ArticlePDF Available

Abstract and Figures

Over large areas, synchronous fluctuations in population density are often attributed to environmental stochasticity (e.g., weather) shared among local populations. This concept was first advanced by Patrick Moran who showed, based on several assumptions, that long-term population synchrony will equal the synchrony of environmental stochasticity among locations. We examine the consequences of violating one of Moran's assumptions, namely that environmental synchrony is constant through time. We demonstrate that the synchrony of weather conditions from regions across the United States varied considerably from 1895 to 2010. Using a simulation model modified from Moran's original study, we show that temporal variation in environmental synchrony can cause changes in population synchrony, which in turn can temporarily increase or decrease the amplitude of regional-scale population fluctuations. A case study using the gypsy moth (Lymantria dispar) provides empirical support for these predictions. This study provides theoretical and empirical evidence that temporal variation in environmental synchrony can be used to identify factors that synchronize population fluctuations and highlights a previously underappreciated cause of variability in population dynamics.
Content may be subject to copyright.
Ecology, 96(11), 2015, pp. 2935–2946
Ó 2015 by the Ecological Society of America
Temporal variation in the synchrony of weather and its
consequences for spatiotemporal population dynamics
The Blandy Experimental Farm, University of Virginia, Boyce, Virginia 22620 USA
USDA Forest Service, Northern Research Station. Morgantown, West Virginia 26505 USA
Department of Biology, Virginia Commonwealth University, Richmond, Virginia 23173 USA
Department of Environmental Sciences, University of Virginia, Charlottesville, Virginia 22904 USA
Abstract. Over large areas, synchronous fluctuations in population density are often
attributed to environmental stochasticity (e.g., weather) shared among local populations. This
concept was first advanced by Patrick Moran who showed, based on several assumptions, that
long-term population synchrony will equal the synchrony of environmental stochasticity
among locations. We examine the consequences of violating one of Moran’s assumptions,
namely that environmental synchrony is constant through time. We demonstrate that the
synchrony of weather conditions from regions across the United States varied considerably
from 1895 to 2010. Using a simulation model modified from Moran’s original study, we show
that temporal variation in environmental synchrony can cause changes in population
synchrony, which in turn can temporarily increase or decrease the amplitude of regional-scale
population fluctuations. A case study using the gypsy moth (Lymantria dispar) provides
empirical support for these predictions. This study provides theoretical and empirical evidence
that temporal variation in environmental synchrony can be used to identify factors that
synchronize population fluctuations and highlights a previously underappreciated cause of
variability in population dynamics.
Key words: gypsy moth; Lymantria dispar; Moran effect, periodicity; population model; regional
stochasticity; spatial coherence; spatial synchrony; wavelet analysis; wavelet coherence.
A wide variety of species exhibit synchronous
fluctuations in the density of spatially disjunct popula-
tions (Hanski and Woiwod 1993, Liebhold et al. 2004).
This spatial synchrony, hereafter ‘population synchro-
ny,’ implies that the behaviors of local populations are
interrelated over larger areas (Ranta et al. 1997). High
levels of population synchrony mean that local popula-
tion densities change in unison, causing high amplitude
fluctuations in regional (system-wide) population densi-
ty (Heino et al. 1997, Liebhold et al. 2012). Highly
synchronous dynamics can increase the risk of extinction
for rare species, as there can be no rescue effect if all
population densities are simultaneously low (Heino et al.
1997, Abbott 2011). Conversely, synchronous cycles in
population density may allow outbreaking pest species
to escape regulation by mobile natural enemies and
increase the severity of damage (Liebhold et al. 2012).
Consequently, understanding patterns and drivers of
population synchrony may improve our ability to assess
risks to species, whether the focus is conservation or pest
A general result from theoretical models of spatio-
temporal population dynamics is that fluctuations of
spatially disjunct popu lations c an be sync hronized
through relatively weak interactions among populations,
such as coupling (e.g., dispersal) or common forcing
(e.g., shared environmental disturbance). A special case
of shared forcing of particular interest in ecology is the
Moran effect (Royama 1992). This phenomenon is
named for Patrick Moran, who found that the
asymptot ic synchrony of populat io ns g over ned by
identical log-linear, density-dependent dynamics will
equal the level of synchrony in environmental distur-
bances (Moran 1953, Royama 1992). Weather is often
thought to provide this synchronizing disturbance, given
its potential effects on birth/death processes and its
consistent synchrony over s patial scales s imilar to
population synchrony (Moran 1953, Koenig 2002).
The Moran model has been extended to incorporate
systems with nonlinear (Ranta et al. 1997, Engen and
Sæther 2005) and spatially heterogeneous population
dynamics (Peltonen et al. 2002, Engen and Sæther 2005,
Liebhold et al. 2006), and to include dispersal (Ranta et
al. 1998, Kendall et al. 2000). However, although there is
evidence that synchrony of weather conditions can
change through time (Walsh et al. 1982, Haston and
Michaelsen 1997), effe cts of thi s type of temporal
variation on ecological processes have not been ex-
Manuscript received 5 August 2014; revised 23 March 2015;
accepted 11 May 2015. Corresponding Editor: B. J. Cardinale.
Present address: Department of Forestry and Wildlife
Ecolog y, U niv ersi ty of Wiscons in, Madison, Wisconsin
53706 US A. E-mail:
Though t he Moran effect predicts a long- term
equality between environmental and population syn-
chrony, population synchrony is known to vary over
shorter timescales (Ranta et al. 1998). A few studies have
linked this variation to anomalous mean weather
conditions (Forchhammer et al. 2002, Haydon et al.
2003, Cattadori et al. 2005), but we found only two
studies that examined temporal varia tio n in both
environmental and population synchrony. Post and
Forchhammer (2004) linked a long-term, increasing
trend in the synchrony of w inter temperatures to
increases in the population synchrony of caribou in
Greenland. In contrast, Jepsen et al. (2009) examined
short-term changes in synchrony during an outbreak of
Fennoscandian geometrid moths. They observed that
both environmental and population synchrony were
high during the incipient phase of an outbreak, and then
both decreased as the outbreak progressed. Interesting-
ly, they also suggest that this temporary high level of
population synchrony led to an unusually widespread
outbreak of these moths. However, verifying that short-
term changes in environmental synchrony can alter
population synchrony, and subsequently increase the
amplitud e of region al outbreaks , w oul d r eq uire a
theoretical basis and examination of empirical data
spanning more than one population cycle.
The goal of our study is to extend Moran-effect
theory to include temporal variation in environmental
synchrony. We begin by demonstrating that a common-
ly cited source of environmental synchrony, the syn-
chrony of weather, varies substantially through time in
regions throughout the USA. Next, we incorporate
temporal variation in environmental synchrony into
Moran’s original model, which captures the population
dynamics of a wide variety of animals. Using this model,
we determine conditions under which temporal variation
in environmental synchrony can affect population
synchrony and the amplitude of regional population
fluctuations. Finally, we test these theoretical predic-
tions in an empirical case study of the gypsy moth
(Lymantria dispar). This is an ideal system to test these
predictions because, although little is known about
temporal variation in environmental or population
synchrony in this system, there is strong evidence that
weather synchronizes gypsy moth outbreaks (Peltonen
et al. 2002, Hayn es et al. 201 3), and extens ive
spatiotemporal datasets are available.
Temporal patterns in the synchrony of weather
Study of temporal variation in the Moran effect
makes sense only in light of temporal variation in
environmental synchrony, so we began by characterizing
changes in the synchrony of weather conditions through
time. We calculated synchrony in interannual variation
in monthly precipitation totals and monthly averages of
both minimum and maximum daily temperatures from
1895 to 2010, based on readings from 1218 first-order
weather stations in the U.S. Historical Climatology
Network across the 48 conterminous states of the USA
(National Climatic Data Center (NCDC); data available
To explore geographic consistency in patterns
of synchrony of weather, we divided these weather
stations into the nine NCDC climatic regions: the
Northeast, Upper-Midwest, Ohio Valley, Southeast,
South, Southwest, West, and Northwest. We treated
each variable, region, and month separately, for a total
of 324 time series. Prior to synchrony calculations, we
removed a mild positive skew from the precipitation
totals with a square root transformation.
Synchrony between two sites is generally calculated in
a time-invariant manner as the correlation among
measurements for the entire length of the time series,
though some previous studies have calculated correla-
tions within moving windows of 10 or more years to
examine changes in the synchrony of weather through
time (e.g., Ranta et al. 1998, Post and Forchhammer
2004, Bjørnstad et al. 2008). To maximize temporal
resolution and minimize autocorrelation, we measured
synchrony within even shorter 3-yr moving windows.
