Forest Ecology and Management 226 (2006) 110–121
www.elsevier.com/locate/foreco
The dynamics of forest tent caterpillar outbreaks in Québec, Canada
Barry J. Cooke a,*, François Lorenzetti b,1
a
Canadian Forest Service, Northern Forestry Centre, 5320 122nd Street, Edmonton, Alta., Canada T6H 3S5
b
Université du Québec en Outaouais, Département d’informatique et d’ingéniérie,
Gatineau, and Institut Québecois d’Aménagement de la Forêt Feuillue, 58 rue Principale, Ripon, Qué., Canada J0V 1V0
Received 8 September 2005; received in revised form 18 January 2006; accepted 18 January 2006
Abstract
Historical patterns of forest tent caterpillar defoliation over the period 1938–2002 in the province of Québec, eastern Canada, were analyzed in
relation to forest inventory data. The extent of defoliation over time was largely nonstationary and only somewhat periodic; however six major
defoliation episodes could be identified. Individual outbreaks tended to span only 36.6% (13.1% S.E.) of the total area defoliated, suggesting they
are frequently terminated before attaining their maximum potential extent. Although outbreaks tended to recur periodically, they were not perfectly
synchronized across the province. Two core regions, 14 000 and 20 000 km2 in size, located in the northwestern, aspen-dominated boreal forest
region and the southeastern, maple-dominated mixedwood forest region, were found to exhibit cyclic patterns of defoliation, with periodicities of 9
and 13 years, respectively. These oscillations were characterized by strong second-order negative feedback, suggesting regulation by lagged
density-dependent processes. Outbreak cycles in the two core regions were in phase with one another (r = 0.39) until 1963, when a sudden, largescale outbreak collapse occurred in the North during the initial phase of the third cycle. Since that time outbreak oscillations have been completely
out of phase (r = 0.16), leading to a persistent wave-like pattern of outbreak spread back and forth between regions along a northwest–southeast
axis. Within core regions, cycle amplitude varied in a slow and smooth manner, with the phasing pattern of amplitude modulation differing
substantially between regions. Although the timing of population cycle peaks appears to be highly predictable, at least within the core regions, the
levels of defoliation experienced during these peaks appears to be unpredictable and may be modulated by factors yet to be identified.
# 2006 Elsevier B.V. All rights reserved.
Keywords: Insect outbreaks; Spatiotemporal dynamics; Population cycles; Synchronization; Cluster analysis; Time-series analysis; Stationarity; Natural
disturbance forecasting
1. Introduction
Insects are a major source of disturbance in the boreal forest;
however there are very few species whose dynamics are
sufficiently well understood that the timing and extent of
outbreaks can be predicted with any reliability (Cooke et al.,
2006). The most destructive species, such as the conifer-feeding
budworms of the genus Choristoneura (Lepidoptera: Tortricidae), are unquestionably the best studied (MacLean, 1980;
Royama, 1984; Volney, 1989; Campbell, 1993). However, these
species, compared to the less destructive hardwood defoliators,
tend to outbreak so infrequently – every 20–40 years (Blais, 1983;
* Corresponding author. Tel.: +1 780 435 7218; fax: +1 780 435 7359.
E-mail addresses: [email protected] (B.J. Cooke),
[email protected] (F. Lorenzetti).
1
Tel.: +1 819 983 6589.
0378-1127/$ – see front matter # 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.foreco.2006.01.034
Swetnam and Lynch, 1993; Burleigh et al., 2002; Boulanger and
Arseneault, 2004) – that it takes that much more time and effort to
study and understand their dynamics. For example, although we
have been studying budworms in eastern and western North
America for nearly a century, there are still disagreements as to
how and why outbreaks occur (Ludwig et al., 1978; Royama,
1992; Hassell et al., 1999; Royama et al., 2005), and whether or
not their occurrence and impact is at all predictable (MacLean
and MacKinnon, 1997; Gray et al., 2000; Jardon et al., 2003).
It is in this vein that we consider the case of the forest tent
caterpillar, Malacosoma disstria Hbn. (Lepidoptera: Lasiocampidae), a major defoliator of trembling aspen, Populus
tremuloides Michx., and sugar maple, Acer saccharum Marsh,
in mixedwood and hardwood forests throughout North America
(Witter, 1979). Compared to the relatively wasteful needlefeeding insects, the forest tent caterpillar is an efficient forager
that consumes most of the foliage it destroys (Fitzgerald, 1995).
Consequently, there is a strong linear relationship between
B.J. Cooke, F. Lorenzetti / Forest Ecology and Management 226 (2006) 110–121
population density and defoliation (Hodson, 1941) which
breaks down only as population densities exceed the 100%
defoliation threshold.
In eastcentral Canada (i.e. Ontario), forest tent caterpillar
outbreaks are fairly well-synchronized and recur every decade
or so (Sippell, 1962). However, in westcentral Canada (i.e.
Saskatchewan and Manitoba), outbreaks are so asynchronous
as to lack any distinct periodicity (Hildahl and Reeks, 1960).
The forest tent caterpillar, though not as destructive as the
conifer-feeding budworms, can cause substantial mortality of
trembling aspen over large areas (Candau et al., 2002),
suggesting it could be a source of much insight into the
dynamics of other periodically outbreaking, forest-disturbing
Lepidopteran species. However a significant challenge is to
reconcile these major regional differences in outbreak patterns.
