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Keywords:

  • Centaurea diffusa;
  • density dependence;
  • ideal free distribution;
  • insect distribution;
  • Larinus minutus;
  • model;
  • plant–herbivore interactions;
  • resource dilution;
  • Urophora affinis

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

1. The distribution of herbivores among plant patches may be an important factor determining plant population persistence. The resource concentration hypothesis proposes that herbivores are more abundant per unit plant at higher host plant densities and this has been found to occur in many systems. However, the opposite pattern, resource dilution, in which the herbivores are more abundant in low-density patches and situations in which the number of insect herbivores per unit plant remains constant, also occurs.

2. We developed a simulation model to explore how the distribution of insects per plant affects plant population decline and persistence. We varied the numbers of plants per patch and the distribution pattern, i.e. whether insects were found in a resource concentration distribution, a resource dilution distribution or a distribution in which insect abundance increased linearly with plant density.

3. Resource concentration resulted in longer persistence of plant populations. Plant populations declined more rapidly with either weak resource dilution or directly proportional insect distribution patterns. As the intensity of resource concentration increased, the decline in plant population density was reduced, and plant persistence increased because of increasing variance in insect load. Under strong resource dilution, increasing variance in the insect load also led to a reduction in plant population decline and an increase in plant persistence.

4. We complement our model with field data from the diffuse knapweed, Centaurea diffusa biocontrol system. We compared the relationship with plant density of a successful biocontrol agent, Larinus minutus, and an unsuccessful one, Urophora affinis. Larinus minutus density was directly proportional to plant density, while U. affinis showed a resource concentration pattern with higher rates of attack in high-density patches.

5.Synthesis: Patterns of insect distribution with host plant density will alter the extent to which patches of differing plant densities decline or persist. Resource concentration promotes persistence of the insect–plant system because increased herbivore pressure in high-density patches leads to negative density-dependent plant growth. Weak resource dilution and a distribution of insects that is directly proportionate to plant density can accelerate plant population decline. Strong resource dilution leads to positive density dependence with higher population growth in large patches. Our simulation model and field data demonstrate that the relationship between insect distribution and plant densities can influence plant population dynamics and has implications for choices of weed biological control agents.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

It is now commonly acknowledged that insects can influence the abundance of their host plants; however, our understanding of when insects are able to influence plant abundance remains poor (reviewed by Maron & Crone 2006). Spatial variation in herbivore load via insect aggregation on individual host plants has been suggested as a potential regulation mechanism for the populations of both plants and insects (Myers, Monro & Murray 1981; Heard & Remer 2008). Such aggregations may arise through a range of mechanisms that mediate the response of insects to plant density, for example sensory biases (visual vs. olfactory), dispersal biases, food requirements and diet breadth, competitive exclusion and predation (Kunin 1999).

The density of herbivorous insects may be related to the density of their host plants in a variety of ways (Rhainds & English-Loeb 2003). The resource concentration hypothesis states that more dense or larger stands of a plant will recruit more herbivores per unit plant (Root 1973), and this effect will be strongest for specialist herbivores. Some herbivores have been documented to follow a resource concentration type distribution (e.g. Kèry, Matthies & Fischer 2001; Ostergard & Ehrlén 2005; Sholes 2008). However, in other systems, (e.g. Kunin 1999; Elzinga et al. 2005; Fagan et al. 2005), the reverse pattern has been observed. In these cases, plants in sparser stands experience greater levels of herbivory per unit plant, a distribution termed ‘resource dilution’ (Otway, Hector & Lawton 2005).

These differences in density-dependent relationships could potentially influence the persistence of the insect–plant system. Under a resource concentration distribution, we predict that the higher density of specialist herbivores in large patches should increase herbivore damage and decrease plant reproduction or survival. This would allow smaller patches to grow in size or density (negative density dependence, i.e. higher plant population growth rates at low densities) and reduces the likelihood of extinction. Resource dilution could establish the opposite pattern (positive density dependence, i.e. greater plant population growth rates at high densities) as the increased number of specialist herbivores in small patches will reduce the number of plants in these patches making them more extinction-prone.

