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The dynamics of forest tent caterpillar outbreaks across east-central Canada

Barry J. Cooke, Chris J. K. MacQuarrie and Franc̨ois Lorenzetti

B. J. Cooke (barry.cooke@nrcan-rncan.gc.ca), Natural Resources Canada, Canadian Forest Service, Northern Forestry Centre, 5320 – 122nd Street, Edmonton, AB T6H 3S5, Canada. – C. J. K. MacQuarrie, Natural Resources Canada, Canadian Forest Service, Great Lakes Forestry Centre, 1219 Queen St. E. Sault Ste. Marie, ON P6A 2E5, Canada. – F. Lorenzetti, Univ. du Québec en Outaouais, Dépt des sciences sociales (Secteur sciences de la nature/sciences forestières) and Inst. Québécois d’Aménagement de la Forêt Feuillue, 58 rue Principale, Ripon, QC J0V 1V0, Canada.

An analysis of forest tent caterpillar Malacosoma disstria defoliation records from Ontario and Quebec over the period 1938–2002 indicates that outbreaks recur periodically and somewhat synchronously among regions of the two provinces. Cluster analysis revealed that the most strongly periodic, large-scale, synchronized fluctuations occurred within three regions: northwestern Ontario, eastern Ontario/western Quebec and southeastern Quebec. Defoliation in the vast sur-rounding hinterlands tended to be infrequent and sporadic, loosely tracking defoliation in the core outbreak regions. One small cluster in northeastern Ontario stood out as anomalous, as a result of an increasing trend in the duration of periodic defoliation episodes, marked by an unprecedented double-wave of defoliation that persisted from 1992 to 1999. This is the precise area where, in the early 2000s, trembling aspen Populus tremuloides stems were mapped as being in a state of decline of unprecedented severity and extent. Our results suggest forest tent caterpillar has the potential to cause significant impacts on forest health and, hence, carbon budgets in east-central Canada and that the forest tent caterpillar deserves more attention as a model system of forest insect disturbance ecology.

Ecologists for over a century have been fascinated by periodic fluctuations in insect populations (Nicholson and Bailey 1935, Turchin and Taylor 1992). In more recent decades the topic of synchronization of defoliator population cycles has emerged as a critical issue (Kendall et al. 2000, Peltonen et al. 2002), as this is the mechanism most commonly invoked by theorists to explain the simultaneous emergence of disparate infestations and their subsequent coalescence to form large-scale outbreaks (Royama 1992). Some periodically outbreaking forest Lepidoptera systems that have received considerable attention are: larch budmoth Zeiraphera dini-ana in Europe (Baltensweiler 1964, Bjornstad et al. 2002, Klemola et al. 2006), autumnal moth Epirrita autumnata in Fennoscandia (Tenow 1972, Ruohomaki et al. 2000, Klemola et al. 2006), gypsy moth Lymantria dispar in the United States (Johnson et al. 2006), and spruce budworm Choristoneura fumiferana in eastern Canada (Royama 1984, 2005, Royama et al. 2005).

To this list one might add the forest tent caterpillar Malacosoma disstria in east-central Canada. The forest tent caterpillar is a voracious defoliator of hardwood trees through-out North America (Stehr and Cook 1968, Fitzgerald 1995), exhibiting large-scale, periodic outbreaks on trembling aspen Populus tremuloides in much of the boreal forest (Witter 1979). Outbreaks are typically short-lived, persisting 3 yr or less at the stand level, and somewhat longer at the landscape scale (Sippell 1962), although localized infestations have been known to persist for nearly a decade before collapsing

(Shepherd and Brown 1971, Witter et al. 1975). The forest tent caterpillar has been cited as a co-factor in the decline of aspen in Alberta and Ontario, Canada (Candau et al. 2002, Hogg et al. 2002, Man and Rice 2010) and data show that tree mortality increases with the duration of sustained defo-liation by the species (Churchill et al. 1964, Man and Rice 2010, Moulinier et al. 2011).

Much has been said of the regular occurrence of large-scale forest tent caterpillar outbreaks in Canada (Baird 1917, Hildahl and Reeks 1960, Fleming et al. 2000, Cooke et al. 2007), but no study has actually quantified the strength of periodicity, the scale of synchrony, and the degree to which regional populations depart from these oft-cited norms. In this paper we report on regional-scale patterns of forest tent caterpillar defoliation observed in the Canadian provinces of Ontario and Quebec (Fig. 1) from 1938 to 2002. For this study we defined populations of forest tent caterpil-lar as areas within Ontario and Quebec that shared similar spatial and temporal patterns of defoliation intensity. Using defoliation intensity as a proxy measure for population size, we subjected each forest tent caterpillar population in the region to a qualitative and quantitative analysis of the frequency, amplitude, and return interval of outbreaks. Then, to examine the processes driving the pattern of out-breaks within individual populations, we derived popula-tion rates of change from the time series and determined the value and magnitude of density-dependent and lagged density-dependent parameters.

