Spatial dynamics in a host–multiparasitoid community


Dr P. Amarasekare, National Center for Ecological Analysis and Synthesis, University of California Santa Barbara, 735 State Street, Suite 300, Santa Barbara, CA 93101–5504. Tel: (805) 892–2522. Fax: (805) 892–2510. E-mail:


1. The harlequin bug, a herbivore on bladderpod, is attacked by two specialist egg parasitoids Trissolcus murgantiae and Ooencyrtus johnsonii. Ooencyrtus can out-compete Trissolcus in the laboratory, but coexistence is the norm in field populations. Despite the heavy mortality inflicted by the two parasitoids, the host–parasitoid interaction is persistent in all sites that have been studied in southern California.

2. I manipulated inter-patch distances in a field experiment to determine whether spatial processes drive parasitoid coexistence and/or host–parasitoid dynamics. I first tested the hypothesis that the parasitoids coexist via a dispersal–competition trade-off. Both parasitoid species took significantly longer to colonize isolated patches than well-connected patches, suggesting that they have comparable dispersal abilities. Ooencyrtus did not exclude Trissolcus even when inter-patch distances were reduced to 25–30% of those observed in natural populations. These data suggest that parasitoid coexistence can occur in the absence of a dispersal advantage to the inferior competitor.

3. Since the treatments with isolated vs. well-connected patches did not differ in parasitoid composition, I next asked whether isolation would destabilize, or drive extinct, the host–multiparasitoid interaction. No local extinctions of bugs or parasitoids were observed during the 18-month study period. Bug populations in the isolated patches were no more variable than those in the well-connected patches. In fact, temporal variability in the experimentally isolated patches was comparable to that observed in highly isolated natural populations.

4. These data argue against a strong effect of spatial processes on host–parasitoid dynamics. Local processes may mediate both parasitoid coexistence as well as the host–parasitoid interaction.


Understanding how species interactions persist in patchy environments is a central problem in ecology. Theory suggests that spatial dynamics may play a key role in maintaining both competitive and consumer–resource interactions. For example, an inferior competitor may coexist with a superior competitor by virtue of greater ability to disperse among local populations ( Levins & Culver 1971; Hastings 1980; Nee & May 1992; Tilman et al. 1994 ). Predators and prey that engage in locally unstable interactions may persist if there is emigration and immigration among populations ( Murdoch & Oaten 1975; Reeve 1988; Hassell, Comins & May 1991; Jansen 1994).

The situation is more complicated for multi-species systems. Communities in which several consumers specialize on the same resource, or several prey share the same predator or pathogen, will be characterized by competitive as well as consumer–resource interactions. Spatial processes may influence both. The challenge is to separate the effects of spatial processes on competitive interactions within the consumer or resource trophic level from those on interactions between consumer and resource trophic levels. The fact that the data have lagged behind theory is at least partly due to this problem of separation of effects. To date, only a handful of studies have investigated metapopulation processes in multispecies communities ( Harrison & Taylor 1996).

The harlequin bug (Murgantia histrionica (Hahn); Hemiptera: Pentatomidae), a herbivore on bladderpod (Isomeris arborea (Nutt.); Capparaceae), has two specialist egg parasitoids (Trissolcus murgantiae (Ashm.); Hymenoptera: Scelionidae and Ooencyrtus johnsonii (How.); Hymenoptera: Encyrtidae) in southern California. The parasitoids exert heavy egg mortality on the host, with average monthly parasitism rates ranging from 40 to 70% ( Amarasekare 1998, 1999). The heavy mortality notwithstanding, the host–parasitoid interaction is persistent in every population that has been studied in southern California ( Sjaarda 1989; Amarasekare 1998, 1999).

Host–parasitoid metapopulation models (e.g. Murdoch & Oaten 1975; Reeve 1988; Murdoch et al. 1992 ; Taylor 1998) predict that low levels of dispersal among local populations may stabilize host–parasitoid dynamics if the populations have asynchronous dynamics. The interactions between the two parasitoid species may confound this expectation. For example, if parasitoid coexistence is itself driven by inter-patch dispersal (i.e. one species goes extinct in the absence of immigration), then isolation of populations may alter parasitoid coexistence patterns and hence host–parasitoid dynamics. Then, any direct effect of host or parasitoid dispersal on host–parasitoid dynamics will be confounded with an indirect effect due to altered coexistence patterns of the parasitoids. The first step therefore is to determine whether dispersal influences the coexistence of parasitoids.

