typically irrelevant or had a negative impact. Most studies of induced volatiles examine just a single volatile source, which misses the potential importance herbivore densities can have on parasitoid foraging success. Predictions from our model argue for looking at larger populations of plants and herbivores before determining whether a volatile signal has a substantially positive effect on parasitoids. We also argue that if breeding plants for volatile production is going to be a successful strategy, the appropriate volatile production by young plants is needed early in the season if it is to improve parasitoid foraging efficiency.

While our simulation model has identified important parameters that should be studied more closely, several modifications to the model could be made in the future that would improve its value. One assumption we made in this model is that parasitoids are either foraging randomly or foraging in response to signals. We did not allow for parasitoids to change patterns within a lifetime. Other models have shown that evolving parasitoid systems can change host-parasitoid dynamics (Abrams and Kawecki 1999). Therefore, incorporating parasitoid learning into this model would be an important next step.

We specifically chose to focus on a naïve parasitoid entering a field of nonparasitized larvae, rather than following an entire parasitoid population's dynamics over a season. Following parasitoid population dynamics would be an interesting model extension but would require considerably more parameters. Parasitoid and host eclosion are not always synchronized in nature (van der Meijden and Klinkhamer 2000); parasitized herbivores can consume different amounts of foods than their nonparasitized congeners (Fatouros et al. 2005) and parasitized larvae can have different mortality from nonparasitized larvae (Jones 1987). These factors may all alter the relevance of volatiles in host plants over several herbivore generations. In many cases, less efficient individual predators or parasitoids will lead to more stable population dynamics over longer periods of time (van der Meijden and Klinkhamer 2000); therefore, following long-term dynamics could lead to different conclusions.

We framed our research question from the naive parasitoid's perspective: when should a parasitoid follow an induced volatile coming from a plant, and how much of a fitness benefit can it obtain from following the volatile plume? These questions could also be framed from the plant's perspective: how accurate does a plant need to be to attract parasitoids? However, this implies that parasitoids can exert a positive evolutionary pressure on plant fitness. There is some evidence that parasitized Pieris species consume less, and that the plant can gain fitness by recruiting parasitoids (Fatouros et al. 2005). It is also possible, however, that parasitism has no effect on individual plant fitness within a single generation of parasitoids and hosts (Coleman et al. 1999), thus, making the question from the plant's point of view inconclusive (Janssen et al. 2002). To have evolutionary relevance this model needs to be modified to include long term plant fitness.

We hope the model will stimulate future research on the timing and spatial dynamics of herbivore-induced plant volatiles. While these are difficult parameters to measure in natural systems, they appear to be ecologically relevant and are important aspects to study, especially, if this phenomenon is to be applied practically in agriculture.

Acknowledgements

We thank Mathieu Legros for programming assistance. Comments by Coby Schal, Nick Haddad, and anonymous reviewers improved the manuscript. Funding for this research was provided by a National Science Foundation Pre-doctoral Fellowship and by the Keck Center for Behavioral Biology.

Supplementary material

10886_2008_9472_MOESM1_ESM.doc (530 kb)
Table 1 Relative advantage for parasitoids that followed signals, calculated as the number of hosts attacked by parasitoids following signals minus the number attacked by parasitoids randomly foraging, divided by the number attacked by randomly foraging parasitoids. Negative numbers indicate that randomly foraging parasitoids had a higher relative advantage than parasitoids following signals (pink colors accompany negative numbers and blue colors accompany positive numbers. The color intensity reflects the magnitude of the number—see below). The columns are as follows: “Induction” is the induction delay in days, “Relaxation” is the relaxation delay in days, “Density” is the herbivore host density, “Host” is the oldest viable instar host, “Distance” refers to the distance bias of the parasitoid, and “Pattern” is which pattern the parameter combinations were classified as. In the Distance column, “Exp” refers to an exponential signal bias, and “Lin” refers to a linear signal bias (DOC 540 KB).

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Molly Puente
    • 1
  • Krisztian Magori
    • 1
    • 2
  • George G. Kennedy
    • 1
  • Fred Gould
    • 1
  1. 1.Department of EntomologyNorth Carolina State UniversityRaleighUSA
  2. 2.School of EcologyUniversity of GeorgiaAthensUSA

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