Ecography 34: 001–014, 2011 doi: 10.1111/j.1600-0587.2011.07083.x

© 2011 The Authors. Journal compilation © 2011 Nordic Society Oikos Subject Editor: Jacques Régnière. Accepted 28 June 2011

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Figure 1. Cluster map of regions in Ontario and Quebec, Canada with similar spatiotemporal patterns of forest tent caterpillar defoliation between 1938 and 2002 (a) and coincidence between forest tent caterpillar defoliation and incidence of trembling aspen decline in north-central Ontario (b). Areas with the same color belong to the same population. Numbers are assigned to populations by increasing severity of defoliation; box in (a) shows the area highlighted in (b); crosses in (a) show the location of the cluster centroids.

In this study we also examined the patterns and process governing synchronization among and within populations of forest tent caterpillar. We used spatial correlation and covariance analyses to determine if, and over what dis-tance, outbreaks of forest tent caterpillar are synchronized among populations (Peltonen et al. 2002). We then tested the hypothesis that the amplitude of cycling (i.e. the vari-ability in the time series) should be an important factor governing the rate of cycle synchronization (Royama 1980,

Barbour 1990) by examining the degree of synchrony within and among populations. We use our results to pro-vide an explanation for the decline of trembling aspen that occurred in an area of northeastern Ontario in the early 2000s. We sought to determine whether the pattern of outbreak there was anomalous relative to dynamics in the other parts of the insect’s range, and in particular if there was any evidence of an increasing trend in outbreak severity over the entire region.

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Methods

Data

We analysed the occurrence of forest tent caterpillar out-breaks between 1938 and 2002 using forest insect and dis-ease survey (FIDS) records of defoliation intensity in the provinces of Ontario and Quebec. Previous studies have investigated population dynamics of forest tent caterpillar using the global time series of defoliation for Ontario and Quebec (Cooke et al. 2009) and spatial and temporal sub-sets of the same data (Simpson and Coy 1999, Cooke and Roland 2000, Cooke and Lorenzetti 2006). The source data were aerial survey sketch maps of areas exhibiting moder-ate to severe defoliation attributable to forest tent caterpillar. These sketch maps for each year and province were digitized and the original polygons of forest tent caterpillar damage were rasterized by overlaying a grid and determining the severity code for the polygon falling within each grid cell (Cooke and Lorenzetti 2006, Cooke et al. 2009). The data for Ontario were rasterized at a scale of 10 3 10 km grid, while the data from Quebec were rasterized at a scale of 6 3 6 km. The original aerial survey data for Ontario were also recorded in a different fashion from that in Quebec and therefore, after rasterizing, each cell in Ontario took a continuous value between 0 and 1, whereas the Quebec ras-ter cells were coded as either 0 or 1. A preliminary analysis showed the scale of rasterization and the difference in coding between the two provinces had no meaningful effect on the results. The rasterizing procedure resulted in 12 383 cells all of which were located between 43°N and 53°N and 60°W and 95°W (Fig. 1).

Cluster analysis

Hierarchical clustering analysis (Kaufman and Rousseeuw 1990) was used to identify areas with temporally similar dynamics using the time series of defoliation intensity data between 1938 and 2002 for each rasterized cell as the raw data. Previous studies have used this approach to examine spatial and temporal patterns in animal population dynamics over large areas and long time periods (Swanson and Johnson 1999, Williams and Liebhold 2000, Okland and Bjornstad 2003, Aukema et al. 2006, Cooke and Lorenzetti 2006).

In hierarchical clustering, the similarity among the time series of defoliation intensity for cell is used to cluster the cells into groups (Kaufman and Rousseeuw 1990, Venables and Ripley 2002). Similarity among the time series is assessed by computing a distance matrix for all pairs of cells; cells with time-series that are less similar will be separated by a greater distance (Kaufman and Rousseeuw 1990). The distance matrix for the cells is then used as the basis for the cluster-ing. Note that in our application, while the cells are spatial units, the distance matrix is calculated using only the values in the time series (i.e. the intensity of forest tent caterpil-lar defoliation between 1938 and 2002). Thus the distance matrix, the clustering, and the subsequent time-series analysis are not influenced by the spatial relationship among the cells. We used a hierarchical clustering approach whereby an algo-rithm initially considers each time series to be independent

(i.e. a cluster of one) and then proceeds by joining similar time-series until all have been joined (see Kaufman and Rousseeuw 1990 for a comparison of clustering methods). The end-product of the clustering allows the relationships amongst the time series to be visualized as a dendrogram; within the dendrogram, time series that are more related are located closer to each other on the plot (Venables and Ripley 2002). Points in the dendrogram where one or more time series join a branch are called nodes, all time series that join the dendrogram below a given node are considered to be members of the same cluster. Using a hierarchical method with a large number of time series will result in a great many more clusters than can be reasonably analyzed; therefore, it is necessary to ‘prune’ the dendrogram to determine the num-ber of informative clusters.

