Introduction

Chemical information plays an important role in the biology of many species ranging from microbes to mammals (Bell and Cardé 1984; Dicke and Takken 2006; Kats and Dill 1998; Wyatt 2004). The so-called infochemicals (Dicke and Sabelis 1988) provide information on the availability of food or mates, as well as on the presence of competitors or natural enemies. In addition to auditory, tactile, and visual cues, infochemicals are the most important cues for insects, both over short and long range distances (Cardé and Miller 2004; Vet and Dicke 1992). Another well-known example of an infochemical is the sex pheromone emitted by female moths that attracts conspecific males over long distances (Ostränd and Anderbrant 2003; Wall and Perry 1987). Once the chemicals are released, they are freely available for every organism in the food web (Bruinsma and Dicke 2008; Dicke and Baldwin 2010; Turlings et al. 1995). Thus, chemical communication among individuals of one species potentially can be spied upon by a natural enemy (Fatouros et al. 2005; Hedlund, et al. 1996; Wiskerke et al. 1993; Wyatt 2004). On the other hand, chemical information emitted by predators also can potentially be used by prey animals to avoid or escape from predators (Dicke and Grostal 2001; Fraker 2008; Kats and Dill 1998). Most studies on chemical information focus on the response of individuals to chemical cues. However, through changes in the behavior of individuals, chemical mediation of ecological interactions also can play a significant role at the population level (Vet 1999).

Host-parasitoid interactions can be influenced extensively by the exploitation of chemical information. Chemical compounds emitted by the host provide searching parasitoids with information on where to find their hosts. Parasitoids often face a problem known as the reliability-detectability problem (Vet and Dicke 1992). Chemical information emitted by the host is reliable, but usually not well detectable over long distances, as the host is under strong natural selection to be inconspicuous to its natural enemies. Chemicals from the host’s habitat often are better detectable over long distances, but this information is not reliable, because their presence does not necessarily indicate the presence of the host. One way to solve the reliability-detectability dilemma is to exploit chemicals that hosts emit to communicate with conspecifics, such as sex pheromones or aggregation pheromones (Dicke et al. 1994; Fatouros et al. 2008; Hedlund et al. 1996).

Models for host—parasitoid systems have been fruitful for many experimental and theoretical investigations, and have provided ample knowledge on parasitoid population dynamics (Godfray 1994; Hassell 2000; Wajnberg et al. 2008). Spatial aspects are important in parasitoid-host interactions (Tilman and Kareiva 1997; Turchin 1998). Modeling studies that include spatial effects have focused mainly on foraging behavior in environments where resources are heterogeneously distributed (Bukovinszky et al. 2007; Charnov 1976; Haccou et al. 1991; Wajnberg et al. 2012) or focus on temporal stability or on spatio-temporal patterns (Hirzel et al. 2007; Ives 1992; Nguyen-Huu, et al. 2006; Pearce et al. 2007; Schofield et al. 2005). There are few studies that model the effect of chemical information on spatio-temporal parasitoid-host dynamics. Pearce et al. (2007), Puente et al. (2008), and Schofield et al. (2002), studied the effects of chemical information; however, in these studies only the parasitoid responded to chemical information, i.e., herbivore-induced plant volatiles. They, however, did not include a response of the herbivorous host to the chemical information.

In the present study, we modeled how a natural enemy that “eavesdrops” on the chemical communication of its host may affect the population dynamics of the host. Our study system consisted of Drosophila melanogaster, the common fruit fly, and one of its natural enemies, the parasitoid Leptopilina heterotoma. This is a generalist parasitoid that attacks the larvae of a variety of Drosophila species inhabiting a variety of ephemeral substrates (Janssen et al. 1988). Adult female fruit flies emit a volatile aggregation pheromone (Bartelt et al. 1985) that attracts conspecifics and results in aggregated oviposition by female fruit flies on a suitable resource (Wertheim et al. 2006). Leptopilina heterotoma parasitoids exploit the aggregation pheromone of the adult fruit flies to localize their hosts, the larvae of the fruit fly (Wiskerke et al. 1993).

