Diversity, Stability, and the Forecast Challenge in Forest Lepidopteran Predictive Ecology: Are Multi-Scale Plant–Insect Interactions the Key to Increased Forecast Precision?

Abstract

I report on long-term patterns of outbreak cycling in four study systems across Canada and illustrate how forecasting in these systems is highly imprecise because of complexity in the cycling and a lack of spatial synchrony amongst sample locations. I describe how a range of bottom-up effects could be generating complexity in these otherwise periodic systems. (1) The spruce budworm in Québec exhibits aperiodic and asynchronous behavior at fast time-scales, and a slow modulation of cycle peak intensity that varies regionally. (2) The forest tent caterpillar across Canada exhibits eruptive spiking behavior that is aperiodic locally, and asynchronous amongst regions, yet aggregates to produce a pattern of periodic outbreaks. In Québec, forest tent caterpillar cycles differ in the aspen-dominated northwest versus the maple-dominated southeast, with opposing patterns of cycle intensity between the two regions. (3) In Alberta, forest tent caterpillar outbreak cycles resist synchronization across a forest landscape gradient, even at very fine spatial scales, resulting in a complex pattern of cycling that defies simple forecasting techniques. (4) In the Border Lakes region of Ontario and Minnesota, where the two insect species coexist in a mixedwood landscape of hardwood and conifers, outbreak cycle intensity in each species varies spatially and temporally in response to host forest landscape structure. Much attention has been given to the effect of top-down agents in driving synchronizable population cycles. However, foliage loss, tree death, and forest succession at stem, stand, and landscape scales affect larval and adult dispersal success, and may serve to override regulatory processes that cause otherwise top-down-driven periodic, synchronized, and predictable population oscillations to become aperiodic, asynchronous, and unpredictable. Incorporating bottom-up effects at multiple spatial and temporal scales may be the key to making significant improvements in forest insect outbreak forecasting.

1. Introduction

At the intersection of animal population ecology and forest insect pest risk assessment lies an intriguing set of questions that have perplexed theoreticians and empiricists for over a century:

(1)

Why do some animal populations cycle [1]?

(2)

What stabilizes population cycling, allowing it to persist [2,3,4]?

(3)

What is the relationship between food-web species diversity and stability in animal population fluctuations? Is diversity stabilizing [5]?

(4)

What causes so many species of forest Lepidoptera to outbreak periodically [6]?

(5)

What role do top-down and bottom-up factors play in generating cyclic fluctuations [7]?

(6)

What causes cycling populations to synchronize spatially within species [8,9,10]?

(7)

Are patterns of periodic outbreaks in the forest Lepidoptera more consistent with clockwork theory [11], catastrophe theory [12,13], or some hybrid model [14]?

The reason these questions have persisted is because:

(1)

Answering them requires significant amounts of time-series data, with spatial replication and with attention paid to putatively important temporal and spatial co-variates.

(2)

Hypothesis testing requires good models that squarely confront new data. Getting theory and data to speak to one another is a challenge.

(3)

To the extent these systems are nonlinear and stochastic, relevant data accumulate slowly. Cross-scale systems are dominated by ecological surprise that confounds experimenters and resource managers alike.

(4)

These systems are multi-causal, so multiple hypotheses must be explored concurrently, and cannot be studied sequentially.

(5)

Evidence is often equivocal. It may tilt one way under one set of circumstances, or at one spatial and temporal scale, and differently under a different set of circumstances or scales.

(6)

Fierce competition for limited funding amongst rival investigators invested in specific hypotheses has impeded collaboration.

(7)

The “open data” and “open governance” movements that encourage widespread sharing of code and data are a relatively recent development.

As the planet moves into the Anthropocene, the ordinary uncertainties associated with unanswered questions of this type are likely to compound, resulting in an “uncertainty cascade”, as the myriad effects of climate change and landscape change percolate through complex food-webs whose baseline kinetics are poorly understood [15]. There is a growing recognition that we can no longer afford to have ecologists operating as we have been, in isolated silos of science specialization, as planetary change through “the spheres” (e.g., cosmosphere, atmosphere, hydrosphere, lithosphere, biosphere, genosphere, chemosphere) drives unprecedented ecosystem change, resulting in reduced levels of predictability of ecosystem function and rising levels of uncertainty in the global supply of ecosystem services [16]. Process feedback [17,18] and tipping elements [19] abound, resulting in a continuous stream of ecosystem surprises, from inexplicable surges in planetary warming [20], to unexpected levels of extreme fire behavior [21]. The need for open collaboration and integration in ecosystem modeling has never been so urgent, and forest insect disturbance modeling is a significant part of the global equation.