We used two complementary methods to prune the out-put of the hierarchical clustering. First, we calculated the Kelly–Gardner–Sutcliffe (KGS) penalty function (Kelly et al. 1996, White 2010) to obtain a cut-off value. The KGS penalty function uses the clustering hierarchy and the origi-nal dissimilarity matrix to calculate a dissimilarity measure for all levels of the raw dendrogram; the minimum value of the function gives the suggested number of clusters. We also used non-metric multidimensional scaling (NMDS) to produce a ‘stress plot’ (Kruskal and Wish 1978). Stress is calculated from the observed distances between every pair of time series in q dimensional space (Venables and Ripley 2002). Where the stress is minimized suggests an optimal number of clusters, this location can be found by indenti-fying the ‘elbow’ of a stress plot, or the value of q (i.e. the number of clusters), at which there is a significant drop in the stress value as computed by the NMDS (Kruskal and Wish 1978).

After we determined an optimal number of clusters we then computed the time-series of mean defoliation intensity for each population. For simplicity we will refer to the clus-ters of cells that resulted from pruning the dendrogram as ‘populations’ although some are not contiguous in space. We also computed the time series of mean defoliation intensity for the entire region in this study (i.e. Ontario and Quebec). The hierarchical clustering procedure arbitrarily numbers clusters based on the order they appear in the dendrogram thus before proceeding with our analysis we ranked the pop-ulations in terms of overall defoliation intensity and then re-numbered the populations based on their rank (higher numbers mean more defoliation). It was these time-series that were used for all subsequent analyses.

Time series analysis

We used the time series of mean defoliation intensities to determine when forest tent caterpillar outbreaks occurred in each population. We defined an outbreak as occurring when the mean defoliation intensity exceeded the overall mean for the entire time series for two or more years (Babin-Fenske and Anand 2011).

The cyclic behaviour of each forest tent caterpillar popu-lation was investigated and quantified using autocorrelation function (ACF), partial autocorrelation function (PACF), and spectral analyses. The ACF computes the correlation

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defoliation intensities over time by fitting a version of the model that included a time parameter (t) described by the constant a3:

Rt a0 a1 Xt a2 Xt1 a3t (2)

We plotted the values of a2 versus 1 a1 into the parameter plane for (1) to determine the expected pattern of fluctua-tion in population size that would be expected within each regional population (Royama 1992). To permit comparison we also fit (1) to the regional time series and plotted its loca-tion in parameter space as well. Fitting the second-order density-dependent model (1) also allowed us to compute a measure of cycle length, c, for each population from the values of a1 and a2 by:

c a a a 2 arctan 1+ 4 112

2 1( ) ( )æèççç

öø÷÷÷÷ (3)

(Royama 1992). After computing c we plotted the value on the spectral analysis plot for each population to permit comparison between the cycle length predicted based on the second-order density-dependent model (1) and the cycling time predicted by the ACF and spectral analysis.

Outbreak synchrony

We used correlation and covariance analyses to determine the distance over which fluctuations in forest tent caterpil-lar populations are synchronized. We first computed pair-wise correlations between the time series for all populations (not including the regional time series) then plotted these as a function of the distance between the geographic cen-tres (cluster centroids) of the populations. The locations of the centroids were determined by calculating the mean lati-tude and longitude from all cells within the population. We used locally-weighted polynomial regression (lowess) to fit a simple correlation versus distance function to that data. We compared the results of this analysis to the smoothed non-parametric covariance function (SNCF) (Bjornstad et al. 1999, Bjornstad and Falck 2001). We also compared the SNCF results for our data to that from forest tent cat-erpillar in western Canada using data from Peltonen et al. (2002). We also compared the SNCF to SNCFs previously determined for larch budmoth, spruce budworm, western spruce budworm, gypsy moth and mountain pine beetle (data also from Peltonen et al. 2002).

We also examined if the degree of synchrony within populations was correlated to the amplitude of population cycling (Barbour 1990). To compute a measure of syn-chrony within each population we calculated the Pearson correlation coefficient for the time series of defoliation intensity between all pairs of cells in each population, from which we then calculated the mean Pearson correlation for the entire population. We used the natural log of the standard deviation of the mean defoliation intensity for the entire population as a measure of cycling amplitude for in each population. We estimated the strength of the correla-tion between these two values for all populations using the Pearson correlation coefficient.

coefficient between mean defoliation intensities for all points (Xt) in the time series (X1, X1 j), (X2, X2 j), …, (XT, XT j), where T is the total length of the time series and j is a time lag from 0 to T. Note that throughout we follow the nota-tion convention of Royama (1992), thus Xt loge(xt) where xt is the mean defoliation intensity at time t. The correlation coefficients are then plotted versus j, with a high degree of correlation at a given value of j indicating that any two years separated by that amount are likely to have similar levels of mean defoliation intensity. A correlation for a given lag time is assumed to be strong if the coefficients exceed the 95% confidence intervals (CI) for a correlation coefficient of 0 (i.e. the correlation is significantly different from 0). We considered populations with lag coefficients that exceed both the upper and lower confidence intervals to be regularly cyclic and population with lag coefficients that exceed only one confidence interval to be moderately cyclic. The PACF is similar to the ACF, but removes the effect of autocorre-lations caused by the sharing of intermediate time points. Thus for a low-order cyclic population the ACF cycles and damps slowly, while the PACF truncates abruptly after a low number of lags (Royama 1992).