Drosophilid fruit flies tend to aggregate on suitable resources. Forming aggregations can benefit individuals in populations that are subjected to an Allee effect (a negative per capita growth rate at small population sizes [(Allee 1931) (for review, see Wertheim et al. 2005)]. If the population density is low, individuals can have difficulties in finding a mate, or in exploiting a resource (Berec et al. 2001; Wertheim et al. 2005). For instance, drosophilid fruit flies vector yeast to new substrates making it more suitable for their offspring by adding extra food to the resource, but also because yeast competes with fungi that have a negative effect on larval survival (Morais et al. 1995; Rohlfs et al. 2005; Stamps et al. 2012; Wertheim et al. 2002). Another possible advantage of aggregation can be a diluted risk of attack by natural enemies at high population densities [the selfish herd theory (Hamilton 1971)]. This can, for instance, be caused by the fact that a predator only is able to attack a certain amount of prey and, thus, more individuals survive at a high prey density, or that a large group of prey is better able to defend itself than a small group. Host finding and egg laying take time, which limits the number of hosts a parasitoid can parasitize in a fixed period of time. On the other hand, the formation of aggregations also can have costs. Individuals within an aggregation often experience more severe competition for food and mates than when they are on their own. A large group of individuals also can be more conspicuous to natural enemies and more vulnerable to parasites and diseases (Parrish and Edelstein-Keshet 1999).

Here, we addressed the positive and negative effects of using chemical information on the information-emitting species. For this reason, we mainly focused on the population dynamics of D. melanogaster. The use of an aggregation pheromone by D. melanogaster may affect its population dynamics in three ways. First, the use of the aggregation pheromone influences two density-dependent effects: the response to the pheromone promotes the formation of aggregations, which results in a reduction in mortality due to the Allee effect (Lof et al. 2009; Rohlfs et al. 2005; Wertheim et al. 2002). Second, the counteracting effect is that with increasing density, competition increases as well, resulting in larval mortality due to (scramble) competition (Hoffmeister and Rohlfs 2001; Rohlfs and Hoffmeister 2003; Wertheim et al. 2002). The trade-off between these two effects has been investigated (Lof et al. 2009). The present study focusses on a third aspect: the aggregation pheromone used by D. melanogaster can be exploited by their natural enemies to locate their host or prey (Wertheim et al. 2003). This may increase the mortality due to predation or parasitism. To study the effects of chemical information on the population dynamics of D. melanogaster when a parasitoid uses the same infochemicals to find its host, we developed a spatio-temporal model that incorporates odor distribution, the behavioral responses of fruit flies and parasitoids, and the foraging behavior of the parasitoid. It includes larval mortality due either to the Allee effect, or to competition, or to parasitism. In our model, both the parasitoid and the host can respond to chemical information. This is a novel approach, as other host-parasitoid models only consider chemotaxis for the parasitoid and assume random movement by the adult host (e.g., Pearce et al. 2006, 2007; Schofield et al. 2002, 2005).

Methods and Materials

Description of the Model

We developed a dynamic spatial parasitoid—host model that incorporates infochemical concentration, movement of parasitoids and adults of its hosts (both random and directed towards the infochemical source), and the interactions between the parasitoid and its larval host. The complete model and the formulas are found in Supplementary Material S1. Below, we give a brief summary.

Fruit Fly Behavior and Within Generation Population Dynamics

After hibernation (Boulétreau-Merle et al. 2003), fruit flies re-colonize an area with suitable breeding sites at the beginning of the breeding season. At the end of the breeding season, they leave the breeding area to find shelter. Because the winter acts as a system reset, we focused on the dynamics within one season. For results and biological conclusions, we looked at population size and population mortalities after a full season.

The development time from freshly oviposited eggs to adult fruit flies is about 19 d (Ashburner et al. 2005). Our simulation model contained ten non-overlapping fruit fly generations. At the start of each generation, a fixed number of resources (e.g., yeast-infected apples) lay randomly in the simulated orchard. Next, the population dynamics ran for 7 d. In the first 3 d, fruit flies dispersed and reproduced; in days 4–7 the parasitoids dispersed, searched for hosts, and parasitized fruit fly larvae (Fig. 1). The larvae that survived constituted the next adult fruit fly population 12 d later.

Fig. 1
figure 1

Flow chart of the processes in the model. In our model, the time step, ∆t, is 5 min. We simulated10 generations, each generation consisted of seven simulation days

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In our model, we considered female fruit flies and female parasitoids only. The female fruit fly population was divided into three subpopulations according to their current activity. On the resource, the settled flies (with density H S) mated and laid their eggs. When done, they first actively flew away from the resource (leaving flies, with density H L) in a random direction. After one time step, this gave a donut-shaped distribution. This was simulated in an integro-difference equation with a ring-random or ‘ripple’ dispersal kernel (see online Supplementary Material S2) (Allen et al. 2001; Brewster and Allen 1997; Etienne et al. 2002).

Next, they become searching flies (with density H C), flying at random until chemical information directs them towards a suitable resource (chemotaxis). Bartelt et al. (1985) showed that fruit flies (both females and males) responded more strongly to the combination of food odors (especially yeast odors, with density F) and aggregation pheromone (cis-vaccenyl acetate, with density A) than to food odors alone, and that they did not respond to the aggregation pheromone alone. We modeled the response of the searching subpopulations of fruit flies to food odors and the aggregation pheromone as a composite Monod function (Monod 1949). When the searching ends in finding a resource, the searching fly may settle on it.