If outbreak occurrence is truly periodic, then why should the
long-term dynamics differ so strongly between regions?
Spatial analyses of defoliation data from Ontario indicate
that outbreak duration varies regionally in response to
landscape variables such as forest structure, climate, and
elevation (Roland, 1993; Roland et al., 1998; Cooke and
Roland, 2000)—all of which are known, from survivorship
studies in Alberta, to influence temporal processes governing
population growth, including early larval overwintering
survival (Blais et al., 1955; Cooke and Roland, 2003) and
late larval and pupal parasitism (Roland and Taylor, 1997). In
particular, a decade-long survivorship study from Alberta
indicates that outbreaks develop more rapidly in fragmented
forests (Roland, 2005), while a parallel modeling study
suggests this may translate, in the long-run, into more rapid
population cycling (Cobbold et al., 2005).
In this paper we analyze the spatiotemporal pattern of forest
tent caterpillar outbreaks across a large, and different, area – the
province of Québec, in eastern Canada – over the period 1938–
2002. We show how a purely temporal analysis of the aggregate
province-wide data leads to the conclusion that forest tent
caterpillar populations are at best marginally cyclic. Using
cluster analysis on the full space–time data set, we show that
outbreaks are actually highly periodic within certain regions,
but only weakly synchronous between regions. We conclude
that periodic outbreaks are a result of spatially synchronized
oscillatory population fluctuations, but that the cycle-synchronization process varies in strength in time and space.
2. Methods
2.1. Historical insect data
Our analyses were based on the historical forest insect data
base maintained by the Ministère des Ressources Naturelles et
de la Faune du Québec. This is a synthetic data base
summarizing, for the entire province of Québec, the
presence/absence of a large number of forest insect species,
as determined by a variety of federal and provincial institutions,
using a variety of sampling methods and survey criteria that
have varied since the program began in 1938. We focused on the
defoliation mapping component of the database—this having
111
been measured with the greatest degree of consistency among
years and across the landscape. We selected the subset of data
related to forest tent caterpillar, which are gridded at a spatial
resolution of 5 min 5 min of longitude and latitude, and
binary-coded as ‘defoliated’ or ‘not defoliated’. Our data set
comprised 6630 observational cells spanning some
400 000 km2, over the period 1938–2002 (Fig. 1). As illustrated
by Gray et al. (2000), who analyzed the spruce budworm
component of the defoliator database, the coarse-resolution
aerial survey data, though inappropriate for high-resolution
applications, such as stand-level risk assessment, are wellsuited to large-scale pattern analysis. Consequently we report
here on dynamics occurring in fairly large, contiguous regions
between 14 000 and 100 000 km2 in surface area, even though
the database has a spatial resolution of 58 km2.
2.2. Pattern analysis
Temporal patterns of fluctuation in defoliation were
summarized using classical time-series analysis methods,
including spectral analysis and autocorrelation analysis.
Classical time-series methods, however, are very sensitive to
nonstationarity (Chatfield, 1989). Stationarity – the degree of
temporal (or spatial) homogeneity in means (first-order
stationarity) and variances (second-order stationarity) – is a
condition that is often assumed in ecological time-series
analysis, but rarely checked (Turchin, 1990). This is
unfortunate because nonstationarity is a serious impediment
to the interpretation of results from time-series analysis
(Berryman and Turchin, 2001).
Nonstationarity was an immediate concern in this study
because, according to historical fire-tower surveys maps, forest
tent caterpillar outbreaks in 1952 and 1953 were unusually
extensive. Assuming these maps were accurate, we calculated
the area defoliated across the province during six roughly
decadal time intervals and, using a one-sample t-test, computed
the probability that the extensive outbreak of 1948–1957 was
within the range of variability expected from this sample
(Minitab, Minitab Inc., College Station, PA).
Having demonstrated the importance of gross nonstationarity in the aggregate provincial-scale data, we proceeded to a
regional scale analysis, in an attempt to factor out any
nonstationarity and get a clearer picture of the spatiotemporal
dynamics of outbreaks within regions of stationarity. Our
hypothesis was that temporal nonstationarity in the provincialscale time-series was a result of spatial nonstationarity (i.e.
regional variability) in tent caterpillar outbreak dynamics. In
other words, we expected it might be possible to decompose the
nonstationary provincial time-series into well-defined spatial
regions of stationary and nonstationary dynamics. Within the
regions of stationarity, we fully expected to find cyclical
patterns of outbreaks, such as have been reported for the
neighboring province of Ontario, over a similar time period
(Fleming et al., 2000).
Cluster analysis was used to partition the province into areas
where forest tent caterpillar fluctuated synchronously between
epidemic and endemic levels. The temporal dynamics of
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B.J. Cooke, F. Lorenzetti / Forest Ecology and Management 226 (2006) 110–121
Fig. 1. Map of the study area in Québec showing elevation (increasing with shading). Region names are depicted in (A1).
caterpillar populations in 6630 observational cells were
grouped into nine spatially non-contiguous classes, using the
‘‘clara’’ (clustering for large applications) algorithm (Kaufman
and Rousseeuw, 1990) from the R statistical package, version
1.6.2 (Ihaka and Gentleman, 1996). We chose a stopping
criterion of nine clusters in order to ensure that the smallest
cluster contained at least 200 out of 6630 observational cells.