For each time window, we calculated all pairwise
correlations among locations and reported the mean of
these pairwise correlations as synchrony for the middle
year of that time window (Appendix A). Averaging over
n(n 1)/2 pairwise correlations, where n was the number
of locations in the region, helped reduce noise from
stochastic phase slip among oscillations at individual
locations (Appendix A). The minimum possible value of
these average correlations is 1/(n 1) given a constant
variance among locations, so that anti-synchronous
states become less likely as the sample size increases
(Gouhier and Guichard 2014). Alternative concordance
measures of synchrony do not suffer from this contrac-
tion, but range only from 0 to 1 and require a second
step to determine if a given value is synchronous or anti-
synchronous (Gouhier and Guichard 2014). Concor-
dance measures also performed poorly in our zero-heavy
gypsy moth defoliation records. Interestingly, the mean
correlations coefficient and concordance techniques
both indicated few negative values and these negative
were typically close to zero (data not shown).
The temporal scale of fluctuations in the synchrony of
weather may influence how these fluctuations affect
ecological processes. For example, annual fluctuations
in the synchrony of weather might have less of an effect
than longer term changes. Initial visual inspection of
changes in the synchrony of weather conditions through
time revealed apparent periodic behavior, one form of
longer term changes. To inform our simulation model
and statistical analyses, we evaluated the extent of
periodicity in the synchrony of weather conditions using
wavelet analysis (Torrence and Compo 1998, Cazelles et
al. 2007). The continuous wavelet transform is similar to
6 -based-station-data
ANDREW J. ALLSTADT ET AL.2936 Ecology, Vol. 96, No. 11
Fourier analysis in that it breaks down a time series into
its cyclical components but has the additional feature of
characterizing temporal variation in periodicity (Tor-
rence and Compo 1998; details in Appendix B). The
wavelet transform is a convolution of the time series
with a wavelet function, a periodic function resolved in
time and an adjustable cycle length. Repeating this
convolution for all time steps and frequencies provides
the ability to detect temporal variability in periodic
behavior, as displayed in the wavelet spectrum. We
conducted these analyses using a Matlab package that
applies the widely used Morlet wavelet (Cazelles et al.
2007) modified to correct a bias towards low-frequency
signals inherent to traditional wavelet analysis (Liu et al.
2007). While the wavelet transform does not require that
a time series follow a specific distribution, the Morlet
wavelet itself is normally distributed, and normally
distributed data often produce more reliable results
(Jevrejeva et al. 200 3, G rin sted et al. 2004). We
improved the normality of these time series with the
Box-Cox transform (Box and Cox 1964), using the
Matlab function boxcox to determine the maximum
likelihood value of the transformation parameter. The
time series were then transformed to a standard normal
distribution. We tested for significant periodicity using a
hidden Markov model simulation experiment, which
accounts for short-term autocorrelation present in the
time series, without making assumptions about the
structure of that autocorrelation (Cazelles et al. 2014).
Simulation model
Moran’s original work demonstrated that, over the
long term, synchrony among local populations was
equal to the level of environmental synchrony in a
system with identical and linear local population
dynamics (Moran 1953). Given the extensive temporal
variation observed in the synchrony of weather, we used
a simulation model to ask two related questions. First,
does temporal variation in environmental synchrony
cause changes in population synchrony? Second, be-
cause higher, constant levels of population synchrony
are k nown to increase the amplitu de of regional
population fluctuations, we ask if these short-term
changes in population synchrony have an effect on
regional (system-wide) population dynamics.
The model system consisted of i ¼ 1, 2, ..., 100 local
populations, each governed by the second order
autoregressive (AR2) model
ðt 1Þþa
ðt 2Þþn
where x
was log-population density of the local
populations, i, and t is time. The terms a
and a
the strength of direct and delayed density dependence,
respectively, and represented the effects of endogenous
ecological interactions. Th e stochastic term, n
represented exogenous, density-independent disturbance
to the system, as weather conditions might impose.
Values of n
(t) were drawn from a multivariate normal
distribution in which each of the 100 individual elements
had a mean of zero and standard deviation of one. The
correlation among these distributions represented envi-
ronmental synchrony (S
), which varied through time.
Population synchrony (S
) was calculated with the
previously described 3-yr moving window correlations.
The well-characterized AR2 model allowed us to
produce a variety of population behaviors by varying
parameters a
and a
(Royama 1992, Box et al. 1994)
that influence the rate of changes in population
synchrony (Bjørnstad et al. 2008). We considered the
parameter range a
þ 4a
0 and a
1, where, in
stochastic models, the model produces dampened
oscillations towards the equilibrium with an approxi-
mate cycle length of
(Box et al. 1994). The length of population cycles is
unimportant to rates of change in population synchrony
( Bjørn stad et al. 20 08). Therefo re, to red uce the
parameter space, we fixed the cycle length of x
yr, selected the desired value of a
, and varied a
accordingly. The variance and periodicity of x
increase at an accelerating rate as a
!1 (Box et al.
1994). For example, when a
¼ a
¼ 0, all variance in
(t) comes directly from n
(t), and changes in population
synchrony occur immediately. When 0 , a
, 0.5 , the
intrinsic dynamics based on prev ious system states
contribute more to the variance of x
(t), and the rate
of synchronization decreases, though these time series
remain statistically aperiodic (Bjørnstad et al. 2008). As
is decreased further, periodicity and variance increase
rapidly until a
¼1, where x
(t) exhibits neutrally stable
cycles. Throughout this manuscript, we will use a
as a
proxy for the strength of intrinsic regulation and the
variance and periodicity of x
To mimic the naturally occurring fluctuations in the
synchrony of weather, we used a separate AR2 model
ðt 1Þþd
ðt 2ÞþeðtÞð2Þ
that allowed manipulation of the cycle length and the
periodicity of oscillations in S
as previously described
for Eq. 1. Simulation using Eq. 2 produces time series
with zero mean and amplitude dependent on parameter
values. To control these properties, we calculated S
prior to running the population model and then
transformed the S
time series to have the desired mean
and amplitude, defined as one-half of the span
containing 95% of values. Also, based on our empirical
findings, we used 0 S
1 so that S
could be
asynchronous but not anti-synchronous.
To measure the effect of changes in S
on S
, we used
two complementary bivariat e extensions of wavelet
analysis the cross-wavelet spectrum and wavelet coher-
ence (Grinsted et al. 2004, Cazelles et al. 2007; details in
Appendix B). The cross-wavelet spectrum indicates
wavelengths at which both time series share wavelet
power, similar to a covariance, and provides the time-
frequency-resolved phase difference between the series.
Wavelet coherence indicates consistency in phase
difference between two time series with values ranging
from 0 (independent time series) to 1 (phase-locked time
series). Wavelet coherence rises systematically with
increasing cycle length (Maraun and Kurths 2004).
Tests for statistical significance are not appropriate for
simulated data, so to account for this increase we used
the coherence between two random normal distributions
to indicate an expected level of coherence at each cycle
Next, we evaluated the effect of short-term changes in
on the amplitude of fluctuations in regional
population size, X(t) ¼ Rx
. While deviations from the
mean of X(t) ¼0 will clearly not always be high given its
periodicity under some parameter values, we expected
the largest amplitude fluctuations in X(t) to occur when
(t) is high. To evaluate this hypothesis, we fit linear
ordinary least squares (OLS) regressions between S
and the absolute value of X(t), where a positive slope
indicated that deviations in X(t) increased as S
increased. To facilitate comparisons among simulations
with different parameter sets, we standardized X(t)to
zero mean and u nit varia nc e prior to fitting the
regression. Simulations were conducted in Matlab and
were run for 1500 years with the first 500 years discarded
to reduce the influence of initial conditions.
Gypsy moth study system
In its invasive North American range, the gypsy moth
has exhibited cyclical population fluctuations through-
out much of the 20th century, apparently due to delayed
density-dependent mortality caused by a gypsy moth
specific n ucle opolyh edro virus (Dw yer et al. 2 000).
However, extended periods of low gypsy moth density
are common (Allstadt et al. 2013) and thought to result
from high rates of predation by generalist, small
mammal predators in low-density gypsy moth popula-
tions (Elkinton and Liebhold 1990, Elkinton et al.
1996). Since 1989, the introduced fungal pathogen
Entomophaga maimaiga has also been a major source
of density-independent mortality in North American
gypsy moth populations (Hajek 1999), but the density-
dependent viral interactions described previously have
not been disrupted ( Liebhold et al. 2013). Gypsy moth
outbreaks are synchronous over distances up to 1000 km
(Peltonen et al. 2002, Haynes et al. 2009a). The role of
dispersal in gypsy moth population synchrony over
these distances is limited, as female moths in North
American populations are unable to fly and larvae
typically disperse over distances of a few hundred meters
(Mason and McManus 1981). Instead, this synchrony is
thought to be caused by meteorological disturbances
shared among spatially disjunct populations of gypsy
moths and their natural enemies (Haynes et al. 2013).