The “Ecological Forecasting Initiative” [22] is a direct response to this emergent need to encourage ecosystem modelers to get serious about predictive ecology in the Anthropocene. The related “Forecast Challenge” is a specific attempt to foster a culture of continuous incremental improvement and collaborative competition in predictive ecology—an ethos captured succinctly in the PERFICT paradigm—a re-imagined foundation for computational workflows in predictive ecology [23].

Aside from their important role as global biogeochemical processes, the other practical reason for developing enhanced forecasting methods in forest insect population ecology is that the most influential forest insects also happen to be pests of economic importance. Predicting pest occurrences before-the-fact is the key to enabling early detection and rapid response (EDRR) as a part of mitigative action, but it is also the key to enabling adaptations to risks that cannot be mitigated. Continuous improvement in quantitative understanding is the cornerstone of adaptive management [24]. As in climatology, scenarios are helpful for guiding broad thinking about a wide range of potential policy solutions for catastrophic risks [25,26]; but without probabilities associated to scenarios, it is hard to know which options merit serious consideration. A “risk assessment” is, essentially, a low-grade forecast. Why not, then, move, as a community, toward formalizing the link between the ecological factors driving risk and our imperfect knowledge about those ecological drivers? In an economic world, the only convincing way to argue that more knowledge is needed in a risk assessment is to illustrate the relationship between a given knowledge gap and the uncertainty it creates downstream, including the material consequences of that uncertainty.

It was 100 years ago that Craighead [27] gave the first authoritative account of the population ecology of the spruce budworm, Choristoneura fumiferana Clem.—the most important disturbance agent in the Canadian boreal forest. Since that time, two complete outbreak cycles have passed in eastern Canada, and a third is now under way [28]. Just 40 years ago, Royama [29] presented the first coherent, data-driven hypothesis explaining the periodic pattern of spruce budworm outbreaks and the large spatial scale of synchronization. This theory emphasized the top-down role of natural enemies in generating a delayed feedback loop that promotes cycling behavior. It sets aside any bottom-up role for the host-plant or the forest landscape in generating, or modifying, cycling behavior, which was the favored hypothesis through the 1970s [12].

The spruce budworm (SBW) is an early-season defoliator that times early larval emergence with the spring flush of poorly defended new foliage on its preferred host tree species, white spruce (Picea glauca (Moench) Voss) and balsam fir (Abies balsamea (L.) Mill.). White [30] outlined how a bottom-up hypothesis could help explain spruce budworm outbreak cycling. Meanwhile, several studies have shown that the host plant does have significant effects on fecundity, dispersal, and dispersal success of the conifer-feeding budworms [31,32]. Kneeshaw et al. [33] suggested that forest landscape species diversification might be a key means by which violent outbreak cycles could be stabilized, thus resurrecting an old hypothesis—the “silvicultural hypothesis”—that Miller and Rusnock [34] had described as “fallen”.

But after a full century of research on the population dynamics of the spruce budworm, it is fair to ask what is the material evidence that we have advanced our ability to predict the future? How do we know when our research agenda is delivering results? How do we demonstrate impact? How do we evaluate the return on all the investment in reduced uncertainty regarding the factors that influence outbreak dynamics? It is my contention that the “forecast challenge” is an opportunity to reframe how we evaluate our collective understanding of forest pest population dynamics. Forecast modeling is an opportunity to showcase what we know, and evaluate the different contributions to the collective effort to understand what drives outbreaks.

The purpose of this paper is to illustrate how an enhanced understanding of the plant–insect interaction in forest insect population dynamics might be the key to significant advances in forecasting ability. To do this, we start by asking the following: what is it that generates uncertainty in forecast models, and what is the surest path to significantly reducing that uncertainty? Box 1 illustrates what is meant by a “forecast model” and “forecast uncertainty” and shows how forecast uncertainty in an autoregressive time-series model rises significantly when a system’s cycling dynamics are heavily perturbed by a random stochastic factor (or set of factors). Box 1 is based on the autoregressive integrated moving average (ARIMA) model, which is rooted in the analysis of autocorrelation and partial autocorrelation structures in population time-series data [7].

Box 1. Forecast precision as a function of presumed population dynamics for a slow-cycling process. Top two rows (a–e) represent a highly deterministic simulation (u = 0.2; a₁ = 1.96, a₂ = −0.99). Bottom two rows (f–j) represent a highly stochastic simulation (u = 0.7; a₁ = 1.80, a₂ = −0.84). Both simulations generate a ~35 y population cycle (spectra in e, j; c = 37.5 y vs. 34.6 y), with unimodally distributed cycle peak intensities (b,g) that average roughly 6 units of population density (horizontal blue lines in (a,f); vertical in (b,g)). The main difference is that the higher stochasticity simulation in the bottom rows shows a wider range of forecast uncertainty, based on ARIMA(2, 0, 0) fits to the simulation data. The red curve indicates the model’s deterministic dynamics. The blue curve is the forecast, with its 80% and 95% confidence intervals in dark and light grey. The model’s structure is outlined in Appendix A. See Section 2 for details on ARIMA forecasting.