Supplementary analyses (not shown) indicate that our results do
not depend sensitively on the choice of stopping criterion.
The goal of clustering was to identify areas of temporally
coherent dynamics. Because Québec is large and topographically, climatically, and vegetationally complex, we expected
complex spatial patterning in the size, shape, and distribution of
the various clusters, with population clusters behaving
differently in different ecoregions.
For each cluster, an annual defoliation index was defined as a
continuous variable on the interval [0,1] by computing the
average intensity of defoliation over all observational cells in
the cluster for a given year (cell defoliated = 1, cell not
defoliated = 0). An assumption made in subsequent analyses is
that fluctuations in this defoliation index are correlated with
average insect population densities within each cluster. This is
not necessarily the case—and this points to a major and
universal limitation in the use of defoliation data to make
inferences about population dynamics. However, in the absence
of evidence to the contrary, our simplifying assumption seems
reasonable.
Time-series averages for each cluster were then submitted to
autocorrelation analysis. The goals here were to identify
periodic variability that might be induced by a low-order
autoregressive process, and to determine the order of the
regulating process. If tent caterpillar cycles are driven by a
predator–prey type of interaction, then one would expect
significant autocorrelations in a particular range of periodicity,
with strongly positive and negative first and second-order
feedback, respectively, in the partial autocorrelation function
(Royama, 1992).
Spectral analysis was then used to determine whether cluster
time-series were dominated by variation occurring in one or
more frequency classes. Although autocorrelation functions are
capable of identifying between-cluster differences in the
dominant frequency, spectral analysis can be used to identify
differences occurring in multiple parts of the frequency
spectrum. This is especially important in cases where local
population fluctuations may be multifrequential or nonstationary with respect to oscillation frequency or amplitude.
The reason we wanted to investigate the multifrequential
properties of the cluster time-series is because a simple
predator–prey system should exhibit simple, unifrequential
oscillatory behavior, whereas a tritrophic system (with fast
B.J. Cooke, F. Lorenzetti / Forest Ecology and Management 226 (2006) 110–121
113
Fig. 2. Distribution of (a) trembling aspen and (b) sugar maple in the province of Québec. Values mapped are basal areas in m2 of timber per hectare of land. Thick
black outline indicates inventoried area. Outlined polygons in northwestern and southeastern regions represent clusters 8 (aspen-dominated) and 6 (mapledominated), respectively, from Fig. 4.
predator response and slow vegetation response) should exhibit
much more complex dynamics—including truly multifrequential oscillations (e.g. cycles that are stationary in frequency, but
nonstationary in amplitude) (Holling, 1992). After discovering
that even the most stationary cluster time-series exhibited
trends in cycle amplitude, we used complex demodulation (as
described by Bloomfield (2000) and implemented in S-plus
(Insightful Corp.)) to formally test whether cycle amplitude was
indeed varying in a slow, smooth, systematic manner.
2.3. Forest inventory data
Given the variable pattern of forest tent caterpillar outbreaks
across the regions of the province, we proceeded to search for
an association between regional-scale outbreak characteristics
and regional-scale forest attributes. The dependent variables of
interest were the degree of periodicity in outbreak occurrence
(i.e. the tendency for cycle amplitude to be sustained at
consistently high levels), and the period of oscillation. The
independent variables related to the abundance of the primary
host plants: sugar maple and trembling aspen. Basal areas for
each species were derived using provincial forest inventory
data, from the second decadal inventory (1970–1980), gridded
to the same dimensions as those of the defoliator database
(Fig. 2).
Unfortunately, a formal test of association between regionalscale outbreak pattern and forest cover variables was not
possible, due to the high degree of spatial autocorrelation in all
variables and the large size of the derived regions relative to that
of the province. Because of this severely pseudoreplicated
design, the associations reported here, though helpful, are
merely suggestive and should be considered conjectural.
3. Results
3.1. Extent of outbreaks
During the 65 years from 1938 to 2002 the total area
experiencing defoliation by forest tent caterpillar during at least
one of those years summed to 384 540 km2, or 25.0% of the
surface area of Québec. This area is subsequently referred to as
the ‘‘outbreak range’’ as a matter of convenience. Notably,
forest tent caterpillar defoliation was found to occur hundreds
of kilometers north of the line identified by Fitzgerald (1995)
as its northern limit. This was largely a product of unusually
extensive defoliation in the 1950s.
3.2. Nonstationarity in provincial-scale data
Province-wide fluctuations in the area defoliated were
roughly decadal, leading to six distinct cycles over the 65-year
time period of study, the sixth not having been completed by the
end of 2002 (Fig. 3). The time-series, during the 1950s,
appeared to be nonstationarity with regard to the mean, as a
result of unusually extensive defoliation in 1952 and 1953.
When the data set was partitioned into six roughly decadal
time frames, the area defoliated during each was found to vary
from 11% to 97% of the total (mean: 36.6%; S.E.: 13.1%)
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B.J. Cooke, F. Lorenzetti / Forest Ecology and Management 226 (2006) 110–121
3.3. Spatial coherence in defoliation time-series
Fig. 3. Province-wide extent of forest tent caterpillar defoliation, expressed as a
time-series. Vertical dashed lines indicate the six time-frames used in the
analysis of Table 1.
