Contrasting dynamics in the same plant–herbivore interaction

Abstract

Long-term studies of two-species interactions under field conditions are unusual; most long-term field studies are of single species dynamics (1–6). Concurrent long-term studies on the dynamics of the same two interacting species in different locations are very rare. This result has led to the tacit assumption that different cases of the same two-species interaction would involve essentially quantitative differences (e.g., context-specific differences in the numeric values of demographic parameters like fecundity or death rates). Here, we show that for one of the best-known two-species systems (ragwort and cinnabar moth), this finding does not hold. The interaction between the plant and its herbivore is fundamentally different in coastal dunes in The Netherlands and in grasslands in Southeast England. In the first case, the dynamics are cyclic and the interaction involves both direct and delayed density dependence; in the second case, the insect has little impact on plant dynamics and there are no time lags in density dependence. The difference is caused by differences in the importance of seedlimitation in plant recruitment in the two locations.

Recent developments have highlighted the way that abiotic and biotic factors interact in the regulation of animal [vertebrate (1, 2) and invertebrate (3, 4)] and plant (5, 6) single-species dynamics. In reality, of course, species interact with resources, competitors, mutualists, and natural enemies (7). Although the theory of multispecies interactions is relatively well developed (8–10), there are very few tests of this theory using field data. Comparative studies of the dynamics of the same interaction in different ecological settings have not been carried out. Using a replicated plant-herbivore system, we compare and contrast the population processes and mechanisms that influence the observed dynamical patterns. We focus on the interaction between a resource and its consumer. By developing nonlinear statistical models, we illustrate how crucial dynamical effects are contingent on the precise structure of the ecological interaction between a plant and its herbivore. We evaluate the strength and change in plant density dependence (through plant recruitment) and herbivore density dependence (through numerical and functional responses) as the principal determinants of the mechanisms underlying the dynamics of the plant–herbivore interaction.

Methods

Biology and Population Census Methods. The system involves the cinnabar moth (Tyria jacobaeae) L. (Lepidoptera: Arctiidae) and its food plant, ragwort (Senecio jacobeae) L. (Asteraceae). The basic biology of the system is of a food-limited specialist herbivore feeding on a host plant where the dynamics of the plant are principally determined by interspecific competition for recruitment sites. This system is unique in that comparative time series data are available for the cinnabar moth–ragwort interaction over relatively long periods of time: a mesic grassland in Silwood Park (20 yr) and a coastal sand dune in Meijendel (26 yr). The annual censuses of the populations allow a comparative assessment of the form of the interaction between the plant and the herbivore and the influence of each species on the population dynamics of the other. The existence of such coupled time series is fundamental for quantifying the temporal and spatial variability of species interactions.

Cinnabar moth is a univoltine specialist herbivore that feeds almost exclusively on ragwort. Adult moths emerge in May or early June and lay eggs on the lower leaves of the ragwort plants. Larvae pass through five instars and are voracious herbivores, completely stripping plants of all leaves and flowerheads. Ragwort is a monocarpic or short-lived polycarpic perennial species. In the first year after germination, it exists as a rosette plant. It usually flowers in its second year although it can behave as an annual and can behave as a repeat-flowering perennial, especially if cinnabar moth strips the plant of its flowers before seed-fill.

Observations for the time series were collected for the plant and the herbivore simultaneously. At Silwood Park (1981–2000), ragwort density was recorded as flowering stems per m² and cinnabar moth density as egg batches per 0.1 ha. At Meijendel (1975–2000), ragwort density was recorded as plants per 4 m² and similarly cinnabar moth density was estimated as eggs per 4 m².

Time Series Analysis and Model Criticism. We analyze the plant–herbivore interaction by using a set of nonparametric, time-series statistical models. Contributions of moth and plant density (explanatory variables) to changes in moth and plant density (response variables) are considered by using a statistical model in the form:

[1]

Here, Δ_i,(t) is the difference in densities between one time step and the next for the ith species (ragwort or cinnabar moth), γ(x_j) is the set of time-lagged additive functions (of both species) that describe the density dependence within and between species, and ε_(t) is the residual error term. Rather than proposing a specific transformation for each explanatory variable, we use a relatively flexible method for modeling individual terms in a nonparametric (additive) model (11). The central idea of an additive model is to replace the linear function of a covariate with a smoothed function. Our additive time series models then consist of the sum of such functions. These models are classed as nonparametric because we do not impose a parametric form on the functions but instead estimate them through the use of a smoothing kernel (11).