Gypsy moth population dynamics were assessed using
annual aerial defoliation surveys of the northeastern
United States from 1975 to 2009, which indicate the
presence/absence of defoliation at a 2-km resolution
(Liebhold et al. 1997). The proportion of forest area
defoliated by gypsy moth larvae is correlated with gypsy
moth population density (Williams et al. 1991, Liebhold
et al. 1995). We aggregated the 2-km resolution data
into 64 3 64 km grid cells and calculated the proportion
of the larger grid cell defoliated annually. This spatial
scale provided a continuous variable and smoothed
spatial error prevalent over smaller distances, while
maintaining a large sample of spatially disjunct popu-
lations (Haynes et al. 2013). We excluded areas not
generally infested with gypsy moth prior to 1975 (U.S.
Code of Federal Regulations, Title 7, Chapter III,
Section 301.45) to avoid transient dynamics of newly
invaded areas (Bjørnstad et al. 2008), leaving 92 grid
cells over 786 3 896 km from western Pennsylvania to
Maine (Fig. 1 in Haynes et al. [2009a]).
A limitation of these data is that aerial surveys have a
detection threshold of ;30% defoliation (Ciesla 2000) so
low-density gypsy moth population dynamics are not
captured. When calculating the gypsy moth synchrony
time series, one or both cells in an individual pairwise
correlation frequently had zero defoliation in all 3 yr of
a time window, causing those pairwise correlations to be
undefined. Undefined correlations were excluded from
synchrony calculations, reducing the sample size of
synchrony estimates during some time windows, partic-
ularly during the second half of our study period (1995–
2009), when levels of defoliation across the region were
generally low. Although we conducted our analyses
throughout the full study period, we focused interpre-
tation on the period 1975–1995. Prior to analysis, we
fifth-root transformed the zero-heavy defoliation data to
remove a strong positive skew (Allstadt et al. 2013) and
approximate the normal distribution of the Morlet
wavelet (Grinsted et al. 2004).
A previous study linked spatial variation in gypsy
moth population synchrony to synchrony of monthly
totals of precipitation (Haynes et al. 2013), so we
evaluated the effect of temporal variation in monthly
precipitation on gypsy moth dynamics. We focused on
months that coincided with the development of gypsy
moth larvae (April–July), because this life stage typically
causes defoliation and has the highest mortality within a
generation. We obtained precipitation data from the
Parameter-elevation Regressions on Independent Slopes
Model (PRISM; Daly et al. 1994) at a 4-km resolution
and aggregated these values into the same 64 3 64 km
grid cells used for gypsy moth defoliation. We calculated
interannual synchrony of total precipitation for each
month (April–July) as in the weather station analyses.
The periodicity of gypsy moth defoliation, gypsy
moth population synchrony, and synchrony in monthly
precipitation were assessed using wavelet analysis, and
we used cross-wavelet spectrum and wavelet coherency
analyses to detect temporal associations between these
time series. Statistical significance of the wavelet cross-
ANDREW J. ALLSTADT ET AL.2938 Ecology, Vol. 96, No. 11
spectrum and wavelet coherence were tested using
hidden Markov model simulations similar to those
described for wavelet analysis (Cazelles et al. 2014).
Temporal patterns in the synchrony of weather
Patterns of temporal variation in the synchrony of
weather varied among weather variables, months, and
geograph ic regi ons (repr ese nta t ive data in Fi g. 1;
descriptive statistics for all time series in Appendix C).
Yearly estimates of synchrony from all time series
ranged from 0.01 to 1, and ,2.5% of readings were
negative. Synchrony in minimum and maximum tem-
peratures was generally higher than in precipitation with
overall means of 0.4, 0.4, and 0.18, respectively, though
there was conside rable variation depending on the
month of the year and geographic region. Similarly,
the synchrony in temperature displayed higher levels of
variation than synchrony in precipitation (Appendix C).
Statistically significant periodicity occurred in 186 of the
324 time series, 81, 75, and 78 for minimum tempera-
tures, maximum temperatures, and precipitation, re-
spectively. Of these periodic time series, the cycle lengths
ranged from ;4 to 32 yr (the longest length that we
tested) with a median of 12 yr.
Simulation model
In the simulation model, population synchrony (S
tracked environmental synchrony under many condi-
tions (Fig. 2a), particularly when local population
dynamics were weakly or moderately periodic (Fig. 3).
The pattern of temporal variation in S
also influenced
the strength of this association. Coherence between S
and S
was strongest with higher amplitude and more
periodic fluctuations in S
, while the cycle length (Fig. 3)
and the mean level of S
(data not shown) had little
effect. We also observed phase dependence of S
cycles in regional population density, X(t), with higher
during rising and falling phases of the population
cycle (Fig. 2a). This is expected when measuring
synchrony over time periods shorter than the population
cycle length (details in Appendix D). In all cases, the
time-invariant synchrony values of S
and S
equal. That is, the classic Moran effect still applied.
After establishing that changes in S
caused temporal
variation in S
, we tested our second hypothesis that
these short-term changes would alter the amplitude of
fluctuations in regional population density. The largest
fluctuations in X(t) occurred when S
was high, driven
by an increase in S
(e.g., years 925–935 in Fig. 2). The
effect of S
on X(t) was strongest when local popula-
tions were weakly or moderately periodic ( Fig. 4). This
relationship was also enhanced by increased periodicity
of S
, whereas reducing the amplitude or cycle length of
reduced the relationship between S
and the
amplitude of X(t) (Fig. 4).
Case study: the gypsy moth
Forest defoliation due to gypsy moth larvae was high
during the first half of the study period relative to the
second half (Fig. 5a). There was a negative trend in the
area defoliated from 1975 to 1995, and defoliation was
negligible at the regional scale from 1996 to 1999. From
1996 to 1999, 1, 0, 3, and 2 out of 92 grid cells had
detectable defoliati on, respecti vely, compared to a
FIG. 1. Time-varying synchrony (top) of mean daily minimum temperature and (bottom) of total precipitation for the months
of January and June. Results shown for four of nine climatic regions of the United States designated by the National Climatic Data
Center, selected to maximize geographic coverage. Lines indicate the following regions: Northeast (NE), South (S), Rockies and
Plains (RP), and the West (W).
maximum of 61 in 1981. The wavelet spectrum of the
regional defoliation time series provided evidence that
periodic, regional-scale outbreaks occurred from the
beginning of the study through the early 1990s at
distinct cycle lengths of 4–5 and 8–10 yr (Fig. 5b),
though this pattern was not significant for the particular
subset of defoliation data used in this analysis. This
periodic behavior reflected a pattern of a 4–5 yr cycle in
which every other outbreak was larger than thos e
between (Fig. 5a) as observed in earlier studies.
Estimates of gypsy moth population synchrony
ranged from 0.04 to 0.98 during our study period. From
1975 to 1995, there were statistically significant 8–10 yr
cycles in gypsy moth population synchrony, as well as
nonsignificant evidence for 2–3 yr cycles (Fig. 5c). The
8–10 yr cycles of population synchrony coincide with the
8–10 yr cycles in population density, while the 2–3 yr
peaks in population synchrony correspond to the rising
and falling phases of 8–10 yr gypsy moth outbreak
cycles (Fig. 5a, c).
Spatial synchrony in total June precipitation (S
fluctuated periodically with a consistent cycle length
between 8 and 10 yr (Fig. 5e, f; from 1975 to 1995). The
cross-wavelet spectrum showed common power between
and gypsy moth population synchrony at the 8–10
yr cycle length (Fig. 6a), corresponding to the main cycle
in S
and the double peaks of gypsy moth population
synchrony (e.g., 1978–1985 in Fig. 5c). Within this
FIG. 2. Sample time series from simulation. (a) Population synchrony (S
, gray) generally tracks changes in environmental
synchrony (S
, black), but see years 990 forward. (b) Local population densities, x
(t), demonstrating changes in S
through time, t,
where i is the population. Black markers (dots above panel) indicate years with S
. 0.5. (c) Regional (mean) population density,
X(t), through time. The largest fluctuations in X(t) tended to occur when and S
and S
are high. Markers as in (b). Local
population dynamics were moderately periodic (a
¼0.65; see Eq. 1). Fluctuations in S
were highly periodic (d
¼0.95; see Eq.
2) with a cycle length of 24 years, a mean of 0.5, and an amplitude of 0.35. Local population dynamics and variation in S
more periodic as a
approaches 1 and d
approaches 1, respectively.
ANDREW J. ALLSTADT ET AL.2940 Ecology, Vol. 96, No. 11
region, phase angles between t he time series wer e
consistent and near zero. This same area of the spectrum
is also significant when standardized into the wavelet
coherence (Fig. 6b). We did not find significant areas of
wavelet coherence between outbreak synchrony and the
synchrony of precipitation in other months that we
considered (April, May, and July; Appendix E).
Whereas many studies have examined changes in
population synchrony through space, few have exam-
ined temporal variation in population synchrony (Ranta
et al. 1998, Forchhammer et al. 2002, Haydon et al.
2003, Post and Forchhammer 2004, Cattadori et al.