The null ARIMA-based model example in Box 1 is relevant to spruce budworm outbreak cycling, because low-order feedback is thought to regulate spruce budworm population fluctuations [7,29], and the pattern of a dozen outbreaks over 400 years in Québec, Canada has been roughly periodic [35,36], but with some irregular complexity [37,38]. If the autoregressive parameters of a forecast model are not known, or are poorly estimated as a result of such complexity, then the associated forecast will be imprecise. This can happen if assumptions about the source of the cycling behavior are mistaken. For example, it matters whether spruce budworm outbreak cycling is generated by (i) top-down forces (e.g., the delayed action of specialist natural enemies) that may be represented by a low-order autoregressive process [29] or (ii) a mix of top-down and bottom-up forces that would require higher-order models [14].

In the Border Lakes landscape of Ontario and Minnesota, Robert et al. [39] showed that spruce budworm cycling becomes more synchronized and more intense when the forest landscape is dominated by spruce and fir host trees. Robert et al. [40] subsequently showed that this is no coincidence, because in the same landscape, outbreaks of forest tent caterpillar (FTC), Malacosoma disstria Hbn., become more intense and better synchronized when the landscape is dominated by their primary host: trembling aspen, Populus tremuloides Michx. One of the important implications of this result is that forest tree species diversity tends to “stabilize” forest insect pest cycling, by reducing both cycle peak intensities and the spatial scale of outbreak synchronization [41]. A second implication, explored in this paper, is that forecasting future cycle peak intensities may require knowledge of the state of the forest, and inclusion of its effects in simulation forecast models.

That these results are not restricted to just the spruce budworm, but include the forest tent caterpillar, suggests they may extend to any major boreal forest insect pest species. The forest tent caterpillar has a phenology that roughly matches that of the spruce budworm. It overwinters as a diapausing second-instar larva that ecloses in early spring, around the time of budburst, when rapidly expanding succulent foliage becomes accessible [42]. During outbreaks, population densities will rise to cause 100% defoliation [43], and if this continues for several years uninterrupted, host death becomes increasingly certain [44], much as with the spruce budworm. Both insect species tend to space themselves out to minimize starvation effects, although this happens earlier in solitary-feeding spruce budworm (during the second larval stage, in peak springtime) than in the colonial forest tent caterpillar (during the fifth larval stage, in peak summertime). This host-dependency increases the likelihood that host-plant effects at the stem and/or landscape scale may be implicated in the pest species’ cycling dynamics, particularly when spacing behavior is inadequate to attenuate the many harmful effects of over-crowding.

Are multi-scale plant–insect interactions therefore the key to understanding the origins of complex patterns of cycling? There are two divergent approaches one could take to answer this question. Laboratory experiments and spatially distributed process-oriented field studies focusing on quantifying specific bottom-up feedback effects may yield insights that allow us to empirically constrain parametric simulation models of cycling dynamics. Alternatively, a time-series approach would consist of focusing on just one location that has been well-studied, and continue to accumulate time-series data, to see if additional populations and forest covariate data will reduce forecast uncertainty.

In this paper, I revisit some important long-term data sets of spruce budworm and forest tent caterpillar outbreak occurrence, attempting to determine which of the two approaches is most likely to bear fruit. Although we do not have the data to answer the question definitively within the scope of a single review paper, we can break the big question down into more tractable sub-questions for which forest insect data do exist:

• Is outbreak cycling the result of a low-order process that generates precise forecasts?
• Is cycle amplitude constant or variable, with precise or imprecise forecasts?
• If cycle amplitude varies, does it do so slowly, in a way it could lead to enhanced predictability?
• Is there any evidence that slow, deterministic changes in forest landscape structure mediate cycle intensity?

The data sets examined include tree-ring data and defoliation survey data, and come primarily from Québec, Ontario, and Alberta, Canada. I show that, in all data sets, regardless of source data type or region of origin, (1) low-order autoregressive time-series models result in tremendous forecast imprecision, even in very long series (as illustrated in the bottom of Box 1), and (2) variation in cycle peak intensity tends to follow a smooth pattern of steady rise and fall—much as one would expect for a fast, top-down cycling process regulated by slow, bottom-up feedback.

2. Materials and Methods

The general approach used is to fit ARIMA (Auto Regressive Integrated Moving Average) forecast models to various published aggregate time-series of spruce budworm (SBW) and forest tent caterpillar (FTC). ARIMA-based forecasting is relevant to these systems because theory has suggested that low-order autoregressive processes are responsible for population regulation [7,29], and low-order autoregressive models have been used in the past to represent cyclic dynamics in both systems [45,46]. These ARIMA models are then used to generate 60-year forecasts for SBW and 30-year forecasts for FTC, with 80% and 95% confidence intervals. The longer prediction horizon for SBW was used because historical records for that system tend to cover a longer time-frame, and SBW is also thought to cycle more slowly than FTC. After breaking down the aggregate time-series into spatially distinct constituent signals, we ask whether the tremendous uncertainty on model forecasts based on aggregate data is potentially a necessary result of complex patterning at finer spatial scales—patterning that might be plausibly host-related.