Statistical model criticism proceeded by two methods. First, removal of the extreme outliers and refitting the nonparametric models confirmed that the qualitative patterns for the density-dependent structures remain robust. Second, resampling the time series with replacement by using a bootstrap algorithm and again refitting the nonparametric statistical models revealed that these nonlinear time series models provide parsimonious descriptions of the population patterns.

Results and Discussion

It turns out that the long-term population dynamics of both plant and herbivore are fundamentally different at the two sites (Fig. 1). At Silwood Park, the dynamics of both the moth and the plant are noncyclic and relatively stable. At Meijendel, the interaction between ragwort and cinnabar moth is cyclic, with amplitude fluctuations in both plant and herbivore numbers with a period of ≈5 yr. Time-series diagnostics indicate little if any effect of delayed density dependence on either the moth or the plant populations at Silwood Park. In contrast, significant lags at years 1 and 2 suggest that both direct and delayed density-dependent factors play a crucial role in the dynamics of the interaction at Meijendel. There is no evidence for the systematic entrainment of the plant–herbivore dynamics by external drivers at the two sites. Although they occur at roughly the same latitude and experience essentially the same weather systems, there is no evidence from the correlation of the common parts of the time series for synchrony (Moran effects) in either ragwort or cinnabar moth abundance (Fig. 1C). Rather, detailed statistical analyses highlight the importance of nonlinear feedbacks on the dynamics of the moth and herbivore populations at both sites.

Fig. 1.

(A) Time series of the plant (gray dashed line) and herbivore (black solid lines) populations for (i) Meijendel and (ii) Silwood Park. (B) Time-series diagnostics (partial autocorrelation) indicate that delayed density-dependent processes are absent in the ragwort (i)–cinnabar moth (ii) interaction at Silwood Park but prevalent in the plant–herbivore interaction at Meijendel (iii–iv). Horizontal dashed lines represent 95% confidence limits for the autocorrelations. (C) Correlation plots of the common parts of the time series of (i) log ragwort and (ii) log cinnabar moth abundance between the two sites. There is no evidence for environmentally correlated dynamics in either the cinnabar or ragwort series: correlation coefficients: ρ = —0.097 for ragwort populations, ρ = —0.067 for cinnabar populations.

In Dutch sand dunes, ragwort is regulated through rather complex density-dependent processes (Fig. 2). Although direct density-dependent processes (i.e., the effects of plant population 1 yr ago) have an impact on the abundance of the plant population in the present year, there is evidence of delayed density dependence in the ragwort population with a significant time delay 2 yr ago. Simpler demographic models of this interaction (12) mask both the importance of delayed effects and the nonlinearity in the interaction. At Silwood Park, plant dynamics are quite different. Nonlinear time-series analysis demonstrates that only plant density in the previous year had a significant effect on the regulation of the plant population (Fig. 3A). For the dynamics of the moth at Meijendel, there is clear evidence that the insect population is regulated through negative feedbacks acting through both direct and delayed processes. Statistical modeling (Fig. 4) shows that the direct and delayed density-dependent processes have a negative, regulatory effect. In contrast, at Silwood Park, the moth dynamics are governed solely by a direct density dependent process (Fig. 3B).

Fig. 2.

Plant dynamics at Meijendel. Estimated nonparametric regression lines for (square-root) ragwort abundance [plant density (t — 1)]. The most parsimonious model includes the contributory effects of (A) direct density dependence of ragwort {f[plant density (t — 1)]}, (B) delayed density dependence of the moth {f[moth density (t — 2)]}, and (C) the delayed density dependence of ragwort {f[plant density (t — 2)]} on changes in ragwort density. The U-shaped relationships (A and B) are indicative that population growth is minimal at intermediate densities, whereas the N-shaped relationship (C) is indicative of Allee effects operating within the plant population. Thin gray dashed lines are standard errors.

Fig. 3.

Plant and insect dynamics at Silwood Park. Estimated nonparametric regression lines for the ragwort–cinnabar moth interaction. (A) The direct density-dependent effects of ragwort {f[plant (t — 1)]} on changes in ragwort density [plant density (t — 1)]. (B) The direct density-dependent effects of cinnabar moth {f[moth density (t — 1)]} on changes in moth density [moth density (t — 1)]. The L-shaped relationship (A) indicates that the effects of plant biomass on population change is minimal at intermediate and high densities, whereas the N-shaped relationship (B) is indicative of Allee effects operating within the moth population. Thin gray dashed lines are standard errors.

Fig. 4.

