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\begin{document}

\title{Four times out of Europe: serial invasions of the winter moth,
Operophtera brumata, to North America}



\author[1]{Jeremy Andersen}%
\author[2]{Nathan Havill}%
\author[3]{Adalgisa Caccone}%
\author[1]{Joseph Elkinton}%
\affil[1]{University of Massachusetts Amherst}%
\affil[2]{USDA Forest Service}%
\affil[3]{Yale University}%


\vspace{-1em}



  
  \date{June 02, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Reconstructing the geographic origins of invasive species is critical
for establishing effective management strategies. Frequently, molecular
investigations are undertaken when the source population is not known,
however; these analyses are constrained both by the amount of diversity
present in the native region and by changes in the genetic background of
the invading population following bottlenecks and/or hybridization
events. Here we explore the geographical origins of the invasive winter
moth (Operopthera brumata L.) that has caused widespread defoliation to
forests, orchards, and crops in four discrete regions: Nova Scotia,
British Columbia, Oregon, and the northeastern United States. It is not
known whether these represent independent introductions to North
America, or ``stepping stone'' spread among regions. Using a combination
of Bayesian assignment and approximate Bayesian computation methods, we
analyzed a population genetic dataset of 24 polymorphic microsatellite
loci. We estimate that winter moth was introduced to North America on at
least four occasions, with the Nova Scotian and British Columbian
populations likely being introduced from France and Sweden,
respectively; the Oregonian population likely being introduced from
either the British Isles or northern Fennoscandia; and the population in
the northeastern United States likely being introduced from somewhere in
Central Europe. To our surprise, we found that hybridization has not
played a large role in the establishment of winter moth populations even
though previous reports have documented widespread hybridization between
winter moth and a native congener. We discuss the impact of genetic
bottlenecks on analyses meant to determine region of origin.%
\end{abstract}%



\sloppy


\textbf{Title:} Four times out of Europe: serial invasions of the winter
moth, \emph{Operophtera brumata} , to North America

\textbf{Short Title:} Serial invasions of the European winter moth

\textbf{Authors:} Jeremy C. Andersen\textsuperscript{1,*}, Nathan P.
Havill\textsuperscript{2}, Adalgisa Caccone\textsuperscript{3}, Joseph
S. Elkinton\textsuperscript{1}

\textbf{Affiliations:}

\textsuperscript{1}Department of Environmental Conservation, University
of Massachusetts, Amherst

\textsuperscript{2}Northern Research Station, USDA Forest Service,
Hamden, Connecticut

\textsuperscript{3}Department of Ecology \& Evolutionary Biology, Yale
University, New Haven, Connecticut

\textsuperscript{*} Corresponding Author email: jcandersen@umass.edu

\textbf{Abstract:} Reconstructing the geographic origins of invasive
species is critical for establishing effective management strategies.
Frequently, molecular investigations are undertaken when the source
population is not known, however; these analyses are constrained both by
the amount of diversity present in the native region and by changes in
the genetic background of the invading population following bottlenecks
and/or hybridization events. Here we explore the geographical origins of
the invasive winter moth (\emph{Operopthera brumata} L.) that has caused
widespread defoliation to forests, orchards, and crops in four discrete
regions: Nova Scotia, British Columbia, Oregon, and the northeastern
United States. It is not known whether these represent independent
introductions to North America, or ``stepping stone'' spread among
regions. Using a combination of Bayesian assignment and approximate
Bayesian computation methods, we analyzed a population genetic dataset
of 24 polymorphic microsatellite loci. We estimate that winter moth was
introduced to North America on at least four occasions, with the Nova
Scotian and British Columbian populations likely being introduced from
France and Sweden, respectively; the Oregonian population likely being
introduced from either the British Isles or northern Fennoscandia; and
the population in the northeastern United States likely being introduced
from somewhere in Central Europe. To our surprise, we found that
hybridization has not played a large role in the establishment of winter
moth populations even though previous reports have documented widespread
hybridization between winter moth and a native congener. We discuss the
impact of genetic bottlenecks on analyses meant to determine region of
origin.