(Table 1, upper portion). The 1948–1957 outbreak appeared to
be unusually extensive, whether compared to the mean extent of
all six outbreaks (t = 4.85, p < 0.005), or just the other five
(Table 1, bottom portion: t = 19.34, p < 0.001). In 1952, the
most extensive outbreak year on record, forest tent caterpillar
defoliation occurred in 82.5% of the outbreak range,
representing an area of 317 245 km2. When the 1952 and
1953 data were excluded from analysis, the sum area affected
by forest tent caterpillar dropped to 271 614 km2, or 70.6% of
the outbreak range, with most of that reduction coming from the
northern and southern limits of the study area in 1952 and 1953,
respectively. The unusually large extent of the second outbreak
appears to be a statistical anomaly resulting from the brief
expansion of populations into ephemeral latitudes and
elevations. Nonstationarity in the provincial-scale time-series
is thus a spatial phenomenon as much as it is a temporal
phenomenon.
Cluster analysis with k = 9 clusters indicated substantial
regional-scale coherence in the spatiotemporal pattern of
occurrence of forest tent caterpillars (Fig. 4, top frame). Six of
the resulting clusters (numbers 4–9) were strongly spatially
coherent. The three remaining clusters (1–3), which covered
61% of the study area, comprised a diffuse matrix in which the
regional clusters (4–9) were embedded. Cluster 1 was
especially notable for its size (n = 1745 out of 6630 cells)
and location, extending far into the north. Diffuse cluster 2 was
also quite large (1690 cells), extending to the eastern and
southern boundary of the study area. Cluster 3 was smaller (405
cells), concentrated in the high-elevation conifer-dominated
forest region of the Laurentian Mountains.
The temporal dynamic within clusters was also highly
coherent, as evidenced by the small standard deviations on
time-series averages for all nine clusters (Fig. 4, bottom
frames). Individual cluster time-series averages showed
markedly different patterns of fluctuation. The range-delimiting
clusters 1 (to the North) and 2 (to the East) (Fig. 4, map) were
dominated by a single year of defoliation in 1952 and 1953,
respectively. Cluster 3 experienced defoliation occurring in
both years, as well as in 1951.
3.4. Outbreak periodicity
More remarkable, however, was the regularity of quasiperiodic fluctuations in the other six clusters, numbered 4–9.
Clusters 4 and 5 showed only two major episodes – in 1952–
1953 and 1981 – which were separated by three decades of low
activity. The difference between clusters 4 and 5 was the
absence and presence, respectively, of defoliation in 1951.
Table 1
Proportion of surface area defoliated during each of six roughly decadal outbreaks (top), and selected summary statistics (bottom) comparing the extent of outbreak II
to the extent of (a) all six outbreaks, and (b) the five other outbreaks, numbered I, III, IV, V, VI
Outbreak
Time frame
Time span
(years)
I
II
III
IV
V
VI a
1938–1947
1948–1957
1958–1969
1970–1983
1984–1996
1997–2002
10
10
12
14
13
6
(a) I–VI (n = 6)
(b) I, III–VI (n = 5)
Area affected
(proportion per year)
0.240
0.966
0.316
0.445
0.113
0.115
0.0240
0.0966
0.0263
0.0317
0.0087
0.0191
Mean
Standard error
0.366
0.131
0.0344
0.0127
H0: I–VI = II
t-Statistic b
p-Value
4.59
0.006
4.85
0.005
Mean
Standard error
0.246
0.063
0.0220
0.0038
H0: I, III–VI = II
t-Statistic b
p-Value
a
Area affected (proportion
of outbreak range)
11.42
0.000
19.34
0.000
Outbreak VI was not complete at time of analysis, but was spreading southeastward from cluster 8 (Abitibi region) toward cluster 6 (Estrie region).
One-sample t-test (Minitab Inc.) of the null hypothesis that the area affected during the six (or five) outbreak cycles is equal to that experienced during outbreak
cycle II.
b
B.J. Cooke, F. Lorenzetti / Forest Ecology and Management 226 (2006) 110–121
Clusters 8 and 9, in northwestern Québec, showed six obvious
cycles, which varied slowly and smoothly in amplitude. Cluster
number 6, in southeastern Québec, showed five cycles which
also varied slowly and smoothly in amplitude, but with a
different pattern of phasing compared to clusters 8 and 9:
during the period 1960–1983 cycles in cluster 6 were of high
amplitude while those in clusters 8 and 9 were of low amplitude
and short duration. Since that time amplitude has declined in
cluster 6 and increased in clusters 8 and 9. Cluster 7 exhibited
slightly more erratic behavior, in the sense that populations
tended to resurge after an initial transient decline.
Autocorrelation analysis of the nine cluster time-series
showed a tendency toward decadal cyclicity in the four regions
of stationary dynamics (clusters 6–9) where defoliation was
115
most frequent (Fig. 5). (Note we do not attempt to interpret
autocorrelation coefficients for the nonstationary time-series
from clusters 1 to 3.) Cyclicity was especially strong in clusters
6 and 8, where autocorrelation coefficients were significantly
positive at lags of 13 and 9 years, respectively, and where partial
autocorrelation coefficients in both cases were strongly positive
and strongly negative for first and second-order lags,
respectively. In the other two regions (clusters 7 and 9) linear
time-series analysis failed to detect statistically significant
cyclicity and second-order feedback. Notably, clusters 6–9 all
exhibited signs of positive partial autocorrelations, at lags of 12,
9, 8, and 9 years, respectively.
