Journal of Animal Ecology 2008, 77, 757–767
doi: 10.1111/j.1365-2656.2008.01396.x
Spatial population structure of a specialist
leaf-mining moth
Blackwell Publishing Ltd
Sofia Gripenberg1*, Otso Ovaskainen1, Elly Morriën2† and Tomas Roslin1
1
Metapopulation Research Group, Department of Biological and Environmental Sciences, PO Box 65 (Viikinkaari 1),
FI-00014 University of Helsinki, Finland; and 2Institute of Ecological Sciences, Faculty of Earth and Life Sciences,
De Boelelaan 1087, 1081 HV Amsterdam, Vrije Universiteit Amsterdam, the Netherlands
Summary
1. The spatial structure of natural populations may profoundly influence their dynamics. Depending
on the frequency of movements among local populations and the consequent balance between local
and regional population processes, earlier work has attempted to classify metapopulations into
clear-cut categories, ranging from patchy populations to sets of remnant populations. In an alternative,
dichotomous scheme, local populations have been classified as self-sustaining populations generating
a surplus of individuals (sources) and those depending on immigration for persistence (sinks).
2. In this paper, we describe the spatial population structure of the leaf-mining moth Tischeria ekebladella,
a specialist herbivore of the pedunculate oak Quercus robur. We relate moth dispersal to the distribution
of oaks on Wattkast, a small island (5 km2) off the south-western coast of Finland.
3. We build a spatially realistic metapopulation model derived from assumptions concerning the
behaviour of individual moths, and show that the model is able to explain part of the variation in
observed patterns of occurrence and colonization.
4. While the species was always present on large trees, a considerable proportion of the local
populations associated with small oaks showed extinction–recolonization dynamics. The vast
majority of moth individuals occur on large trees.
5. According to model predictions, the dominance of local vs. regional processes in tree-specific
moth dynamics varies drastically across the landscape. Most local populations may be defined
broadly as ‘sinks’, as model simulations suggest that in the absence of immigration, only the largest
oaks will sustain viable moth populations. Large trees in areas of high oak density will contribute most
to the overall persistence of the metapopulation by acting as sources of moths colonizing other trees.
6. No single ‘metapopulation type’ will suffice to describe the oak–moth system. Instead, our study
supports the notion that real populations are often a mix of earlier identified categories. The level
to which local populations may persist after landscape modification will vary across the landscape,
and sweeping classifications of metapopulations into single categories will contribute little to
understanding how individual local populations contribute to the overall persistence of the system.
Key-words: dispersal, leaf miner, local and regional dynamics, sources and sinks, spatially
structured population model, trees as islands.
Journal of Animal Ecology (2007) doi: 10.1111/j.1365-2656.2007.0@@@@.x
Introduction
The spatial structure of natural populations may have a
profound impact on their dynamics (Hanski & Gilpin 1997;
Tilman & Kareiva 1997; Hanski 1999; Hanski & Gaggiotti
*Correspondence author. E-mail: [email protected]
†Present address: Department of Multitrophic Interactions,
Netherlands Institute of Ecology, PO Box 40 (Boterhoeksestraat 48),
6666 ZG Heteren, the Netherlands.
2004). Depending on the frequency of movements between
different locations, the dynamics of local populations may
be more influenced by either local or regional processes
(Thomas & Kunin 1999). In this context, some authors
(notably Harrison 1991, 1994; Harrison & Taylor 1997) have
classified the spatial structuring of metapopulations into
distinct categories, ranging from patchy populations (with
frequent interaction between individuals inhabiting different
habitat patches) through classic metapopulations (characterized
by little dispersal and marked extinction–colonization dynamics)
© 2008 The Authors. Journal compilation © 2008 British Ecological Society
758
S. Gripenberg et al.
to collections of highly subdivided remnant populations
(with essentially no migration between the local populations).
Other authors, such as Thomas & Kunin (1999) and Ovaskainen
& Hanski (2004), have emphasized that all these population
types may be described more clearly as special cases of a general
continuum, based on the relative roles of underlying processes.
However, few studies to date have attempted to describe
natural systems using such an integrated approach.
Another categorization applied frequently to local populations linked by dispersal is based on ‘sources’ as opposed to
‘sinks’ (Pulliam 1988). While the above-mentioned classification
of populations is conducted at the level of entire metapopulations, the source–sink concept is used commonly to describe
local populations within a metapopulation (e.g. Boughton
1999; Foppen, Chardon & Liefveld 2000; Caudill 2003).
Conventionally, local populations producing a net surplus of
individuals are defined as source populations, while populations
in which local recruitment is insufficient to balance local
mortality are referred to as sinks (Pulliam 1988). Nevertheless,
the source–sink concept has often been examined without
reference to the exact spatial setting of the local populations.
If a population with surplus individuals (a potential source
population) is located far from other populations, most of the
individuals leaving the population may in fact never immigrate
to other populations. When assessing source–sink dynamics
and the contribution of individual local populations to the
system as a whole, we should therefore do so preferentially in
an explicitly spatial context.