Previous models by Heard & Remer (2008) and Myers (1976) considered patterns of insect distributions on plant, but not the influence of this on host-plant populations. Here we evaluate the effect of contrasting patterns of insect distribution on the host-plant populations. To investigate this, we created a simulation model for a hypothetical insect–plant system in which the insects were pre-dispersal seed predators. Our model assumes that insects are able to reduce the populations of their host plant; this is the basic premise of the enemy release hypothesis (Keane & Crawley 2002) and weed biological control. Patches had different numbers of plants, and insects were differentially distributed across those patches following either a resource concentration pattern, a resource dilution pattern or directly proportional with the number of plants in the patch. We varied the strength of resource concentration or dilution. For example, as the resource concentration pattern strengthens, increasing numbers of insects occur in the larger patches and fewer in the smaller ones. We predicted that increasing variance in insect load (insects per plant) between patches would increase persistence times (less extinction). Although our model is based on pre-dispersal seed predators; we predict that the model is applicable to other herbivore guilds that indirectly reduce plant reproduction. We then illustrate our simulation results with an observational study of the diffuse knapweed biocontrol system and consider the distributions of two different insect species with contrasting levels of weed control.

Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Model details

Plant populations

We created a simulation model in R (R Development Core Team 2009) to test whether the insect distribution patterns that are driven by plant density alter the extent of plant population persistence and rate of population decline. Our modelled herbivores are pre-dispersal seed predators that attack the seed-head (or other type of fruiting body) and destroy a set proportion of seeds. Insects are able to move freely between plant patches. However, as plant recruitment is local to the patch, the model is not spatially explicit. The modelled plants are annuals.

The only density-dependent mechanisms present in the model are (i) the maximum number of plants in a given patch is limited by a carrying capacity, described below, and (ii) insect reproduction in a given patch is limited by the availability of seed-heads for offspring development. No additional density-dependent plant reproduction factors exist in the model to ensure that changes in the plant population because of insect herbivory are clearly evident and not altered by plant density-dependent mechanisms.

We started the model with twenty plant patches, with the number of plants in each patch drawn from the exponential distribution with a rate of 0.01 (resulting in a mean patch size of 100 plants). Using the exponential distribution gives many small and a few large patches (left skew), a distribution of patch sizes often seen in invading populations (Moody & Mack 1988; Bishop 2002; Müllerováet al. 2005). We define the total population as the sum of all plants in all patches, and each patch is a subpopulation. The initial number of plants in the patch sets the patch carrying capacity, which is the maximum number of plants the patch can support. In each patch, plants can be of varying sizes – the number of seed-heads per plant was taken from a normal distribution with a mean of 75 and SD of 10, censored so that minimum seed-heads per plant equals zero. We then calculate the total number of seed-heads in each patch.

Insect distribution in relation to plant patch size

We started the model with 10 insects per plant in the total population. The insects are then distributed across the patches following power relationships as shown in Fig. 1a and described below. Figure 1b shows how these total numbers convert to insect load. This form was chosen because it best matches the verbal description of Root (1973), it asymptotes to zero (insect load cannot be negative nor can insects be present on non-existent plants) and we can distinguish between weak and strong resource dilution. This is the same form as the relationship between weevil and sawfly densities on figwort Scrophularia nodosa (Andersson & Hambäck 2011). Andersson & Hambäck (2011) predicted a curvature of −0.5 based on scaling of olfactory information with patch size and suggest that departures from this value indicate differences in insect search behaviour (they reported curvature values of −0.15 and −0.53 for sawflies and weevils on figwort, respectively). The curvature parameter determines whether the distribution follows a resource concentration, resource dilution pattern or is directly proportional to plant densities. If the curvature is one, this equation gives a direct proportional pattern between plant density and insect load (Fig. 1) or the ideal free distribution (Kennedy & Gray 1993). For resource concentration, curvature is >1, and insect load is lower in small plant patches, but higher in large patches, compared with the direct proportional pattern. The further the curvature value is from one, the stronger the pattern. When the curvature is <1, resource dilution occurs, and plants in small patches have a higher insect load, and plants in large patches have a lower load compared with the direct proportional pattern. Weak dilution occurs when the curvature parameter is between 0 and 1, while a negative curvature parameter represents strong resource dilution. Under weak resource dilution, a small patch has a lower total abundance of insects than a large patch, but plants within a small patch will have a higher individual load. Under strong resource dilution, a small patch has both more insects overall and a higher load than a large patch (Fig. 1).

image

Figure 1.  Patterns of insect distribution modelled: directly proportional (curvature θ = 1) to plant population, resource concentration (curvature = 2) and resource dilution (weak: curvature = 0.5; strong: curvature = −0.1). The total number of insects (a) was calculated as described in the text and was the same under all three distributions. We then calculated the corresponding insect load (= insects per plant; b) by dividing the total number of insects by the number of plants in the patch.