The bug appears to be suppressed well below the density set by its resources ( Amarasekare 1998). Hence, the two parasitoids are competing for a shared limiting resource. They engage in strong asymmetric larval competition, and Ooencyrtus excludes Trissolcus in laboratory experiments ( Sjaarda 1989). In the field, however, the parasitoids coexist in the majority of local populations. The few patches with one parasitoid species always consist of Trissolcus ( Amarasekare 1998, 1999). Coexistence in the field may result from a competition–dispersal trade-off ( Levins & Culver 1971; Hastings 1980). For example, Trissolcus may counteract its competitive inferiority by being a superior disperser. A superior dispersal capability would allow Trissolcus to establish in patches that Ooencyrtus cannot colonize, and to counteract exclusion by Ooencyrtus in patches that both species colonize.

If parasitoid dispersal does not influence coexistence, one can proceed to investigate the role of host dispersal in maintaining the host–multiparasitoid interaction. The high parasitism rates observed suggest the potential for the parasitoids to overexploit the hosts and drive them extinct. The parasitoids exhibit large fluctuations in abundance, but bug populations in the two-parasitoid patches show little or no fluctuations (P. Amarasekare, unpublished manuscript). If host population stability results because host dispersal among patches moderates population fluctuations (cf. Murdoch et al. 1992 , 1996; Nisbet et al. 1992 ), one would expect destabilization of dynamics when patches are isolated with respect to the bugs’ dispersal capability.

Here I report the results of a field experiment designed to test the role of inter-patch dispersal in parasitoid coexistence and host population dynamics. I discuss the results in light of other empirical studies on spatial dynamics of host–parasitoid interactions.

Natural history

Isomeris, the host plant of the harlequin bug, is a coastal sage scrub endemic with a naturally patchy distribution ( Goldstein et al. 1991 ). It produces secondary compounds known as glucoisinolates that render it unpalatable ( Nuss 1983). In fact, Isomeris supports only two other species of insects, the flea beetle and the pollen beetle, neither of which is a significant competitor for the harlequin bugs ( Sjaarda 1989; Amarasekare 1998). Harlequin bugs also lack natural predators, which may be a result of sequestering secondary compounds contained in the host plant ( English 1983; Nuss 1983). Preliminary experiments have shown the bug to be unpalatable to bird and lizard predators (Boyd Collier, personal communication). The only known natural enemies of the bug are two egg parasitoids T. murgantiae and O. johnsonii. Local dynamics in this system therefore consist of the multiparasitoid – single host interaction.

Ooencyrtus johnsoni is both gregarious and engages in superparasitism ( Sjaarda 1989; Amarasekare 1998). One to three adults may emerge from one host egg ( Walker & Anderson 1933). Superparasitism is absent in the solitary T. murgantiae ( Sjaarda 1989; Amarasekare 1998). Only one adult develops within a host egg. The bugs have three generations per year: spring, summer and autumn ( Wilford-Beanan & Hanscom 1982), while the two parasitoids have about nine generations per year ( Maple 1937; Huffaker 1941; Sjaarda 1989).

The naturally patchy distribution of the host plant creates a hierarchical spatial structure for bugs and parasitoids. For instance, individual bushes are aggregated into discrete patches that are separated by an uninhabitable matrix of annual grasses and weeds. On a landscape scale, the patches themselves are aggregated into collections that suggest a metapopulation structure. Mark–recapture experiments show frequent movement of bugs within patches (38–43%), but only infrequent movement among patches (2·4–2·7%). Mean, median and modal dispersal distances (including inter-patch dispersal events) within a generation were 13 (± 3) m, 4·5 m, and 8 m, respectively ( Amarasekare 1998). These distances are comparable to the mean interbush distances (5–6 m) but are much smaller than the mean inter-patch distances (60–74 m) observed in natural populations. These mark–recapture data combined with an analysis of spatial variation in abundances served to establish that a patch of host plants constitutes the local population for bugs and parasitoids ( Amarasekare 1998).

Experimental design and methods

If the two parasitoids coexist through a dispersal–competition trade-off, Ooencyrtus should exclude Trissolcus once the latter’s dispersal advantage is eliminated. One can test this prediction by experimentally manipulating inter-patch distances. When inter-patch distances are large relative to the dispersal capability of the inferior disperser (Ooencyrtus), Trissolcus should be able to colonize all patches, but Ooencyrtus may be missing from some patches. Hence, one expects to see a mixture of Trissolcus-only and two-parasitoid patches. When inter-patch distances are small relative to the dispersal capability of Ooencyrtus, there will be no dispersal advantage to Trissolcus. Hence, one expects to see the exclusion of Trissolcus in all patches. On the other hand, if coexistence is not driven by a dispersal–competition trade-off, the parasitoids should coexist in both treatments.