For host-specific insects specialized on trees, the landscape
offers a distinct spatial structure, where – using a classic metaphor
by Janzen (1968) – individual trees might be thought of as
‘islands’ of suitable habitat embedded in a ‘sea’ of unsuitable
matrix habitat. However, trees often exhibit an irregularly
clumped distribution (e.g. Condit et al. 2000; Frost & Rydin
2000; Atkinson et al. 2007), and hence host individuals will
range from well-connected to highly isolated. How will this be
reflected in the spatial population structure of insect herbivores?
In this study we use the leaf-mining moth Tischeria ekebladella
(Bjerkander), a specialist herbivore of the pedunculate oak
Quercus robur (L.), as a model system to explore the spatial
population dynamics of an insect associated with a patchily
distributed host tree species. To relate dispersal to the spatial
configuration of host trees, we build a spatially realistic
metapopulation model which we validate against observations
on insect distribution. We use the model to assess to what
extent the distribution of host trees determines the dynamics
of the moth. Specifically, we aim to quantify the relative roles
of local and regional processes, and to identify which
local populations may be classified as sources, which as sinks,
in an explicitly spatial setting.
Materials and methods
STUDY SYSTEM
In Finland, the leaf-mining moth T. ekebladella is associated exclusively
with the pedunculate oak, Q. robur. In other parts of its range, it will
also feed on other oak species and on sweet chestnut Castanea sativa,
but these alternative host species are lacking from the Finnish
landscape. T. ekebladella has a univoltine life cycle in Finland: the
moths fly in June and early July, when eggs are laid on the fresh
foliage of oak trees. Some weeks later the eggs hatch, and the larvae
feed as leaf miners inside the oak leaves throughout the summer. In
the autumn, the larvae drop to the ground along with the abscised
leaves. Pupation occurs inside the leaves in early spring, and the
moths emerge some 5 weeks later.
At our study site, the island of Wattkast in south-western Finland,
the location and size of all oak trees higher than 0·5 m (n = 1868) has
been mapped (Gripenberg & Roslin 2005). Here, the oak has a
highly aggregated distribution with some individuals being very
isolated (Fig. 1a). Several previous findings suggest that processes at
the metapopulation level affect the distribution of T. ekebladella
among potential host trees on Wattkast. First, we have found that
tree-specific differences in host-induced mortality do not suffice to
explain the local presence or absence of T. ekebladella (Gripenberg
Fig. 1. Spatial distribution and patterns of
occupancy of oak trees. (a) Map of Wattkast
showing the location of all (n = 1868) oak
trees on the island. The rectangle shows the
outline of the area enlarged in (d). (b) Location
of 97 small oak trees surveyed for the presence
or absence of Tischeria ekebladella throughout
2003–07. The more years that a tree was
occupied for, the darker its symbol. (c)
Location of large oak trees (all occupied by
T. ekebladella): White circles show 20 oak
trees surveyed 2003–07, white quadrats
show 16 trees sampled in 2004 and black
triangles show 22 trees sampled in 2006.
Symbol size reflects tree height. (d) Location
of 69 small trees from which T. ekebladella
was removed experimentally in 2005 and
2006. Trees that were colonized in both 2006
and 2007 are depicted as black circles, grey
circles indicate trees that were colonized in
either of the years, while white circles show
trees which remained uncolonized.
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Animal Ecology, 77, 757–767
Spatial population structure of T. ekebladella 759
& Roslin 2005). Secondly, survival rates of moth larvae vary largely
independently of each other at any spatial scale larger than the
individual tree (Gripenberg & Roslin 2008). Hence, there are no
patterns of local moth survival which could account for a large-scale
association between the relative connectivity of trees and the presence
of T. ekebladella (Gripenberg & Roslin 2005).
THE METAPOPULATION MODEL
To describe the spatial population structure of T. ekebladella, we
built a spatially realistic metapopulation model. Before constructing
the full model, we first describe two of its components: the dispersal
process and the dependence of local population size on tree size.
Modelling the dispersal process
The scale of dispersal is a key element of any metapopulation model.
In T. ekebladella, dispersal is a two-step process. First, larvae may
drift through the landscape inside leaves abscised in the autumn.
Secondly, adult moths (emerging from the abscised leaves in the
following spring) disperse through active flight. A pilot study
suggested that passive dispersal of larvae inside leaves is of secondary
importance compared to active dispersal of adult moths (see Supplementary material, Appendix S1). We will therefore focus upon
dispersal by adults. We assume that the individuals follow a random
walk both within the habitat patches (oaks) and in the remaining
matrix. Additionally, we assume that the individuals show edgemediated behaviour, leaving the oak trees less frequently than
would be predicted by a pure random walk process. To simplify the
landscape structure, we assume that oak crowns are circular in
shape. We do not have direct measurements of crown diameters, but
adopt the relationship between crown and trunk diameters quantified
for another oak species, Q. suber (L.): dC = 2·25 + 0·15 dT (Paulo,
Stein & Tomé 2002), where dC is the crown diameter (in metres) and
dT is the diameter of the trunk (in centimetres). We parameterized
the diffusion model both with maximum likelihood and Bayesian
methods using data on the distribution of the offspring of dispersing
female moths (see Supplementary material, Appendix S2).