Spectral analysis confirmed the tendency toward weakly
periodic, decadal fluctuations in two core regions (Fig. 5, insets).
Fig. 4. Map (top panel) and time-series averages (bottom panels) resulting from cluster analysis of defoliation data. Darker shading on map indicates higher elevation,
as in Fig. 1. Time-series averages (thick line) are plotted standard deviation (thin line) for each colored cluster represented in map. Clusters are indexed according to
increasing number of years of defoliation. Dashed vertical lines in lower frames indicate the year 1963, when populations collapsed everywhere except cluster 7.
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Fig. 5. Autocorrelation (main frames) analysis of cluster-based time-series averages. Autocorrelations are plotted as step function in black; partial autocorrelations as
bars. Spectral analyses shown as inset (Daniell smoother with spans = {3}). Vertical bars on spectra indicate 95% confidence interval, with bandwidth as horizontal
cross. Arrowheads on spectra for clusters 6 and 8 indicate strong (i.e. low-order autoregressive) periodicity at 12.8 and 9.1 years, respectively.
In cluster 8 the decadal peak was closer to 9 years; in cluster 6 it
was closer to 13 years. In both clusters higher frequency
harmonics were observed in the 5y and 7y range. These were
largely due to lack of fit of a sinusoidal model to the inherently
squared waves produced by binary data—a common phenomenon when Fourier methods are applied to non-sinusoidal timeseries (Bloomfield, 2000). At the same time it is worth noting the
erratic behavior of the cluster 7 time-series, where outbreak
cycles were briefly interrupted in both 1962 and 1972 (Fig. 4), and
whose spectrum exhibited distinct 5y and 3y periodicity (Fig. 5).
3.5. Regional variation in outbreak timing and severity
Correlations among cluster time-series averages indicated
that synchrony was highest between clusters 4 and 5 (r = 0.84),
which were adjacent to and intermingled amongst one another
(Fig. 4). Synchrony was lowest between clusters 1 and 6
(r = 0.08), which were separated by the hundreds of kilometres
occupied principally by clusters 4 and 5 (Fig. 4). When
correlations were computed over the time period 1954–2002 (to
eliminate the extensive outbreak of 1952–1953 common to
most clusters), synchrony was again highest between clusters 4
and 5 (r = 0.95), but very low between core clusters 6 and 9
(r = 0.07). Cluster 6 (Estrie region) and cluster 9 (Témiscamingue region) are separated by 500 km of highly variable
topography which includes the St. Lawrence River Valley to the
South and the Laurentian mountains and the Hydroelectric
Réservoirs Cabonga and Gouin to the North (Figs. 1 and 4).
Complex demodulation confirmed that decadal cycles in all
regions varied in amplitude in a slow and smooth manner.
B.J. Cooke, F. Lorenzetti / Forest Ecology and Management 226 (2006) 110–121
117
Fig. 6. Patterns of amplitude modulation in time-series averages for four clusters showing moderate periodicity. Smooth curves in black illustrate low-frequency
trend in decadal cycle amplitude, as fitted by complex demodulation (pass and stop frequencies = 1/1000 and 1/14 for all four clusters; centering frequency = {1/12.8,
1/10.7, 1/9.1, 1/10.7} for clusters 6–9, respectively).
These low-frequency trends differed among regions, with
clusters 8 and 9 of Abitibi-Témiscamingue exhibiting lowamplitude cycles from 1960 to 1990 and cluster 6 of Estrie
exhibiting the opposite trend (Fig. 6). Cluster 7 exhibited a
pattern of amplitude modulation somewhat in between these
two, largely a result of a clear spike in 1962 that was not present
in the other regions (Fig. 6).
3.6. Synchrony breakdown
Close inspection of the cluster time-series averages (Fig. 4)
revealed that cyclic patterns of forest tent caterpillar abundance
in clusters 9 and 6 started off more-or-less synchronized with
one another, with decadal cycles occurring in 1942–1944 and
1952–1954, and a third synchronous cycle initiated in 1962.
After this point, the provincially synchronous 10-year cycle
broke down into regional components. As early as 1968 decadal
oscillations in each had slipped completely out of phase.
Moreover, this phase-lag, estimated to be 6 years in length, or
one half-cycle, has persisted ever since. The last cycle in cluster
6 peaked in 1993; previous cycles had peaked in 1968 and 1981.
The last cycle in clusters 8 and 9 peaked in 2001; previous
cycles there had peaked in 1988 and 1975.
A closer look at the regional differences in time-series
revealed that 1963 was a year of decline across most of Québec,
but not in cluster 7. After declining in 1964, cluster 7
populations rebounded in 1966, whereas cluster 9 populations
did not rebound until a decade later (1972–1975). Thus it
appears that 1963 is the first identifiable point in time where
trajectories began to diverge and inter-regional synchrony
began to break down. Population indices for cycle III in cluster
6 and clusters 8 and 9 peaked in 1968 and 1975, respectively,
demonstrating that the breakdown in synchrony was sudden and
severe. Complete and persistent asynchrony was achieved in
less than one cycle.