2005, Henden et al. 2009). We demonstrate that the
synchrony of weather conditions often varies through
time, and our simulation model results indicate that this
variation can cause detectable changes in population
synchrony under many conditions. Additionally, the
resulting temporal variation in population synchrony
can alter the amplitude of fluctuations in regional
population density. The gypsy moth case study provides
suggestive empirical evidence for these theoretical
predictions. These results indicate that studying tempo-
ral variation in synchrony may provide insights into
mechanisms causing population synchrony and increase
understanding of population dynamics over large spatial
The synchrony of weather fluctuated through time in
regions throughout the United States. As in ecology,
FIG. 3. Wavelet coherence, indicated by color, between S
and S
from the simulation model, in relation to the periodicity of
fluctuations in S
and S
. S
had a mean of 0.5, with amplitude and cycle length as labeled. A coherence of 1 indicates a perfect
linear association. Local population dynamics and variation in S
become more periodic as a
approaches 1 and d
1. Wavelet coherence was measured at the expected cycle length of S
and the values shown are the average of 25 simulations.
Wavelet coherence increases systematically with the cycle length at which it is measured. As a visual guide, contours contain areas
where wavelet coherence was greater than 95% of simulated null series.
most work in atmospheric sciences on the synchrony of
weather conditions (referred to as spatial coherence) has
emphasized variation through space rather than through
time (Kutzbach 1967, Walsh et al. 1982). In one
exception, Haston and Michaelsen (1997) identified
changes in synchrony of precipitation over a 400-yr
period in southern California, linked to planetary-scale
atmospheric circulation patterns (i.e., the El-Nin
Southern Oscillation) that alter storm paths through
the area. Atmospheric circulation patterns are somewhat
periodic (e.g., Wunsch 1999, Frauenfeld et al. 2005) and
may cause the statistical periodicity frequently observed
in the synchrony of weather, though such an analysis is
beyond the scope of this paper. Whether these processes
are truly periodic is a matter of debate (e.g., Wunsch
1999). Regardless, our finding that population synchro-
ny will track environmental synchrony through time is
general to other forms of variation as well. Periodicity of
varying degrees merely provided a convenient way to
characterize variability in environmental synchrony in
the rest of our study.
In the simulation model, we found that the relation-
ship between temporal variation in environmental
synchrony and population synchr ony depended on
properties of the fluctuations of both environmental
synchrony and local population density. Unsurprisingly,
effects of e nvironmental synchrony on population
synchrony were strongest when fluctuations in environ-
mental synchrony were large in amplitude. Strongly
periodic fluctuations in environmental synchrony also
enhanced this relationship, representing longer term
changes in synchrony to which populations had time to
respond. Similarly, highly periodic local population
dynamics inhibited the transfer of environmental syn-
chrony to population synchrony because highly periodic
populations have a trajectory that is relatively impervi-
ous to the influence of environmental stochasticity over
the short timescales we are examining (Bjørnstad et al.
2008). However, even among species known for their
periodic population dynamics, few if any reach the
highest levels of population periodicity considered in our
simulation model (Kendall 1998, Liebhold and Kamata
2000). Because weak to moderate periodicity is common
in natural populations, temporal changes in the syn-
chrony of weather may drive changes in the population
synchrony of a wide range of ecological systems. In these
systems, this variation in the strength of the Moran
effect provid es anothe r method of ve rif yi ng that
population synchrony is caused by environmental
The gypsy moth case study pr ovid es empiri cal
evidence of temporal variation in the synchrony of
weather driving fluctuations in population synchrony, as
might be expected given the regular oscillations in the
synchrony of June precipitation and weakly periodic
gypsy moth population dynamics (Liebhold et al. 2000).
The case study als o demonstrates that the linkage
between population and environmental synchrony
phenomenon can be useful in identifying potential
mechanisms causing population synchrony, particularly
in systems with limited dispersal. Previous work linked
synchrony in precipitation totals from all months with
geographic variation in the synchrony of gypsy moth
outbreaks (Haynes et al. 2013). We have apparently
narrowed down the synchronizing effect to total June
precipitation, at least during periods of widespread
gypsy moth outbreaks. The mechanism through which
precipit ation synchro nize s gy psy moth popu lat io ns
remains unclear. Weather may synchronize gypsy moth
populations directly through effects on mortality or
survivorship, or indirectly such as through effects on
oak masting and predators of the gypsy moth that
depend on acorns for winter survival (Haynes et al.
2009a, 2013).
In our model, as in Moran (1953) and Bjørnstad et al.
(2008), local population dynamics are governed by a
FIG. 4. Regression slopes between the temporary level of environmental synchrony, S
(t), and the amplitude of fluctuations in
regional population density,
, for local population dynamics and patterns of periodicity in S
(t). Positive slopes indicate larger
variability in jX(t)j when levels of S
(t) are high. Periodicity of S
(t) is indicated by line color, with d
¼1, 0.75, 0.5, 0.25, and
0 for blue, green, red, teal, and purple. Local population dynamics and S
(t) become more periodic as a
and d
approach 1.
Fluctuations in S
(t) had amplitude and cycle length of (a) 0.35 and 18 years, (b) 0.15 and 18 years, and (c) 0.35 and 6 years.
was standardized to 0 mean and standard deviation of 1 prior to analysis.
ANDREW J. ALLSTADT ET AL.2942 Ecology, Vol. 96, No. 11
constant second-order autoregressive model with no
dispersal among populations. High levels of dispersal
may dampen temporal variability in population syn-
chrony (Ranta et al. 1998), and shifts in local population
dynamics can also cause changes in synchrony through
time (Henden et al. 2009). Additionally, nonline ar
population dynamics (Ranta et al. 1997, Engen and
Sæther 2005) and spatial heterogeneity (Peltonen et al.
2002, Engen and Sæther 2005, Liebhold et al. 2006)
affect overall levels of synchrony and the decay of
synchrony through space, but it is less clear how they
would affect variation through time. More theoretical
work is needed to determine if the impacts of temporal
variation in synchrony are maintained in more complex
models. However, empirical results from the gypsy moth
case study suggest that temporal variation in environ-
mental stochasticity can influence the synchrony of
populations governed by nonlinear trophic interactions
(Dwyer et al. 2004, Allstadt et al. 2013).
Consistently high levels of population synchrony are
known to promote large, regional-scale fluctuations in
population densities that can increase the risk of rare
species extinction or widespread outbreaks of pest
species (Heino et al. 1997, Liebhold et al. 2012). Our
results indicate that short-term variation in population
synchrony, caused by changes in environmental syn-
chrony, can also influence the amplitude of regional
density fluctuations. This finding offers an explanation
for observed dynamic patterns of regional gypsy moth
outbreaks, in which each large outbreak (occurring at 8
10 year intervals) tends to be followed by a smaller
outbreak 4–5 years later (Fig. 5a; Johnson et al. 2006,
FIG. 5. Time series of (a) regional defoliation by gypsy moths, (c) gypsy moth population synchrony, (e) synchrony of total
June precipitation, and (b, d, f ) corresponding wavelet spectra. (a) Defoliation totals were fifth-root transformed and then
standardized to zero mean and unit variance. Peaks in the 4–5 and 8–10 year cycles are indicated by black and gray arrows,
respectively. Open circles indicate years with defoliation in fewer than 10 grid cells. (b, d, f ) Red areas within the wavelet spectrum
indicate higher power (evidence for periodicity); blue areas denote lower power. Dashed lines contain regions of statistically
significant periodicity. Below the thick curved lines, power values are subject to edge effects and must be interpreted with care.
Haynes et al. 2009b). Previous theoretical work has
hypothesized that these smaller outbreaks may be
caused by inter- or intraspecific interactions, such as
dispersal among areas with variable predation pressure
(Bjørnstad et al. 2010) or induced defenses of the host
trees (Elderd et al. 2013). However, our results indicate
that this pattern may instead be a consequence of
temporal variation in the synchrony of weather, as the
larger o utb rea ks occurred when the synchron y of
weather, and therefore population synchrony, was high
and the smaller outbreaks occurred when the synchrony
of weather was low. This suggests that monitoring for
unusually synchronous weather conditions might pro-
vide early warning of unusually widespread pest
outbreaks. Temporal variation in environmental and
population synchrony may also be relevant to the
conservation of rare species because in current popula-
tion viability analyses, the degree of population syn-
chrony is typically assumed to be constant through time
(e.g., Akc¸ akaya and Root 2002), thereby ignoring the
possibility of recurring peri ods of high population
synchrony and potentially underestimating extinction
The findings presented here suggest a new role of
weather in the cyclical population dynamics of many
animals. Early studies indicated that dynamics of insects
and small mammals may be primarily driven by, or
indeed track, temporal variation in meteorological
conditions (e.g., Elton 1924, Davidson and Andrewar-
tha 1948). However, more rigorous searches have failed
to yield evidence for population density tracking
meteorological conditions (Martinat et al. 1987, Elkin-
ton and Liebhold 1990). Though meteorological cycles
influence populations in a variety of ways (Stenseth et al.