Testing these predictions requires replicating the natural spatial structure of the system. To this end I created experimental archipelagos of host plant patches on a 25-ha site on the UC Irvine campus. The Isomeris plants used in the patches were grown from seed for 3 years in the UC Irvine greenhouses and transplanted in the field in 1995. All seeds were collected from a nearby natural population to eliminate any confounding genetic effects on plant quality. The two treatments (Near and Far) each consisted of three replicate archipelagos. Individual archipelagos were separated by distances of at least 150 m. Each archipelago contained seven patches, and each patch consisted of four equally spaced Isomeris bushes. Inter-patch distance in the Near treatment was 20 m, which is within the dispersal range of both bugs and parasitoids ( Amarasekare 1998). It is also the smallest inter-patch distance observed in natural collections of patches. Inter-patch distance in the Far treatment was 50 m, which is comparable to the mean inter-patch distance observed in natural populations (60 ± 12 m) and was the largest distance that could be used within the area available. According to mark–recapture data ( Amarasekare 1998), only 4% of the bugs moved a distance larger than 20 m within a generation, and < 2% traversed distances exceeding 50 m.

In June 1996, 64 bugs were released in the central patch of each archipelago. After 4 weeks had elapsed, 24 adults of each parasitoid species were released in the central patch. The resulting densities (16 bugs m−2 and 6 parasitoids m−2) were at the high end of typical summer densities. Each patch was supplemented with 168 fresh bug eggs (42 m−2) to facilitate parasitoid colonization.

Patches were censused at monthly intervals from June 1996 to December 1997. This period covered five bug generations and 14–15 parasitoid generations. I counted the number of eggs and adult harlequin bugs on each bush. I quantified the density of each life-history stage as the number of individuals of that stage on the bush divided by the canopy surface area (calculated by approximating the surface area to that of a spheroid). During each monthly census I marked with coloured wire all newly laid egg clusters on the I. arborea bushes being surveyed for population dynamics. After 30 days had elapsed, which ensured all eggs of the cohort had hatched, I collected all marked egg clusters. Eggs were examined under a dissecting microscope. Eggs from which harlequin bug nymphs had emerged were clearly distinguishable from parasitoid emergences. The two parasitoids also had distinctive methods of emergence. The larger Trissolcus chewed a large hole from the top, while the smaller Ooencyrtus tended to emerge from the side or the bottom through a smaller hole. This made it possible to score accurately the fate of all hatched eggs. Monthly parasitism rate for each species was quantified as the number of eggs parasitized by that species divided by the total number of eggs.

Statistical analyses

Parasitoid colonization ability

I quantified colonization ability as the inverse of the time taken for each species to colonize the peripheral patches from the central release patch. Since each treatment consisted of three replicate archipelagos with seven patches each, I computed the average time to colonization per replicate archipelago. I used these averages as the dependent variable in a two-way anova. If a dispersal–competition trade-off exists, Trissolcus should be faster at colonizing patches in the Far treatment while both species should be equally fast at colonizing patches in the Near treatment. Hence, one would expect a significant Species × Treatment interaction in the two-way anova. On the other hand, if both species have comparable dispersal abilities but respond to the spatial structure defined in the experiment, one might expect a significant Treatment effect but not a Species or Species × Treatment effect.

Parasitoid coexistence

If the two parasitoids coexist via a dispersal–competition trade-off, one would expect to see the exclusion of Trissolcus in the Near treatment and a mixture of Trissolcus-only and two-parasitoid patches in the Far treatment (see above). This means that the fraction of eggs parasitized by Trissolcus should decline to zero over time in the Near treatment, while the fraction of eggs parasitized by Ooencyrtus should increase. In contrast, both species should exhibit non-zero parasitism rates in the Far treatment. One would expect parasitoid densities to exhibit a similar pattern. I used repeated measures anova to compare the temporal trajectories of the fraction of eggs parasitized (and parasitoid density) in the two treatments. If a dispersal–competition trade-off exists, the temporal trajectories of the fraction parasitized and parasitoid density for each species should be different in the two treatments. Hence, one would expect a significant Species × Treatment × Time interaction. I used both univariate and multivariate analyses to test for an interaction effect.

In repeated measures anova, tests for main (between-subject) effects involve a comparison of the mean within-subject response across levels of the between-subjects factor ( SAS 1993; von Ende 1993). In this case, the main effects of Species and Treatment will be tested by comparing the sums of the fraction parasitized (or density) over the repeated measures divided by the square root of the number of repeated measures in a standard two-way anova. Hence, this analysis ignores any effect of time (e.g. correlation of adjacent observations) and should be considered only if the effects of Time, Species × Time, or Treatment × Time interactions prove to be insignificant.

The basic assumptions of anova require that observations be independent and normally distributed, and that error variances be homogeneous ( Winer, Brown & Michaels 1991; Sokal & Rohlf 1995). Parasitism data were arcsine-transformed and parasitoid densities log-transformed so that they should conform to these requirements. These transformations also satisfy the requirement of repeated measures anova that the dependent variable has a multivariate normal distribution ( SAS 1993; Winer et al. 1991 ).