We tested if forest tent caterpillar populations cycle at more than one frequency using spectral analysis. Spectral analysis complements the ACF because ACF are only capa-ble of identifying cycling at the dominant frequency. For this analysis we used a fast Fourier transform with modified Daniell smoothers and plotted the smoothed periodogram of our results (Venables and Ripley 2002). Peaks of equal magnitude in the periodogram indicate that a population is cycling at more than one frequency. We tested the domi-nance of peaks in the periodogram produced by the spec-tral analysis by plotting the cumulative periodogram and examining which frequencies exceeded the 95% limit for the maximum deviation from a spectrum with no dominant frequency (Venables and Ripley 2002). Finally, we expressed the results of both periodograms in terms of cycle length (the inverse of frequency) to allow a direct comparison to the ACF and PACF analyses.

Density-dependence of population fluctuations

We investigated the processes driving cyclic behaviour in each forest tent caterpillar populations by modeling the rela-tionship between population rates of change and population size in a given year. For this analysis we used the mean defo-liation-intensity data as a proxy measure for the size of the population within each regional population between 1938 and 2002. We modeled the rate of change in mean defolia-tion intensity of forest tent caterpillar populations in each population as a linear second-order pure density-dependent process (sensu Royama 1992):

Rt a0 a1Xt a2 Xt1 (1)

Where Rt loge(xt 1/xt) or the rate of change in population size (mean defoliation intensity) from year t to year t 1, a0, a1 and a2 are constant parameters describing the intercept (a0), density-dependent (a1) and lagged density-dependent (a2) processes. We also searched for non-stationarity in mean

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Figure 2. Kelly–Gardner–Sutcliffe (KGS) function (a) and stress plot (b) used to determine number of clusters for subsequent analy-ses. KGS plot shows a local minimum at 5 clusters. Stress plot was determined from non-metric multidimensional scaling of 12 383 time-series of forest tent caterpillar defoliation between 1938 and 2002 for forests in Ontario and Quebec, Canada.

Figure 3. Dendrogram showing the hierarchical relationship amongst nine clusters after pruning. Clusters were determined using a hierarchical clustering (Euclidian distances with complete linkage) of forest tent caterpillar defoliation intensities recorded between 1938 and 2002 for forests in Ontario and Quebec, Can-ada. Similarity amongst clusters decreases from the bottom to the top of the dendrogram. Height is a relative measure of where in the hierarchical clustering cells and clusters are joined to the dendro-gram and is the inverse of similarity.

All analyses were done in the R statistical computing environment, ver. 2.12.0 (R Development Core Team 2010). The clustering analysis was done using the clara function in the cluster package (Kaufman and Rousseeuw 1990). All time series analyses were done using the acf, pacf, and spec-trum functions from the stats package (R Development Core Team 2009) and the cpgram function (cumulative periodo-gram) from the MASS package (Venables and Ripley 2002). All correlations were fit using the cor function from the stats package (R Development Core Team 2009). Equations (1) and (2) were fit to the mean defoliation intensity for each population using the lmList function in the nlme package (Pinheiro et al. 2009). The locally-weighted polynomial regression was determined using lowess also from the stats package; SNCFs were calculated using function Sncf in the ncf package (Bjornstad 2009).

Results

Cluster analysis

The hierarchical clustering produced a complex dendro-gram from the 12 383 cells. The KGS function had a local minimum at 5 clusters (Fig. 2a). The stress plot showed no evidence of an elbow (Fig. 2b). In this case we apply the rule-of-thumb to avoid dimensions of q that reduce the stress below 5% unless the value of q will also result in a significant reduction in the observed stress (Kruskal and Wish 1978). The stress for 9 clusters was 5.09%. Given the large geo-graphic area covered by the data, we therefore selected the less conservative estimate of nine clusters for our analyses, although this is more than the number suggested by the KGS penalty function, the difference in between 5 and 9 clusters was 2 which we deemed to be acceptable.