FIG. 6. The (a) cross-wavelet spectrum and (b) wavelet coherence between gypsy moth population synchrony and synchrony of
total June precipitation. Dashed lines indicate areas of the spectra that are statistically significant. Arrows indicate the phase
difference between the two time series, where a right-facing arrow indicates that the time series are in phase and a left-facing arrow
means that the series are in anti-phase. Arrows pointing up indicate that synchrony of June precipitation led synchrony of
defoliation by a fraction of a cycle length.
ANDREW J. ALLSTADT ET AL.2944 Ecology, Vol. 96, No. 11
2003), population cycles are now generally thought to
arise from trophic interactions (Berryman 1996, Sten-
seth 1999, Myers and Cory 2013), whereas the primary
observed role of weather is synchronization of dynamics
(Moran 1953, Royama 1992). The results presented here
provide new evidence for the importance of meteoro-
logical conditions to regional population dynamics.
Specifically, we have learned that while population
cycles may not be directly driven by meteorological
cycles, changes in the synchrony of weather might be an
important driver of the amplitude of animal population
oscillations at regional scales.
We thank A. Evan, J. Walter, and E. Luzader for their
assistance, and J. Fox, N. Yoccoz, and other anonymous
reviewers for their helpful comments. This research was funded
by a National Science Foundation grant (DEB 1020614) to
K. J. Haynes.
Abbott, K. C. 2011. A dispersal-induced paradox: synchrony
and stability in stochastic metapopulations. Ecology Letters
Akc¸ akaya, H. R., and W. Root. 2002. RAMAS GIS: linking
spatial data with population viability analysis (version 4.0).
Applied Biomathematics, Setauket, New York, USA.
Allstadt, A. J., K. J. Haynes, A. M. Liebhold, and D. M.
Johnson. 2013. Long-term shifts in the cyclicity of outbreaks
of a forest-defoliating insect. Oecologia 172:141–151.
Berryman, A. A. 1996. What causes population cycles of forest
Lepidoptera? Trends in Ecology and Evolution 11:28–32.
Bjørnstad, O. N., A. M. Liebhold, and D. M. Johnson. 2008.
Transient synchronization following invasion: revisiting
Moran’s model and a case study. Population Ecology 50:
Bjørnstad, O. N., C. Robinet, and A. M. Liebhold. 2010.
Geographic variation in North American gypsy moth cycles:
subharmonics, generalist predators, and spatial coupling.
Ecology 91:106–118.
Box, G. E., and D. R. Cox. 1964. An analysis of transforma-
tions. Journal of the Royal Statistical Society Series B
(Methodological) 26:211–252.
Box, G. E., G. Jenkins, and G. Reinsel. 1994. Time series
analysis: forecasting and control. Third edition. Prentice
Hall, Upper Saddle River, New Jersey, USA.
Cattadori, I. M., D. T. Haydon, and P. J. Hudson. 2005.
Parasites and climate synchronize red grouse populations.
Nature 433:737–741.
Cazelles, B., K. Cazelles, and M. Chavez. 2014. Wavelet
analysis in ecology and epidemiology: impact of statistical
tests. Journal of the Royal Society Interface 11:20130585.
Cazelles, B., M. Chavez, G. C. de Magny, J. F. Gue
gan, and S.
Hales. 2007. Time-dependent spectral analysis of epidemio-
logical time-series with wavelets. Journal of the Royal Society
Interface 4:625.
Ciesla, W. M. 2000. Remote sensing in forest health protection.
Forest Health Technology Enterprise Team Report number
00-03. USDA Forest Service Remote Sensing Applications
Center, Salt Lake City, Utah, USA.
Daly, C., R. P. Neilson, and D. L. Phillips. 1994. A statistical–
topographic model for mapping climatological precipitation
over mountainous terrain. Journal of Applied Meteorology
Davidson, J., and H. G. Andrewartha. 1948. The influence of
rainfall, evaporation and atmospheric temperature on
fluctuations in the size of a natural population of Thrips
imaginis (Thysanoptera). Journal of Animal Ecology 17:200
Dwyer, G., J. Dushoff, J. S. Elkinton, and S. A. Levin. 2000.
Pathogen-driven outbreaks in forest defoliators revisited:
building models from experimental data. American Natural-
ist 156:105–120.
Dwyer, G., J. Dushoff, and S. H. Yee. 2004. The combined
effects of pathogens and predators on insect outbreaks.
Nature 430:341–345.
Elderd, B. D., B. J. Rehill, K. J. Haynes, and G. Dwyer. 2013.
Induced plant defenses, host–pathogen interactions, and
forest insect outbreaks. Proceedings of the National Acad-
emy of Sciences USA 110:14978–14983.
Elkinton, J. S., W. M. Healy, J. P. Buonaccorsi, G. H. Boettner,
A. M. Hazzard, and H. R. Smith. 1996. Interactions among
gypsy moths, white-footed mice, and acorns. Ecology 77:
Elkinton, J. S., and A. M. Liebhold. 1990. Population dynamics
of gypsy moth i n Nor th America. Annual Review of
Entomology 35:571–596.
Elton, C. S. 1924. Periodic fluctuations in the numbers of
animals: their causes and effects. Journal of Experimental
Biology 2:119–163.
Engen, S., and B.-E. Sæther. 2005. Generalizations of the
Moran effect explaining spatial synchrony in population
fluctuations. American Naturalist 166:603–612.
Forchhammer, M. C., E. Post, N. C. Stenseth, and D. M.
Boertmann. 2002. Long-term responses in arctic ungulate
dynamics to changes in climatic and trophic processes.
Population Ecology 44:113–120.
Frauenfeld, O. W., R. E. Davis, and M. E. Mann. 2005. A
distinctly interdecadal signal of Pacific ocean-atmosphere
interaction. Journal of Climate 18:1709–1718.
Gouhier, T. C., and F. Guichard. 2014. Synchrony: quantifying
variability in space and time. Methods in Ecology and
Evolution 5:524–533.
Grinsted, A., J. C. Moore, S. Jevrejeva, et al. 2004. Application
of the cross wavelet transform and wavelet coherence to
geophysical time series. Nonlinear Processes in Geophysics
Hajek, A. E. 1999. Pathology and epizootiology of Entomo-
phaga maimaiga infections in forest Lepidoptera. Microbiol-
ogy and Molecular Biology Reviews 63:814.
Hanski, I., and I. P. Woiwod. 1993. Spatial synchrony in the
dynamics of moth and aphid populations. Journal of Animal
Ecology 62:656668.
Haston, L., and J. Michaelsen. 1997. Spatial and temporal
variability of southern California precipitation over the last
400 yr and relationships to atmospheric circulation patterns.
Journal of Climate 10:1836–1852.
Haydon, D. T., P. E. Greenwood, N. C. Stenseth, and T.
Saitoh. 2003. Spatio-temporal dynamics of the grey-sided
vole in Hokkaido: identifying coupling using state-based
Markov-chain modelling. Proceedings of the Royal Society B
Haynes, K. J., O. N. Bjørnstad, A. J. Allstadt, and A. M.
Liebhold. 2013. Ge ographi cal vari ati on in the spatial
synchrony of a forest-defoliating insect: isolation of environ-
mental and spatial drivers. Proceedings of the Royal Society
B 280:1753.
Haynes, K. J., A. M. Liebhold, T. M. Fearer, G. Wang, G. W.
Norman, and D. M. Johnson. 2009a. Spatial synchrony
propagates through a forest food web via consumer–resource
interactions. Ecology 90:2974–2983.
Haynes, K. J., A. M. Liebhold, and D. M. Johnson. 2009b.
Spatial analysis of harmonic oscillation of gypsy moth
outbreak intensity. Oecologia 159:249–256.
Heino, M., V. Kaitala, E. Ranta, J. Lindstro
m, M. Heino, V.
Kaitala, E. Ranta, and J. Lindstro
m. 1997. Synchronous
dynamics and rates of extinction in spatially structured
populations. Proceedings of the Royal Society B 264:481–
Henden, J. A., R. A. Ims, and N. G. Yoccoz. 2009.
Nonstationary spatio-temporal small rodent dynamics: evi-
dence from long-term Norwegian fox bounty data. Journal of
Animal Ecology 78:636645.
Jepsen, J. U., S. B. Hagen, S.-R. Karlsen, and R. A. Ims. 2009.
Phase-dependent outbreak dynamics of geometrid moth
linked to host plant phenology. Proceedings of the Royal
Society B 276:41194128.
Jevrejeva, S., J. Moore, and A. Grinsted. 2003. Influence of the
Arctic Oscillation and El Nin
o-Southern Oscillation (ENSO)
on ice conditions in the Baltic Sea: the wavelet approach.
Journal of Geophysical Research: Atmospheres (1984–2012)
Johnson, D. M., A. Liebhold, and O. N. Bjørnstad. 2006.
Geographical variation in the periodicity of gypsy moth
outbreaks. Ecography 29:367–374.
Kendall, B . E . 1998. The macroecology of populati on
dynamics: taxonomic and biogeographic patterns of popula-
tion cycles. Ecology Letters 1:160–164.