Odor Distribution

Recently mated female D. melanogaster disseminate the aggregation pheromone as a slowly evaporating fluid (Bartelt et al. 1985). Searching fruit flies and parasitoids can detect this volatile (A) in the air, together with food odors (F). As we assumed that there is no wind, these odors thus diffuse randomly, i.e., they spread out in all directions at the same rate. Because odor diffuses in three dimensions, while we modeled in two dimensions, we introduced a loss term to represent odor molecules that get out of reach of the insects in the vertical dimension (de Gee et al. 2008).

Parasitoid Behavior and Within-Generation Dynamics

As from the fourth simulated day, the larvae that emerged from fruit fly eggs were amenable to parasitism. From that moment on, we started modeling the dynamics of the female parasitoid population. The parasitoids were divided into the same three activity states as the adult fruit flies.

On the resource, foraging parasitoids (with density P F) search for unparasitized hosts to oviposit in. We modeled parasitism as a Holling type II functional response (Holling 1959), which incorporates a saturating maximum parasitism rate. This response is parameterized by the host density, the search efficiency of L. heterotoma, and the handling time, i.e., the time between detecting a host and subsequently resuming the search for a next host. The rate at which foraging parasitoids leave a specific resource was estimated by using host-density dependent patch residence times from a study by Van Lenteren and Bakker (1978). They showed that the patch residence time of L. heterotoma increases with increasing numbers of hosts present on the patch.

Leaving parasitoids (with density P L) first actively fly away from the resource in a random direction, just as fruit flies do (ring-random dispersal, see online Supplementary Material S2). In the air, searching parasitoids (with density P C) use chemical information to locate a resource with fruit fly larvae. Leptopilina heterotoma has an innate response to the aggregation pheromone of D. melanogaster and some other Drosophila species (Hedlund et al. 1996; Wiskerke et al. 1993). Leptopilina. heterotoma also responds more strongly to the combination of food odors and aggregation pheromone than to food odors alone (Dicke et al. 1985; Wertheim et al. 2003). We used the same response function as for fruit flies, although with different parameter values.

Between-Generation Population Dynamics

Apart from parasitism, scramble competition and an Allee effect influence local larval D. melanogaster survival, so larval survival rate is highest at intermediate larval densities. At high densities, competition can cause high mortality. At low densities, harmful fungi may cause a high mortality of fruit fly larvae (Rohlfs et al. 2005; Rohlfs 2006). In D. melanogaster, adult fruit flies inoculate the resource with yeasts before egg-laying (Morais et al. 1995). This has two beneficial effects: first, it increases the amount of food for the larvae. Second, by competing with disadvantageous fungi, yeast reduces the fungal growth.

We assumed that parasitism does not affect the behavior of the larvae, and that the Allee effect and competition affect parasitized and unparasitized larvae equally. The surviving female larvae constitute the next adult female generation, and the adults that emerge in situ from their pupa immediately begin to search for a suitable resource. Thus, the next generation adults start by searching.

The development from larvae to adults is not always synchronized between parasitoid and host (Godfray 1994). In our system, the development time for L. heterotoma is approximately three times longer than for D. melanogaster. Therefore, there is a delay in time of two fruit fly generations before parasitoid larvae develop into adults. In this study, we focused on the costs and benefits of communicating through an aggregation pheromone for the fruit fly population dynamics; therefore, we focused on the dynamics of the host. Because L. heterotoma is a generalist parasitoid, attacking more than one host species, it is not likely that its population dynamics is affected very strongly by that of D. melanogaster. Therefore, the parasitoid dynamics was not modeled explicitly. Instead, each generation started with a parasitoid population that either had a fixed size, or a size that was proportional to the present fruit fly population. In both cases, the parasitoids started with a random distribution in the area.

Simulation Set-Up

We simulated one summer, consisting of ten discrete fruit fly generations. Per generation, we simulated three dispersal/reproduction days for the fruit fly population followed by four dispersal/oviposition days for the parasitoid population, each day consisting of 12 h, divided in time steps (Δt) of 5 min (Fig. 1). Non-volatile aggregation pheromone is excreted only by fruit flies in the first 3 d of the generation; thereafter, there is only evaporation. Food odors are produced during all seven simulation days. The next 12 d that complete a generation do not require spatial simulations: we just assess the number of larvae that survive and constitute the next adult fruit fly population. No adult mortality within a generation is incorporated in the model.