The nine populations of forest tent caterpillar in Ontario and Quebec ranged in size from 54 to 8952 cells and were organized into discrete, localized populations embedded within a single large, regional population (Fig. 1a). Most (5/9) populations were contiguous; the rest were also con-tiguous for the most part, with only small, localized regions separated from the main body of the population (e.g. popu-lations 3, 7 and 8). The exception was population 6 which had two relatively large, disjoint components, both located in northwestern Ontario. When we compared the clustering relationship amongst the populations to their geographical locations we found that clusters located close to each other on the dendrogram (Fig. 3) were also located close together in space (Fig. 1a). For instance population 4 and 9 are closely related (Fig. 3) and one is imbedded within the other (Fig. 1a), while population 5 is both distinct from all other

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Figure 4. Mean ( 1 SD) defoliation intensity caused by forest tent caterpillar observed from aerial surveys between 1938 and 2002 of Ontario and Quebec (a) and nine regional populations with similar spatial-temporal patterns of defoliation (b). See Fig. 2 for locations of populations. Solid black line in (a) and (b) is the mean defoliation intensity for the overall time series (Ontario and Quebec; n 44 yr); broken lines in (b) are the mean defoliation intensity for the populations. Letters denote where the overall defoliation intensity exceeded the Ontario and Quebec mean for more than two years; stars indicate where the overall mean was exceeded for only one year. Note that not all populations experienced all outbreaks. Red lines are means, grey lines are 1 standard deviation; in (b) values in parentheses are the num-ber of cells in each population.

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Figure 5. Results of autocorrelation (ACF), partial autocorrelation (PACF) and spectral analysis (fast Fourier transform) of the time series of forest tent caterpillar defoliation intensity between 1938 and 2002 in Ontario and Quebec. Broken lines in ACF and PACF plots are Bartlett bands and denote the upper and lower 95% CI; lag values that exceed the Bartlett bands are values significantly from 0 (indicated by ∗ in the ACF). Open circle in the periodogram shows the dominant cycle length (i.e. the return interval or frequency of outbreaks); closed circle shows the cycle length computed from the parameters of the second-order pure density-dependent model (see Methods); the vertical bar in the periodogram is the coverage probability for the confidence interval.

Figure 6. Results of autocorrelation (ACF), partial autocorrelation (PACF) and spectral analyses of the time series of forest tent caterpillar defoliation intensity between 1938 and 2002 for nine populations in Ontario and Quebec. Notation as in Fig. 5.

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Figure 7. Cumulative periodograms of the spectral analyses in Fig. 5 and 6. Broken lines are the 95% limit for the maximum deviation from a spectrum with no dominant frequency. The dominant cycle length is where the cumulative periodogram first exceeds the broken lines.

Density-dependence of population fluctuations

Parameter estimates from the second-order density-depen-dent model (1) were not consistent with the patterns in the PACF (Table 1). Significant first-order density-dependence was detected in only 2 populations (Table 1, populations 1, and 4); second-order density-dependence was detected in 5 of 16 populations (Table 1, populations 1, 3, 7, 8 and 9).

clusters in the dendrogram (Fig. 3) and in space (Fig. 1a). This suggests the clustering and pruning procedures gave a clustering arrangement that reflected biological processes, giving regions with shared temporal patterns.

Time series analysis

We identified six forest tent caterpillar outbreaks of more than two years in the Ontario and Quebec time series that occurred in 1943–1944; 1951–1954; 1962–1966; 1975–1978; 1989–1992; and 2000–2002 (A–F, Fig. 4a). We also identified two ‘mini-outbreaks’ of one year each in 1972 and 1981 (denoted with stars in Fig. 4a). The largest mean intensity of defoliation across Ontario and Quebec was coincident with the 1951–1954 outbreak (cycle B, Fig. 4a). The return interval between outbreaks varied within and among populations (Fig. 4b) with most (8/9) having outbreaks that occurred at approximately 9–14 yr intervals and that, qualitatively, appear to have been well-synchronized among populations. The exception was population 1 which experienced infrequent outbreaks in a pattern that was both aperiodic and trendless (Fig. 4b).

The quantitative analyses of cyclic behaviour (Fig. 5, 6) were consistent with the qualitative characterizations of the time series plots. Mean defoliation intensity across the entire region exhibited moderately cyclic behavior (Fig. 5). Amongst the populations, most (7/9) exhibited some degree of cyclic behaviour (Fig. 6). Populations 6–8 had lag coef-ficients between 5–15 yr that exceeded the upper and lower Bartlett bands both (i.e. the 95% CI) which is typical of populations with regular, cyclical behaviour. The 95% confi-dence intervals are indicated on the ACF plot by the Bartlett bars (broken lines in Fig. 5 and 6). Population 4 exhibited moderately cyclic behaviour (i.e. lag 4–9 yr coefficients did not fall below the lower Bartlett band); as did populations 3 and 9; but with the opposite pattern (i.e. lag 10–15 yr coefficients failing to rise above the upper Bartlett band). No evidence of cyclic behavior was detected in populations 1 and 2 (Fig. 6).

The PACF analysis showed first-order coefficients were always positive and second-order coefficients were always negative (Fig. 5, 6). All populations had first-order coefficients that exceeded the 95% CI in the PACF plots; most second-order coefficients were significant as well, except in popula-tion 2. Higher order coefficients in all populations tended to vary between positive and negative values but almost never exceeded the 95% CI (i.e. were not significant).