Kendall, B. E., O. N. Bjørnstad, J. Bascompte, T. H. Keitt, and
W. F. Fagan. 2000. Dispersal, environmental correlation,
and spatial synchrony in population dynamics. American
Naturalist 155:628636.
synchrony and the Moran effect. Ecography 25:283–288.
Kutzbach, J. E. 1967. Empirical eigenvectors of sea-level
pressure, surface temperature and precipitation complexes
over North America. Journal of Applied Meteorology 6:791–
Liebhold, A., J. Elkinton, D. Williams, and R. M. Muzika.
2000. What causes outbreaks of the gypsy moth in North
America? Population Ecology 42:257–266.
Liebhold, A., J. Elkinton, C. Zhou, M. Hohn, R. Rossi, G.
Boettner, C. Boettner, C. Burnham, and M. McManus. 1995.
Regional correlation of gypsy moth (Lepidoptera: Lyman-
triidae) defoliation with counts of egg masses, pupae, and
male moths. Environmental Entomology 24:193–203.
Liebhold, A., and N. Kamata. 2000. Population dynamics of
forest-defoliating insects. Population Ecology 42:205–278.
Liebhold, A., W. D. Koenig, and O. N. Bjørnstad. 2004. Spatial
synchrony in population dynamics. An nual Review of
Ecology, Evolution, and Systematics 35:467–490.
Liebhold, A. M., K. W. Gottschalk, E. R. Luzader, D. A.
Mason, R. Bush, and D. B. Twardus. 1997. Gypsy moth in
the United States: an atlas. General Technical Report NE-
233. Northeastern Forest Experiment Station, USDA Forest
Service, Radnor, Pennsylvania, USA.
Liebhold, A. M., K. J. Haynes, and O. N. Bjørnstad. 2012.
Spatial synchrony of insect outbreaks. Pages 113–125 in P.
Barbose, D. Letourneau, and A. Agrawal, editors. Insect
outbreaks revisited. Wiley-Blackwell, Hoboken, New Jersey,
Liebhold, A. M., D. M. Johnson, and O. N. Bjørnstad. 2006.
Geographic variation in density-dependent dynamics impacts
the synchronizing effect of dispersal and regional stochas-
ticity. Population Ecology 48:131–138.
Liebhold, A. M., R. Plymale, J. S. Elkinton, and A. E. Hajek.
2013. Emergent fungal entomopathogen does not alter
density dependence in a viral competitor. Ecology 94:1217–
Liu, Y., X. San Liang, and R. H. Weisberg. 2007. Rectification
of the bias in the wavelet power spectrum. Journal of
Atmospheric and Oceanic Technology 24:2093–2102.
Maraun, D., and J. Kurths. 2004. Cross wavelet analysis:
significance testing and pitfalls. Nonlinear Processes in
Geophysics 11:505–514.
Martinat, P. J. 1987. The role of climatic variation and weather
in forest insect outbreaks. Pages 241–268 in P. Barbosa and
J. C. Schultz, editors. Insect outbreaks. Academic Press, San
Diego, California, USA.
Mason, C., and M. McManus. 1981. Larval dispersal of the
gypsy moth. The gypsy moth: research toward integrated pest
management. US Department of Agricul ture Technical
Bulletin 1584:161–202.
Moran, P. A. P. 1953. The statistical analysis of the Canadian
lynx cycle II: synchronization and meteorology. Australian
Journal of Zoology 1:291–298.
Myers, J. H., and J. S. Cory. 2013. Population cycles in forest
lepidoptera revisited. Annual Review of Ecology, Evolution,
and Systematics 44:565–592.
Peltonen, M., A. M. Liebhold, O. N. Bjørnstad, and D. W.
Williams. 2002. Spatial synchrony in forest insect outbreaks:
roles of regional stochasticity and dispersal. Ecology 83:
Post, E., and M. C. Forchhammer. 2004. Spatial synchrony of
local populations has increased in association with the recent
Northern Hemisphere climate trend. Proceedings of the
National Academy of Sciences USA 101:92869290.
Ranta, E., V. Kaitala, J. Lindstro
m, and E. Helle. 1997. The
Moran effect and synchrony in population dynamics. Oikos
Ranta, E., V. Kaitala, and P. Lundberg. 1998. Population
variability in space and time: the dynamics of synchronous
population fluctuations. Oikos 83:376–382.
Royama, T. 1992. Analytical population dynamics. Chapman
and Hall, London, UK.
Stenseth, N. C. 1999. Population cycles in voles and lemmings:
density dependence and phase dependence in a stochastic
world. Oikos 87:427–461.
Stenseth, N. C., G. Ottersen, J. W. Hurrell, A. Mysterud, M.
Lima, K.-S. Chan, N. G. Yoccoz, and B. A
dlandsvik. 2003.
Studying climate effects on ecology through the use of
climate indices: the North Atlantic Oscillation, El Nin
Southern Oscillation and beyond. Proceedings of the Royal
Society B 270:2087–2096.
Torrence, C., and G. P. Compo. 1998. A practical guide to
wavelet analysis. Bulletin of the American Meteorological
Society 79:61–78.
Walsh, J. E., D. W. Allen, and M. B. Richman. 1982. Spatial
coherence of monthly precipitation in the United States.
Monthly Weather Review 110:272–286.
Williams, D. W., R. W. Fuester, W. W. Metterhouse, R. J.
Balaa m, R. H. Bullock, and R. Chianesei. 1991. Oak
defoliation and population density relationships for the
gypsy moth. Journal of Economic Entomology 84:1508
Wunsch, C. 1999. The interpretation of short climate records,
with comments on the North Atlantic a nd Southern
Oscillations. Bulletin of the American Meteorological Society
Ecological Archives
Appendices A–E are available online:
ANDREW J. ALLSTADT ET AL.2946 Ecology, Vol. 96, No. 11
... During these outbreaks, L. dispar larvae reach high population levels causing forest defoliation over large regions. These outbreaks have been well-studied and L. dispar population dynamics are characterized by both periodic oscillations and spatial synchrony across large spatial extents (Johnson et al. 2005(Johnson et al. , 2006Allstadt et al. 2013Allstadt et al. , 2015Haynes et al. 2019). ...
... We note that the increase in synchrony from the 1931-1940 interval to the 1975-1984 interval could have arisen as an artefact of the change from mapping defoliation from ground to aerial surveys. Also, observed changes in L. dispar synchrony may reflect changes in the synchrony of weather (Allstadt et al. 2015), so it is difficult to identify the causes of these changes with certainty. Allstadt (2015) analyzed historical defoliation map data from across the L. dispar range from 1975 to 2009 aggregated to 64 km cells. ...
... Also, observed changes in L. dispar synchrony may reflect changes in the synchrony of weather (Allstadt et al. 2015), so it is difficult to identify the causes of these changes with certainty. Allstadt (2015) analyzed historical defoliation map data from across the L. dispar range from 1975 to 2009 aggregated to 64 km cells. This range of years overlapped with our analysis of synchrony in defoliation among New England states from 1924 to 2016 (Fig. 2c). ...
Full-text available
The population dynamics and impacts of non-native species often change following their initial establishment, with impacts either increasing or decreasing over time. The reasons why the abundance of an invading species may change are varied but often reflect changes in the way in which populations interact with resident communities. Here we analyze changes in the outbreak dynamics of Lymantria dispar (formerly known to as the “gypsy moth”), a Eurasian foliage-feeding insect that has been established in N. America for ca. 150 years. We find that during the course of this species’ presence in N. America, it has continually exhibited population dynamics in which populations reach outbreak levels, resulting in defoliation of large forested areas. However, there is evidence of some changes in both the periodicity and synchrony of these outbreaks. We hypothesize that the accidental introduction of an entomopathogenic nucleopolyhedrosis virus around 1906 resulted in populations shifting from a pattern of sustained outbreaks to oscillatory dynamics with periodic outbreaks synchronized over large distances. We analyze historical L. dispar population data that provide some evidence in support of this hypothesis. There is also evidence that the more recent establishment of the fungal pathogen Entomophaga maimaiga has caused a decrease in the amplitude of L. dispar outbreaks since its emergence in 1989.
... Previous studies have documented synchronous fluctuations in abundance for wide-ranging species, including avian species [6,7]. The driving forces behind these synchronous fluctuations are dispersal and environmental effects, including the Moran effect [8], which proposes that fluctuations among populations with the same density-dependent structure are synchronized by strong density-independent factors (typically weather-related) [9,10]. Although the Moran effect was developed to explain fluctuations occurring simultaneously among geographically distinct populations of a single species, it can also be applied to closely related species [11], species with similar density-dependent population structures [9,12], and species with similar life histories [12]. ...