Insect dynamics at Meijendel. Estimated nonparametric regression lines for (square-root) moth abundance [moth density (t — 1)]. The most parsimonious model includes the contributory effects of direct density dependence of the moth {f[moth density (t — 1)]} (A), delayed density dependence of the moth {f[moth density (t — 2)]} (B), and the delayed density dependence of ragwort {f[plant density (t — 1)]} on changes in moth density (C). The U-shaped relationships (A and B) are indicative that population growth is minimal at intermediate densities, whereas the N-shaped relationship (C) is indicative of Allee effects operating within the plant population. Thin gray dashed lines are standard errors.

Nonlinearities are evident in the interaction between the plant and its specialist herbivore. At Meijendel, there is evidence that the moth has a delayed density-dependent effect on plant growth rate (Fig. 2B). At Silwood Park, however, there is no statistical evidence for either a direct or a delayed effect of the moth on the growth rate of ragwort. The effects of the plant on the specialist herbivore also show marked nonlinearities. At Meijendel, the plant has a positive effect on changes in moth density when at low density but can act to inhibit moth population growth rate at high densities (Fig. 4C). In contrast, at Silwood Park, there is no evidence for either a direct or delayed effect of ragwort on the growth rate of the moth.

In years when cinnabar moth is common and ragwort is rare, there is mass defoliation of the plant and virtually no seed is set. In years when ragwort is abundant, the cinnabar moths are satiated and there is very little impact on total seed production. However, linking individual moth or plant performance to dynamics is not necessarily straightforward (13, 14), and it is differences between the sites that lead to these idiosyncratic population dynamic responses. At Meijendel, where the vegetation is open and there is plenty of bare sand for plant recruitment, the population dynamics show a significant delayed density component. Plant recruitment at this site from the seed bank or directly from germination is not microsite limited. At Silwood Park, however, the vegetation is closed and there is little bare soil. At this site, the plant–herbivore interaction is weakly coupled through direct density-dependent processes. Our analysis shows that both the direct and delayed components of the effects of cinnabar moth on the population dynamics of ragwort are negligible at Silwood. A suite of additional density-dependent factors (such as interspecific plant competition mediated by rabbits, the impact of disturbance leading to mass recruitment of the plant, and the role of competitors and/or natural enemies on the cinnabar moth) are potential mechanisms for the differences in the observed dynamics of the cinnabar moth–ragwort interaction between the two sites (12, 15–18). For instance, although the species assemblages on ragwort are equivalent (12), parasitoids seem be more influential in Meijendel than in Silwood Park and may play a role in driving the 5-yr cycle in insect abundance observed in the Dutch system (15). Short-term insect exclusion experiments at Silwood Park using systemic insecticides (11) indicate an influential role for competitors such as the flea beetle Longitarsus jacobaeae. Nonlinear density-dependent processes influence the dynamics of the ragwort and cinnabar and interaction between the plant and the herbivore. Differences between the sites are primarily driven by differences in the processes of plant recruitment and herbivory. These different kinds of interactions between the sites indicate that, although the density-dependent processes of herbivory and intraspecific competition are common to both systems, the rank importance of the component elements is a variant property of the site-specific plant–herbivore interaction.

To reiterate, our key finding here is that the same plant–herbivore system shows fundamentally different dynamics at the two sites. At Silwood Park, direct density-dependent mortality and mass plant recruitment resulting from soil disturbance (principally by rabbits) act to stabilize the plant–herbivore system, but plant and herbivore dynamics are clearly uncoupled. At Meijendel, time delays, and in particular delayed density dependence acting on the insect are instrumental in determining the plant–herbivore population dynamics. To explore these qualitatively different patterns (i.e., coupling or not, importance of time delays) and the ecological mechanisms underlying them requires an evaluation of appropriate mechanistic models. Choosing between different model structures to identify the most appropriate model for each site (using modern likelihood techniques and model selection criteria; ref. 19) is a challenge that will be developed in future work.

This study demonstrates how contingencies such as different density-dependent mechanisms can influence the sign, the magnitude, and the form of the population effects on ecological interactions. Ecological interaction strengths are traditionally thought to be indeterminate in their response to experimental perturbation (20). That the structure of this two-species interaction is contingent, stochastic, and nonlinear alerts us to the possibility of misinterpretation of the sign and magnitude of the interaction for reasons quite different from those associated with the type of experiment used to study interactions in species assemblages. The implication from the ragwort–cinnabar moth system is that ecological experiments need to examine species interactions over considerable lengths of time to explain appropriately the type, form, and strength of species interactions.