An ARIMA forecast model includes three classes of terms, with the number of these terms specified by parameters p, d, and q. The parameter p indicates the number of autoregressive (AR) terms in the model and the parameter q indicates the number of moving average (MA) terms in the model. The number of difference terms in the integrated (I) model is represented by parameter d. In the models presented here, the data are never differenced (i.e., d = 0), so we are effectively examining ARMA(p, q) model formulations. This is appropriate for situations where any cycling is purely endogenous in origin, i.e., where the series is not influenced by an exogenous trend or cycle, as one would expect in a model host–parasitoid system observed in a constant environment, as theorized in our Box 1 null hypothesis.

The general form of the ARMA(p, q) model is as follows:

X_t − α₁X_t−1 − … − α_pX_t-p = ε_t + θ₁ ε_t−1 + … + θ_q ε_t−q,

(1)

where X is the state variable of interest, t is discrete time, α represents the strength of regulatory feedback of order p, ε is measurement error, θ is the measurement lag effect, and q represents the persistence strength of the measurement error lag. For an endogenously cycling AR process, p ≥ 2. The higher the selected p, the higher the assumed dimensionality of the system, and the greater the opportunity for more complex cycling dynamics, but the greater the risk of forecast model overfitting. The moving average term, q, attempts to describe lag effects that influence system measurement, but not system dynamical behavior. For example, we might want to employ a lag MA term in the case of survey data, if positive detections in year t influence survey efforts in year t + 1, or in the case of tree-ring data, where the “physiological preconditioning” effect of a tree’s status in year t influences its growth rate in year t + 1 [47], which introduces a measurement and inference lag that has nothing to do with the driving input of concern—in our case, insect population dynamics. The higher the number of ARMA model terms, p + q, the greater the opportunity for the forecast model to represent the observed process and predict future observations, but with the risk of overfitting to historical data, effectively under-estimating the hidden influence of unmeasured driving covariates.

The time-series that we subject to ARIMA forecast analysis were derived from four study areas distributed across the spruce–aspen sub-boreal forest of North America (Figure 1). Each sub-study is described in turn. In each case, detailed methods of data acquisition are described in the primary sources cited. Here, only brief summaries are given.

• Spruce budworm (SBW) tree-ring data in Québec

Boulanger and Arseneault [35] developed a 450-year long chronology of spruce budworm outbreak activity in eastern Québec (centered near Rimouski, 48.4390° N, 68.5350° W) by coring church timbers and scanning for major growth reductions that can only be attributable to insect herbivory. Boulanger et al. [36] did the same for a slightly larger area in southern Québec, centered around Beauce (46.0522° N, 70.8177° W), some 400 km to the south. The area sampled lies within the Appalachian Mountain region and belongs to the eastern sugar maple (Acer saccharum Marsh.)–yellow birch (Betula alleghaniensis Britt.) subdomain [50]. Detailed methods of sample preparation and data processing are described in the original works.

The data are considered jointly for the purpose of developing a southeastern regional forecast model, and separately to examine the degree of synchrony between the two series and the pattern of periodicity within each series. With a separation distance of just 400 km between chronology centers, the theory of synchronized top-down-driven cycling [7,29] would predict a high degree of synchronization for an insect such as SBW that often flies hundreds of kilometers [51,52]. The algorithm ampd() from the R package AMPD (Automatic Multiscale-based Peak Detection) was used to process the time-series for the periodic occurrence of outbreak peaks.

2.

Forest tent caterpillar (FTC) defoliation data across Canada

Cooke et al. [53] presented a 64-year long record of forest tent caterpillar defoliation across Canada, building on earlier studies focusing on Québec [49] and eastern Canada [54]. Each year, from 1938–1995, the Forest Insect and Disease Surveys (FIDS) unit of the Government of Canada mapped moderate-to-severe defoliation of trembling aspen in each province using a combination of fire towers and fixed-wing aircrafts. After 1995, this survey responsibility was transferred to the appropriate provincial authority. Aerial surveys in all provinces are ground-checked with point-wise ground surveys to confirm the identity of the defoliator species. The area surveyed spans the southern half of the boreal forest, including the southern hemi-boreal zone [55]. Detailed insect survey methods are described in the original works.