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The number of insects in a given patch i at time t (xi,t) is calculated as:

  • image(eqn1)

where yi,t is the number of plants in patch i at time t, Σixi,t is the total number of insects present in the total population at time t, summed over all patches and θ is the curvature parameter. Tables of all symbols used are available in Appendix S1 of the Supporting Information.

We hypothesized that increasing the absolute distance from one of the curvature parameter would increase variance in insect numbers and load among the patches. We calculated the variance of insect number and load on a standardized population using curvature parameters ranging from 3 to −1 to determine how variance changes, and used those curvature values subsequently in model simulations.

Insect reproduction and damage to plants

We modelled insect reproduction using this equation:

  • image(eqn2)

where each patch produces xi,t insects and ∑ixi,t+1 represents the total number of insects in the second generation. Insect reproduction in each patch is determined by their reproductive potential, r, the number of seed-heads available in that patch, si,t and the proportion of seed-heads escaping attack, e. Each insect can produce eight offspring (rx; values used by Heard & Remer (2008) and Myers (1976) are similar) if seed-heads are available for those offspring. Any offspring produced beyond the number of available seed-heads die – a seed-head can produce only one insect. This was performed primarily to simplify the model but is analogous with the situation in many insect species where oviposition pheromones deter a second oviposition to reduce cannibalism (Dip.: Tephritidae, Prokopy, Ziegler & Wong 1978; Lep.: Pieridae, Dempster 1997; Col.: Coccinellidae, Martini et al. 2009).

In the field, even when insect densities are high, some seed-heads will not be attacked. The proportion of seed-heads that escape attack characterizes the search efficiency of the insect. Escape from herbivory may occur because of mismatches between plant and insect phenology (Singer & Parmesan 2010; Bourchier & Crowe 2011). We refer to this variable as seed-head escape, e, and each generation is sampled from a uniform distribution ranging from 0% to 20% of the seed-heads in a patch. While these seed-heads are unavailable for insect reproduction, they produce seeds. A seed-head will also escape attack if there are insufficient insects to attack all seed-heads. Thus, the total number of seed-heads in a patch that escape insect attack, Ti,t, is:

  • image(eqn3)

Plant reproduction (flowering plant to flowering plant) is a function of the number of seed-heads in a patch (si,t; determined by the number of plants in a patch), the number of seed-heads that escape attack (Ti,t), the impact of an insect when it attacks a seed-head (a) and a reproduction constant (ry). When no herbivory occurs, average plant reproduction is 7.5 flowering plants for each flowering plant. This is in line with Heard & Remer (2008); four plants plant−1 year−1), Myers & Risley (2000); 6.3–0.53 knapweed plants plant−1 year−1) after including density-dependent plant reproduction and initial patch size density of 1–9 plants m−2, and Rees & Paynter (1997); 25 scotch broom plants plant−1 year−1) if sites were available for plant colonization. The number of new plants produced by the patch i (pi,t+1) is calculated by:

  • image(eqn4)

The insect impact parameter (a) determines the proportion of seed-heads (5%) in the patch that are able to reproduce when attacked. When seed-heads are not attacked, each seed-head produces one seed. If a = 1, then no attacked seed-heads reproduce; if a = 0, insect attack has no effect. As the modelled plants were annuals, all plants in the previous generation (Σipi,t) were removed from the model. For the next generation, all of the insects produced (Σixi,t+1) were reallocated across the plant patches as described above (eqn 1).

Output

To consider short-term (transient) dynamics, we ran the model for 10, 20 and 30 generations, redistributed the insects across the plant populations each generation and conducted 1000 simulations. We report the plant population size (total number of plant individuals summed across all patches, referred to as the total population) and number of plant patches (=patches) present after 10, 20 and 30 generations. A patch was present if it had at least one plant.

We then ran the model 1000 times for 1000 generations and considered persistence time, i.e. the number of generations required for plant populations to go extinct. Insect populations become extinct in the generation immediately after plant extinction. We report the proportion of runs in which the plant populations become extinct and the mean time to extinction of those populations.