\textbf{Keywords:} Approximate Bayesian computation, region of origins,
invasive species, biosecurity

\textbf{Introduction:}

In light of the unprecedented number of introductions of nonnative
species (Mack et al., 2000), one of the most pressing research needs for
evolutionary biologists and ecologists is to identify the factors that
influence the establishment of species that have negative ecological and
economic impacts (Suarez \& Tsutsui, 2008). Multiple introductions
(Dlugosch \& Parker, 2008), including cryptic ones (Roman, 2006), are
thought to play an important role in providing the diversity required to
overcome genetic bottlenecks associated with the establishment of
populations in novel ecosystems (Darling, Bagley, Roman, Tepolt, \&
Geller, 2008; Facon, Pointier, Jarne, Sarda, \& David, 2008). However,
when multiple geographically disjunct populations of an invasive species
become established, it is often unclear whether the species is a serial
invader (i.e., each population was introduced independently) or whether
the separate populations represent establishment from within the
invasive regions under a ``stepping stone'' model (see Cerwenka,
Alibert, Brandner, Geist, \& Schliewen, 2014; Lombaert, Guillemaud,
Cornuet, Malausa, Facon, \& Estoup, 2010; Oficialdegui et al., 2019;
Tonione, Reeder, \& Moritz, 2011 for examples). Identifying which mode
of introduction occurred (serial invader or stepping stone) is necessary
for the study of genetic and ecological factors that drive invasion
success as independent populations are necessary for robust
hypothesis-based testing (Kang, Buckley, \& Lowe, 2007), and this
information is also crucial for focusing management efforts (Floerl,
Inglis, Dey, \& Smith, 2009).

When reconstructing regions of origins, and determining the numbers of
introductions of a focal organism, ideally historical records should be
observed and robust genetic analyses performed (e.g., Lynch \&
Saltonstall, 2002; Schwenk, Brede, \& Streit, 2008). Unfortunately,
historical records may not exist for all introduced species, and it is
not uncommon for an introduced species to go unnoticed for long periods
of time before becoming an invasive pest. Genetic analyses have the
ability to independently reconstruct regions of origins, and in some
instances provide estimates for the times of introductions
(Auger-Rozenberg et al., 2012; Barker, Andonian, Swope, Luster, \&
Dlugosch, 2017; Javal et al., 2019; Lesieur et al., 2019; Lombaert et
al., 2010; Oficialdegui et al., 2019; Zardus \& Hadfield, 2005).
However, the power of these analyses are constrained by numerous factors
including the underlying genetic structure of the species, the number of
generations since the introduction, the effective size of the founding
population(s), the strength of the bottleneck the population(s)
experienced, and/or the presence of differing selective pressures in the
native and introduced regions. As such, one common finding is for
introduced populations to be reconstructed as genetically ``distinct''
from all sampled source populations (e.g., Barker et al., 2017; Wu et
al., 2015). This result could be due to the tendency for commonly
implemented Bayesian genetic clustering algorithms to over-split
populations (Frantz, Cellina, Krier, Schley, \& Burke, 2009) or an
artifact generated during the interpretation of results (Lawson, Van
Dorp, \& Falush, 2018).

Here we explore the invasion history of the economically damaging
defoliator the winter moth, \emph{Operophtera brumata} L. (Lepidoptera:
Geometridae). In its native distribution across Europe, North Africa,
and western Asia, winter moth defoliates a wide range of tree and shrub
species (Ferguson, 1978). Populations of winter moth in Europe have been
used as a model for the study of population ecology (Varley, Gradwell,
\& Hassell, 1973), and this species has been critically important for
understanding the importance of spatial-synchrony (Jepsen et al., 2009)
and synchrony of hatch with host tree bud-burst (Embree, 1965 ,Varley \&
Gradwell, 1960, Visser \& Holleman, 2001) -- a factor studied in other
invasive defoliator populations as well (e.g. Hunter \& Elkinton, 2000).
The invasion history of winter moth in North America has been well
documented, with populations of winter moth first reported in the 1930's
in Nova Scotia (Embree, 1967; MacPhee, 1967; MacPhee, Newton, \& McRae,
1988), the 1950's in Oregon (Kimberling, Miller, \& Penrose, 1986), the
1970's in British Columbia (Gillespie, Finlayson, Tonks, \& Ross, 1978),
and in the 1990's in coastal regions of northeastern United States
(Elkinton et al., 2010; Elkinton, Liebhold, Boettner, \& Sremac, 2014).
These populations are thought to have been introduced by the movement of
infected nursery stocks (Ferguson, 1978). However, where in Eurasia
these populations were introduced from, and whether these represent a
single introduction that was then spread across North America, or
multiple introductions (or some combination of these) is unclear.
Previously, a genetic examination of the invasion history of winter moth
in North America was conducted, but was unable to discern these patterns
due to low levels of mitochondrial DNA diversity in both introduced and
native samples (Gwiazdowski, Elkinton, DeWaard, \& Sremac, 2013).

To overcome this limitation, we examine the invasion history of winter
moth in North America using polymorphic microsatellite loci amplified
from individuals collected across its native and introduced regions. We
specifically examine how many times winter moth was introduced to North
America, and when possible, determine the specific source location.
Lastly, we comment on the role of hybridization between winter moth and
a North American congener the Bruce spanworm (\emph{O. bruceata} Hulst),
and the effects of genetic bottlenecks on the establishment of invasive
winter moth populations.