We assessed the effect of chemical information usage by both fruit flies and their parasitoids on the population dynamics of fruit flies by comparing fruit fly abundance and persistence for five different combinations of response types to chemical information: fruit flies that disperse randomly (Dm0) or can use both food odors and aggregation pheromone (DmFA), combined with parasitoids that disperse randomly (Lh0), use food odors (LhF), or use both food odors and aggregation pheromone (LhFA). These can be combined into six different combinations. However, we assumed that parasitoids cannot do better than fruit flies with respect to the aggregation pheromone. Therefore, only the combinations Dm0-Lh0, Dm0-LhF, DmFA-Lh0, DmFA-LhF, and DmFA-LhFA were simulated. In the simulations with a fixed number of parasitoids, we set the parasitoid level at 0, 300, 500, 700, or 900. In the simulations where the number of parasitoids at the beginning of a new generation was a fixed fraction of the number of fruit flies present, the number of parasitoids was 0.125 times that of the fruit flies.

We considered a spatial domain of 90 × 90 m. This was divided into 512 × 512 cells with side length of 0.1758 m. To mitigate boundary effects, we enlarged the simulated area to 180 × 180 m, with the actual domain in the center. On this enlarged domain, we used periodic boundary conditions for the odor distribution and for fruit fly and parasitoid populations. In periodic boundary conditions, the left boundary of the domain is connected with the right boundary, and the top boundary with the bottom boundary. This assures that the influx of flies and parasitoids into the domain is equal to the outflow. The enlarged area eliminates possible boundary effects for the odors. In the center of the domain, we simulated an orchard of 60 × 60 m with abundant resources (1 apple m−2). To mimic the natural situation, for each new generation of flies, 3,600 new apples were randomly allocated. At the beginning of the simulation, we released 4,000 adult fruit flies randomly distributed in the orchard. We simulated each combination three times with different realizations of the resource distributions to verify the consistency of the results.

To investigate the implications of using chemical information by fruit flies while a natural enemy “spies” upon this information, we kept track of the percentage mortality of fruit fly larvae due to the Allee effect, due to competition, and due to parasitism for the different scenarios. With this output, we specifically investigated what mortality factor (“Allee effect”, “competition” or “parasitism”) or combination of mortality factors (“parasitism and Allee effect” or “parasitism and competition”) caused fruit fly larvae mortality. We also investigated whether the formation of aggregations by fruit flies in response to the aggregation pheromone resulted in a diluted risk of parasitism.

The numerical solution of the model equations (see Supplementary Material S2) consists of two steps. First, odor evaporation, odor diffusion, adult fruit fly motion, and parasitoid motion are solved using the integro-difference (IDE) approach (as in Neubert et al. 1995; Powell et al. 1998). Next, the population dynamics are simulated.

Statistics

For both situations, fixed number of parasitoids (N = 500) or fixed fraction of parasitoids (1 parasitoid per 8 fruit flies), the development of the female fruit fly population was studied over the first six generations (during the fast population growth). As stated above, each simulation started with 4,000 female fruit flies. In each following generation, the size of the adult female fruit fly population was calculated as half the surviving number of fruit fly larvae produced by the last generation. As the numbers varied over several orders of magnitude, we analyzed the logarithm (base 10) of these population sizes. We fitted random coefficients models, allowing each simulation to have its own quadratic regression over generations, but all starting from the same intercept [log(4,000)]. The five distinguished groups can have different mean regression coefficients for the linear and quadratic terms. The random coefficient model is a type of linear mixed model. It was fitted using PROC MIXED of the SAS software program (version 9.2). The regression lines were compared pairwise between groups with F-tests, and the predicted log(counts) at generation 6 were calculated and compared between the groups (t-tests) to quantify population development. As ten pairwise comparisons were done both for the F-tests and t-tests, we used as threshold for the P-value 0.05/10 = 0.005, by applying the Bonferroni method.

In each generation, fractions of fruit flies either survived or died due to the Allee effect, competition, or parasitism. Per generation, the distribution of fruit flies over the four response categories, which we called a response pattern, was studied by using multinomial likelihood taking into account overdispersion. The response patterns were allowed to depend on the five distinct treatments. Next, a comparison of the response patterns among the five treatment groups was done using approximate F-tests. The F-test statistics were calculated as the mean change in deviance due to the treatment group, divided by the estimated extra scale parameter. To check treatment effects on the individual response categories (Allee, competition, parasitism, and survival), both overall and pairwise comparisons between treatments were made per response category by using approximate F-tests. The statistical analysis of the response patterns was done by programming in R (version 2.14.2). Separate analyses were done for the cases of fixed number of parasitoids and fixed percentages of parasitoids.