We varied key parameters (plant reproduction, insect impact, insect reproduction and seed-head escape) to assess how dependent our results were on each variable. We chose the parameters because of a priori assumptions about their influence on rates of population decline. These parameters had a single value for the main analysis. For each parameter, we endeavoured to cover the range of values that produced a result between complete extinction after 1000 generations and no decline in the plant population. We ran the model 100 times for both 30 generations and 1000 generations to obtain varying curvature values and assessed the same responses as above.

To determine how different patterns of insect distribution alter the density dependence of plant reproduction, we removed plant carrying capacity and ran the model for 1000 simulations under varying curvature values for just two generations. For each simulation, we calculated the change in plant population in each patch by dividing the patch population in Generation 2 with the patch population in Generation 1 (>1 plant population increases, <1 plant population decreases). We used the nlme package in R (Pinheiro et al. 2009) to calculate the average slope of the relationship between the relative change in plant population (Gen. 2/Gen. 1) and the number of plants in each patch in Generation 1. Simulation was treated as a random effect. We used 95% confidence intervals to assess whether the slope was significantly different from zero. Positive slopes occur when large patches produce more offspring per plant than small patches (positive density dependence). Negative slopes indicate negative density dependence and occur when small patches produce more offspring per plant than large patches.

Observational study

Study system and sites

Diffuse knapweed (Centaurea diffusa Lam., Asteraceae) is a biennial or short-lived perennial invasive weed in North America from Colorado to British Columbia. In its second or third year, it produces up to 1500 seed-heads (median 60; this study) and dies after seed production. Here, we document the distribution of two common seed-head herbivores that oviposit in the seed-heads: Larinus minutus Gyllenhal (Col.: Curculionidae) and Urophora affinis Frauenfeld (Dip.: Tephritidae). Urophora affinis larvae form galls in the seed-head, while L. minutus larvae eat the entire contents of the seed-head. Larinus minutus eliminates U. affinis when they co-occur in a seed-head (Crowe & Bourchier 2006). Neither species moves between seed-heads as larvae. The introduction of U. affinis was not associated with apparent changes in knapweed abundance, while the recent decline of diffuse knapweed has been attributed to L. minutus (Myers et al. 2009).

Our two study sites were in the southern Okanagan Valley of British Columbia, Canada – a meadow above Vaseux Lake (49°17′45.97″, −119°31′34.21″, 384 m a.s.l.) and a meadow near the White Lake Observatory (49°19′12.65″, −119°37′46.43″, 549 m a.s.l.). At both sites, diffuse knapweed has declined overall (Myers et al. 2009), but dense patches are still present, resulting in a wide distribution of patch sizes.

Density measurements

In July 2008, we chose 80 flowering plants at each of the two sites. To select plants, we ran a series of arbitrarily selected transects along the site. Focal plants along transects were chosen by blindly taking 10–20 paces then identifying the nearest neighbour. This design ensured that we had a good representation of all density levels across the meadow. We measured the number of flowering plant stems in a 1 m2 quadrat surrounding the focal plant.

We harvested half the focal plants in early August and the second half in mid-September, to determine whether competition between the two insects could influence the observed pattern between insect density and plant density as predicted by Kunin (1999). In August, seed-heads often contain both species. By September, however, L. minutus had consumed U. affinis galls and larvae.

Seed-head herbivores

To determine the level of seed-head attack by the larvae, we assessed sufficient seed-heads on each plant to achieve an accuracy of 90% (E = 0.1) and confidence interval (Z) of 1.645 (90% confidence) for each plant under the binomial distribution with finite population sizes (Krebs 1999). In September, some insects had emerged, but either their damage or gall remained. In these cases, we scored the species as present.

Data analysis

For seed-head herbivores, the appropriate measure of insect load is the number of insects per seed-head (although for other feeding guilds, other definitions are more appropriate, e.g. Otway, Hector & Lawton 2005). We counted every insect in the seed-heads. In some cases, more than one insect per seed-head was present, i.e. insect load was greater than one. This occurred either because the seed-head contained multiple U. affinis galls (Harris 1980) or because several L. minutus (eggs or small larvae) were sometimes present in August, although by September only one was ever present. If seed-heads could only support one insect, insect load would equal the proportion of seed-heads infested.

We determined whether the L. minutus and U. affinis loads on a plant were related to plant density using Spearman’s rank correlation in R (R Development Core Team 2009) as data did not meet the assumptions of normality and homoscedascity.