\textbf{Materials and Methods:}

\emph{Sample collection}

Winter moth males were collected using pheromone-baited traps (Elkinton
et al., 2010; Elkinton, Lance, Boettner, Khrimian, \& Leva, 2011) from
locations in Europe, North Africa, and western Asia, as well as from the
four regions in North America, where established winter moth populations
have been recorded (Nova Scotia, British Columbia, Oregon, and the
northeastern United States, Figure 1). In addition, larval individuals
and adult females, which are wingless and do not fly, were
opportunistically collected (see supplemental Appendix S1 Table S1 for
complete collection information, including life stages).

After collection, adult moths were placed in glassine envelopes (Uline
Corporation, USA) and stored at either -20\selectlanguage{ngerman}°C or -80°C, and larval
caterpillars were placed in 95\% ethanol and stored at -20°C. For many
of the moths included in our analysis, collection and genotype
information was previously reported (e.g., Andersen, Havill, Caccone, \&
Elkinton, 2017; Andersen et al., 2019a,b, In Press) (Supplemental
Appendix S1 Table S1).

\emph{Microsatellite genotyping}

Genomic DNA was extracted using the EZNA® Tissue DNA extraction kit
(Omega Bio-tek; Norcross, Georgia), following the manufacturer
protocols. For adult males, prior to extraction, the wings and genitalia
were removed and stored as vouchers. For adults and larvae, the
remaining body parts were then homogenized, using 3/16'' stainless steel
beads (GlenMills Inc.; Clifton, New Jersey) with a FastPrep-24 Sample
Homogenizer (MP Biomedicals, Santa Ana, California). After extraction,
24 polymorphic microsatellite loci (Havill et al., 2017) were genotyped
at the DNA Analysis Facility on Science Hill at Yale University, using a
Thermo Fisher Scientific 3730xl DNA Analyzer. Fragment lengths were
determined using the microsatellite plugin in the software program
Geneious v. R11 (https://www.geneious.com) in comparison to the GeneScan
500 LIZ size standard (Thermo Fisher Scientific; Waltham,
Massachusetts).

Only individuals from which \selectlanguage{english}[?] 20 microsatellite loci were successfully
amplified were included in analyses. In addition, since winter moth has
been reported to hybridize with Bruce spanworm in all of its invaded
regions (Andersen et al., 2019a) the dataset was further filtered to
remove hybrids by comparing assignment probabilities based on 12
polymorphic loci that co-amplify in both species (described below).
Microsatellite genotypes are provided as a tab-delimited
Structure-formatted supplemental file titled
``WinterMothOriginsStructure.txt''.

\emph{Population genetics statistics}

For each locality in Europe, North Africa, and western Asia from which
\selectlanguage{english}[?]10 winter moth individuals were collected, standard population genetic
statistics were estimated from the microsatellite genotypes scores,
using GenoDive (Meirmans \& Van Tienderen, 2004). In the introduced
region, we prioritized sampling a small number of individuals from a
large number of locations in each region to obtain a broader
representation of genetic diversity (see Suarez \& Tsutsui, 2008).
Null-allele frequencies for each locus were estimated using Dempsters EM
method as implemented in GenePop (Raymond \& Rousset, 1995; Rousset,
2008).

\emph{Bayesian sample assignment}

To assign individuals to genetic clusters, a two-step approach was
taken. First, genotypes for all North American samples were added to the
dataset presented in Andersen et al. (2019a), and the probability of
assignment (\emph{Q} ) of sampled individuals to one of two distinct
genetic clusters (\emph{K} ) representing either pure winter moth or
pure Bruce spanworm was calculated using Structure v.2.3.2 (Falush,
Stephens, \& Pritchard 2003; Pritchard, Stephens, \& Donnelly, 2000).
These analyses were based on the analysis of 12 polymorphic
microsatellite loci that co-amplify between the two species, and ten
independent analyses were run using the admixture model, correlated
allele frequencies, and default settings, with random starting values,
runtimes of 1,000,000 generations, and burn-in periods of 100,000
generations. Results were then summarized across runs using Clumpak
(Kopelman, Mayzel, Jakobsson, Rosenberg, \& Mayrose, 2015), and hybrid
individuals were identified as those receiving scores of \emph{Q}
\textless{} 0.75 to both the Bruce spanworm and the winter moth genetic
clusters. Hybrid individuals were then removed from the dataset, and the
filtered dataset (\selectlanguage{english}[?] 20 polymorphic loci for each individual) was used to
estimate values of \emph{Q} for all individuals (both native and
introduced regions) for values of \emph{K=} 2 through\emph{K} = 14 in
Structure using the run parameters described above. To determine the
optimal number of clusters present in the dataset, the \selectlanguage{english}[?]\emph{K}
statistic (Evanno, Regnaut, \& Goudet, 2005) was calculated in
StructureHarvester (Earl \& vonHoldt, 2012), and independent runs were
again summarized for major and minor partition schemes using Clumpak.