These data are treated in aggregate for the purpose of developing a national-scale forecast model, then disaggregated in two ways. First, as in [56], the data were disaggregated via time-series clustering, using a hierarchical cluster analysis based on six clusters. Six was chosen as the stopping criterion for clustering because there were six outbreak cycles observed in the 64 years of study, and there were six regions covered: Alberta, Saskatchewan, Manitoba, Ontario, Québec, Maritimes. Second, as in [49], we focused on just the subset of Québec data south of 49° N, to examine disaggregated data in the two disparate regions where trembling aspen and sugar maple dominate, namely: Abitibi-Temiscamingue (“AT”; aspen), and Eastern Townships (“ET”; maple), representing a separation distance of ~600 km.

With a separation distance of 600 km between defoliation cycling clusters, the theory of synchronized top-down driven cycling [7] would predict a low degree of synchronization for an insect such as the FTC that typically flies short distances, and rarely hundreds of kilometers [57].

3.

Trembling aspen tree-ring data and FTC outbreaks in central Alberta

We revisit trembling aspen tree-ring data gathered from a densely sampled grid of 128 sites near Cooking Lake, Alberta [48], located in the aspen parkland forest region [50]. The landscape is a morainal till that is dominated by trembling aspen, with balsam poplar (Populus balsamifera L.) and white spruce forming a minor component totaling less than 5% of any plot. Radial increment was measured in 384 trembling aspen stems distributed over a 20 km × 20 km area. A section was taken at the base of each tree. Sections were dried at 40 °C for several days, sanded, and polished. Annual growth rings were resolved using a 10–60× magnification stereo-microscope with a range of light sources. Each ring was dated and measured to the nearest 0.01 mm using an ocular micrometer. Sectional chronologies were cross-dated by examining the cross-correlation among ring width profiles, particularly with regard to high-frequency fluctuations in ring width.

The dominant factor affecting trembling aspen ring widths across central Alberta is defoliation by forest tent caterpillar, although drought is a statistically significant climatic determinant of growth in the aspen parkland (Table 1 in [50]). Although it is not possible to predict climatic fluctuations driving trembling aspen growth patterns, it should be possible to forecast fluctuations in FTC numbers, if these fluctuations are periodic and spatially synchronous. As with the first two study systems, an ARIMA forecast model was developed for the aggregate data from Cooking Lake.

4.

SBW and FTC tree-ring data in Ontario and Minnesota

The Border Lakes landscape encompasses a ~20,000 km² ecoregion that straddles the border between Minnesota (USA) and Ontario (Canada) at the hemiboreal transition between the Laurentian mixedwood and boreal forest regions. Forest composition is mixed hemiboreal [58], with a high proportion of boreal tree species (e.g., jack pine (Pinus banksiana Lamb), black spruce (Picea mariana (Mill.) B.S.P), white spruce (Picea glauca (Moench) Voss), balsam fir (Abies balsamea (L.) Mill.), paper birch (Betula papyrifera Marsh.), aspens (Populus tremuloides Michx., P. grandidentata Michaux)), as well as several species near the northern limit of their range, such as white pine (Pinus strobus L.), red pine (P. resinosa Ait.), and red maple (Acer rubrum L.).

Outbreak histories of SBW and FTC were reconstructed by sampling tree-rings from 100 mixedwood sites containing 50 white spruce and 50 trembling aspen sample locations. These data were aggregated from the level of individual trees to sites to subareas of sites in close proximity (i.e., within 25 km), thereby generating 16 spatially distributed SBW outbreak chronologies, and 15 spatially distributed FTC outbreak chronologies, with a high degree of congruency in the spatial distribution of reconstruction chronologies. Detailed methods of outbreak reconstruction for SBW and FTC are described by [37,38], respectively.

As with the other three study systems, forecast models were developed for the aggregate data. The disaggregated data (separated by a hierarchical clustering algorithm and analyzed in three earlier papers [39,40,41]) were reviewed for patterning that departed from the expectations of the simple top-down theory of outbreak cycling [7]. The chronologies in this study design were dispersed over a smaller area than either of the first two studies, but larger than the third—all of the plots being contained within a network spanning just 200 km × 200 km (Figure 1). At this small spatial extent, a top-down theory of outbreak cycling [7] would predict high synchrony between cycling populations, both for a long-range disperser such as SBW, and a short-range disperser such as FTC. Previously published analyses confirm that the degree of synchrony is generally high in both SBW [39] and FTC [40], but drops considerably when host forests are less abundant [41]. However, none of the previous papers examined whether the aggregated data lead to an imprecise forecast model.

All data transformations and analyses were conducted using the R statistical software package ver. 4.4.1 [59].

3. Results

3.1. Spruce Budworm Tree-Ring Data in Québec

The composite tree-ring data from eastern and southern Québec indicated a reasonably high degree of outbreak periodicity, leading to a 60-year forecast of additional outbreak cycles expected to peak just before 2020 and again around 2040 (Figure 2). The forecast was imprecise, however, as the predicted intensity of the next two cycles could vary from low to moderate to high intensity (Figure 2a). At the time of writing, in 2024, an intense outbreak did eventually emerge in Québec. However, with foci in northeastern Québec and northwestern Québec, it still had not affected the areas sampled here, in southeastern Québec.