3.7. Relation to forest cover
A host-tree species distribution map for the province shows
that while northwestern Québec (cluster 8) is dominated by
trembling aspen, southeastern Québec (cluster 6) is dominated
by sugar maple (Fig. 2). Thus there appears to be an association
between outbreak periodicity and forest type, with the 9-year
outbreak cycle occurring in the aspen-dominated boreal forest
region and the 13-year outbreak cycle occurring in the mapledominated tolerant hardwood forest region. An association
consisting of only two regions can hardly be considered a
statistically robust basis for inference. However, it is an
accurate description of the patterns observed during the
sampling period of 1938–2002 in the province of Québec.
4. Discussion
4.1. Predicting the maximum extent of defoliation during
outbreaks
The range of forest tent caterpillar outbreaks in the north and
east of Québec appears to be limited by the Monts Groulx
mountains of the North Coast and the Chic-Chocs mountains of
the Gaspé peninsula (Figs. 1 and 4). Outbreaks are more
common in the low-lying pocket of the Saguenay River valley
(islands of clusters 4 and 5) than in the Northern Laurentian
mountains immediately north and south of the Saguenay River
(cluster 2). Topography thus appears to be an important factor
limiting the duration and frequency of outbreaks in Québec.
The extent of defoliation across the province appears
somewhat periodic; however it varies greatly among decadal
cycles. The fact that individual decadal outbreaks never spread
to cover the entire outbreak range is not in itself surprising.
What is surprising is just how small a proportion of the outbreak
range that individual outbreaks tend to cover: a third, on
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B.J. Cooke, F. Lorenzetti / Forest Ecology and Management 226 (2006) 110–121
average, and often as little as a tenth. In contrast, the 1950s
episode was exceptionally extensive, covering more than 95%
of the outbreak range. This suggests outbreaks could potentially
cover a much larger area than they actually tend to.
4.2. Cause of cycling
The strong periodicity in defoliation cycles in the core areas
of northwestern and southeastern Québec suggests that they are
associated with population cycling—the sort of cycling that is
caused, for example, by delayed feedbacks between predators,
herbivores, and host plants. Of course, population cycling can
be caused by other forces, such as periodic forcing by an
exogenous environmental variable (Williams and Liebhold,
1995), and such effects are, admittedly, statistically indistinguishable from cyclicity arising from delayed feedback
(Hunter and Price, 1998). However many population studies
have implicated delayed density-dependent parasitism as a
critical agent responsible for tent caterpillar population cycling
(Myers, 1988; Roland and Taylor, 1997; Rothman and Roland,
1998; Roland, 2005).
Notably, if the periodicity of outbreaks is tied directly with
the cycling of insect populations, this leads to the conjecture
that the less severe and less extensive defoliation cycles that
occurred, for example, during 1960–1990 in cluster 8 in
northwestern Québec and during 1938–1950 and 1985–2002 in
cluster 6 in southeastern Québec, may be associated with
intermediate population levels which failed to reach the
extreme levels necessary for severe and prolonged defoliation.
4.3. Mechanism of synchrony breakdown
The breakdown in forest tent caterpillar cycle synchrony
initiated in 1963 was, initially, surprising to us. A careful
review of the literature, however, revealed that (1) forest tent
caterpillars eggs at high altitudes in western Canada failed to
hatch in the spring of 1963 (Gautreau, 1964), thus leading to the
decline of that outbreak; (2) forest tent caterpillar during the
1962–1966 cycle in Ontario did not occur in significant
numbers in the northern region (Daniel and Myers, 1995),
possibly because hatchlings there died in May 1963 as a result
of a late spring frost (Forest Insect and Disease Survey, 1963, p.
51). The cycle collapse in northern Ontario occurred despite an
increasing trend in 1962, and a forecast for widespread
outbreak in 1963. And, notably, the cluster 9 region of Québec
is adjacent to this part of Ontario where outbreak did not
materialize. Consequently, it seems likely that poor spring
weather was responsible for the desynchronization of tent
caterpillar population oscillations in Québec. The hypothesis is
attractive because of the aforementioned pattern of population
rebounding in 1962–1963, 1965–1966 and 1972 in cluster 7.
This sort of pattern could be a result of recurring meteorological
perturbations that repeatedly fail to terminate a population
cycle.
Typically, climatic perturbations are thought of as a
synchronizing force. Peltonen et al. (2002) suggested that
the spatial scale of population synchrony in cyclic forest insects
– including forest tent caterpillar – should be equal to the spatial
scale over which climatic phenomenon are autocorrelated.
However, Cooke and Roland (2003) describe a mechanism in
the forest tent caterpillar system whereby climatic perturbations, even if spatially autocorrelated, could act as desynchronizing perturbations. They provide data and arguments
suggesting that the likelihood of prolonged population collapse
depends not only on the severity of the weather perturbation
(which is density-independent), but also on (1) the susceptibility and vulnerability of caterpillars to perturbation, and (2)
the abundance of natural enemy populations—all of which are
density-dependent. Although weather variables may be
correlated over very large spatial scales, the factors that
mediate their impact – such as population density and quality –
may not be. Thus it is hypothesized that (1) density-dependent
mediating processes can turn ordinary climatic perturbations
into extraordinary climatic shocks, and (2) cycling populations,
once put out of phase, are no longer subjected to the same
regime of climatic perturbations.