The univariate tests for within-subjects effects in repeated measures anova require the sphericity assumption ( Winer et al. 1991 ; SAS 1993; von Ende 1993). Violation of this assumption leads to inflated F statistics. One solution is to adjust the degrees of freedom of the F-test to make it more conservative ( von Ende 1993). Throughout I use the Greenhouse–Geisser adjusted probabilities for the significance levels associated with the respective F-tests.

I used a polynomial transformation of the repeated measures ( SAS 1993) to look at the linear, quadratic, cubic, etc. trends over time. This allowed me to detect the pattern and rate of divergence, if any, of the different treatments. For example, the linear component quantifies the pattern of change over time, quadratic component the rate of change over time, and the cubic, the rate at which this rate itself changes ( Winer et al. 1991 ).

I measured the fraction parasitized and parasitoid density in each patch within the six archipelagos at monthly intervals from June 1996 to December 1997. For each date, the average parasitism and density data per replicate archipelago were obtained, yielding three replicate observations for each treatment combination and a total of 12 observations per date. However, using all 18 repeated measures in the analysis proved problematic since the number of dependent variables (18) exceeded the total number of observations per date (12), thus providing insufficient degrees of freedom for the multivariate analyses ( Winer et al. 1991 ). Since host generations are demarcated by seasons, the most logical approach was to compute average parasitism and parasitoid density per season. These averages yielded six repeated measures corresponding to the following seasons: summer 96, autumn 96, winter 97, spring 97, summer 97 and autumn 97.

Host population dynamics

If parasitoid dispersal does not influence coexistence, then it is possible to test hypotheses about the role of host dispersal in stabilizing host population dynamics. Despite heavy parasitism, host populations in nature fluctuate very little. This stability may result from host dispersal among patches. If so, one would expect greater host population fluctuations when patches are isolated sufficiently to restrict immigration.

I first investigated the colonization ability of bugs. Bugs should have difficulty in colonizing patches that are isolated with respect to their dispersal capability. Hence, one would expect the average time to colonization to be greater in the Far treatment relative to the Near treatment. I used a t-test for unequal variances to compare times to colonization in the two treatments. This is a more conservative test than the one that assumes homogeneity of variances ( Zar 1984; Sokal & Rohlf 1995).

I used two approaches to quantify dispersal effects on host population stability. First, I compared temporal variability in the two dispersal treatments using a t-test. I used the ‘metapopulation’ (i.e. each archipelago of seven equidistant patches) as the experimental unit since I was interested in stability at the metapopulation scale. To this end, I measured the temporal variability of each patch within an archipelago and computed the mean temporal variability across patches for each replicate archipelago. If dispersal among local populations confers metapopulation stability, one expects significantly lower mean temporal variability in the Near treatment compared to the Far treatment.

I quantified temporal variability as the Standard Deviation (SD) of the logarithm of consecutive population censuses (cf. Murdoch & Walde 1989). Since I censused all patches within all replicate archipelagos, it is not necessary to make a correction for spatial variance due to sampling effects ( Stewart-Oaten et al. 1995 ). Logarithmic transformation creates problems when zero values are observed in the data. Stewart-Oaten et al. (1995) suggest several methods for dealing with zeros (see also Murdoch et al. 1996 ). I chose the option of adding a constant (one-sixth of the smallest density or fraction parasitized) to the zero observations. This is the method that appears to have the fewest drawbacks ( Stewart-Oaten et al. 1995 ). Since I am interested in the relative variability across treatments rather than in the absolute variability of any treatment combination, choice of this particular method over any other is unlikely to pose a problem.

The above approach of comparing the mean temporal variability does not reveal any differences between temporal trajectories in the two treatments. I used repeated measures anova to determine whether the population trajectories in the two treatments are qualitatively different. For example, patches in the Far treatment may not only exhibit greater fluctuations, but they may drift to zero in the absence of stabilizing effects of dispersal ( Murdoch et al. 1996 ). Patches in the Near treatment on the other hand, may converge on a stable equilibrium.

If the above expectations hold in the experiment, one should see a significant Time × Treatment interaction in the repeated measures anova. Since population densities in each treatment are likely to change over time, one may also expect to see a significant effect of Time. As before, I used a polynomial transformation of the repeated measures to detect any significant trends over time.