The AMPD algorithm, using a sensitivity parameter of s = 21, identified ten outbreak intervals over the 440-year long period (Figure 2a). The last three cycles (VIII, IX, X) were all quite sinusoidal and were synchronized in both phasing and intensity between the two constituent regions. However, during the previous three centuries, only one outbreak interval exhibited such high synchrony: interval IV, 1740–1780. During the other six intervals, I–III and V–VII, the average correlation between regional outbreak chronologies was less than zero. The distribution of pairwise correlation coefficients across the ten intervals was extremely variable, with two prominent modes appearing at correlations of −0.1 and 0.7 (Figure 2b). Indeed, dropping the sensitivity parameter of AMPD down to s = 6 revealed the existence of 12 additional low-intensity sub-cycles in the composite series, all during intervals I–VII, such that major intervals could be subdivided into decadal sub-intervals during which the outbreak cycle was peaking in either southern Québec or northern Québec, but not both. In fact, during prolonged periods, intervals I–III and V–VII, outbreak sub-cycles consistently peaked first in eastern Québec and later in southern Québec (blue vs. red dots in Figure 2a). During the first period, intervals I-III, the time-lag between eastern and southern Québec cycle peaks was 20–40 years. During the second period, intervals V–VII, the time-lag between eastern and southern Québec cycle peaks was roughly 20 years. This marked lack of synchrony at the faster time-scale, within major intervals, occurred despite the fact that the composite series exhibited relatively strong periodicity (Figure 2c), with strongly positive first-order feedback and strongly negative second-order feedback (Figure 2d). A spectral analysis (Figure 2e) suggested the eastern Québec series was cycling at a slightly faster frequency (37.5 y) than the southern Québec series (50.0 y), consistent with the observation that eastern Québec peaked decades before southern Québec in 6 of 10 intervals.

The two series were asynchronous not just at the faster within-interval time-scale, but also at the slowest possible time-scale, across all cycles (blue vs. red dashed curves in Figure 2a). While the eastern Québec series was peaking in cycle intensity at the start and end of the series (intervals I–II and VII–X), outbreak cycles in the southern component were peaking at the middle of the series (III–V). The low-frequency trends in cycle intensity mirrored one another in the two regions, despite these budworm populations being separated by only 400 km.

3.2. Forest Tent Caterpillar Defoliation Data across Canada

As reported by [56], FTC, in aggregate, exhibits fairly periodic behavior across Canada in 1938–2001 (Figure 3). However, the process is noisy enough that the forecast for 2002–2032, based on an ARIMA(2, 0, 1) model, is remarkably imprecise (Figure 3a). The source of the noise, which is the source of the forecast imprecision, is revealed when the aggregate time-series is decomposed via cluster analysis (Figure 3b): the cycling is not spatially synchronized. Moreover, the regional clusters exhibit very little local periodicity at all. They are nonstationary in mean and variance, and exhibit high skewness and kurtosis, making them unsuitable for time-series analysis [53].

What is remarkable about each series is that despite the fact that each is dominated by singular spike anomalies (Figure 3b) that move about unpredictably from region to region across the country (Figure 3c), the anomalies collectively occur on a periodic schedule, resulting in a periodic aggregate (Figure 3a). The areas where FTC are cycling are so small that they do not appear in a six-cluster decomposition. It is not until the decomposition employs 12 or more clusters that one begins to observe small pockets of periodic behavior [57]. This analysis reveals that this is a system where synchronized outbreak cycling is not the most important question to be answered. Far more important to understand is what drives the anomalous departures from synchronized cycling. Are they a product of a bottom-up resource pulse?

When the FTC defoliation data are limited to just the province of Québec, the patterns that emerge from a nine-cluster sub-model for Québec are exactly those reported by [50]. The FTCs in Québec exhibit periodic behavior in just two regions, in the northwest and southeast sectors: the Abitibi-Temiscamingue (AT) district, and the Eastern Townships (ET) (Figure 4). Cluster 8 in AT spans 40,890 km²; cluster 6 in ET spans 24,940 km². This represents just 2.3% and 1.4% of the FTC outbreak range in Canada, at 1,739,652 km². Identifying clusters this small in the full national-scale dataset would require roughly 50 clusters.

3.3. Trembling Aspen and FTC-Caused Growth Reductions in Central Alberta

From 1919–1998 ten intervals were observed where trembling aspen growth rates dropped well below the 0.65 mm threshold of impact caused by drought, and is more typically associated with defoliation by forest tent caterpillars (Figure 5). Although these growth reductions occurred somewhat regularly every 7–10 years, half were severe (IV, V, XI, IX, X), with the series mean dropping to the 0.65 mm threshold, and half were not (I, II, III, VII, VIII). The lack of regularity in amplitude variability led to an extremely imprecise forecast using an ARIMA (2, 0, 1) forecast model.