For the diluted risk of parasitism, we studied the percentage parasitism per resource. Its relation to larval density was investigated. A diluted risk of parasitism was shown if the percentage parasitism decreased with local larval density. To check whether the ability to use chemical information affected the risk of parasitism, we studied the local percentage parasitism for the five combinations of infochemical use by fruit flies and L. heterotoma. We also checked whether there were differences in the density-dependent percentages parasitism between the simulations with a fixed number of parasitoids (500) and a fixed fraction of parasitoids (1 adult parasitoid per 8 adult flies).

Results

Infochemical Use Affects Population Growth and Establishment

Figure 2 shows the development of female fruit fly population sizes over the first six generations (and beyond). For fixed number of parasitoids and fixed fraction of parasitoids the patterns are comparable. Note, however, that the population growth or decline is more extreme for the fixed number of parasitoids. In an earlier study (Lof et al. 2008), we found that the use of infochemicals by fruit flies had a positive effect on their population growth. In this study, we found that infochemical use by fruit flies still had a positive effect even in the presence of a natural enemy that can exploit this information.

Fig. 2
figure 2

The dynamics of the total fruit fly population in the orchard (60 × 60 m), for all 10 generations. a The simulations were run with a fixed total number of 500 parasitoids each generation. b The simulations were run with a fixed fraction of parasitoids each generations (Lh:Dm = 1:8). The five lines represent the following situations: Dm0-Lh0 ● and black drawn line; Dm0-LhF ○ and black dashed line; DmFA-Lh0 ■ and grey dashed line; DmFA-LhF □ and grey dotted line; DmFA-LhFA ◊ and drawn grey line. Dm0 Flies that disperse randomly, DmFA Flies that use both food odor and aggregation pheromone, Lh0 Parasitoids that disperse randomly, LhF Parasitoids that use food odors, LhFA Parasitoids that use both food odor and aggregation pheromone

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For both situations, fixed number and fixed fraction of parasitoids, the total number of fruit flies in the orchard in the first six generations was, according to pairwise comparisons of the six regression lines, not significantly different between DmFA-LhF and DmFA-LhFA groups (F 2,10 = 0.18, P = 0.84 for fixed numbers, and F 2,10 = 0.19, P = 0.83 for fixed fraction). All other pairwise comparisons yielded highly significant differences (P < 0.001 for all other comparisons). The total number of fruit flies in the orchard increasesd fastest when fruit flies responded to chemical information and parasitoids did not (DmFA-Lh0). Both the DmFA-LhF and DmFA-LhFA simulations where parasitoids were able to use some or all chemical information grew slightly slower. Furthermore, when fruit flies were not able to use chemical information, the fruit fly populations went towards extinction in all replicates when parasitoids were able to use food odors, and in two out of three replicate simulations when parasitoids were unable to use chemical information. The decline was faster for the Dm0-LhF simulations than for the Dm0-Lh0 simulations.

For a fixed number of parasitoids, the population size grew fastest for group DmFA-Lh0, with predicted log(population size) after six generations (± SE) of 4.89 ± 0.03. For the groups where parasitoids could use chemical information (DmFA-LhF and DmFA-LhFA) the predicted mean log(size) is 4.50 ± 0.03. If the fruit flies could not use chemical information, then the predicted mean log(size) is 3.34 ± 0.03 for parasitoids unable to use chemical information (and 3.04 ± 0.03 for parasitoids able to use chemical information). We conclude that when flies can respond to odors their population size at generation 6 is roughly 30 (≈101.5) times larger than when they cannot. When parasitoids are able to respond to odors, this results in a 50 % decrease of the fruit fly population (0.5 ≈ 10−0.3).

For a fixed fraction of parasitoids, the predicted means (log(size) ± SE) at generation six differ in a less extreme way: 4.16 ± 0.03 (for DmFA-Lh0), 4.03 ± 0.03 (for both DmFA-LhF and DmFA-LhFA), 3.51 ± 0.03 (for Dm0-Lh0), and 3.30 ± 0.03 (for Dm0-LhF). When fruit flies can respond to odors, their population size at generation six is roughly 5 (≈100.7) times larger than when they cannot. When parasitoids are able to respond to odors, this results in a 33 % decrease of the fruit fly population (0.67 ≈ 10−0.17).