In theory, the synchronizing forces of spatially autocorrelated perturbations (Moran, 1953) and/or inter-population
migration (Barbour, 1990) should be sufficient to re-synchronize oscillating populations that are temporarily set out of phase
by climatic shocks. So why have caterpillar population
oscillations in clusters 6 and 8 remained out of synchrony
for what is now 40 years? We hypothesize that the failure of tent
caterpillar oscillations to re-synchronize after 1963 is because
the distances between these populations is too large relative to
either (1) the inter-population migration rate, or (2) the spatial
scale over which subsequent climatic perturbations were
autocorrelated, or (3) the degree of homogeneity among
endogenous forces governing cyclicity in the two regions.
This third possibility is especially attractive, because of the
apparent association between outbreak periodicity and forest
type in the two core areas. It is unclear to us exactly why
trembling aspen should lead to a faster rate of population
cycling than sugar maple, and, as forewarned, it may even be a
spurious correlation. However aspen is generally thought of as a
higher-quality host than maple (Nicol et al., 1997; Lorenzetti
et al., 1999; Panzuto et al., 2001), and this could account for the
higher rate of cycling in the aspen-dominated boreal forest.
More data are required before a model can be built to test this
hypothesis.
4.4. Predicting future outbreak cycles
Given the large influence of huge, remote areas on the sum,
province-wide pattern of defoliation, we are pessimistic about
the possibility of gains in predictability of defoliation occurring
at the provincial scale. Where we are more optimistic is in those
core areas of northwestern and southeastern Québec where
defoliation is highly periodic, and therefore somewhat
predictable—at least in terms of timing.
Predictability of population cycling within these core
regions of cyclicity is offset, unfortunately, by an unexplained
pattern of slow variability in cycle amplitude (Fig. 6). The
amplitude of oscillations in clusters 6 and 8 in particular
B.J. Cooke, F. Lorenzetti / Forest Ecology and Management 226 (2006) 110–121
appears to vary in a smooth manner, as if the cycle maxima
were being modulated by some slow-changing variable.
Without knowing what controls the level of defoliation during
a population cycle, it is impossible to predict, long in advance,
the level of damage that will occur during a given cycle; all we
can do is treat cycle amplitude as a random variable with a
given mean and variance. In this regard, it appears that, in both
core regions, roughly half of all population cycles result in
severe and prolonged defoliation.
Knowing that forest tent caterpillar populations in cluster 6
peaked last in 1995 and that they exhibit a periodicity of 13
years, we predict, with an unknown level of confidence, that the
next cycle in that region will peak in 2008. In the other core area
of periodicity – clusters 8 and 9 in northwestern Québec –
populations last peaked in 2001. With a periodicity of 9 years,
the next cycle peak is thus expected in 2010. The severity of
defoliation during these cycles is not predictable this early in
advance because we do not yet know what modulates the
amplitude of local population cycles.
Notably, should the northwestern cycle arrive a year earlier
than expected and the southeastern cycle arrive a year later,
then the two regional cycles would coincide temporally, in
2009. This, in theory, could lead to the sort of unusually
extensive and prolonged defoliation that was observed during
the 1951–1954 outbreak, with defoliation occurring in the
rarely-defoliated, and more remote clusters 1 and 2. For this to
happen, all that would be required, according to the outbreak/
moth dispersal theory of Royama (1980), is extensive
reciprocal migration of female moths between regional
clusters 6 and 9. The probability of reciprocal migration
occurring at this spatial scale is impossible to estimate from our
limited knowledge of moth dispersal rates and distances,
although wind-assisted, long-range, mass-flights of forest tent
caterpillar moths are a documented phenomenon (Brown,
1965).
Defoliation by forest tent caterpillar has been identified,
along with drought and site conditions, as one of the important
co-factors in hardwood forest decline, including the 1980s
decline of sugar maple in Québec (Payette et al., 1996) and the
more recent decline of trembling aspen in Alberta (Hogg et al.,
2002) and Ontario (Candau et al., 2002). Based on our analysis,
those concerned about forest tent caterpillars in the maplesugar producing regions of southeastern Québec should
immediately begin monitoring the health of their trees on an
annual basis. If forest tent caterpillar populations begin to rise
to the level of several egg masses per tree, noticeable
defoliation can be expected. At that point, monitoring should
intensify so that quantitative estimates of population levels are
available for numerous locations. Similarly, insect populations
in northwestern Québec should also be monitored, on the offchance that the next boreal population cycle develops more
rapidly than anticipated. If observations in Ontario are
representative, then a relatively short interval between
outbreaks (e.g. only 3–6 years between successive outbreaks,
as opposed to the normal interval of 9–13 years) may
significantly increase the risk to the forest resource (Candau
et al., 2002).
119
4.5. Nonstationarity in spatially aggregated time-series
Knowing, now, that forest tent caterpillar populations in
Québec vary regionally in their dynamics (Fig. 5), it is
instructive to look back at the marginally cyclic provincial scale
defoliation time-series (Fig. 3), and reconsider the broader issue
of nonstationarity in spatially aggregated time-series data.
In most forest insect defoliation studies, the spatial scale of
analysis is fixed to that of a whole jurisdictional unit, such that
there is no recourse when it is found that the jurisdiction-wide
defoliation time-series appears nonstationary in mean or
variance. In some studies (e.g. Candau et al., 1998; Fleming
et al., 2000; Liebhold et al., 2000) the time-series data are
analyzed untransformed—which may seriously violate the
stationarity assumption of time-series analysis. In others (e.g.