3.4. SBW and FTC Tree-Ring Data in Ontario and Minnesota

Ref. [39] identified four major outbreak cycles of SBW in the Border Lakes landscape over the period 1837–2005. However, the pattern of periodicity was somewhat ambiguous, which resulted in a highly imprecise 60-year forecast, whether a low-order ARIMA(2, 0, 0) model was used (Figure 6a) or a higher order (7,0,1) model (Figure 6b). Meanwhile, [40] identified ten cycles of highly variable intensity of FTC in the Border Lakes landscape over the period 1876–2006. The pattern of periodicity was, as with SBW, somewhat ambiguous, which resulted, again, in a highly imprecise 30-year forecast, whether a low-order ARIMA(2, 0, 0) model was used (Figure 6c) or a higher order (7,0,1) model (Figure 6d).

Ref. [41] demonstrated that one of the reasons for the ambiguity in cycling behavior in either species in the Border Lakes was the effect that forest composition across the study area has on the intensity of cycling in each insect species. Different areas cycle differently depending on whether they are dominated by hardwoods or conifers, with the intensity of outbreaks of the conifer defoliator, SBW, rising with increased conifer content, and the intensity of outbreaks of the hardwood defoliator, FTC, rising with increased hardwood content. Indeed, this spatial relationship between host and defoliator appears to extend from space into time (Figure 7).

The fact that the Minnesota landscape is relatively rich in hardwoods and the Ontario landscape is relatively rich in conifers is what drives the modern ends of the modeled series in Figure 7 apart. The authors in [41] further suggested that it may be defoliation-driven successional change in forest landscape structure, from either spruce to aspen or vice versa, that may be governing this “see-saw” pattern of outbreak cycling. They propose a working model of outbreak cycle stabilization driven by a reciprocal landscape-scale plant–insect interaction. If the landscape is heavily dominated by either spruce or aspen, the corresponding defoliator species will dominate. When the landscape is maximally diversified, in terms of species composition and patchiness, this minimizes the impact of each insect by stabilizing the amplitude of outbreak cycling.

4. Discussion

Although there are signs of robust periodicity in both the SBW and FTC systems, in both Québec and Ontario, the patterns of outbreak are not consistent with the simple idea of spatially synchronized cycling arising from spatially autocorrelated weather effects or dispersal acting on a low-order feedback process such as one might expect from a top-down-driven predator–prey system. Outbreak cycles in these systems tend to exhibit extreme variability, and at least some of the variability is associated with the type of forest landscape in which the focal insect is found. This is significant, because forecasts based on low-order autoregressive models are extremely imprecise, and the imprecision is rooted in the extreme variability in peak cycle intensity. Even at very fine spatial scales where insect dispersal is likely to be sufficient to connect every sample population with every other sample population, outbreak cycling in FTC is insufficiently periodic and insufficiently spatially synchronized to generate a precise forecast of the timing and intensity of the next impact cycle.

The extreme variability in cycle peak intensity arises at two distinct time-scales. At the faster time-scale between successive cycles, major outbreak cycles are very often preceded or followed by minor cycles that do not meet the standard threshold of “outbreak”. This results in a muted autocorrelation function (e.g., Figure 2c) and thus an imprecise forecast. This extreme variability in cycle peak intensity is frequently associated with poor synchrony in cycling between locations (Figure 2b). For FTCs across Canada, the level of synchrony is remarkably low, with regional cluster time-series being dominated by aperiodic spike anomalies that are only periodic in aggregate. It is not clear at all what drives these spike anomalies in the FTC system. The most likely candidate is a sudden flush of disturbance-loving trembling aspens resulting in a “resource-pulse-driven eruption” (sensu [61]), similar to the manner in which bark beetle outbreaks may be driven to remarkably high intensities [62]. However, one cannot rule out the possibility of either anomalously favorable weather at those times and places, or an absence of natural enemies.

At the slower time-scales, all four study systems exhibited a slow modulation of cycle peak intensity. For SBW tree-ring data in Québec (study 1), it is not clear what might be causing the centuries-long cycle in outbreak cycle peak intensity (Figure 2a dashed lines). It cannot be the cooler climate through the “Little Ice Age” because the trends in the two regions, separated by only 400 km, oppose one other. For FTC defoliation data in Québec (study 2), host species type appears to be associated with similarly distinct patterning, with the aspen and maple-dominated regions of northwestern and southeastern Québec cycling out of phase with one another. A clue to this behavior may lie in the Border Lakes (study 4), where the most definitive evidence gathered to date indicates that host forest landscape structure governs cycle intensity and synchrony. This constitutes the strongest proof available that species-diverse forests are less prone to intensive and extensive outbreaks of forest Lepidoptera. It is also consistent with the observation that bottom-up factors shape SBW outbreak synchrony across Québec [63].