For each value for \selectlanguage{english}[?]\emph{K} with a distinct peak representing a
positive rate of change identified using StructureHarvester, the
summarized `popfile' of cluster membership coefficients for the major
mode calculated in Clumpak was used to create a distance matrix using
the `dist' function in R v. 4.0.0 (R Core Team, 2020). The resulting
matrices were then used to calculate `NeighborNet' networks using
SPLITSTREE v.4.14.2 (Huson \& Bryant, 2006), and the outputs were
examined to identify geographic patterns.

\emph{Approximate Bayesian computation}

To determine whether populations of North American winter moth in
distinct geographic regions were the result of a single introduction to
Nova Scotia (the first introduced region recorded in North America) that
was then subsequently spread to additional locations in North America
(i.e., following a stepping-stone model), or whether each invasive
population represents a novel introduction (i.e., a serial introduction
model), or some combination of these, we compared the relatedness of
each invasive population to each other and to the ``Eastern European'',
``Central European'', and ``Western European'' winter moth genetic
clusters previously reported in Andersen et al. (2017, In Press) using
approximate Bayesian computation (ABC), as implemented in the software
program DiyABC v.2.1.0 (Cornuet et al., 2008). For these analyses,
thirty individuals were selected randomly from each of the three
European clusters and from each of the four invasive regions. Ideally,
we would be able to perform comparisons of all possible scenarios that
include representatives from all native clusters and invasive regions,
however; the number of possible scenarios increases at an unmanageable
rate with each taxon added (e.g., there are 10,395 possible
``scenarios'' in a seven-taxa analysis). Therefore, we utilized an
approach similar to ``tournament-ABC'' presented in (Stone et al.,
2017).

As in Stone et al. (2017), we use a series of hierarchical ABC analyses
where subsets of scenarios are first compared in ``tournaments'' to
reduce computational complexity. Here, we first fixed the relationship
among the Eastern, Central, and Western European genetic clusters
following Andersen et al. (2017), where it was determined that the
Central European cluster was likely the result of admixture between the
Eastern and Western clusters following the post-glacial recolonization
of the European continent after the last glacial maximum. To this
topology, we also added an unsampled ``ghost'' population to represent a
possible extra-European origin for each invasive population. Tournament
scenarios were then built sequentially, following the documented order
of the invasion history (graphical representations of scenarios from
each tournament are presented in Supplemental Appendix Figures S1-S4).
The first tournament compared four scenarios where the Nova Scotia
population could have originated from one of the European clusters or
the extra-European ``ghost'' population. In the second tournament, five
scenarios were compared testing the relationship of the Oregon
population to each putative source population with the relationship of
the Nova Scotia population set based on the ``best'' scenario from
Tournament 1. In the third tournament, six scenarios were compared
testing the relationship of the British Columbia population to each
putative source population with the relationships of the Oregon and Nova
Scotia populations set based on the ``best'' scenario from Tournament 2.
Finally, in the fourth tournament, seven scenarios were compared testing
the relationship of the Northeastern United States population to each
putative source population with the relationship of the British
Columbia, Oregon, and Nova Scotia populations set based on the ``best''
scenario from Tournament 3. For each tournament, a reference table of
1,000,000 generations per scenario was generated. Under each scenario we
included multiple parameters to allow for changes in population sizes,
following splitting/merging events, and included the potential for a
genetic bottleneck for each invasive population, default mutation model
parameters, the minimum mean mutation rate set to 1 x
10\textsuperscript{-5}, and maximum values for the mean and individual
locus coefficient P's were both set to 1.0. As per Andersen et al.
(2017, In Press), we removed four loci with especially large allelic
ranges (02339, 00925, 02191, and 12042) to improve the shape of the
cloud of simulated datasets. We calculated three one sample summary
statistics (mean number of alleles, mean genetic diversity, and mean
size variance) and three two sample summary statistics (\emph{F}
\textsubscript{ST}, classification index, and
{[}d\selectlanguage{english}\selectlanguage{greek}µ{]}\textsuperscript{2} distance). For each tournament, the scenario
representing the ancestral origin of each invasive population was
determined by comparing the results from the \emph{Logistic
Regression}test implemented in DiyABC based on comparisons of 1\% of
simulated datasets closest to the observed data. Model checking for each
tournament was performed by comparing the results from a principle
components analysis (PCA) that included the supported scenario as part
of the \emph{Perform Model Checking} analysis.