As we calculated insect load on the plant rather than total number of insects in the patch, a positive slope in response to density is indicative of resource concentration, a negative slope indicates resource dilution and slope of zero indicates a direct proportional response between insect and plant densities.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Model

Variance in insect load and numbers increased with both the strength of resource concentration or resource dilution (Fig. 2). As expected, variance in load was lowest when insect load was directly proportional to plant density (i.e. curvature equals 1).

image

Figure 2.  Variance in insect load (insects per plant) and numbers (log) on plant patches following redistribution under different curvature parameters. Total plant population was 275 in 10 patches containing 5, 10, 15, 20, 25, 30, 35, 40, 45 and 50 plants, respectively. The total number of insects distributed among the plants was 2750 (10 insects per plant when curvature = 1). When curvature = 1, there is no variation in the number of insects per plant in the different plant patches, and when curvature = 0, there is no variation in insect load across in the patches (variance = 0). Above the x-axis, s.RD refers to strong resource dilution, w.RD to weak resource dilution, DP to the directly proportional pattern and RC to resource concentration.

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Both the number of plant patches and the total population declined over time following the introduction of insect herbivores with all insect distribution patterns (Figs 3 and 4). Total population decline was greatest when insect pattern was either directly proportional to plant density or followed a weak resource dilution pattern (Fig. 3). The reduction in the number of patches was greater under the direct proportional pattern and resource dilution (both weak and strong) than resource concentration; this difference became greater over time (Fig. 3), but at high resource concentration, all patches remained after 30 generations when curvature was >1.75. More extreme curvature values (i.e. increasing strength of the pattern) were associated with less reduction in the total population.

image

Figure 3.  Mean (±SD) total plant populations (top) and total number of plant patches (bottom) remaining after 10, 20 and 30 generations under a range of curvature parameters. The mean value of each run is represented by the closed black symbol, while each simulation (1000) is represented by the open grey symbol. Curvature parameter values >1 indicate resource concentration, =1 indicate a directly proportional relationship with plant density, 0–1 weak resource dilution and <0 strong resource dilution. Above the x-axis, s.RD refers to strong resource dilution, w.RD to weak resource dilution, DP to the directly proportional pattern and RC to resource concentration.

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image

Figure 4.  Proportion of simulations where plant populations persisted beyond 1000 generations (left) and mean (±SD) time to extinction of runs where all populations became extinct (right). The mean value of each run is represented by the closed black symbol, while each simulation (1000) is represented by the open grey symbol; at a curvature of 2, extinction of the plant population occurred in only one simulation only, and no extinctions occurred when curvature equalled 2.5 or 3. Above the x-axis, s.RD refers to strong resource dilution, w.RD to weak resource dilution, DP to the directly proportional pattern and RC to resource concentration.

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Persistence of the insect–plant system was greater with resource concentration (Fig. 4). When curvature equalled 2, all populations survived, so we did not run the model for curvatures of 2.5 or 3. Plant populations persisted longer as the curvature parameter increased from 1 or decreased from 0, (Fig. 4).

Resource concentration and dilution caused opposing patterns of plant density dependence (Fig. 5). Strong resource dilution caused positive density dependence as more plant offspring were produced in the larger plant patches leading to a positive relationship between rate of change in patch population and patch size. Resource concentration caused negative density dependence as more offspring per plant were produced in smaller patches. No density dependence in plant reproduction was evident when insects responded in a weak resource dilution or direct proportional pattern (i.e. slopes were not significantly different from zero, Fig. 5).

image

Figure 5.  Impact of the curvature value on density dependence of plant reproduction. Mean slope of relationship (with 95% confidence intervals) between the relative change in plant population (Gen. n+1/Gen. n) and the number of plants in each patch in Generation n is presented. A positive slope refers to positive density dependence (plants in larger patches produce more offspring), while negative slopes indicate negative density dependence. If the slope does not differ from zero, no density dependence was observed. Above the x-axis, s.RD refers to strong resource dilution, w.RD to weak resource dilution, DP to the directly proportional pattern and RC to resource concentration.