When constructing the population dynamic model (below), we
use the parameterized diffusion model to calculate two quantities
characterizing the movement process. First, Rij is defined as the
probability with which an individual originally in tree i will visit tree
j before it dies. Secondly, Ti is the time that an individual currently
in tree i is expected to spend in tree i within its lifetime. Compared
to traditional, kernel-based approaches (e.g. Hanski & Ovaskainen
2000; Baguette 2003; Moilanen 2004; Fujiwara et al. 2006; Chapman,
Dytham & Oxford 2007), this dispersal model adds spatial realism to
the movement process. As the movements of individual moths are
affected by the trees they encounter, the probability Rij does not
depend solely on the sizes of and distance between trees i and j, but
also on the sizes and spatial locations of the remaining oak trees.
Similarly, the mean time Ti that an individual spends in tree i is
affected by the actual configuration of trees surrounding the focal
tree i. In a highly fragmented landscape of circular tree crowns, both
Rij and Ti can be calculated analytically without the need to simulate
the movement process (see Supplementary material, Appendix S2).
Scaling local population size to host tree size
In the context of our metapopulation model, local population sizes
reflect the local pool of potential migrants. To investigate whether
population size scales directly with tree size, we sampled 75 trees of
variable size [mean girth at breast height (GBH) = 70 cm, standard
deviation (SD) = 59 cm] within a dense oak stand on Wattkast in the
autumn of 2004. On each tree, we examined a sample of approximately
100 leaves (mean = 104 leaves tree−1, SD = 21 leaves tree−1) and counted
the total number of leaf miners present.
To test whether leaf miner density per leaf changes with tree size,
we modelled miner density (the number of miners divided by the
total number of leaves in the sample) as a function of tree size
(GBH), assuming a log link function and Poisson distributed errors.
The analysis was implemented in  version 9·1 ( ).
There was no detectable relationship between tree size and the
number of leaf miners per number of examined leaves [the coefficient
estimate for GBH was 0·0002 on the scale of the log link function,
standard error (SE) = 0·0006, P = 0·66]. As all sampled trees were
located in the same oak stand (and should thus have been equally
accessible to the moth), T. ekebladella does not seem to favour leaves
on trees of any particular ontogenetic stage or stature.
The amount of leaves on a tree was estimated using information
in an independent data set (K. Schönrogge, unpublished data),
resulting in the relationship log(leaf number) = 0·92 + 2·55 log(GBH)
(see Supplementary material, Appendix S3).
Construction of the population dynamic model
To develop a spatially realistic metapopulation model, the information
on moth dispersal and local population sizes derived above was
integrated as follows:
1. Based on the information on how local population size scales
with tree size (above), we assume that the number of leaf miners zi(t)
on an occupied tree i in year t is proportional to the total number of
leaves on the tree, Ai, so that zi(t) is Poisson distributed with mean
c1Ai, where c1 is the mean number of leaf miners per leaf in occupied
trees. Because we assume that population size is constant within
occupied trees, we ignore the potential time lag it might take for a
local population to build up after colonization.
2. A fraction c2 of the larvae is assumed to emerge as adult
females and become mated. The number of such females, denoted
by bi(t), is Poisson distributed with mean c1c2Ai. These females are
assumed to move independently of each other according to the
diffusion model. We denote the number of females that originate
from trees other than tree i and ever visit tree i by mi(t). Assuming
that the number of moths is large, and the movement probabilities
Rij are small, mi(t) can be approximated by a Poisson distribution
with mean µi(t) = Σj≠iRjibj(t) (Ovaskainen & Hanski 2004). When
also taking females originating from tree i into account, the total
number of mated females that visit tree i is ni(t) = bi(t) + mi(t).
3. We assume that the time that a female visiting tree i spends in
the tree within its lifetime is distributed exponentially with mean Ti.
Hence, the total amount of time qi(t) spent in tree i by all females visiting the tree is gamma-distributed with parameters ni(t) and Ti.
4. Within trees, females are assumed to lay eggs at a constant rate
of 1/t*, where the parameter t* is the mean amount of time required
to oviposit one egg. With this assumption, the number of eggs ai(t)
laid on tree i is Poisson distributed with parameter qi(t)/t*.
5. We classify a tree as being occupied if it receives at least one egg.
We note that the model derived here applies specifically to an organism
with discrete generations. While the model actually predicts the
number of eggs laid in a tree, we make the assumption that the treespecific number of leaf miners is proportional to the estimated
number of leaves on the tree. There are two reasons for making this
simplifying assumption. First, the pattern of similar miner densities
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Animal Ecology, 77, 757–767
760
S. Gripenberg et al.
across trees is supported by empirical data (e.g. Roslin et al. 2006).
Secondly, any explicit modelling of density dependence would seem
dubious given the lack of empirical data on the density-dependence
of relevant processes across all stages of the life cycle (for densitydependence in larval survival, cf. Roslin et al. 2006).