\textbf{Results:}

\emph{Microsatellite genotyping}

After filtering to include only individuals with genotype scores from [?]
20 microsatellite loci, 1,588 samples were retained for subsequent
analyses. When the North American samples were analyzed using the 12
polymorphic microsatellite loci that co-amplify between Bruce spanworm
and winter moth, four individuals were classified as being Bruce
spanworm and four individuals were identified as probable hybrids. The
final dataset therefore included 1,580 pure winter moth individuals.

\emph{Population genetics statistics}

Standard population genetic statistics were calculated for 53
populations from the native distribution of winter moth, as well as from
each of the four invasive North American populations (Supplemental
Appendix S1 Table S2). Populations had on average 7.8 alleles per locus
(\selectlanguage{ngerman}± 1.71 alleles per locus), with the invasive populations having equal
to, or greater allelic diversity than the native populations (average of
8.06 ± 2.05 alleles per locus). The greatest allelic diversity was
observed in the population from Pan\selectlanguage{polish}č\selectlanguage{english}evo, Serbia (average of 12.04
alleles per locus), and the population with the lowest allelic diversity
was Reykjav\selectlanguage{ngerman}ík, Iceland (average of 3.42 alleles per locus). As per
previous winter moth population genetic analyses, all populations showed
evidence of deviations from Hardy-Weinberg Equilibrium (P \textless{}
0.05 for all).

\emph{Bayesian sample assignment}

On average, negative log-likelihood scores for the independent Structure
runs increased from \emph{K} = 2 through \emph{K} = 13, before
decreasing at \emph{K} = 14 (Supplemental Appendix S1 Figure S5). Based
on the \selectlanguage{english}[?]\emph{K} method implemented in StructureHarvester, the optimal
partition scheme was determined to be \emph{K} = 3 (Supplemental
Appendix S1 Figure S6). However additional peaks, potentially
representing additional partition schemes, were detected at \emph{K =}
6, \emph{K} = 8, and \emph{K} = 13. Individual probabilities of
assignment (\emph{Q} ) for major modes for values of \emph{K =} 3,
\emph{K =} 6, \emph{K} = 8, and \emph{K} = 13 (Figure 2) show the
clustering of the invasive populations relative to those in the native
range. Major modes for values of \emph{K=} 2 through\emph{K} =14 are
presented in Supplemental Appendix S1 Figure S7. A summary of the
biogeographic patterns based on the distance matrix analysis of the
population membership coefficients (Structure ``popfiles'') for \emph{K
=} 6, \emph{K} = 8, and \emph{K} = 13 are presented graphically in
Supplemental Appendix S1 Figure S8, Figure 3, and Supplemental Appendix
S1 Figure S9, respectively.

\emph{Approximate Bayesian computation}

Tournament comparisons of invasion scenarios indicated that each of the
four invasive populations in north America were more closely related to
populations from Europe than to each other, or to an unsampled
extra-European ``ghost'' population, suggesting four separate
introduction events from Europe for winter moth (Figure 4). Comparison
of the Nova Scotia population to the Western European, Central European,
and Eastern European genetic clusters, indicated that it was most likely
introduced from Central Europe (Supplemental Appendix S1 Figure S10a),
and this relationship received high support based on logistic regression
analysis (P = 0.98). The Oregon population most likely originated from
Western Europe (Supplemental Appendix S1 Figure S10b), and this
relationship received high support based on logistic regression analysis
(P = 0.96). The British Columbia population most likely represents an
additional independent introduction from Central Europe (Supplemental
Appendix S1 Figure S10c), and this relationship received high support
based on the logistic regression analysis (P = 1.00). The population in
the northeastern United States population was also reconstructed as a
third introduction from Central Europe (Figure 4), and this relationship
was also highly supported (P = 1.00). Based on examinations of the
posterior estimates, each of the invasive populations experienced a
strong genetic bottleneck when they diverged from European populations
\textasciitilde{}100 ya (Supplemental Appendix S1 Table S3).
Visualization of the PCAs for the supported scenario from each
tournament based on the \emph{Perform Model Checking} analysis in
DiyABC, indicated that posterior values from simulated datasets formed a
distinct cloud encompassing the sample dataset (Supplemental Appendix S1
Figures S11 through S14).