Spectral analyses indicated decadal-scale cycle lengths (i.e. approx. 10 yr or more between outbreaks) for the entire region and for all populations (open circles in Fig. 5, 6). Plotting the cumulative periodogram supported this obervation (Fig. 7). Computing the cycle length from a1 and a2 (Table 1) using (3) tended to support the results of the spectral analysis. Most (7/9) populations and the region were determined to have oscillations 8 yr, which we took as approximately decadal-scale (closed circles in Fig. 5, 6); however, for one population the computed cycle lengths was shorter (i.e. 8 yr) than those predicted by the spectral analysis (Fig. 6; population 6) and for another the computed cycle length was larger (i.e. 12 yr) than predicted (Fig. 6; population 9).

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Table 1. Parameter values for the linear second-order pure density-dependent model (Rt a0 a1 Xt a2 Xt1) for nine local populations of forest tent caterpillar in Ontario and Quebec. See text for an explanation of the variables. A significant p value ( 0.05) indicates the para-meter value is different from 1.

Population ao p a1 p a2 p

1 2.2763264 0.01 0.25006365 0.05 0.2573413 0.032 1.2769767 0.03 0.29624028 0.26 0.2413190 0.213 1.3462537 0.01 0.22431331 0.16 0.5723353 0.014 1.0790707 0.02 0.26994433 0.02 0.1319586 0.275 0.9668106 0.15 0.14994252 0.64 0.5736492 0.086 1.7366018 0.01 0.52911670 0.07 0.2636901 0.187 1.1480694 0.01 0.10109707 0.62 0.2997897 0.048 1.0632331 0.01 0.09402646 0.60 0.4974493  0.019 0.4716255 0.28 0.13263505 0.82 0.3291089 0.02

Table 2. Parameter values for the linear second-order pure density-dependent model with an additional time variable (Rt a0 a1 Xt a2 Xt1a3t) for nine local populations of forest tent caterpillar in Ontario and Quebec. See text for an explanation of the variables. A significant p value ( 0.05) indicates the parameter value is different from 1.

Population ao p a1 p a2 p a3 p

1 2.064836 0.92 0.25003041 0.06 0.2575557 0.03 0.000107 0.992 28.626067 0.47 0.29592937 0.26 0.1289317 0.60 0.014966 0.453 9.187135 0.75 0.21640200 0.19 0.5723817  0.01 0.003969 0.794 4.442601 0.86 0.26999367 0.02 0.1340376 0.28 0.001700 0.895 15.728475 0.86 0.09660692 0.82 0.5651344 0.09 0.008494 0.856 15.207758 0.59 0.54774400 0.07 0.2543905 0.21 0.006820 0.637 5.977356 0.86 0.10074820 0.63 0.3011903 0.04 0.002443 0.888 9.468380 0.74 0.06862721 0.73 0.4859215  0.01 0.004252 0.779 12.739931 0.74 0.12194371 0.84 0.3296309 0.02 0.006704 0.73

Only population 1 exhibited significant first- and second-order density-dependence. The addition of a time term to (1) had no effect on the results (Table 2).

Plotting the fitted values of a1 and a2 (Table 1) into the parameter plane for (1) showed all forest tent caterpillar pop-ulations had second-order density-dependent parameter val-ues consistent with damped oscillations that, in the absence of stochastisity, decrease in amplitude with time as the popu-lation approaches stability (Fig. 8; populations in region IV). In the presence of stochasticity these populations would be expected to have recurrent cycles. Populations 4 and 9 had parameter values close to those that would be expected for asymptotic growth towards a stable population size (region I in Fig. 8). We also observed that the location of the popula-tions in the parameter plane reflected spatial patterns seen in the map (Fig. 1); notably, populations 1 and 2 and the provincial (Ontario and Quebec) population (‘p’ in Fig. 8) aggregated near to each other.

Outbreak synchrony – synchrony between populations

The pairwise synchrony between populations rapidly decayed as the distance between the centroids of the regional populations increased (Fig. 9). Populations with 100 km between their centroids (Fig. 1) tended to be most correlated (SNCF and correlation coefficients 0.7) with those sepa-rated by 800 km the least correlated (SNCF and correla-tion coefficients 0.2). However, that neither the correlation function nor the SNCF approached 0 indicates even the most separated populations would be expected to have somewhat similar dynamics. These results should be interpreted with

caution though. In constructing the SNCF we found the Sncf function failed with only 9 clusters in the dataset; there-fore to construct the SNCF plot we entered each population twice. The Sncf function uses a bootstrap resampling proce-dure to compute the value of the spatial covariance, thus our procedure may have the effect of overestimating the covari-ance among clusters depending on how many times the same cluster was selected twice. We assume the effect on our results was minimal as the dataset is re-sampled 1000 times to con-struct the SNCF. Moreover, the correlation function showed a similar pattern and its construction was not influenced by the method used to construct the SNCF.