Because only the product of the parameters c1 and c2 affects the
model behaviour, we combined them as β = c1c2. Similarly, the
absolute values of the parameters Ti and t* need not be estimated
independently, as only their ratio matters for the number of eggs
that individual moths lay in a given tree. When estimating the
parameters of the movement model (see Supplementary material,
Appendix S2), we fixed t* to t* = 1/30 (d–1). Hence, our estimates for
the parameters Ti are compatible with this value. Finally, as the
parameters t*, Ti and Rij were estimated from independent data (see
Supplementary material, Appendix S2), the parameter β is the only
free parameter in the metapopulation model. To allow for temporal
variation in environmental conditions, we assume β to be lognormally distributed with mean µ and SD = σ. We estimated µ and
σ by matching the model prediction with the empirically observed
fraction of occupied trees (0·64) and its SD (0·05) using a data set of
97 small oaks surveyed over a 5-year period (see next section). We
first simulated the model for a transient of 100 years, and then
simulated 1000 replicates of the 5-year interval. The parameters µ
and σ were adjusted until they matched the empirically observed
values with an accuracy of two digits, leading to parameter estimates
of µ = 6·5 × 10–6 and σ = 0·17.
The model derived here is a patch-occupancy approximation of
an individual-based model. In other words, inference about patterns
of occupancy and colonization is based on assumptions about the
behaviour of individual moths. In classical models of metapopulation
dynamics, local extinctions and colonizations are usually modelled
as two different processes. However, in the current model there is no
fundamental difference between the colonization of the natal tree
and the colonization of other trees, as the moths emerge from leaves
that may already have moved some distance from the natal tree.
A similar approach was adopted to study metapopulation dynamics
of the butterfly Melitaea cinxia (Ovaskainen & Hanski 2004).
EMPIRICAL DATA: SPATIAL DISTRIBUTION AND
DYNAMICS OF T. EKEBLADELLA
Model predictions were tested against empirical data on the
tree-specific occurrence of T. ekebladella on Wattkast. Naturally, we
were not able to assess the presence or absence of leaf miners on all
of the 1868 trees on the island. Hence, our study focuses upon several subsets of the trees which were studied in various level of detail
between 2003 and 2007.
The local presence or absence of T. ekebladella was studied on a
set of 97 small (1–4 m) trees during 2003–07 (Fig. 1b). These trees
were small enough for each part to be reached from the ground. In
each autumn of the 5-year study period, we visited the trees and
examined all leaves for the presence of leaf miners.
To assess the effect of tree size on the occurrence of T. ekebladella,
we also acquired data on the occurrence of T. ekebladella on a set of
larger trees (Fig. 1c). Throughout 2003–07, 20 medium-sized oak
trees (3–8 m) located in an area of high oak density were surveyed
for the presence of absence of leaf miners (survey design described
by Gripenberg, Salminen & Roslin 2007). In addition, in 2004 and
2006 we sampled a total of 38 large trees (8–20 m) for the presence
or absence of leaf miners: in 2004, we sampled 16 trees located in
various parts of the island, in 2006, we sampled 22 more. From each
of the 16 trees surveyed in 2004, 18 branch tips (each comprising a
sample of approximately 100 leaves) were cut down from various
parts of the tree crown, resulting in a total sample of 1820–2037
leaves per tree. For the 22 trees investigated in 2006, 30 branch tips
of around 50 cm were cut down and examined for the presence of
leaf miners (R. Kaartinen, unpublished data).
To explore the potential of T. ekebladella to colonize unoccupied
trees, we created targets for colonization by removing experimentally
any leaf miners present on 69 small (1–3 m) trees in the north-western
corner of Wattkast (Fig. 1d). All mined leaves were picked off
manually in early September in 2005 and 2006 (the average number
of miners per tree were generally low; in 2005 mean = 23, SD = 28
and in 2006 mean = 7, SD = 12 leaf miners per tree). In both years
following the experimental extinctions (2006 and 2007), we revisited
the trees and examined all leaves to assess which trees had been
colonized in a single moth generation.
ASSESSING MODEL FIT AND DERIVING KEY
PREDICTIONS
Model fit
To assess how well the metapopulation model predicts patterns of
occupancy, we compared model predictions to empirical data on
leaf miner distribution across 97 small trees and 5 years. As we used
the average occupancy level in the same data to parameterize the
model (parameter β), we assessed model fit by two metrics that are
independent of the overall occupancy level. A given occupancy level
may reflect either high colonization rate, balanced by high extinction
rate, or low colonization rate, balanced by low extinction rate. We
therefore first compared the observed turnover rate (the total number
of colonization and extinction events within the 5-year period) to
the one predicted by the model. As a second measure of model
performance, we examined how well the model predicts the
observed fraction of years that a given tree was occupied [i.e.
(number of years occupied)/5]. To test if the tree-specific model
prediction (defined as the fraction of years the model predicts each
tree to be occupied out of 5000 simulated years) explains a significant
amount of the variation in the real data, we built a generalized linear
model assuming a logit link function and binomially distributed
errors. The model was fitted in  version 9·1 ( ).
As an independent test of model-predicted colonization, we used
data from the 69 experimentally vacated trees. Here, we compared
the model prediction to the real data (fraction of years out of 2 that
a tree was colonized) using a generalized linear model exactly as
described above.