Full-text available
As global temperatures continue to rise, population or spatial synchrony (i.e., the degree of synchronization in the fluctuation of demographic parameters) can have important implications for inter- and intraspecific interactions among wildlife populations. Climatic fluctuations are common drivers of spatial synchrony, and depending on the degree of synchronization and the parameters impacted, synchrony can increase extinction probabilities. Although citizen science is an inexpensive method to collect long-term data over large spatial scales to study effects of climate changes on wildlife, few studies have used citizen science data to determine if this synchrony is occurring across populations and species. We used 21 years of citizen science nesting data collected on Eastern Bluebirds ( Sialia sialis ) and Carolina Chickadees ( Poecile carolinensis ), two widespread North American species with similar life histories and abundant data, to assess the degree of synchrony between and within their populations in the southeastern United States. We found little evidence of synchronous fluctuations in the nesting parameters of hatching success, hatchability, and fledging success between and within species, nor did we observe consistent patterns towards increased or decreased synchrony. Estimates of nesting parameters were high (≥ 0.83) and showed little variability (relative variance ≤ 0.17), supporting the hypothesis that parameters that strongly contribute to population growth rates (i.e., typically fecundity in short-lived species) show little interannual variability. The low variability and lack of synchrony suggest that these populations of study species may be resilient to climate change. However, we were unable to test for synchronous fluctuations in other species and populations, or in the survival parameter, due to large gaps in data. This highlights the need for citizen science projects to continue increasing public participation for species and regions that lack data.
... Resolving these gaps in understanding is urgent in light of accelerating global change. Changes in synchrony are associated with climatic variation (Allstadt et al., 2015;Cattadori et al., 2005;Hansen et al., 2013;Kahilainen et al., 2018;Ong et al., 2016;Post & Forchhammer, 2002, 2004 and recent studies suggest that some systems are becoming more or less synchronous in association with climate trends (Defriez et al., 2016;Di Cecco & Gouhier, 2018;Koenig & Liebhold, 2016;Ojanen et al., 2013). The degree to which climate shifts cause changes in synchrony remains underexplored but is now recognised as likely to be important (Hansen et al., 2020;Özkan et al., 2016). ...
Full-text available
Spatial synchrony is a ubiquitous and important feature of population dynamics, but many aspects of this phenomenon are not well understood. In particular, it is largely unknown how multiple environmental drivers interact to determine synchrony via Moran effects, and how these impacts vary across spatial and temporal scales. Using new wavelet statistical techniques, we characterised synchrony in populations of giant kelp Macrocystis pyrifera, a widely distributed marine foundation species, and related synchrony to variation in oceanographic conditions across 33 years (1987–2019) and >900 km of coastline in California, USA. We discovered that disturbance (storm‐driven waves) and resources (seawater nutrients)—underpinned by climatic variability—act individually and interactively to produce synchrony in giant kelp across geography and timescales. Our findings demonstrate that understanding and predicting synchrony, and thus the regional stability of populations, relies on resolving the synergistic and antagonistic Moran effects of multiple environmental drivers acting on different timescales. Spatial synchrony is a ubiquitous feature of population dynamics, but it is largely unknown how multiple environmental drivers interact to determine synchrony via Moran effects, and how these impacts vary across spatial and temporal scales. Using new wavelet statistical techniques, we characterized synchrony in populations of giant kelp, a widely distributed marine foundation species, and related synchrony to variation in oceanographic conditions. We discovered that disturbance and resources—underpinned by climatic variability—act individually and interactively to produce synchrony across geography and timescales, demonstrating that predicting regional population stability relies on resolving the synergistic and antagonistic Moran effects of multiple environmental drivers acting on different timescales.
... Such synchrony in demographic rates has been demonstrated in other sympatric migratory bird species, for example in productivity and survival in canvasback Aythya valisineria and redhead A. americana ducks (Péron and Koons 2012). We assume that synchrony in demographic rates between sympatric species can be explained by overall similar responses to environmental conditions throughout the annual cycle, consistent with other studies in animal ecology (Rachlow and Bowyer 1991, Ranta et al. 1997, Allstadt et al. 2015. Thus, we anticipate that conservation planning for altering Ross's goose Snow goose Figure 5. Correlations between female snow goose and Ross's goose population growth, adult survival, adult fidelity, juvenile survival, juvenile fidelity and per capita production of young using all posterior samples. ...
Full-text available
Dynamics of free‐ranging animal populations can result from complex interplays of survival, recruitment and movement. Yet incomplete understanding of demography impedes conservation strategies intended to modify population dynamics of focal species. We estimated survival and per capita production of young, as well as emigration and immigration, from 1997 to 2017 in Ross's goose Anser rossii and lesser snow goose Anser caerulescens caerulescens, which are sympatric species of migratory birds that nest in the central Canadian Arctic at one of the largest breeding colonies in North America. We formed age‐structured integrated population models (IPMs) for each species that jointly analyzed live and dead encounter data as well as breeding adult population size and fecundity data to understand drivers of population dynamics. We compared the demography between species because both species increased during the 1990s and early 2000s yet thereafter snow geese declined, while Ross's geese continued to increase, then stabilized and similarly declined. Declines in Ross's and snow goose populations were caused by reduced per capita production of young, and juvenile survival, as well as increased adult and juvenile emigration. Stronger declines in juvenile survival in snow geese explain their earlier population decline compared to Ross's geese. Despite the divergence in population trends in Ross's and snow geese, we found strong synchrony in demographic rates which suggested substantial emigration from this colony and similar responses to environmental conditions. Direct estimation of demographic patterns in the IPM framework permitted hypothesis testing and inference about the role of immigration, even though immigrant sources were unsampled. We provide a novel m‐array implementation specific to a multi‐state Burnham model which greatly improved computational efficiency and convergence of posterior estimates. Our findings are an important reminder of the role that permanent movements can play in animal demography and metapopulation structure.
... It is also noteworthy that dispersal, species interactions, and local population dynamics are likely to be influenced by temporal changes in the hydrological regime. Such temporal variation in the drivers of synchrony could lead to long-term temporal changes in spatial synchrony itself, as reported in other studies (Allstadt et al., 2015;Post & Forchhammer, 2004;Sheppard et al., 2016). ...
Spatial synchrony is the correlation between the temporal dynamics of local populations. This pattern may be driven by spatially correlated environmental variation (i.e., Moran effect), dispersal and trophic interactions. Investigating geographic patterns of synchrony can help disentangle the relative importance of these drivers. Using fish abundance data from long-term ecological research (17 years) in the Upper Paraná River floodplain, we studied the relative roles of dispersal distance, density dependence differences, and environmental synchrony in determining spatial synchrony of the most common species in this floodplain. We also investigated the geography of spatial synchrony by estimating modularity and site-level contributions to synchrony and anti-synchrony networks. We found positive spatial synchrony for most species, but levels were relatively low. For most species, our explanatory matrices were poorly related to spatial synchrony. We detected modular structures in some species networks, which reflected complex spatial patterns in synchrony. We also detected sites with high importance to spatial synchrony patterns that could be managed to increase metapopulation stability. The variable levels of spatial synchrony for fish species in the Upper Paraná River floodplain implies the need to monitor several sites to understand their dynamics in this region. Also, some migratory species of high importance to regional fisheries, such as Prochilodus lineatus, may deserve special monitoring attention due to the increased regional extinction risk associated with their high levels of spatial synchrony. Finally, we speculate that hydrological manipulation from upstream reservoirs should consider the timing of water releases to avoid spatially correlated population declines.
... For instance, species may be synchronous at one timescale and compensatory at other timescales (Downing et al., 2008;Vasseur et al., 2014), they may be synchronous in certain life history stages but asynchronous in others (Lasky et al., 2016), and they may be synchronous under some environmental conditions and asynchronous in others (Xu et al., 2015). A wide range of processes can influence species dynamics and correlations in species fluctuations, including environmental variation (Allstadt et al., 2015;Tredennick et al., 2017), biotic interactions (Pedersen et al., 2016), variability in species demographic rates (Jucker et al., 2014), and dispersal . While all of these processes may affect synchronous versus compensatory dynamics, many have not been explored in a timescalespecific manner. ...
Full-text available
Synchronous dynamics (fluctuations that occur in unison) are universal phenomena with widespread implications for ecological stability. Synchronous dynamics can amplify the destabilizing effect of environmental variability on ecosystem functions such as productivity, whereas the inverse, compensatory dynamics, can stabilize function. Here we combine simulation and empirical analyses to elucidate mechanisms that underlie patterns of synchronous versus compensatory dynamics. In both simulated and empirical communities we show that synchronous and compensatory dynamics are not mutually exclusive but instead can vary by timescale. Our simulations identify multiple mechanisms that can generate timescale‐specific patterns, including different environmental drivers, diverse life histories, dispersal, and non‐stationary dynamics. We find that traditional metrics for quantifying synchronous dynamics are often biased towards long‐term drivers and may miss the importance of short‐term drivers. Our findings indicate key mechanisms to consider when assessing synchronous versus compensatory dynamics and our approach provides a pathway for disentangling these dynamics in natural systems.