Outbreak synchrony – synchrony within populations

The degree of population synchrony within populations was correlated to the pattern of fluctuation within populations as characterized by time-series variances (r 0.947; Fig. 10). The populations with the highest variances and highest with-in-population synchrony (populations 5, 8 and 9) are also those that tended toward sustained cycling (Fig. 6). Note, the mean Pearson correlation for population 1 is absent as it proved too computationally challenging for the resources we had access to.

Discussion

Forest tent caterpillar populations in Ontario and Quebec exhibit a range of dynamic behaviours, from stationary, periodic eruptions in small focal regions (populations 3–9), to periodic eruptions with an increasing trend in outbreak

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Figure 8. Location of populations in the direct and lagged density-dependent parameter plane based on the fitted values of a1 and a2 from the function Rt a0 a1Xt a2Xt1. See text for the explanation of variables. The regional time series (Ontario and Quebec; Fig. 4a) is indicated by p. Small graphs in the plot show the theoretical relationship between population size and time for a population inhabiting the given region of density-dependent parameter space. Symbols around the numbers indicate if the population was classified by the autocor-relation function analysis (Fig. 5 and 6) as regularly cyclic (squares); moderately cyclic (diamonds); or non-cyclic (circles). Inset: the location of all 16 populations in full parameter space (notation as in Royama 1992).

occurrence over time (i.e. first-order non-stationarity; popu-lation 2), and a non-stationary pattern of episodic eruptions of variable extent and duration that spans 73% of the insect’s range (population 1). We did not investigate the causes of these dynamic patterns; however they do have simple eco-logical interpretations, which we put forth here as working hypotheses. The periodic behaviours in populations 3–9 and their association with positive and negative first-order and second-order feedback suggest population regulation by delayed density-dependent processes, such as through a predator-prey or host-parasitoid interactions.

The dominant size of the non-stationary population (population 1; Fig. 1) is noteworthy for its influence on the global time-series (Fig. 4a). We point out that the auto-correlation structure of population 1 is very similar to that of the global time-series (Fig. 7), but once this dominat-ing non-stationarity is partitioned out of the global time-series (i.e. during the clustering procedure), the periodic behaviour in the remaining clusters is revealed (Fig. 4b). Synchrony among population clusters was also high (Fig. 9), with the one major outbreak that did occur in population 1 being well synchronized with the 1951–1954 outbreak that affected all the other populations (outbreak B, Fig. 4). We interpret this result to mean that population 1 occupies a region of marginal habitat for forest tent caterpillar, where population fluctuations follow behaviour in the other populations only if conditions (e.g. weather and tree health)

at the time of the outbreak permit. Finally, we observed that all populations (and thus the entire region) had autoregres-sive parameters typical of those expected to have recurrent cycles in the presence of stochasticity (Fig. 8, inset in region IV; Royama 1992).

The ability of insects to disperse is thought to play a role in the synchronization of outbreaks. In this study outbreak synchrony was remarkably high (ca 500 km, Fig. 9) for an insect thought to have only a ‘modest’ capacity for disper-sal (Peltonen et al. 2002). Indeed, our forest tent caterpillar outbreak cycles – observed in eastern Canada – were more synchronized than in a similar analysis of data from western Canada (Peltonen et al. 2002; Fig. 9, inset). However, the for-est tent caterpillar population, and three of the other species (larch bud moth, western spruce budworm, mountain pine beetle) analysed in Peltonen et al. (2002) inhabit mountain-ous regions (Fig. 9) whereas the topography of Ontario and Quebec is relatively flat. Climatic differences between moun-tains and the boreal plain of central Canada could explain this pattern. We propose an alternate hypothesis. If moun-tains act as a barrier to dispersal then populations inhabiting mountainous areas should be less synchronous than those that live in non-mountainous regions. This hypothesis also predicts that cycle synchrony among populations may be a function of landscape complexity and not the insect’s life his-tory. We would therefore predict that populations of forest insects inhabiting regions with less complex topography are

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Figure 9. Synchrony decay among regional populations as a function of distance between cluster centroids (Fig. 1). Thick black line is the spatial non-parametric covariance function (SNCF); thin black lines are 95% bootstrap confidence intervals; grey dots are spatial correla-tions among time series of mean defoliation intensity for all possible pairs of forest tent caterpillar populations; grey line is the smoothed correlation function fit to the spatial correlations. Inset: SNCF curves re-drawn from Peltonen et al. 2002 for larch bud moth (lbm) in Europe, gypsy moth (gm) in the eastern United States, spruce budworm (sbw) in eastern Canada; and mountain pine beetle (mpb), western spruce budworm (wsbw) and forest tent caterpillar (ftc) in western Canada.

more likely to be synchronized. Understanding the effect of topography on cycle synchrony could be important to man-aging outbreaks, in part, because it would suggest the range around incipient outbreaks that should be surveyed to detect other outbreaks. Alternately, it may be that the forest tent caterpillar’s dispersal capacity has been under-estimated, or dispersal is not the primary factor influencing the spatial scale of cycle synchronization in eastern Canada.