Causes of Mortality and Size of Drosophila Population

In all simulations with a fixed number and fixed fraction of parasitoids at the start of each generation, we saw the effect of the local parasitoid—host interactions on the numbers in the orchard as a whole (see Fig. 2). For the fixed fraction of parasitoid numbers, the Drosophila population stayed between 6 103 and 15 104 individuals, whereas this range was much larger for the simulations with a fixed number of parasitoids (1 103 to 15 105). Thus, the relative density of the host and parasitoid matters. The interaction at the local scale with Allee effect, competition, and parasitism emerges also in the fates of the total larval population (see online Fig. S3): the Allee effect shows a diminishing impact when the total larval population size is between 104 to 3 105 individuals (Fig. S3a and e), while above that number the effect of competition increases (Fig. S3b). It is noted, that for the one population where the adult fruit flies did not respond to odors, the mortality due to the Allee effect of their larvae was lower than when they can. The spatial distribution of the adult fruit flies and consequently that of the larvae differed between those replicates: the colonization was not yet complete. Therefore, local larval densities were higher when they could not use odor information. Parasitism is always present, but it is only an important mortality cause for larval population sizes large enough for the Allee effect to be overcome, and small enough for competition not yet to have impact (Fig. S3c and g). Thus, as expected, the Drosophila larval population size drove the survival and the distribution over the different mortality causes. Hence, the larval population size and distribution is affected by the ability to use chemical information by the adults. When fruit flies can use chemical information, more fruit flies find a resource, and more eggs are laid. Consequently, the use of chemical information does affect the initial rate of population growth or decline as was seen in Fig. 2.

Relative Contributions of Factors for Larval Mortality Over Generations

Figure 3 shows the distribution of the mortality and survival of the larval population in each generation for the fixed number of parasitoids (Fig. 3a–e) and the fixed fraction of parasitoids (Fig. 3f–j). In the online Table S4, first, the results of the overall comparison of the five situations with respect to the distribution of the larvae over the categories Allee, competition, parasitism, and survival are shown. In almost all generations, the overall test (see S4, exception generation 10 for fixed fraction of parasitoids) indicates a significant difference (P <0.05) between the five different scenarios for the response to odors for fixed number of parasitoids and fixed fraction of parasitoids. Therefore, we report the results of the pairwise comparisons in online Table S5. When looking per generation for both the fixed number and fixed fraction of parasitoids, we see that these always give rise to different patterns for the Allee effect (except the last generation in the fixed fraction simulations). Parasitism also is affected by the five different situations (except in generation 8 for the fixed number of parasitoids). Competition is not affected in the fixed fraction simulations, whereas it is in the last six generations for the fixed number of parasitoids. Survival in the first six generations is significantly different for the five different situations in the fixed number and fixed fraction simulations. After the sixth generation, the overall difference is sometimes significant and sometimes not.

Fig. 3
figure 3

Local percentage mortality of fruit fly larvae per generation. The simulations were run a–e with a fixed number of 500 parasitoids each generation and f–j a fixed fraction of parasitoids (Lh:Dm = 1:8). The abilities of the fruit flies and parasitoids are (a) + (f) Dm0-Lh0, (b) + (g) Dm0-LhF, (c) + (h) DmFA-Lh0, (d) + (i) DmFA-LhF, and (e) + (j) DmFA-LhFA. The bars depict, per generation, the cumulative percentage mortality due to Allee effect (black), competition (dark grey), and parasitism only (light grey) and percentage survival (white). Dm0 Flies that disperse randomly, DmFA Flies that use both food odor and aggregation pheromone, Lh0 Parasitoids that disperse randomly, LhF Parasitoids that use food odors, LhFA Parasitoids that use both food odor and aggregation pheromone

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The ability of fruit flies to use chemical information affects the distribution over the mortality causes of their offspring. If fruit flies can respond to chemical information, larval mortality due to the Allee effect decreases in the first five generations (Fig. 3c–e and h–j). Moreover, the percentage mortality due to parasitism increases. Both effects are caused mainly by the increasing population size. After the fifth generation, larval competition increased so strongly that it impeded further population growth (Fig. 3c–e) in the simulations with a fixed number of parasitoids. In the simulations with a fixed fraction of parasitoids, severe competition never took place because the fruit fly population size was never large enough for competition to become important. If fruit flies are not able to respond to chemical information, a small effect in time is observed for percentage larval mortality due to the Allee effect or competition, compared to fruit flies, responsive to chemical information (Fig. 3a–b) in the simulations with a fixed number of parasitoids, while the Allee effect seems to be overcome in later generations in the simulations with a fixed fraction of parasitoids (Fig. 3f–g).

Effect of the Parasitoid Number (Fixed Number Simulations)

The number of parasitoids in the orchard affects fruit fly persistence. When fruit flies cannot use chemical information, the population can persist only at low parasitoid pressure (Table 1). When fruit flies can use chemical information, they can co-exist in the presence of a larger parasitoid population. The presence of more parasitoids delayed the population growth (data not shown). This is caused mainly by the fruit fly population needing more time to overcome the Allee effect due to higher parasitism. The use of infochemicals by parasitoids delays the population growth even more. When parasitoids can use chemical information, more parasitoids settle on a resource, and thus, more larvae are parasitized.