Colonization ability of parasitoids

If the parasitoids coexist via a dispersal–competition trade-off, one would expect a significant Species × Treatment interaction in a two-way anova on time to colonization. The results indicate otherwise ( Table 1). Neither the interaction nor the Species main effect was significant. The Treatment effect, however, is significant. Both Trissolcus and Ooencyrtus took longer to colonize patches in the Far treatment (mean ± SE: Trissolcus = 3·2 ± 0·4 months; Ooencyrtus = 2·4 ± 0·2 months) compared to the Near treatment (mean ± SE: Trissolcus = 2 ± 0·5 months; Ooencyrtus = 1·8 ± 0·1 months). These results suggest that the two parasitoid species have comparable dispersal abilities at the spatial scales (20 m vs. 50 m) studied.

Table 1. . Species and inter-patch distance effects on time to colonization: results of two-way anova
Species × Treatment10·270·70·4262

Coexistence patterns of parasitoids

Under the dispersal–competition trade-off hypothesis, one would also expect a significant Species × Treatment × Time interaction in a repeated measures anova of fraction parasitized and/or parasitoid density.

Table 2 summarizes the results. Both multivariate and univariate analyses yielded a non-significant Species × Treatment × Time interaction. This means that the parasitism patterns by the two species did not differ between the two treatments ( Fig. 1). The Treatment × Time interaction was also non-significant, suggesting that there was no difference between treatments when parasitism rates were averaged over species. There was, however, a significant Species × Time interaction suggesting that the two species exhibited different temporal patterns of parasitism when averaged across treatments. The parasitoids exhibit a characteristic seasonal pattern with the fraction of eggs parasitized by Trissolcus declining as that by Ooencyrtus increases ( Amarasekare 1998, 1999). The fact that this pattern was preserved when averaging over treatments further reinforces the absence of a strong treatment effect. In fact, the time series of the fraction of eggs parasitized shows that the two parasitoid species coexisted in both treatments and exhibited the same seasonal pattern ( Fig. 1).

Table 2. . Repeated measures anova for the fraction of eggs parasitized in the two dispersal treatments
Multivariate analysis
d.f. (num, denom)Wilk’s LambdaFP
Time4, 50·20583·08710·1487
Time × Species5, 40·09777·38550·0378*
Time × Treatment5, 40·43621·03380·5011
Time × Species × Treatment5, 40·77890·22700·9323
Univariate analysis of within-subject effects
d.f.Type III SSFP adjusted
Time × Species51·00127·480·0086*
Time × Treatment50·07330·550·5602
Time × Species × Treatment50·02510·190·7933
Error (Time)401·0708
Analysis of between-subject effects
d.f.Type III SSFP
  1. Note: (i) The other statistics in the multivariate analyses (Pillai’s Trace, Hotelling–Lawley Trace, and Roy’s Greatest Root) yielded probabilities identical to those obtained for Wilk’s Lambda. (ii) Univariate analyses are based on Greenhouse–Geisser adjusted probabilities which make the F-test more conservative with respect to the violation of the sphericity assumption.

Species × Treatment10·00220·090·7696
Figure 1.

Monthly parasitism rates for the dispersal experiment, June 1996 – December 1997. The short dashed line represents Trissolcus, and the solid line, Ooencyrtus. The values represent means and standard errors computed over three replicate archipelagos. In order to ensure clarity, each species trajectory is depicted with only plus or minus error bars. The top panel represents the Far treatment (inter-patch distance = 50 m), and the bottom panel, the Near treatment (inter-patch distance = 20 m).

These results based on repeated measures are also mirrored in the between-subjects analysis that is based on the time averages of parasitism ( Table 2). The Species × Treatment interaction is non-significant, as is the Treatment main effect. The Species main effect is again highly significant.

Polynomial transformation of repeated measures was used to quantify the nature of temporal trends. The linear trend was non-significant, while the quadratic trend was marginally significant for the Species main effect (F = 5·22, d.f. = 1, 8, P = 0·0517). The cubic and quartic trends for Species were highly significant (Cubic: F = 23·24, d.f. = 1, 8, P = 0·0013; Quartic: F = 40·54, d.f. = 1, 8, P = 0·0002) reflecting the highly nonlinear patterns of parasitism exhibited by the two parasitoid species ( Fig. 1). Trends for the Species × Treatment interaction were not significant, suggesting that the rates of change over time in parasitism and parasitoid density in the two treatments were statistically indistinguishable.

Repeated measures anova for parasitoid density yielded qualitatively similar results ( Table 3). The Species main effect was highly significant, as was the Species × Time interaction. None of the other interaction effects were significant. The cubic and quartic trends of the polynomial contrasts for Species were again highly significant (Cubic: F = 25·9, d.f. = 1, 8, P = 0·0009; Quartic: F = 14·64, d.f. = 1, 8, P = 0·005). All trends for the Species × Treatment interaction were non-significant, suggesting that temporal fluctuations in densities did not differ between treatments. The only difference in the analysis based on density was the significant effect of Time ( Table 3), which shows that overall densities (averaged over both species and treatments) fluctuated over time. The fact that neither parasitoid species showed an increase in population fluctuations in the Far treatment argues against the possibility that inter-patch dispersal stabilizes parasitoid population fluctuations.