For both sets of empirical data, we calculated two additional
measures of model fit by comparing observed and expected Spearman’s rank correlation coefficients (rS) between tree-specific model
predictions and empirical data. First, we examined the probability
with which the match between the observed pattern and model predictions could have been generated by chance alone. To do so, we
computed the correlation coefficient rS between the model-predicted
and observed number of years for which a tree was occupied (for the
97 trees), and between model predictions and the number of years in
which a tree became colonized (for the 69 trees). We then randomized
the real pattern of occupancy or colonization and calculated rS
between the model prediction and the randomized data. We
repeated the randomizations 10 000 times. If the observed rS value
was outside the 95% range of the randomizations, we concluded that
the fit between the model-predicted and observed patterns of occupancy
or colonization, respectively, exceeded significantly the match expected
by chance alone.
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Animal Ecology, 77, 757–767
Spatial population structure of T. ekebladella 761
Second, to examine whether the model alone could explain all
variation in the data, we compared the observed rS value to that
expected if the pattern had been generated by the model. To do so,
we computed the correlation coefficient rS between the model-predicted
long-term probability of occupancy and a 5-year-long sample
period from the model simulation. By repeating the 5-year sampling
1000 times, we established the range of deviations generated by
sampling alone. If the observed rS value was outside the 95% range
of this distribution, the empirically observed pattern was probably
influenced by factors not included by the model. A similar evaluation
was performed for colonizations on the 69 experimentally vacated
trees, but as in this case colonizations were observed for 2 years
only, we compared the mean model prediction to simulations of 2-year
periods.
Table 1. Occurrence and dynamics of Tischeria ekebladella on 97
small trees surveyed throughout 2003–07. The column ‘Old’ gives the
number of occupied trees that were also occupied in the previous year,
column ‘New’ shows the number of newly colonized trees and
column ‘Extinct’ shows the number of unoccupied trees on which leaf
miners were found in the previous year
Year
Old
New
No.
Extinct occupied
No.
unoccupied % occupied
2003
2004
2005
2006
2007
–
52
49
45
42
–
17
13
10
17
–
11
20
17
13
34
28
35
42
38
63
69
62
55
59
65
71
64
57
61
Model predictions
Once constructed and validated, we used the metapopulation model
to calculate a set of key entities reflecting the spatial structuring of
the moth population on Wattkast.
To establish the level to which trees of different size contribute to
the overall metapopulation size, we calculated a measure of expected
local population size for each tree by multiplying its model-predicted
probability of occupancy by its estimated number of leaves (reflecting
the number of leaf miners; see ‘Scaling local population size to host
tree size’). To assess the contributions of local recruitment vs. inflow
of individuals from elsewhere, for each tree we calculated the proportion of individuals being of local origin. Here, we first simulated
the model for 5000 years, and then calculated what proportion of
the leaf miners on each tree were the progeny of females that fed on
the same tree as larvae.
Finally, we classified each local population as a ‘source’ or a
‘sink’, based on two different criteria: first, for each tree, we assessed
how the local moth population would develop in the absence of any
immigration. To do so, we simulated the dynamics on each tree in
isolation. Starting with a situation where the tree was occupied, we
assessed the probability with which the tree was still occupied after
5 years (mean over 10 000 simulations, computed separately for
trees with diameter 1, 2, ... , 90, 91 cm). Secondly, we included the full
landscape of trees in the simulation, and assumed that only the focal
tree was occupied initially. As a measure of the contribution of the
focal tree to the overall persistence of the system, we calculated the
number of trees occupied by the end of the 5-year period (mean of
100 simulations, computed separately for each of the 1868 trees). If
more than one tree was occupied (i.e. if the local population had
more than replaced itself ), the focal tree was considered a source.
Results
DISTRIBUTION AND DYNAMICS OF T. EKEBLADELLA
T. ekebladella is relatively widespread on Wattkast. The
proportion of the 97 small study trees occupied by the species
remained roughly constant throughout the 5-year study
period: leaf miners were found on 57–71% of these trees
(Table 1). However, the turnover rate of local populations
inhabiting these small trees was relatively high (Fig. 1b,
Table 1). In contrast, local populations on larger trees seemed
more permanent: T. ekebladella was present on all the 20
medium-sized trees in each of the study years. As leaf miners
were also found on all the large trees surveyed in 2004 (n = 16)
and 2006 (n = 22), respectively, the species appears to be
present on large trees on Wattkast regardless of their relative
isolation (Fig. 1c).
The dynamic nature of local populations on small trees was
also evidenced by patterns of colonization. Of the 69 small
trees that were subject to our experimental extinction
treatment in 2005 and 2006, more than half were colonized by
the following year (Fig. 1d). In 2006, 44 trees (64%) were
colonized, and in 2007 leaf miners were found on 40 (60%) of
the trees. While the proportion of trees colonized was roughly
similar for both years, the exact trees colonized varied
between the 2 years (Fig. 1d), suggesting that permanent
differences in tree quality were not the main factor behind the
colonization pattern.
MODEL FIT
The diffusion model fitted very well to the data used for its
parameterization (see Supplementary material, Appendix
S2), suggesting that the movement process can be described
sufficiently accurately as a simple random walk. The mean
dispersal distance of adult females (as estimated by maximum
likelihood methods) was 87 m (see Supplementary material,
Appendix S2).