... Climate patterns can synchronize population dynamics through space and time (Allstadt et al., 2015;Black et al., 2018;Kilduff et al., 2015;Koenig & Liebhold, 2016;Moran, 1953). For example, synchrony among North American migrating bird populations is related to increased temperature covariance across the continent (Koenig & Liebhold, 2016). ...
Environmental forces can create spatially synchronous dynamics among nearby populations. However, increased climate variability, driven by anthropogenic climate change, will likely enhance synchrony among spatially disparate populations. Population synchrony may lead to greater fluctuations in abundance, but the consequences of population synchrony across multiple scales of biological organization, including impacts to putative competitors, dependent predators, or human communities, are rarely considered in this context. Chinook salmon (Oncorhynchus tshawytscha) stocks distribute across the Northeast Pacific, creating spatially variable portfolios that support large ocean fisheries and marine mammal predators, such as killer whales (Orcinus orca). We rely on a multi‐population model that simulates Chinook salmon ocean distribution and abundance to understand spatial portfolios, or variability in abundance within and among ocean distribution regions, of Chinook salmon stocks across 17 ocean regions from Southeast Alaska to California. We found the expected positive correlation between the number of stocks in an ocean region and spatial portfolio strength; however, increased demographic synchrony eroded Chinook salmon spatial portfolios in the ocean. Moreover, we observed decreased resource availability within ocean fishery management jurisdictions but not within killer whale summer habitat. We found a strong portfolio effect across both Southern Resident and Northern Resident killer whale habitats that was relatively unaffected by increased demographic synchrony, likely a result of the large spatial area included in these habitats. However, within the areas of smaller fishing management jurisdictions we found a weakening of Chinook salmon portfolios and increased but inconsistent likelihood of low abundance years as demographic synchrony increased. We suggest that management and conservation actions that reduce spatial synchrony can enhance short‐term ecosystem resilience by promoting the stabilizing effect multiple stocks have on aggregate Chinook salmon populations and overall resource availability.
... The potential explanation is that less precipitation and lower soil organic matter shaped the grasslands on the western Tibetan Plateau with the characteristics of low productivity and smaller species (Wu et al., 2016). Low-productivity communities generally correspond to less grazing than high-productivity communities (Allstadt et al., 2015). In addition, small species are often more tolerant to livestock grazing than large ones (Osem et al., 2004). ...
Climate change and human activities have profoundly changed the structure and functioning of alpine grassland ecosystems on the Tibetan Plateau, the most critical ecological safety shelter for Asia. However, it remains unclear to what degree human activity intensity has impacted the alpine grasslands of the Tibetan Plateau. Here we quantify human activity intensity on alpine grasslands of the Tibetan Plateau based on the relationship between actual and potential net primary production. We found that human activity intensity decreased by 16.1% from 2000 to 2017 across the alpine grasslands, which might be driven by recent ecological conservation policies, especially reductions in livestock numbers. Critical thresholds, which show marked grassland responses to different levels of human disturbances, were identified for each ecozone. The net primary production of dry grasslands on the western ecozones was more resistant to human disturbances but with lower resilience than other alpine grasslands on the plateau. Our findings are beneficial to design practical countermeasures to adapt to climate change and recover damaged grasslands on Tibetan Plateau.
Full-text available
Knowing pests’ spatiotemporal distribution patterns is essential for forecasting population outbreaks and designing control tactics or long-term management plans. The family Noctuidae is one of the largest families of the Lepidoptera order. The noctuid’s moths are well represented in all zoogeographic regions in various habitats and have immeasurable ecological and economic importance. Although the species’ ecology has been extensively studied, little is known about the spatial and temporal distribution patterns of noctuid moths in an agroecosystem. Therefore, in this study, the spatial and temporal fluctuations in the abundance of 24 important species in the family were quantified. Yellow light traps were mounted in 11 different selected localities of the Multan district. The maximum species abundance was observed in September but declined in December, January, and February. Spatial contour maps were used to determine the species’ dissemination over space. Meteorological factors such as temperature and humidity showed a significantly positive correlation, while rainfall showed a significantly negative correlation, with species richness. The maximum species abundance was recorded in crop areas as compared to forest areas. This study provides a scientific basis for developing and timely applying control strategies for localized pest control.
Full-text available
Recent studies indicate that environmentally-driven (spatial) population synchrony (i.e., the ‘Moran effect’) may change under global warming, affecting extinction probabilities of populations/species. However, the reliability of the few methodologies used to quantify temporal changes in spatial synchrony has not been evaluated yet. We thus confront existing methods, and a new flexible one, with simulations of various population dynamics’ scenarios.
Full-text available
Spatial synchrony, that is, correlated population fluctuation over wide geographical areas, has been detected in diverse taxa and over various geographical scales. The most commonly suggested mechanisms to explain Spatial synchrony include dispersal, and regional stochasticity (i.e., "the Moran effect"). We analyzed landscape-scale historical outbreak data for six forest insect species: spruce budworm (Choristoneura fumiferana), western spruce budworm (C. occidentalis), larch bud moth (Zeiraphera diniana), forest tent caterpillar (Malacosoma disstria), mountain pine beetle (Dendroctonus ponderosae), and gypsy moth (Lymantria dispar). We used a recently developed statistical method (the nonparametric covariance function) for quantifying the magnitude and spatial range of synchrony in both outbreak and corresponding weather data. The varying dispersal capabilities of the species enabled us to speculate on the relative importance of dispersal vs. the Moran effect as potential mechanisms behind the observed patterns. Our results indicated that spatial synchrony was not directly associated with dispersal capabilities at the spatial scales considered. In contrast, the spatial correlation in weather variables was high enough to account for the levels of synchrony observed in the outbreak data. Therefore, the Moran effect appeared to be the more dominant process affecting the spatial dynamics of these species at the landscape scale. In general, however, the synchrony in outbreaks declined more steeply with geographical distance than the correlation in the weather variables, breaking with the predictions of Moran's theorem. A more detailed analysis of gypsy moth outbreak data showed that local dynamics varied considerably in a spatially dependent manner. The existence of such variation violates one of the assumptions of the Moran's theorem, namely, that the dynamic properties of disjunct populations are identical. We used a simple theoretical model to demonstrate that such geographical variation in local population dynamics may indeed force synchrony to decline more rapidly with distance than the correlation in the environment.
In the analysis of data it is often assumed that observations y1, y2, …, yn are independently normally distributed with constant variance and with expectations specified by a model linear in a set of parameters θ. In this paper we make the less restrictive assumption that such a normal, homoscedastic, linear model is appropriate after some suitable transformation has been applied to the y's. Inferences about the transformation and about the parameters of the linear model are made by computing the likelihood function and the relevant posterior distribution. The contributions of normality, homoscedasticity and additivity to the transformation are separated. The relation of the present methods to earlier procedures for finding transformations is discussed. The methods are illustrated with examples.
We explore extinction rates using a spatially arranged set of subpopulations obeying Ricker dynamics. The population system is subjected to dispersal of individuals among the subpopulations as well as to local and global disturbances. We observe a tight positive correlation between global extinction rate and the level of synchrony in dynamics among the subpopulations. Global disturbances and to a lesser extent, migration, are capable of synchronizing the temporal dynamics of the subpopulations over a rather wide span of the population growth rate r. Local noise decreases synchrony, as does increasing distance among the subpopulations. Synchrony also levels off with increasing r: in the chaotic region, subpopulations almost invariably behave asynchronously. We conclude that it is asynchrony that reduces the probability of global extinctions, not chaos as such: chaos is a special case only. The relationship between global extinction rate, synchronous dynamics and population growth rate is robust to changes in dispersal rates and ranges.
Evaluates the hypothesis that if a climatic anomaly that favours an increase in fecundity and/or survival persists over several consecutive generations, its effects on a forest insect population may be multiplicative, and after some years of continuous increase the "released' population will cause noticeable defoliation. Mechanisms by which weather might cause changes in forest insect abundance are outlined; indirect effects are more likely to be significant, eg by influencing the level of stress in the host plant, which in turn affects its nutritional quality, chemical defences or digestibility. Outbreaks of spruce budworm Choristoneura fumiferana, forest tent caterpillar Malacosoma disstria and southern pine beetle Dendroctonus frontalis are used as examples. The nature of temporal and spatial variation in climatic patterns also needs to be introduced into analysis and interpretation. On balance, there is probably a rather low upper limit on the amount of variability in pest population levels that can be explained by weather variables. -P.J.Jarvis
When Keith (1963) published his ‘Wildlife’s 10-year cycle’, available information on the theme was minimal. Many theories were no more than conjectures. In 1961, realizing that further theorizing would get him nowhere, Keith and a team of researchers from the Wisconsin school of wildlife ecology, launched a long-term field study on snowshoe hare (Lepus americanus) populations near Rochester, Alberta. A number of important papers from this study have appeared since then, including the monograph (Keith and Windberg, 1978) that provides a nearly complete 15-year set of demographic data. I shall call this work ‘the Rochester study’.