\textbf{Discussion:}

Reconstructing the invasion pathways for non-native pests represents a
critically important step for the prevention of additional introductions
(Le Roux \& Wieczorek, 2009), and can help the implementation of
biosecurity programs for particular pest species and their relatives by
identifying the most likely entry routes (e.g., Maxwell, Vettraino,
Eschen, \& Andjic, 2014). Moreover, reconstruction of the invasion
history is crucial for effective biological control, as it enables the
identification of regions from which to evaluate natural enemies (e.g.,
Goolsby et al., 2006). For evolutionary and ecological studies of
factors that influence the probability of establishment of invasive
species and how non-native species adapt to their introduced
environments and ecosystems, (Allendorf \& Lundquist, 2003; Dlugosch \&
Parker, 2008; Lavergne \& Molofsky, 2007), identifying the number of
introductions of an invasive organism is critical (Sakai et al., 2001).
Unfortunately, reconstructing the invasion histories of non-native
organisms can both computationally demanding and/or biologically
untenable due to the combined effects of genetic bottlenecks,
hybridization, and rapid evolution (Buhk \& Thielsch, 2015; Ficetola,
Bonin, \& Miaud, 2008; McEvoy, Higgs, Coombs, Karcetin, \& Starcevich,
2012; Mesgaran et al., 2016; Prentis, Wilson, Dormontt, Richardson, \&
Lowe, 2008). Using a combination of Bayesian clustering and approximate
Bayesian computation methods, we find that invasive populations of
winter moth in Nova Scotia, British Columbia, and the northeastern
United States were all introduced separately from Central Europe, and
that the invasive population in Oregon was introduced from Western
Europe (Figures 3 and 4). Distance analyses of the coefficient of
membership assignments from our Bayesian clustering analyses, suggest
that the invasive population in Nova Scotia is most closely related to a
population of winter moth in Orleans, France, and that the invasive
population in British Columbia is most closely related to a population
of winter moth in Uggvallen, Sweden (Figure 3), representing potential
source localities for both Canadian populations.

The relationships of the American populations were less clear based on
distance analyses, however, with the Oregon population being closely
related to a large number of populations from the British Isles and
northern Fennoscandia, and the northeastern United States population
being unrelated to any sampled European population. In a recent study of
winter moth in Fennoscandia, we determined that the population there was
introduced to the region \textasciitilde{}2,000 ya from the British
Isles, either via dispersal across the North Sea or by human-mediated
dispersal (Andersen et al. In Press). Therefore, without finer-scale
genomic analyses (e.g., genotype-by-sequencing), we will unlikely be
able to determine which of these two locations (British Isles or
northern Fennoscandia) are the source of the Oregon population. The
northeastern United States population, in contrast to all other sampled
invasive populations, was clearly distinct from other winter moth
populations, including the invasive population in Nova Scotia that can
be found only a short distance away across the Bay of Fundy. While it is
possible that we have yet to sample the source of this invasive
population, given our extensive sampling of the native distribution of
winter moth, we believe this is unlikely. For example, the only regions
that we did not sample from which winter moth has previously been
reported are Japan, Taiwan, and the Russian far-east (Troubridge \&
Fitzpatrick, 1993), and in those locations, records of winter moth are
most likely misidentifications of different species that are native to
those regions (Nakajima, 1991). In addition, our inclusion of an
unsampled ``ghost'' population in our DiyABC analyses to represent a
possible extra-European source was not supported in any tournament (P \selectlanguage{english}[?]
0.01 in all analyses). Lastly, as part of ongoing efforts to study the
evolution of the genus \emph{Operophtera} , we have worked with
collaborators in both the Russian far-east and in Japan to collect
samples using traps baited with the winter moth sex-pheromone, and based
on preliminary DNA-barcoding results all samples that were collected in
these regions have been native \emph{Operophtera} species (NPH
unpublished data). Therefore, we believe that the genetic distinctness
of the northeastern United States population is likely the result of a
strong genetic bottleneck and/or rapid-local adaptation following its
introduction from Central Europe.

\emph{Hybrid origins}

Hybridization has long been known to play an important role in the
evolutionary trajectories of species and populations (Allendorf, Leary,
Spruell, \& Wenburg, 2001), and the promotion of the establishment of
invasive species (e.g., Allendorf \& Lundquist, 2003; Benvenuto,
Cheyppe-Buchmann, Bermond, Ris, \& Xavier, 2012; Mesgaran et al., 2016;
Sakai et al., 2001). Soon after the discovery of an invasive population
of winter moth in the northeastern United States, hybridization between
the non-native winter moth and the native Bruce spanworm was
demonstrated by sequencing the G6PD nuclear gene (Elkinton et al., 2010;
2014). Subsequent studies have found that multigenerational
hybridization is occurring between these two species in the northeastern
United States (Havill et al., 2017), and that hybridization between the
two species has occurred in all of the locations that winter moth has
established (Andersen et al., 2019a). In a recent study along a transect
running west (primarily Bruce spanworm) to east (primarily winter moth)
in Massachusetts with traps spaced approximately 10 km apart,
\textasciitilde{}1\% of surveyed individuals were hybrids though in a
distinct hybrid zone between the two species hybridization rates of over
10\% were reported at several locations (Griffin, Chandler, Andersen,
Havill, \& Elkinton, In Press). Therefore, we were surprised that only
four individuals among our samples were classified as hybrids,
suggesting that hybridization has not played a role in the establishment
of winter moth populations, however, this result could be an artifact of
our analyses given that only 12 of the sampled 24 loci have been shown
to consistently co-amplify between the two species (Havill et al.,
2017). Alternatively, given that the only hybrid individuals were
detected in Oregon, a region from which winter moth has virtually
disappeared after its initial establishment, it is also possible that
some type of hybridization to extinction may be occurring in this
system. This possibility needs to be examined further, perhaps with
genome scans to look for introgression between the species, as it could
present an example of hybridization between native and non-native
species having a positive impact, counter to the ``hybridization to
extinction'' paradigm that puts the overwhelming emphasis on risks to
native species (Rhymer \& Simberloff, 1996).