The metapopulation model predicts a rapid increase in
the likelihood of occurrence of T. ekebladella with tree size.
Hence, on large trees, the species is expected to be present with
a very high probability. In this respect, the data fitted the
model well (Fig. 2a). On smaller trees, the likelihood of
occurrence is more variable – as also evident in the data
(Fig. 2a). Here, the local presence or absence of the species is
expected to be influenced more strongly by other factors than
tree size, notably immigration from surrounding trees.
PATTERNS OF OCCUPANCY
For the 97 small trees surveyed throughout 2003–07, there
was a clear and statistically significant positive relationship
between the model-predicted and observed rates of occupancy
2
(Fig. 2b; logistic regression, χ1 = 28·1, P < 0·001), suggesting
that the spatial processes described by the model explain a
significant part of overall variation in tree occupancy. The
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S. Gripenberg et al.
number of turnover events (transitions from occupied to
empty or empty to occupied) in the empirical data was 118
(Table 1), whereas the model prediction had a mean of 96
(95% confidence range 79–115). Hence the model slightly
underestimated the empirically observed turnover rate.
The Spearman’s rank correlation coefficients between
model predictions and empirical observations showed that
the model explains part of but not all the variation in the data.
The Spearman’s rank correlation coefficient for the relationship
between the model-predicted and observed rates of occupancy
was rS = 0·33. This value is significantly higher than that
expected by chance: 95% of the rS values for model predictions
vs. randomized patterns fell between –0·20 and 0·20. Nevertheless, discrepancies between model predictions and observed
patterns cannot be attributed to chance alone. The correlation
between the observed time–series and the predicted value was
significantly lower (rS = 0·33) than that of model-predicted
long-term occupancy vs. 5-year series picked from model
simulations (mean 0·89, 95% of the rS values falling within the
interval 0·84–0·92).
COLONIZATION OF UNOCCUPIED TREES
The model explained a statistically significant proportion
2
( χ1 = 3·7, P = 0·05; Fig. 2c) of patterns of colonization of the
69 small trees. Nevertheless, the Spearman’s rank correlation
between model-predicted and observed colonization (rS =
0·15) fell within the 95% range of the 10 000 correlations
calculated among randomized patterns and model predictions
(–0·24–0·24), due probably to a lack of power associated with
the limited empirical material. Similarly, the observed value
fell outside the 95% range of rS values calculated between the
model-predicted long-term occupancy and individual 2-year
periods from model simulations (mean 0·77, range 0·67–
0·85). Hence the model prediction correlates positively with
the observed colonizations, but the model explains only part
of the variation in these data.
MODEL PREDICTIONS
Fig. 2. Model predictions vs. empirical data. (a) Model-predicted
relationship between tree girth at breast height and probability of
occupancy (small black dots). The white circles show the empirically
observed occupancy status of 155 trees (white circles; 0 = unoccupied
or 1 = occupied). The data refer to 2006, except for 16 large trees
which were surveyed in 2004. (b) Model-predicted probability of
occupancy vs. the empirically observed fraction of years (out of 5) for
which each of 97 small (1–4 m) oak trees was occupied. The curve is
based on logistic regression ( χ12 = 28·1, P < 0·001). (c) Model-predicted
vs. empirical rates of colonization of 69 trees that were cleared
experimentally of leaf miners in 2 years. In all the panels, individual
data points have been displaced slightly vertically to show
overlapping values.
While the oak population on Wattkast is dominated strongly
by small trees, a disproportionate part of the moth population
is associated with large trees (Fig. 3). The relative dominance
of large trees is also evidenced by how much more individuals
of local origin contribute to populations on large trees than
to populations on small trees (Fig. 4a). Nevertheless, the
contribution of local vs. regional processes to tree-specific
moth dynamics is not determined by tree size alone, but varies
considerably across the landscape (Fig. 4a). For trees in
well-connected clusters of oaks, the predicted proportion of
individuals colonizing their native tree is very low (< 1%;
Fig. 4b). In contrast, on more isolated trees, local dynamics
will dominate, as long as the tree is large enough to sustain a local
moth population that is larger than the number of immigrating
individuals. On the most isolated large trees, up to 96% of the
leaf miners are predicted to be the progeny of female moths
having fed on the same tree as larvae (Fig. 4b).
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Animal Ecology, 77, 757–767
Spatial population structure of T. ekebladella 763
In the absence of immigration, populations of T. ekebladella
on small trees (GBH < 50 cm) will not persist, whereas large
trees (GBH > 150 cm) can support long-persisting populations
even in isolation (Fig. 5a). Hence, populations on small trees
may be classified as ‘sinks’ in the classical sense, whereas
populations on large trees are self-sustained. Nevertheless, if
a large tree is located far from other oaks, many emigrating
moths will be lost in the matrix, and its overall contribution to
the persistence of the system may be relatively small, adding
scatter to the general relationship (Fig. 5a,b). Thus, the
degree to which a tree will act as a ‘source’ of individuals
colonizing other trees will depend both upon its size and its
spatial location in relation to other trees.
Discussion
Fig. 3. The contribution of trees of difference size to the overall
population of Tischeria ekebladella on Wattkast. Grey bars show
the proportion of the total pool of moths that are associated with
trees of different size (as predicted by the metapopulation model).