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Varying the key parameters demonstrated that the differences we observed between the insect distribution patterns were not dependent on the parameters chosen. Resource concentration always lead to a higher total population, more plant patches and longer persistence times, while directly proportional and weak resource dilution patterns were associated with a lower plant population and shorter persistence times. When seed-head escape or plant reproduction was high (above 20% or 0.12 respectively) or insect impact low (below 0.93), insects did not affect plant populations regardless of the pattern. In the short term, increasing insect impacts, decreasing seed-head escape or decreasing plant reproduction strengthened the effect of the different patterns (curves were steeper). In the long term, however, intermediate levels of these values had the strongest effect. Variation in insect reproductive capacity had relatively little effect on the plant population parameters. Full results are presented in Appendix S2 of the Supporting Information.

Observational field study

Larinus minutus load was negatively corrected with the density of knapweed flowering stems at White Lake in August (Table 1), a pattern consistent with resource dilution. At Vaseux Lake and at White Lake in September, the number of L. minutus per plant was not related to plant density (Table 1).

Table 1.   Spearman’s rank correlation coefficient results of the relationship between the density of diffuse knapweed bolts and its seed-head herbivore load
 Spearman’s rho P-valuePattern
Larinus minutus load
 White Lake August−0.480.0016RD
 White Lake September−0.160.34No pattern
 Vaseux Lake August−0.0970.56No pattern
 Vaseux Lake September0.0450.79No pattern
Urophora affinis load
 White Lake August0.410.0086RC
 White Lake September0.550.0004RC
 Vaseux Lake August0.580.0001RC
 Vaseux Lake September0.160.32No pattern

Urophora affinis loads increased with increasing density of knapweed flowering stems in both months at White Lake and in August at Vaseux Lake (Table 1). In September at White Lake, no pattern with density was observed.

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

The relationship between the density of insects and their host plants can influence the rate of decline of plant populations and the persistence of plant patches. We have shown that a resource concentration pattern stabilizes the number of plant patches and slows the rate of population decline. Similarly, strong resource dilution can slow the rate of plant population decline although the number of patches decreases with time. In contrast, a weak resource dilution or direct proportional pattern of insect herbivores in response to plant density accelerates plant population decline.

The consistency of our overall findings with different parameter sets shows that this outcome is robust as long as the insects can reduce plant population size. The strength of this relationship increases as insect impact increases or overall plant reproduction decreases (either via the number of seeds produced or the number of seed-heads that escape insect attack). Changes in insect reproduction have relatively little effect on the strength of the pattern as this is primarily limited by the number of available seed-heads.

We know of only two models that previously addressed the effects of spatial aggregation of herbivores on their host plants, and neither explicitly tested the resource concentration hypothesis nor the effects of a resource dilution pattern (Myers 1976; Heard & Remer 2008). Myers (1976) model asked whether aggregated distributions of eggs could regulate insect populations, but it did not include variation in plant population density. She showed that clumping could stabilize the insect–plant system, while overdispersion could lead to overexploitation and extinction. In Heard & Remer’s (2008) model, increased egg clumping in response to plant rarity led to inverse density dependence of plant reproduction. They concluded that the plant–insect system can be stabilized if insect oviposition responds to plant abundance so that eggs are aggregated on rare plants. Our results agree with these conclusions.

Both the models of Heard & Remer (2008) and Myers (1976) focused on how insect behaviour might result in different patterns of insect distribution. In contrast, we evaluate the effect of contrasting patterns of insect distribution on the host-plant population, regardless of the mechanism/s generating those patterns. Because the variance of insect load between patches increases with the levels of resource concentration or dilution, allowing some plants escape herbivore attack (Heard & Remer 2008), both resource concentration and dilution can reduce the extent of plant population decline.

These ideas have not been well-explored for any enemy–victim system, although Nicholson–Bailey host–parasitoid models have been used to investigate the impact of aggregation behaviour of the consumer on the host (for reviews, see Briggs & Hoopes 2004 and Mills & Getz 1996). They do not, however, explicitly compare resource concentration and resource dilution mechanisms. Resource dilution, in particular, is neglected (Briggs & Hoopes 2004) even though negative density dependence is common in host–parasitoid systems [approximately 25% of reviewed cases showed evidence of negative density dependence (Walde & Murdoch 1988)]. Similar to our results, these models show that increasing the level of host density-dependent aggregation stabilizes populations (Rohani, Godfray & Hassell 1994), and results in a trade-off between the persistence of the system and the ability of the parasitoid to suppress the density of the host (Mills & Getz 1996).