In study three, trembling aspen tree-ring data from central Alberta exhibited three outbreak cycles of low intensity (I, II, III) followed by three cycles of high intensity (IV, V, VI), followed by four cycles of mixed intensity, two low (VII, VIII) and two high (IX, X) (Figure 5). Successive outbreaks move about systematically from one part of the study to the next, and this century-long slow motion is related to spatial patterns of host forest cover measured in 1995 (see Figures 2–7 in [48]). However, it is not clear how qualitative changes in host quality through time might be affecting the time sequence of cycles of varying amplitude.

One clear way that trees can exert a local bottom-up effect on herbivory is through adjustments in nutritional status or induced defenses, as has been hypothesized for SBW [30], spruce budmoth, Zeiraphera canadensis Mut. and Free. [64], and larch budmoth, Zeiraphera diniana Gn. [65]. However, there are two additional mechanisms by which stand- and landscape-scale forest tree-species diversification may stabilize high-intensity cycling (Figure 8), and thus reduce the risk of attack by Lepidopteran pests [66]. The first is through the direct effect of non-host forest on dispersal losses, as occurs with western spruce budworm [67]. The second is through the indirect effect of forest diversity on natural enemy community diversity [68]—which constitutes an interaction between top-down and bottom-up effects. Roland [46,69,70] has shown that outbreaks of FTCs are strongly conditioned by this sort of top-down/bottom-up interaction whereby host forest landscape structure alters natural enemy mobility and thus rates of parasitism.

Although it may be argued that forest insect forecasting is not often an operational goal of forest and pest managers, pest risk assessment frequently is. Pest risk assessment is the art and science of efficiently collating everything we know about pest species population dynamics, and assembling it into some sort of predictive context. Recent large-scale risk assessments of mountain pine beetle [71] and SBW [72] explored uncertainties as a central feature of analysis, clarifying the relationship between knowledge gap, research priority, and the importance of learning in the do-learn-adapt cycle of adaptive pest risk management [73]. Both systems exhibit “cross-scale” eruption dynamics [74,75], where stochastic nonlinear process interactions are capable of generating monumental ecosystem surprise, including effects on the global-scale biogeochemistry of carbon sinking [17,18]. If powerful bottom-up effects are manifest locally, at the level of trees and stands, such a nonlinearity could be a significant source of asynchronous behavior that could run afoul on the assumptions of linearity and homogeneity intrinsic to simple forecasting approaches. Are multi-scale plant–insect interactions therefore the key to increased forecast precision? The issue is not just what happens at the scale of microns or millimeters or meters, or over the course of a feeding session or a season or even a population cycle, but across stands and landscapes, and over the course of multiple cycles and even centuries. Bottom-up effects are scale-crossing effects.

It is fair to ask whether results presented here for two focal boreal forest insect pest species are likely to extend to other cycling forest Lepidoptera in Canada, or around the world. It is possible that other systems do not respond this way; however, this remains to be seen. These two systems dominate the Canadian boreal landscape and may serve as a useful template for studying complex spatial dynamics in other systems. The tree-ring records and defoliation records selected for analysis are amongst the longest-term and largest-scale in existence in Canada. Different conclusions from different data series might be possible; however, this also remains to be seen.

Finally, it must be conceded that the long-term series presented here all terminate within the interval 1998–2006, around the time the climate began warming rapidly. For that reason, climate change was not explored as a specific driver of cycling activity. The focus was on the more traditional clash between the top-down versus bottom-up hypotheses of cycling behavior. The demonstrated failure of the ARIMA forecast modeling approach therefore has more to do with environmental factors occurring in earlier time periods than with anthropogenic climate warming occurring during more recent decades. It is not only possible, but likely, that more advanced modeling methods, such as simulation, will be needed to handle the more recent changes in dynamics that are surely occurring under climate change.

5. Conclusions

The diversity-stability question is age-old. I ask whether this might be the missing link in defoliator predictive ecology, i.e., whether it is the key to improving forecast model precision and performance. Results here indicate that the major forest Lepidopteran pests of eastern Canada do not cycle synchronously, and this lack of regularity and synchrony in cycling leads to a serious impediment to forecasting pest occurrences in time. Disaggregating composite time-series can reveal complex spatiotemporal patterning that goes beyond what one expects from a simple Royamian autoregressive model of top-down feedback. This complexity includes slow variations occurring at decadal and multi-decadal time-scales that are inconsistent with low-order feedback as represented in a simple ARIMA forecast model. Including bottom-up effects in a more sophisticated simulation model may be the next logical step in large-scale, long-term defoliator predictive ecology.