The black line shows the frequency distribution of trees among size
classes.
The spatial population structure of any species will depend
both on the distribution of its habitat, and on its own propensity
to cross the distances separating local habitat patches (e.g.
Baguette, Petit & Quéva 2000; Roslin 2000; Moilanen &
Nieminen 2002). In this paper, we have described the spatial
population structure of a host-specific moth using a combination
Fig. 4. Model-predicted proportion of leaf
miners of local origin as function of (a) girth
at breast height and (b) spatial location. In
(b) the largest symbols correspond to cases
where almost all (96%) the individuals on a
tree are the progeny of local moths. The
histogram shows the frequency distribution
of trees in different categories.
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Animal Ecology, 77, 757–767
764
S. Gripenberg et al.
Fig. 5. Contributions of individual populations to the persistence of the moth
metapopulation of Wattkast, as predicted by
the model. The broken line in (a) shows the
probability that a tree of a given size remains
occupied for a period of 5 years in the
absence of any immigration. The dots in (a)
show the expected number of trees occupied
5 years after moths have been introduced to
a given focal tree, assuming that Tischeria
ekebladella was initially absent from the
remaining 1867 trees. A value higher than 1
implies that the tree is a ‘source’ (i.e. moths
emigrating from the focal tree have been
successful in colonizing at least one other
tree). (b) Location of ‘sinks’ (black squares)
and ‘sources’ (white circles). For sources,
symbol size has been scaled to reflect
differences in the number of trees that the
model predicts to be occupied five years after
introduction. The histogram shows the
frequency of ‘sinks’ (black bar) and ‘sources’
of different strength (white bars).
of empirical data and modelling. Our results illustrate that
T. ekebladella defies classification into any of the earlier
proposed, single metapopulation types (cf. Harrison 1991,
1994; Harrison & Taylor 1997). While different parts of the
system could, in principle, be assigned to different types and
the overall system hence be described as a compound mixture,
our model will rather depict them all as variations on the same
underlying processes.
A key process is dispersal. The movement range of T. ekebladella is clearly limited compared to the scale of the study
area of 5 km2. In dense oak stands, individuals will move
freely enough to form a ‘patchy population’ (sensu Harrison
& Taylor 1997), with most of the individuals reproducing in a
tree actually immigrating there from somewhere else. In
the parts of the landscape where oaks are sparse, the rate of
successful immigration will be very limited. Hence, although
the basic process behind individual movements would remain
the same, the spatial distribution of the host tree will result in
fundamentally different flows of individuals in different parts
of the landscape.
Earlier attempts to classify metapopulations into different
categories are based largely on the relative frequency of local
extinction and colonization events, and on the rate of migration
compared to local recruitment (Harrison 1991, 1994; Harrison
& Taylor 1997; see also Thomas & Kunin 1999). Our model
does not make any conceptual distinction between these rates,
but models them as different aspects of the same fundamental
processes. Individuals are simply assumed to emerge somewhere, after which they keep moving and reproducing during
the rest of their adult lifetime (cf. Ovaskainen & Hanski
2004). Classic extinction–colonization dynamics (sensu Hanski
& Simberloff 1997) will occur on only a fraction of the host
trees, the small oaks, which comprise the majority of the host
population. Large trees – albeit fewer in numbers – will host
the majority of moth individuals and sustain large and
long-lived populations.
How host trees of different size and connectivity contribute
to overall metapopulation size and persistence is illustrated
by our analysis of ‘sources’ and ‘sinks’. As a key distinction to
sources and sinks sensu Pulliam (1988), we stress that the
current analysis does not rely on local differences in habitat
quality. Instead, what affects the balance between local
recruitment and regional migration in our model is landscape
geometry. Unless subsidized with individuals from surrounding
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Animal Ecology, 77, 757–767
Spatial population structure of T. ekebladella 765
populations, local populations on small trees will rapidly go
extinct (cf. Connor, Faeth & Simberloff 1983). Populations on
larger trees will be typically self-sustaining net exporters of
individuals, sending out emigrants to the surrounding
landscape. However, even large trees may not work as effective
sources unless located closely enough to other populations.
This illustrates the importance of addressing causal processes
underlying distributional patterns before, for instance,
making applied management decisions. Removing an isolated
source may have few consequences, whereas removing a
well-connected source may result in the large-scale collapse of
several associated sinks.
The current model is built on a series of assumptions, some
of which may be too simplistic in relation to our study system.
That our model fails to account for all complexities of the real
system is suggested by the fact that it accounts for less variation
than we would expect had the observed pattern emerged from
only the processes assumed. Establishing the exact reasons for
these discrepancies is beyond the scope of this paper, and we
can only speculate about underlying causes.
Several features of the current analysis may lend themselves
to critique. For example, trees might differ in quality (e.g.