Table 3. . Repeated measures anova for parasitoid densities in the two dispersal treatments
Multivariate analysis
d.f. (num, denom)Wilk’s LambdaFP
Time5, 40·10167·06800·0407*
Time × Species5, 40·10027·18030·0396*
Time × Treatment5, 40·21982·83920·1669
Time × Species × Treatment5, 40·75050·26590·9106
Univariate analysis of within-subject effects
d.f.Type III SSFP adjusted
Time × Species519·13474·750·0123*
Time × Treatment5 4·99271·240·3172
Time × Species × Treatment5 1·27380·320·7955
Error (Time)4032·1968
Analysis of between-subject effects
d.f.Type III SSFP
Treatment1 1·46951·860·2097
Species × Treatment1 0·03140·040·8469
Error8 6·3204

Colonization patterns of bugs

The bugs colonized patches in both Near and Far treatments within 2 months of the initial release (mean time to colonization ± SE: Near = 1·77 ± 0·45 m; Far = 1·72 ± 0·20 m; n = 6 archipelagos, one-tailed t-test, P = 0·46). These results suggest that the distance of 50 m does not provide a significant barrier to colonization. The number of colonizers was small (1–2 bugs per patch), and population densities in both treatments remained low (maximum density ≤ 1 m−2; Fig. 2a). These results are consistent with the earlier dispersal study ( Amarasekare 1998). While most bugs (98%) tend to stay within patches about 2% move among patches within a generation, which should be sufficient for colonization of empty patches.

Figure 2.

Time series of adult bug (top panel) and egg (bottom panel) densities. The solid line represents data for the Far treatment, and the dashed line, data for the Near treatment. The values represent means (± SE) computed over three replicate archipelagos.

Bug population dynamics

No local extinctions of bugs were observed in any of the patches during the 18-month study period. This is consistent with the persistent bug–parasitoid interactions observed in the natural populations, including the smallest and the most isolated ones.

Contrary to expectations, temporal variability was not greater in the Far treatment. This was true both for adult bug density and egg density ( Table 4; Fig. 2).

Table 4. . Temporal variability in egg and adult bug density in the two dispersal treatments
Mean ± SE
Mean ± SE
t statisticP (one-tailed)
  1. Note: one-tailed t-tests for unequal variances were used, which provide a more conservative test.

Adult density
10·7261 ± 0·08870·7899 ± 0·0698  
20·9605 ± 0·15121·1110 ± 0·04  
30·7726 ± 0·13481·0882 ± 0·1054  
Treatment mean ± SE0·8197 ± 0·07160·9964 ± 0·1034− 1·400·1164
Egg density
11·3775 ± 0·11631·3297 ± 0·0385  
21·2541 ± 0·15141·2773 ± 0·1385  
31·3624 ± 0·04041·1657 ± 0·1982  
Treatment mean ± SE1·3314 ± 0·03891·2576 ± 0·04830·65130·2601

Repeated measures anova that compared temporal trajectories across treatments yielded similar results ( Tables 5 & 6). There was a significant effect of Time, indicating that densities fluctuated over time, but the non-significant Treatment × Time interaction suggests that the nature of adult or egg density fluctuations was not different in the two treatments. As can be seen from the between-subjects analysis ( Tables 5 & 6) mean egg and adult densities were also not different between treatments.

Table 5. . Repeated measures anova for adult harlequin bug density in the two dispersal treatments
Multivariate analysis
d.f. (num, denom)Wilk’s LambdaFP
Time4, 10·009924·84330·1492
Time × Treatment4, 10·0541 4·37280·3425
Univariate analysis of within-subject effects
d.f.Type III SSFP adjusted
Time × Treatment40·22071·510·2749
Error (Time)160·5841
Analysis of between-subject effects
d.f.Type III SSFP
Table 6. . Repeated measures anova for egg density in the two dispersal treatments
Multivariate analysis
d.f. (num, denom)Wilk’s LambdaFP
Time4, 10·017314·16030·1964
Time × Treatment4, 10·022410·89700·2230
Univariate analysis of within-subject effects
d.f.Type III SSFP adjusted
Time × Treatment42·46762·50·1642
Error (Time)163·9481
Analysis of between-subject effects
d.f.Type III SSFP

Adult density showed highly significant quadratic, cubic and quartic effects of time (Quadratic: F = 11·13, d.f. = 1, 4, P = 0·0289; Cubic: F = 13·85, d.f. = 1, 4, P = 0·0204; Quartic: F = 10·92, d.f. = 1, 4, P = 0·0298), while egg density showed significant linear and quartic effects (Linear: F = 29·74, d.f. = 1, 4, P = 0·0055; Quartic: F = 19·34, d.f. = 1, 4, P = 0·0117;). These results are consistent with the nonlinear fluctuations observed ( Fig. 2). However, the treatment effect was non-significant for both egg and adult density, indicating that temporal trends were not different across treatments.