Our field results were consistent with the findings from the model. We found that the less effective biological control agent, Urophora affinis, followed a resource concentration pattern. In contrast, the more effective agent, Larinus minutus, followed either a directly proportional or resource dilution pattern. In September at Vaseux Lake, no relationship existed between U. affinis load and plant density, and overall U. affinis numbers had declined, likely due to competition with L. minutus. This confirms Kunin’s (1999) view that competitive exclusion between insect species can alter the relationship of insects with plant density.

While our model uses the number of plants per patch as the density measure, in the field we had to use density in the area surrounding the focal plants as diffuse knapweed patches were impossible to delineate accurately. Overall, a discrepancy exists in the literature between observational studies that tend to measure plant density and experimental studies that manipulate patch size. Rhainds & English-Loeb (2003) manipulated both plant density and patch size in experiments with tarnished plant bug (Lygus lineolaris, Hem.: Miridae) on strawberry plants. Adult bugs responded to neither patch size nor patch density; however, the nymphs responded positively to patch density in the first generation and to patch size in the subsequent two generations. This suggests that responses to the two variables are likely to be similar. Different insect species locate plants using different mechanisms (e.g. active searching vs. passive settlement). As such, we might expect that some settlement or oviposition behaviours may be sensitive to patch size, while others are sensitive to plant density. Further comparisons between the responses to patch size and density are needed.

Differences in the rates of plant population decline will have community level implications: herbivorous insects may function as classic keystone species if they have strong top-down effects on their host plant (Carson, Cronin & Long 2004). A reduction in a community dominant will result in an increase in other members of the plant community (Carson & Root 2000). However, as a resource dilution pattern will reduce smaller patches, leaving larger ones, it may not promote species coexistence to the same extent. Long, Mohler & Carson (2003) experimentally demonstrated that the specialist herbivore Trirhabda virgata (Col.: Chrysomelidae) responded in a resource concentration pattern to patches of its host, meadow goldenrod (Solidago altissima). Attack by the beetle led to a decline of the host and allowed other plants in the community to increase. The effect on dominant plants by specialist herbivores following a resource concentration pattern has never been experimentally compared with that of specialist herbivores following resource dilution patterns.

Our results suggest that the pattern of insect distribution with plant density will alter the extent to which patches of differing plant density will decline, and thus release non-dominant plant species from competition. Our study also has implications for weed biological control. The goal of weed biological control is to reduce populations to levels where they no longer require additional control (McFadyen 1998). Complete eradication of well-established invasive species is rarely successful (Myers et al. 2000), and there has been only one putative case of eradication via biological control (coconut moth in Fiji; Kuris 2003). Therefore, an ideal weed biological control agent would be one that can rapidly reduce the weed populations, but that can also persist long term. However, these attributes may trade-off. One way this could be achieved is if an agent had dual strategies whereby it follows a weak resource dilution or directly proportional pattern when plants are at relatively high densities, but alters its strategy to one of resource concentration at lower host plant densities. For example, Capman, Batzli & Simms (1990) showed that the response of the common sooty-winged skipper butterfly to patch size depended on whether the patches were at low or high densities. Egg clumping is a mechanism that could lead to resource concentration or dilution, and this has previously been suggested as a desirable trait of biological control agents (Myers 1976; Cappuccino 2000; Heard & Remer 2008). The effect of egg clumping on plant populations, however, is likely to depend on whether clumping is on high- or low-density hosts.

In conclusion, we show that response by insect herbivores to plant density can have major effects on the rate of decline and persistence of the host-plant populations (and, by extension, on the insect–plant system). Such effects are likely to influence the structure of plant communities and should be considered in the evaluation of potential weed biocontrol agents.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

We would like to thank Alana Phelps, Cielle Stephens and Chris Thoreau for assistance in the field and laboratory. Rich FitzJohn helped with programming in R and the graphical abstract. Steve Heard, Michelle Tseng, Diane Srivastava, and Iain Taylor gave helpful feedback on various drafts of this manuscript. Funding was provided by an NSERC grant to JHM and a UBC 4YF to AEAS. We would also like to thank the Nature Trust of British Columbia for allowing the use of their land.

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  7. Acknowledgements
  8. References
  9. Supporting Information
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Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Appendix S1. List of all parameters and variables used in the model.

Appendix S2. Impact on results of varying parameters chosen.

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