Memmott, Day & Godfray 1995; Mopper & Simberloff 1995;
Egan & Ott 2007), thereby excluding T. ekebladella from
certain trees in many or most years. Nevertheless, independent
data suggest very limited tree-to-tree differences and argue
against a critical role of tree-specific differences in quality for
the distribution of our study species (Gripenberg & Roslin
2005, 2008; Roslin et al. 2006). Alternatively, the empirical
data may be ridden by errors. However, we expect sampling
error to be low, because every leaf was inspected on each tree
and field tests suggest a very low probability of scoring ‘false
absences’ (A. Tack, unpublished). The reasons for the imperfect
model fit may therefore likely be found in our assumptions
regarding local population sizes and the dispersal process.
The relationship between GBH and leaf numbers (see Supplementary material, Appendix S3) is a rough approximation,
which inevitably brings inaccuracy to our estimates of local
population sizes. With regard to dispersal, our model is based
on very simplistic assumptions regarding moth movement
through the landscape. In the densest networks of oaks,
individual trees will often be part of complex oak vegetation.
While such vegetation is actually three-dimensional, we
modelled diffusion in two dimensions. Moreover, if there is
any component of active search behaviour, isolated oak trees
may be reached with a higher probability than envisaged by
our model (e.g. Harrison 1989; Conradt et al. 2000). Finally,
what lies between the oaks may also affect movement, as
demonstrated by several empirical studies (e.g. Kareiva 1985;
Jonsen, Bourchier & Roland 2001; Haynes & Cronin 2003).
Future studies may then refine our view of local population
sizes and moth dispersal, but in the current context we
conclude that the metapopulation model explains sufficient
parts of the observed occupancy pattern to advance our
understanding of key processes.
Of the processes inferred, several come with important
implications for the dynamics of both the insect and the host.
From the perspective of the host tree, variation in the
relative persistence of local insect–plant associations will
probably affect patterns of herbivore damage. Because herbivory may be very costly to a plant (e.g. Herms & Mattson
1992), young and isolated trees may benefit from reduced
levels of herbivory (cf. Janzen 1970; Connell 1971). As recent
work suggests that herbivory will generally cause larger
costs to plants than thought earlier (Crawley 1985, 1997;
Louda & Rodman 1996; Maron & Gardner 2000), there may
then be a factual link between spatial location, tree size and
fitness.
From the perspective of the herbivore, population turnover
on small and isolated trees may affect interspecific interactions
between T. ekebladella, its natural enemies and other herbivores:
on many small trees, there will be no T. ekebladella for the
natural enemies to attack, and from some trees occupied by
the moth the parasitoids may be missing (Faeth & Simberloff
1981; Lei & Hanski 1997; van Nouhuys 2005). On the other
hand, on trees not occupied by T. ekebladella, other oakassociated herbivores may benefit from competitive release
from T. ekebladella.
The current results are clearly specific to the oak–T. ekebladella
system on Wattkast, and should not be applied uncritically
to other systems. However, we expect that our results can
reflect general patterns in the spatial structure of insect
populations associated with trees. Many such insects are
likely to have a limited dispersal ability (e.g. van Dongen,
Matthysen & Dhont 1996; Rickman & Connor 2003; Eber
2004), and given the clumped distribution of many tree species
(e.g. Condit et al. 2000; Frost & Rydin 2000; Kunstler et al.
2004; Atkinson et al. 2007) it seems likely that many insect
populations may exhibit similar spatial structuring. Nevertheless, even species sharing the very same habitat network
might respond to landscape structure in very different ways
(Gutierrez et al. 2001; Roslin & Koivunen 2001; van Nouhuys
& Hanski 2002; Biedermann 2004), and before generalizations
can be made we must inevitably wait for future work on
further species. However, our work on T. ekebladella does
offer a beginning, and a point for comparison. If Janzen
(1968) compared host trees to islands, then T. ekebladella will
certainly see them as an archipelago dominated by large
islands, and parts fusing into actual mainlands. Local differences in the structure of this archipelago will drastically
affect the flow of individuals among individual islands,
and also the types of ecological and evolutionary dynamics
that we expect to see on different trees. No tree is then completely an island.
Acknowledgements
The manuscript was improved substantially by comments from two anonymous
reviewers. We thank all students and fieldworkers who have participated in the
yearly leaf miner surveys. Riikka Kaartinen provided data on the distribution
of Tischeria ekebladella on 22 large oak trees, and Ayco Tack and Katja
Bonnevier made substantial contributions to the collection of data. Karsten
Schönrogge kindly provided the data used to infer the relationship between tree
GBH and leaf numbers. The study was supported financially by the Academy
of Finland (projects 213457, 211173 and 111704), the Entomological Society of
Helsinki and the Waldemar von Frenckell Foundation.
© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Animal Ecology, 77, 757–767
766
S. Gripenberg et al.
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Handling Editor: Ottar Bjornstad
Supplementary material
The following supplementary material is available for this article.
Appendix S1. Passive dispersal of larvae in abscised leaves.
Appendix S2. Estimation of movement parameters.
Appendix S3. Assessment of local population sizes.
This material is available as part of the online article from:
http://www.blackwell-synergy.com/doi/full/10.1111/j.13652656.2008.01396.x.
(This link will take you to the article abstract).
Please note: Blackwell Publishing is not responsible for the
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© 2008 The Authors. Journal compilation © 2008 British Ecological Society, Journal of Animal Ecology, 77, 757–767