Comparisons of experimental and natural populations

The above results suggest that inter-patch dispersal does not reduce temporal variability in the host population at the spatial scales studied. It is possible that dispersal may stabilize dynamics in populations that are isolated by distances larger than those used in the experiment. I had been studying three isolated patches in the Irvine-Newport area (mean inter-patch distance ∼ 10 km), which gave me the opportunity to compare temporal variability between the experimental and highly isolated natural populations. The latter are small populations with five to six Isomeris bushes, and hence comparable in size to the experimental populations. Both parasitoids were present in these patches during the study period from June 1996 to December 1997. Hence, parasitoid composition was not a confounding factor in this comparison.

The comparison between natural and experimental populations represented an unbalanced design since only three isolated natural patches remain in the Irvine-Newport beach area (a result of extensive habitat destruction). Hence, I used General Linear Models Procedure ( SAS 1993).

The results show that temporal variability in the highly isolated natural populations is comparable to that observed in the experimental populations (mean variability ± SE: Experimentally isolated = 0·82 ± 0·07; Naturally isolated = 0·77 ± 0·20; GLM contrast analysis, P > 0·05). The power of detecting an effect may be low since only three natural populations were present. However, the actual values observed for the natural patches are very close to those in the experimental populations ( Fig. 3), suggesting similar temporal fluctuations. A post hoc power analysis indicates that even with 50 patches, the power of detecting a difference as small as that observed is only about 30%.

Figure 3.

. The range of temporal variability observed in experimental and natural populations. The black dots represent the mean, and the open circles, the minimum and maximum variability.


I investigated the role of dispersal in parasitoid coexistence and host–parasitoid dynamics in a host–multiparasitoid community. Parasitoid coexistence was not affected by experimental manipulation of inter-patch distances at the 20 m – 50 m scale. Since parasitoid dispersal did not appear to influence coexistence, I next asked whether host dispersal could stabilize host dynamics and hence maintain the host–multiparasitoid interaction. Results of this analysis were also negative. Temporal variability was not greater in experimentally isolated populations. The magnitude of the variability observed was comparable to that of natural populations that are isolated by much larger distances (≥ 10 km) than were used in the experiment.

Lack of statistical power is unlikely to be the reason for these negative results. First, the experiment was well replicated at both local and metapopulation scales. Secondly, the Species main effect and Species × Time interaction effect were highly significant, suggesting that the design was sufficiently powerful to detect the other main effects and interactions had they existed. Thirdly, the data are obviously very close in both treatments.

A second issue is whether the appropriate scales on which spatial processes operate were represented in the experiment. The experimental archipelagos were based on the spatial structure observed in natural collections of host plant patches. The inter-patch distances used were based on previous data on dispersal, and were also comparable to the distances observed in natural populations. Hence, the natural spatial structure was well represented in the experiment. The data in fact suggest that the parasitoids respond to the spatial structure recreated in the experimental archipelagos, but that they do so in a comparable manner, i.e. both species took significantly longer to colonize the more isolated patches. This result argues against a dispersal–competition trade-off. In nature the parasitoids coexist in the smallest and most isolated natural patches, and the superior competitor was found to be absent from patches that had lower egg productivity but not from those that were isolated by distance ( Amarasekare 1998, 1999).

While parasitoid dispersal may not influence coexistence, host dispersal may contribute to the persistence of the host–parasitoid interaction. Despite heavy parasitism, the system is not characterized by local extinctions ( Amarasekare 1998). Moreover, host populations fluctuate very little in nature (P. Amarasekare, unpublished manuscript). Host immigration among extant populations may prevent extinction and stabilize populations by reducing fluctuations (cf. Murdoch et al. 1992 ; Nisbet et al. 1992 ). Such a rescue effect will depend strongly on inter-patch distance ( Hanski, Moilanen & Gyllenberg 1996; Hanski & Gilpin 1996). Hence, isolated populations should exhibit greater fluctuations than well-connected ones. While it is possible that the rescue effect may operate at inter-patch distances greater than 50 m, temporal variability in natural populations isolated by tens of kilometers was no greater than that exhibited by experimental patches separated by 50 m.