\emph{The effects of genetic bottlenecks}

Genetic bottlenecks play an important role in the establishment of
invasive species (Dlugosch \& Parker, 2008; Suarez \& Tsutsui, 2008),
with numerous examples of instances where multiple introductions have
been important for overcoming propagule pressures (Kolbe et al., 2004;
Lavergne \& Molofsky, 2007; Simberloff, 2009) and even an example of how
bottlenecks may have aided the establishment of an invasive species
(Tsutsui, Suarez, Holway, \& Case, 2000). Interestingly, here we find
evidence for multiple introductions of winter moth to North America, and
that all four invasive populations have experienced dramatic bottlenecks
in terms of the reductions of their effective population sizes
(Supplemental Appendix S1 Table S3). Yet, we find no evidence for
reductions in genetic diversity of these populations, as all invasive
populations had as great or greater allelic diversity than populations
found from across Europe (Supplemental Appendix S1 Table S2). As such,
winter moth represents an ideal system to conduct comparative analyses
on factors that influence establishment and ecological impact as each
introduced population represents a unique and independent data point.

\emph{Distance analyses as a complement to ABC analyses}

Historically, straightforward phylogenetic methods have been used to
reconstruct the origins of invasive populations, particularly asexual
organisms (e.g., Havill, Montgomery, Yu, Shiyake, \& Caccone, 2006; Qin
\& Gullan, 1998). However, for sexual organisms where recombination and
larger effective population sizes makes the results from phylogenetic
inference ambiguous, a popular workflow for determining the origin of an
introduced population includes the following steps: 1) to identify
distinct genetic clusters either using Bayesian algorithms such as those
implemented in Structure, FastStructure (Raj, Stephens, \& Pritchard,
2014), and Admixture (Alexander \& Lange, 2011), and/or to use measures
of genetic distance (e.g., Latreille, Milesi, Magalon, Mavingui, \&
Atyama, 2019; Negawo et al., 2020; Rahi et al., 2020); 2) to create a
random subset of equal-numbered individuals from each genetic or
geographic cluster; and 3) to compare potential introduction scenarios
using approximate Bayesian computation. Unfortunately, methods for the
interpretation of ``admixed'' populations (i.e., populations with mixed
probabilities of assignment) are needed as populations with assignment
to multiple genetic clusters is a common result (as reviewed in Lawson
et al., 2018). We believe that distance-based clustering of the
population coefficients of assignment from Bayesian clustering
algorithms (such as the Structure `popfiles') presents a rapid and
useful approach for the reconstruction of the regions of origins of
nonnative populations, particularly when populations in the native range
are highly admixed and/or have limited genetic diversity, as we saw with
populations of winter moth. This approach is particularly attractive in
that it is almost instantaneous (after clustering runs have completed
that is). Additionally, the approach removes the need for the
investigator to define arbitrary cutoffs for population assignments. For
example, in instances when individuals have mixed probabilities of
assignment based on Bayesian assignment (e.g., \selectlanguage{english}\emph{Q [?]} 0.75 to any
one cluster when averaged across Structure runs), assigning samples or
populations to distinct clusters might not be possible visually but is
trivial for distance-based clustering algorithms, like the one
implemented in R.

\emph{Conclusions}

Here we find that winter moth is a serial invader of North American
forests and orchards, with at least four introductions from Europe.
These populations were introduced from a diversity of locations in
Western and Central Europe. Most notable is the fact that populations in
Nova Scotia and the Northeastern United States are genetically distinct
from each other, despite having only \textasciitilde{} 300 km separating
surveyed populations in Maine and Nova Scotia. Given the availability of
a sequenced genome (Derks et al., 2015), and its historical use in
population ecology (Varley \& Gradwell 1960; Varley et al., 1973), we
hope that our work encourages the use of winter moth as a model organism
for comparative studies of the genomic factors that influence the
establishment of invasive species. Lastly, we hope that our method for
the interpretation of Structure results can provide rapid and accurate
inferences into the geographic regions of origins of non-native species.