Table 1 Fruit fly persistence for increasing number of parasitoids present, for different combinations of the ability to respond to chemical information by the fruit fly and the parasitoid
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Diluted Risk of Parasitism?

For simulations with a fixed number of parasitoids, we did not find a diluted risk of parasitism for higher numbers of larvae per resource. On the contrary, the percentage parasitism increased with increasing numbers of fruit fly larvae on a resource (Fig. 4). The increase in parasitism with number of larvae present on a resource occurred for all simulations. However, when the number of parasitoids was fixed, we found more variation in percentage parasitism after the strong population growth of the host (Fig. 4c–d). This indicates that even though there is locally no diluted risk of parasitism, global dilution of risk exists when not enough parasitoids are present. Handling a host and laying an egg costs time [30 sec for L. heterotoma (Wertheim 2001)]. When many larvae are present, the handling time sets the upper limit to how many larvae L. heterotoma can parasitize in a fixed time interval. When the fruit fly population is large, consequently, the total number of eggs deposited on all the resources also will be very large. Therefore, the parasitoid cannot reach the same high percentage parasitism on all resources. When the number of parasitoids is fixed, and the fruit fly population is large, we found high percentage parasitism only in a part of the resources.

Fig. 4
figure 4

Larval mortality due to parasitism for each resource depicted for larval density on resource in simulations with a fixed number of 500 parasitoids; each generation. Depicted are generation a 3, b 5, c 7, and d 9 for the simulations where both fruit flies and parasitoids could respond to both food odors and aggregation pheromone (DmFA-LhFA)

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In the case where the number of parasitoids is a fixed fraction of the fruit fly population numbers, the variation in percentage parasitism does not increase when the fruit fly population reaches its carrying capacity. Per resource, only a maximum number of 70 Drosophila larvae were present. At these local densities, almost no variation in percentage parasitism existed in the simulations with a fixed number of parasitoids either. In our simulations, at the same larval densities for a fixed fraction of parasitoids, the percentage parasitism was 10 to 20 % higher than with a fixed number of parasitoids. Therefore, we conclude that in the fixed fraction simulations the parasitoids had enough time to exploit all resources efficiently.

Discussion

The response of insects to chemical information has been studied in great detail both in the laboratory and in the field (reviewed in Bell and Cardé 1984; Dicke and Baldwin 2010; Dicke and Grostal 2001; Kats and Dill 1998; Fatouros et al. 2008; Wertheim et al. 2005). Predators and parasitoids commonly use chemical cues originating from the host’s habitat (plant volatiles) or cues originating from the host’s chemical communication (for instance sex-pheromones) to locate their host (Bruinsma and Dicke 2008; De Boer and Dicke 2004; De Moraes et al. 1998; Fatouros et al. 2005; Shiojiri et al. 2001; Turlings et al. 1995). The exploitation of chemical cues of the host or the host’s habitat by predators or parasitoids often results in a higher attack or parasitism rate (Wertheim et al. 2003; but see Tentelier and Fauvergue 2007). To our knowledge, the consequences of the ability to use chemical information on population dynamics have not been addressed in a modeling study when both parasitoid and host can respond to the same chemical information. Several modeling studies, however, have addressed parasitoid—host dynamics for systems where only the movement of parasitoids is influenced by chemical information (Pearce et al. 2007; Puente et al. 2008; Schofield et al. 2005).

Effects of the Use of Chemical Information by Host

Consistent with previous studies (Lof et al. 2008, 2009), we found that the use of chemical information by fruit flies enhanced their own population growth rate, even when parasitoids were present. In addition, we found that fruit flies that use chemical information, i.e., food odors and the aggregation pheromone, can persist with more parasitoids present than in the situation where they disperse only randomly. When fruit flies use chemical information, more fruit flies find the resources. Therefore, more eggs are laid per resource, fruit flies more easily overcome the Allee effect, and the population is able to survive higher parasitism pressure.

Effects of Spying Parasitoids

In the present study, we showed that the ability to use chemical information by both parasitoid and host affects the population dynamics of the host. In accordance with experimental results of Wertheim et al. (2003) for the same experimental system, we found that when parasitoids exploited chemical information, the average percentage parasitism was higher. As a result, the population growth rate of fruit flies is lower, and it takes longer to overcome the Allee effect. This negative effect is even stronger when fruit flies are not able to use chemical information and have to find the resources by random dispersal. Protection from predators is viewed as an important selective advantage to being a group member in an aggregation (Parrish and Edelstein-Keshet 1999). In our modeling study, we did not find local diluted risk of parasitism at higher larval densities. Instead, we found that percentage mortality of larvae due to parasitism increased with larval density on a resource.

