Present address: Department of Multitrophic Interactions, Netherlands Institute of Ecology, PO Box 40 (Boterhoeksestraat 48), 6666 ZG Heteren, the Netherlands.

# Spatial population structure of a specialist leaf-mining moth

Article first published online: 14 APR 2008

DOI: 10.1111/j.1365-2656.2008.01396.x

© 2008 The Authors. Journal compilation © 2008 British Ecological Society

Additional Information

#### How to Cite

Gripenberg, S., Ovaskainen, O., Morriën, E. and Roslin, T. (2008), Spatial population structure of a specialist leaf-mining moth. Journal of Animal Ecology, 77: 757–767. doi: 10.1111/j.1365-2656.2008.01396.x

#### Publication History

- Issue published online: 14 APR 2008
- Article first published online: 14 APR 2008
*Received 7 June 2007; accepted 3 February 2008**Handling Editor: Ottar Bjornstad*

### Keywords:

- dispersal;
- leaf miner;
- local and regional dynamics;
- sources and sinks;
- spatially structured population model;
- trees as islands

### Summary

- Top of page
- Summary
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- References
- Supporting Information

- 1The 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).
- 2In 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 km^{2}) off the south-western coast of Finland. - 3We 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.
- 4While 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.
- 5According 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.
- 6No 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.

### Introduction

- Top of page
- Summary
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- References
- Supporting Information

The spatial structure of natural populations may have a profound impact on their dynamics (Hanski & Gilpin 1997; Tilman & Kareiva 1997; Hanski 1999; Hanski & Gaggiotti 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) 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

- Top of page
- Summary
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- References
- Supporting Information

#### 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 & 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 edge-mediated 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.): *d _{C}* = 2·25 + 0·15

*d*(Paulo, Stein & Tomé 2002), where

_{T}*d*is the crown diameter (in metres) and

_{C}*d*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).

_{T}When constructing the population dynamic model (below), we use the parameterized diffusion model to calculate two quantities characterizing the movement process. First, *R _{ij}* is defined as the probability with which an individual originally in tree

*i*will visit tree

*j*before it dies. Secondly,

*T*is the time that an individual currently in tree

_{i}*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

*R*does not depend solely on the sizes of and distance between trees

_{ij}*i*and

*j*, but also on the sizes and spatial locations of the remaining oak trees. Similarly, the mean time

*T*that an individual spends in tree

_{i}*i*is affected by the actual configuration of trees surrounding the focal tree

*i*. In a highly fragmented landscape of circular tree crowns, both

*R*and

_{ij}*T*can be calculated analytically without the need to simulate the movement process (see Supplementary material, Appendix S2).

_{i}##### 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 sas version 9·1 (proc genmod).

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:

- 1Based on the information on how local population size scales with tree size (above), we assume that the number of leaf miners
*z*(_{i}*t*) on an occupied tree*i*in year*t*is proportional to the total number of leaves on the tree,*A*, so that_{i}*z*_{i}(*t*) is Poisson distributed with mean*c*_{1}*A*, where_{i}*c*_{1}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. - 2A fraction
*c*_{2}of the larvae is assumed to emerge as adult females and become mated. The number of such females, denoted by*b*(_{i}*t*), is Poisson distributed with mean*c*_{1}*c*_{2}*A*. 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}*i*and ever visit tree*i*by*m*(_{i}*t*). Assuming that the number of moths is large, and the movement probabilities*R*are small,_{ij}*m*(_{i}*t*) can be approximated by a Poisson distribution with mean*m̃*(_{i}*t*) = Σ_{j≠i}*R*(_{ji}b_{j}*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*n*(_{i}*t*) =*b*(_{i}*t*) +*m*(_{i}*t*). - 3We assume that the time that a female visiting tree
*i*spends in the tree within its lifetime is distributed exponentially with mean*T*. Hence, the total amount of time_{i}*q*(_{i}*t*) spent in tree*i*by all females visiting the tree is gamma-distributed with parameters*n*(_{i}*t*) and*T*._{i} - 4Within 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*a*(_{i}*t*) laid on tree*i*is Poisson distributed with parameter*q*(_{i}*t*)/*t**. - 5We 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 tree-specific 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 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 density-dependence in larval survival, cf. Roslin *et al*. 2006).

Because only the product of the parameters *c*_{1} and *c*_{2} affects the model behaviour, we combined them as β = *c*_{1}*c*_{2}. Similarly, the absolute values of the parameters *T _{i}* 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

*T*are compatible with this value. Finally, as the parameters

_{i}*t**,

*T*and

_{i}*R*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 log-normally 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

_{ij}^{−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 sas version 9·1 (proc genmod).

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 (*r _{S}*) 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

*r*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

_{S}*r*between the model prediction and the randomized data. We repeated the randomizations 10 000 times. If the observed

_{S}*r*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.

_{S}Second, to examine whether the model alone could explain all variation in the data, we compared the observed *r _{S}* value to that expected if the pattern had been generated by the model. To do so, we computed the correlation coefficient

*r*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

_{S}*r*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.

_{S}##### 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

- Top of page
- Summary
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- References
- Supporting Information

#### 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).

Year | Old | New | Extinct | No. occupied | No. unoccupied | % occupied |
---|---|---|---|---|---|---|

2003 | – | – | – | 63 | 34 | 65 |

2004 | 52 | 17 | 11 | 69 | 28 | 71 |

2005 | 49 | 13 | 20 | 62 | 35 | 64 |

2006 | 45 | 10 | 17 | 55 | 42 | 57 |

2007 | 42 | 17 | 13 | 59 | 38 | 61 |

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 (Fig. 2b; logistic regression, = 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 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 *r _{S}* = 0·33. This value is significantly higher than that expected by chance: 95% of the

*r*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 (

_{S}*r*= 0·33) than that of model-predicted long-term occupancy vs. 5-year series picked from model simulations (mean 0·89, 95% of the

_{S}*r*values falling within the interval 0·84–0·92).

_{S}#### colonization of unoccupied trees

The model explained a statistically significant proportion ( = 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 (*r _{S}* = 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

*r*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.

_{S}#### model predictions

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).

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

- Top of page
- Summary
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- References
- Supporting Information

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 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 km^{2}. 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 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 oak-associated 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

- Top of page
- Summary
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- References
- Supporting Information

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.

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- Top of page
- Summary
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- References
- Supporting Information

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### Supporting Information

- Top of page
- Summary
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- References
- Supporting Information

**Appendix S1.** Passive dispersal of larvae in abscised leaves.

**Appendix S2.** Estimation of movement parameters.

**Appendix S3.** Assessment of local population sizes.

Please note: Blackwell Publishing is not responsible for the content or functionality of any supplementary material supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.

Filename | Format | Size | Description |
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JANE_1396_sm_AppendixS1.doc | 25K | Supporting info item | |

JANE_1396_sm_AppendixS2.doc | 93K | Supporting info item | |

JANE_1396_sm_AppendixS3.doc | 26K | Supporting info item |

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.