Theory predicts that the amplitude of cycling (i.e. the variability in the time series) should be an important factor governing the rate of cycle synchronization (Royama 1980, Barbour 1990). We found that synchrony within forest tent caterpillar populations had a positive correlation with the variances of the population time-series. This result is con-sistent with the predictions of Royama (1980) and Barbour (1990). We could find no other examples of studies that have examined the relationship between cycle synchronization and outbreak amplitude in insect systems. In forest tent cat-erpillar populations the correlation we observed may partly explain why the spatial scale of synchronization is so large in this system (Fig. 9). Based on these two observations, we hypothesize there are three ‘nodes’ of cyclic activity in east central Canada; one in northwestern Ontario (population 8), one in eastern Ontario/western Quebec (population 9) and a third in southeastern Quebec (population 5) that we

predict act as ‘pace-makers’ for population dynamics across the entire region.

Populations of forest tent caterpillar in Ontario and Quebec do not appear to have undergone any major range-wide changes in their dynamics (i.e. the length or duration of outbreaks). However, a single exception to this conclu-sion is correlated with effects on forest health. In the early 2000s a 500 000 ha area of declining trembling aspen was mapped in northeastern Ontario (Candau et al. 2002), the bulk of which falls within the cells occupied by population 2 (Fig. 1b). We hypothesize that the anomalous forest tent caterpillar dynamics observed in population 2 may explain this incidence of trembling aspen decline because the for-est tent caterpillars within population 2 caused eight con-secutive years of defoliation between 1992 and 2000 (Fig. 1; Cooke et al. 2009). If trembling aspen trees are not be able to withstand sustained forest tent caterpillar herbivory then the decline coincident with population 2 occurred because the trees were not given the opportunity to recover to a normal state of health. While anecdotal, this hypothesis explains why less trembling aspen decline was observed in trees within the regions of populations 1, 6 and 9 that border population 2 (Fig. 1b), because the forest tent caterpillar in those popula-tions crashed, or were not at outbreak, between 1993 and 1996 (Fig. 4). By extension then, if the duration or frequency of

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Figure 10. Correlation between synchrony within populations and the amplitude of population cycling for forest tent caterpillar popula-tions in Ontario and Quebec. As in Fig. 8, symbols indicate how the population was classified by autocorrelation function analysis.

forest tent caterpillar outbreaks were to increase (e.g. in response to global climate change) there could be significant implications for the overall health of the boreal forest in Canada.

Conclusion

Our results support previous findings that the forest tent cat-erpillar system is sensitive to climate and driven by predator–prey dynamics (Roland et al. 1998, Cooke and Lorenzetti 2006, Cooke et al. 2007, Babin-Fenske and Anand 2011). Understanding the role of cycle synchronization and its inte-gration with these other processes will be important to derive effective models and strategies for managing forest tent cater-pillar outbreaks. However, while robust cycling is observed in most populations, we also found that few populations actu-ally experienced significant defoliation during all six outbreak cycles. Moreover, the locations where forest tent caterpillar populations fluctuated most synchronously were those areas where cycling was most robust. These two observations lead us to suggest a role for high-amplitude cycling in the outbreak dynamics of forest tent caterpillar. We propose that high-am-plitude cycling predisposes forest tent caterpillar populations to synchronization in the first place. While the cause of sustained high-amplitude cycling warrants investigation, a parsimoni-ous interpretation of the spatial pattern of synchronization is that the synchronous clusters are generated by spatial patterns of migration within and among populations (Barbour 1990).

Any study that seeks to understand the causes of cycle syn-chronization should consider the supporting role of cycling properties in pre-disposing forest tent caterpillar populations, and possibly other systems, to synchronization.

In this paper we have demonstrated that a careful analy-sis of crude survey data can provide immediate insight into issues of concern to forest managers. More importantly our results show the forest tent caterpillar has the potential to cause significant impacts on forest health in east-central Canada should the pattern of outbreaks change within and among populations which could ultimately have significant economic and environmental effects (Kurz et al. 2008). Finally, in comparison to some other well-studied forest insect systems (e.g. spruce budworm, gypsy moth) the forest tent caterpillar has received much less attention in the eco-logical literature. Based on our experience in this study we suggest that the species deserves more attention as a model system of forest insect disturbance ecology.

Acknowledgements – We thank Dean Anderson (USDA Forest Ser-vice, Rhinelander, WI) and Brent Joss (Natural Resources Can-ada, Canadian Forest Service, Edmonton, AB) for collating the defoliation data from Ontario. Ronald Fournier (Natural Resources Canada, Canadian Forest Service, Sault Ste. Marie, ON) graciously provided the trembling aspen decline data. We also thank Andrew Liebhold for his helpful comments which greatly improved this paper. BJC and CJKM contributed equally to this work.

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