One potential reason for the absence of a strong spatial effect is the strong seasonality in this system. Models that predict stabilizing effects of dispersal require local populations to exhibit asynchronous dynamics ( Reeve 1988; de Roos, McCauley & Wilson 1991; Murdoch et al. 1992 ; Hassell et al. 1991 , 1994; Jansen 1994). Strong seasonality may prevent such asynchrony at the spatial scales on which individuals are capable of dispersing.

Another possibility is that strong local interactions override the effect of spatial processes. There is no doubt that spatial processes play a crucial role in colonizing new habitats and expanding species ranges. The relatively rapid northward spread of the bug and parasitoids from Baja California ( Walker & Anderson 1933; Sjaarda 1989) provides ample evidence of this. However, spatial processes do not appear to have a strong impact on coexistence or host–parasitoid dynamics at the spatial scales that define local populations. Harrison, Thomas & Lewinsohn (1995) observed a similar result in their study on the coexistence of insect herbivores on ragwort. Superior and inferior competitors alike exhibited high dispersal rates relative to distances that separated natural patches, suggesting that a dispersal–competition trade-off was unlikely to be driving herbivore coexistence.

Interestingly, all studies that report strong spatial effects on consumer coexistence or consumer–resource dynamics involve communities that are characterized by frequent local extinctions (e.g. Huffaker 1958; Walde 1991, 1994; Antonovics et al. 1994 ; Janssen et al. 1997 ; Lei & Hanski 1998). In contrast, published field studies that did not find any effects of spatial processes all involve persistent interactions in which the resource populations exhibit stable dynamics ( Myers, Monro & Murray 1981; Briggs 1993; Murdoch et al. 1996 ; this study). It is possible that local density-dependent processes ameliorate antagonistic interactions in these systems (see review by Harrison & Taylor 1996). For example, Murdoch et al. (1996) hypothesize that a mechanism operating on very small spatial scales may be stabilizing red scale populations in southern California. A local mechanism may operate in the harlequin bug system as well. Previous data ( Sjaarda 1989; Amarasekare 1998) suggest that the dominant competitor Ooencyrtus is superior at larval competition while the inferior competitor Trissolcus is more efficient at exploiting unparasitized hosts. Larval competition by Ooencyrtus may reduce the impact of the more efficient Trissolcus, thus preventing over-exploitation and stabilizing host dynamics. This possibility is investigated elsewhere ( Amarasekare 1999).

The apparent dichotomy between locally stable systems and those characterized by extinction–colonization dynamics is reflected in the dichotomy of modelling approaches. In the patch occupancy framework ( Levins 1969, 1970; Levins & Culver 1971; Hastings 1980; May 1994), local dynamics occur on a much faster scale than metapopulation dynamics, and always lead to local extinctions. Local extinctions result from the exclusion of inferior competitors by superior ones, or from over-exploitation of resources by consumers. In such systems, extinction–colonization dynamics are mandatory for the maintenance of competitive or consumer–resource interactions. The alternative framework is one that explicitly describes local dynamics within patches ( Murdoch & Oaten 1975; Reeve 1988; Murdoch et al. 1992 ; Jansen 1994, 1995). Here, local and spatial dynamics occur on comparable time scales. In discrete models of this type local populations tend to be unstable and extinction-prone (e.g. Reeve 1988; Hassell et al. 1991 , 1994), while in continuous models populations tend to be cyclic (e.g. Murdoch & Oaten 1975; Crowley 1981; Murdoch et al. 1992 ; Nisbet et al. 1992 ). In both discrete- and continuous-time models, low levels of dispersal every generation reduce fluctuations and stabilize dynamics. Unlike in the patch occupancy framework, local extinctions are not observed because immigration rescues populations from extinction.

The data are unambiguous on the importance of spatial processes on systems characterized by extinction–colonization dynamics. It is much more difficult to elucidate the role of spatial processes in systems that do not exhibit frequent local extinctions. In such systems one has to deal with the possibility that local processes themselves may be stabilizing the interaction. Available data are too sparse to make any generalizations ( Harrison & Taylor 1996), but the few published studies do suggest that strong local interactions may override or obscure the effects of spatial processes on host–parasitoid interactions that are relatively persistent.


This research was supported by NSF grants DEB-9057331 and DEB-9627259 to S. Frank, a dissertation improvement grant (DEB-9623801), and two fellowships to the author: University of California Irvine School of Biological Sciences Research Fellowship, and a University of California Regents Dissertation Fellowship. The author was supported by a postdoctoral fellowship from the National Center for Ecological Analysis and Synthesis (funded by NSF DEB-9421535, University of California Santa Barbara and the state of California) during final preparation of the manuscript. J. Bascompte, W. Murdoch and two anonymous referees provided helpful comments on the manuscript.

Received 18 November 1998;revision 5 April 1999