\textbf{Acknowledgements:}

The authors would like to thank the many winter moth enthusiasts who
helped collect samples throughout this research project. A complete list
of all collaborators can be seen in Supplemental Appendix S1 Table S1.
We would specifically like to thank Jeff Boettner for his many years of
organizing and spearheading winter moth collection events, DeAdra Newman
and Brian Griffin for laboratory assistance, and Michelle Labbe and
Rodger Gwiazdowski for comments on earlier versions of this manuscript.
We would also like to thank Ron Weeks at USDA APHIS for encouraging our
research into the population genetics of winter moth. Funding was
provided by grants from USDA APHIS AP17PPQS\&T00C068, AP18PPQS\&T00C070,
and AP19PPQFO000C125, awarded to JSE, and USDA Forest Service, Northern
Research Station award 17-CR-11242303-066 to AC.

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\textbf{Data Accessibility:}

Genotype scores for all samples are provided in the Structure-formatted
supplemental file titled ``WinterMothOriginsStructure.txt''.

\textbf{Author Contributions:}

All authors contributed equally to the writing of the manuscript. JCA
and NPH performed genotyping, JCA conducted analyses, AC provided
laboratory access, and JSE coordinated sample collection and secured
funding.



\textbf{Tables and Figures:}

\textbf{Hosted file}

\verb`image1.emf`  available at \url{https://authorea.com/users/388368/articles/503181-four-times-out-of-europe-serial-invasions-of-the-winter-moth-operophtera-brumata-to-north-america}

\textbf{Figure 1.} Winter moth sample localities in the Pacific
Northwest (top left); northeastern United States and Nova Scotia (top
right); and in Europe, North Africa, and western Asia. Sample localities
are colored following the results presented in Figure 3, except that the
Icelandic, Spanish, Tunisian, southern Italian, and Georgian populations
are shaded roughly following their assignments for \emph{K} =13 in
Figure 2.

\textbf{Hosted file}

\verb`image2.emf`  available at \url{https://authorea.com/users/388368/articles/503181-four-times-out-of-europe-serial-invasions-of-the-winter-moth-operophtera-brumata-to-north-america}

\textbf{Figure 2.} Major modes detected using CLUMPAK for supported
partitions based on the results presented in Supplemental Appendix S1
Figure S6. Samples are grouped by country, and locality, except in North
America, where for clarity they are grouped by geographic region. Thin
dark lines are used to differentiate sample localities, and thick dark
lines to separate countries. Countries in the native range of winter
moth are ordered roughly from west (left) to east (right).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3.} NeighborNet analysis of the population coefficient of
assignments for the major mode of \emph{K} = 8 as summarized by CLUMPAK.
Label names for populations within broader geographic clusters have been
removed for clarity.

\textbf{Hosted file}

\verb`image4.emf`  available at \url{https://authorea.com/users/388368/articles/503181-four-times-out-of-europe-serial-invasions-of-the-winter-moth-operophtera-brumata-to-north-america}

\textbf{Figure 4.} DiyABC result from the final tournament that included
all four invasive populations. Time along the y-axis is not drawn to
scale. For each population, changes in colors represent different
population size parameters (values presented in Supplemental Appendix S1
Table S3).

\textbf{Supplemental Appendix S1:}

\textbf{Table S1.} Locality information

\textbf{Table S2.} Population genetic summary statistics

\textbf{Table S3.} DiyABC Posterior estimates for Tournament 4

\textbf{Figure S1.} Graphical representation of scenarios from DiyABC
Tournament 1

\textbf{Figure S2.} Graphical representation of scenarios from DiyABC
Tournament 2

\textbf{Figure S3.} Graphical representation of scenarios from DiyABC
Tournament 3

\textbf{Figure S4.} Graphical representation of scenarios from DiyABC
Tournament 4

\textbf{Figure S5.} Negative log-likelihood results for Structure runs
from \emph{K} = 2 through \emph{K} = 14

\textbf{Figure S6.} Results from the [?]\emph{K} method implemented in
StructureHarvester

\textbf{Figure S7.} Major Modes for all values of \emph{K}

\textbf{Figure S8.} NeighborNet for \emph{K} =6

\textbf{Figure S9.} NeighborNet for \emph{K} =13

\textbf{Figure S10.} DiyABC supported Scenarios from Tournaments 1, 2,
and 3.

\textbf{Figure S11.} PCA of posterior values for Tournament 1

\textbf{Figure S12.} PCA of posterior values for Tournament 2

\textbf{Figure S13.} PCA of posterior values for Tournament 3

\textbf{Figure S14.} PCA of posterior values for Tournament 4

\selectlanguage{english}
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