Volney, 1988; Williams and Liebhold, 2000a,b), a log
transformation is used to stabilize the time-series variance.
The justification for log-transfomation is that (i) it is standard
practice in the case of point-wise population data (Royama,
1992), and (ii) defoliation is merely a surrogate of population
density. There is some logic to this argument; however it is not
entirely correct, because – as noted in Section 1 – above a
certain intermediate density threshold – which is estimated to
be roughly three egg bands per inch of host-tree DBH (Hodson,
1941) – the defoliation response saturates, as it attains its
maximum value of 100%. Consequently, in years when
population density in a given area exceeds the 100% defoliation
threshold, the defoliation time-series carries no information
about the insect’s population dynamics. If this happens
frequently, then it is not at all clear that log-transformation
will accomplish its intended effect. The log-transformed
defoliation series may be more stationary, but carry less
population dynamics information.
It is largely for this reason that we chose not to formally
analyze the provincial-scale defoliation time-series data
(Fig. 3). Log-transformation may stabilize variance, but it
does not solve the bigger problem of temporal nonstationarity
arising from regional effects (i.e. spatial nonstationarities
embedded within the spatial aggregate).
In our case, cluster analysis on the full space–time data set
solved the problem of temporal nonstationarity through a
process of spatial decomposition. What we found is that much
of the temporal nonstationarity in the provincial aggregate data
could be attributed to (1) nonstationary outbreak dynamics
occurring in the northern and eastern fringe of the species’
range (clusters 1 and 2), and (2) asynchronous population
oscillations occurring in two ends, southeast and northwest, of
the species’ regional distribution (cluster 6 versus clusters 8 and
9). These results are not surprising, in that they are consistent
with the idea that (1) species dynamics are less stable at the
edges of their distribution, and (2) periodic insect outbreaks are
the result of spatially synchronized population oscillations
(Royama, 1992) with the spatial scale of synchronization
varying depending on the effective distance between population
clusters and the degree of spatial correlatedness in environmental perturbations (Moran, 1953; Barbour, 1990; Liebhold
and Kamata, 2000; Peltonen et al., 2002). What is novel about
120
B.J. Cooke, F. Lorenzetti / Forest Ecology and Management 226 (2006) 110–121
our study is that it illustrates how time-series cluster analysis
can be fruitfully applied to sequential spatial data (e.g. annual
defoliation maps) when the driving forces influencing
spatiotemporal dynamics are more temporal than spatial (i.e.
dominated by time-delayed density-dependent processes such
as those causing population cycling). Nonstationarity thus may
be more than just a violation of the assumptions of time-series
analysis; it may be an ecological phenomenon worthy of study
on its own merit.
Previous forest insect studies have attempted to examine
such regional effects by partitioning the space–time data using
arbitrary spatial partitioning methods (e.g. Royama, 1984;
Royama et al., 2005; Candau et al., 1998; Williams and
Liebhold, 2000a). However our study illustrates how and why,
for long time-series spanning multiple outbreak cycles,
clustering based on time-series may provide superior results.
5. Conclusion
Forest tent caterpillar outbreaks in Québec are nearly cyclic
in their pattern of recurrence; however it would be an
oversimplification to state that these cycles are well-synchronized. Synchronous cycles are observed within two core
regions covering a small fraction of the province’s surface area,
in northwestern and southeastern Québec. Between regions,
outbreak cycles are not at all well-synchronized. Thus the
dynamics of forest tent caterpillar outbreaks in Québec appear
to be intermediate in complexity—not as well-synchronized as
in Ontario, but better synchronized than in the western prairie
provinces. This points to the value of a regional approach to
national-scale exercises such as carbon accounting: while one
region may be acting as a carbon source, neighbouring regions
may be acting as a carbon sink.
Our study shows that it is not the mere existence of outbreak
cycles that needs explaining. In the case of forest tent
caterpillar, we also need to explain: (1) why two core regions
separated by only 500 km should vary so strongly in outbreak
periodicity; (2) why populations in the intervening territory
should be non-cyclic; (3) why inter-regional synchrony should
break down so suddenly and so persistently in 1963. We view
these not as mere details, but as key features of tent caterpillar
outbreak oscillations in need of explanation. They are
characteristic across the range of the insect, and may be
characteristic of other species as well.
From a forest manager’s perspective, there are two major
reasons for studying insect disturbance ecology. First, pattern
analysis tells us something about the processes that generate
disturbance, and this is important if we are going to actively
manage and mitigate insect pest damage. Second, disturbance
ecology tells us something about insects as ecosystemstructuring processes, and this is important if we are going
to maintain integral landscapes. Insects are not just pests; they
are keystone species in the ecological community. So whether
the goal is pest management for sustaining timber yields or
emulating natural disturbance for the purposes of forest
certification, a long-term approach to insect population
dynamics research is critical.
Acknowledgements
Bruno Boulet, Ministère des Ressources Naturelles et Faune
du Québec (MRNFQ), graciously provided access to digital
historical insect data. Louis Morneau, MRNFQ, provided
critical documentation explaining intimate details of the survey
methods (which are available upon request). David Gray and
Richard Fleming of the Canadian Forest Service provided
helpful comments on an earlier version of the manuscript. We
also thank Esa Ranta and two anonymous reviewers for their
helpful comments.
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