Ecological Costs of Chemical Communication

Predation and parasitism are important mortality factors for many insect herbivores. As usage of chemical information in locating prey or hosts is especially advantageous when searching for cryptic prey, predation and parasitism might be expected to exert a strong selective pressure on intra-specific communication by chemical information. Nevertheless, as pheromones are crucial to many aspects of herbivore life history, radical alterations of these compounds can be disadvantageous despite their exploitation by predators and parasitoids (but see Raffa et al. 2007).

In Drosophila, larval parasitism is an important mortality factor (Allemand et al. 1999; Fleury et al. 2004; Janssen et al. 1988; Wertheim et al. 2003). Since the larval parasitoid L. heterotoma exploits the aggregation pheromone of the adult fruit flies to localize its hosts, we expected that the use of aggregation pheromone by D. melanogaster would increase the percentage mortality due to parasitism in the larvae of D. melanogaster, as was also found in the field (Wertheim et al. 2003). However, in this model study, we did not find evidence for an ecological cost of the use of aggregation pheromone by D. melanogaster with respect to increased risk of parasitism. A possible explanation for this discrepancy is the difference in experimental setup. In our simulation, we did not compare two types of resources, but two types of parasitoids, a ‘wild-type’ parasitoid that can respond both to food odors and its hosts aggregation pheromone, and a hypothetical ‘mutant’ parasitoid that can respond only to food odors. This simulation potentially can show the added effect of the response to aggregation pheromone by the parasitoid, while the field situation shows the preference for the resource with both food odors and aggregation pheromone. This is one of the advantages of modeling; it can make comparisons possible that are difficult or impossible to test in real life. Here, we could extract the effect of the fruit fly aggregation pheromone solely on parasitism rates by comparing parasitism rates when parasitoids can use both food odors and aggregation pheromone, and parasitism rates when parasitoids can use only food odors or no odors at all, while keeping all other properties of the parasitoid’s behavior unchanged. Because the parasitoid that we studied has an innate response to its host’s aggregation pheromone and to the odors produced by its host’s habitat, this comparison cannot easily be made in a field experiment.

For our study, we were interested in positive and negative effects of the use of aggregation pheromone by fruit flies. Therefore, we focused on the dynamics of the host. To make these dynamics transparent, we excluded possible effects caused by the dynamics of the parasitoid, by assuming that the number of parasitoids present in each generation was either constant or equal to a fixed proportion of the fruit fly population. We expect that the actual dynamics of L. heterotoma lies closest to the fixed proportion of the fruit fly population. Because L. heterotoma is a generalist, it can switch to other Drosophila species when the density of D. melanogaster is low, or even to an alternative host habitat. Hence, it is not likely that it would go extinct when D. melanogaster is not present. On the other hand, one expects that when D. melanogaster is abundant, the density of L. heterotoma would increase (possibly after a time lag).

Our results indicate that parasitism rates where parasitoids can use only food odors are close to the parasitism rates where parasitoids can use both food odors and its host’s aggregation pheromone. A possible explanation for this question may be that the patch-leaving rules were estimated from an experiment of Van Lenteren and Bakker (1978) in an environment where hosts were scarce and the host distribution was clustered. In our experimental setup, both host habitats and hosts were abundant, and because of the random initial distribution of the fruit flies, almost all apples were occupied. Finding an apple (by only using food odors) is often sufficient to find hosts, and, due to the high larval densities on the apples, parasitoids spend a long time on the patch before leaving. Searching for an occupied host habitat only takes a small fraction of the parasitoid’s time. Most of its time is spent foraging on the apple. To test our assumptions, it would be interesting to study whether, in abundance of hosts and host habitats, parasitoids indeed continue to forage with the same decision rules or whether they can adjust their behavior. Furthermore, in our model, parasitoids do not distinguish between patches based on the larval density on the patch. When they find a patch, they settle and start foraging. Only the patch residence time is affected by the number of hosts on the patch. To test whether this assumption is correct, it would be necessary to test whether parasitoids avoid patches with very high larval densities, where their offspring are likely to die because of scramble competition between the hosts.

In this study, we did not find significant differences in the percentage mortality of fruit fly larvae and fruit fly population size between the simulations where parasitoids could use only food odors on the one hand, or the simulations where they could also exploit the aggregation pheromone of D. melanogaster on the other hand. However, this does not imply that there is no cost with respect to parasitism when parasitoids can respond to chemical information. The fruit fly population increases at a slower rate (both for the fixed number and the fixed fraction of parasitoids) and has a lower carrying capacity (only at a fixed fraction of parasitoids) when parasitoids can use chemical information as compared to the simulations where they can search only randomly. This, however, is already the case when parasitoids can respond only to food odors.