Gene flow at the leading range edge: The long‐term consequences of isolation in European Beech (Fagus sylvatica L. Kuhn)

Isolation is expected to lead to negative impacts on populations due to a reduction in effective population size and gene flow, exacerbating the effects of genetic drift, which might be stronger in peripheral and fragmented populations. Fagus sylvatica (European beech) in southern Sweden presents a gradient of isolation towards the leading range edge of the species. We sought to determine the impact of long‐term isolation on genetic diversity and population genetic structure within populations of this species.


| INTRODUC TI ON
Peripheral populations often display decreasing density as environmental conditions depart from the optimum (Brown, 1984) such that the range edge of a species presents a matrix of increasingly naturally isolated populations the further they exist from the core of the species distribution. Considering that current range shifts are driven by contemporary climate change, peripheral populations are important for species migration, population growth and persistence (Hampe & Petit, 2005;Parmesan & Yohe, 2003;Walther et al., 2002). Highly fragmented migration fronts consisting of isolated populations are shaped by founder effects, that can lead to correlative reductions in allelic number and heterozygosity, decreasing genetic diversity and genetic bottlenecks (Comps, Gömöry, Letouzey, Thiébaut, & Petit, 2001;Eckert, Samis, & Lougheed, 2008;Nei, Maruyama, & Chakraborty, 1975;Young, Boyle, & Brown, 1996).
The consequences of isolation are larger for small populations, which are vulnerable to genetic drift (Ellstrand & Elam, 1993).
Persistent reductions in gene flow can also increase the risk of inbreeding depression and genetic differentiation of outlier populations (Eckert et al., 2008;Ellstrand & Elam, 1993;Ouborg, Vergeer, & Mix, 2006), potentially compromising the adaptability of a species and the resilience of populations to environmental change (Jump & Penuelas, 2005;Willi & Fischer, 2005). Outcrossing trees can be disproportionately sensitive to a reduction in pollen-mediated gene flow owing to their often high levels of heterozygosity that may mask deleterious recessive alleles, which if expressed can lead to a reduction in fitness (Bacles & Jump, 2011).
Widespread forest fragmentation is a consequence of an estimated loss of 13 million hectares of forests per year over the past decade (FRA, 2010). However, the effects of isolation in fragmented forest populations are difficult to measure because trees are longlived and multiple generations are required to fully realize potential effects on population genetic variation and structure. The inconsistency in results from fragmentation studies has been described as the paradox of forest fragmentation genetics (Kramer, Ison, Ashley, & Howe, 2008). Organisms with long generation times, such as trees, may experience an effective lag to recent fragmentation events as it can take several generations for the impacts of disturbance to change population genetic structure (Aguilar, Quesada, Ashworth, Herrerias-Diego, & Lobo, 2008;Bacles & Jump, 2011;Mona, Ray, Arenas, & Excoffier, 2014). This lag is reflected in the inconsistent empirical evidence existing for the effects of fragmentation on tree populations (Kramer et al., 2008). However, natural range edges have been subject to population isolation longer than recently fragmented forests, making such populations particularly valuable for measuring the effects of isolation in long-lived species.
Given the need to better understand the impact of population isolation, we sought to determine how isolation impacts genetic diversity within populations of the long-lived, wind-pollinated tree species, Fagus sylvatica (European beech). We used a gradient of increasingly isolated forest patches found at the northern range edge of F. sylvatica in Sweden using a digitized historic map of regional beech distribution to accurately characterize the level of isolation at each study site.
We measured contemporary gene flow and pollen-mediated dispersal rates to assess the effect of isolation on the genetic structure of the adult and seedling cohorts of the species. We hypothesized that in the adult cohort, long-term isolation experienced at the range-edge shape the underlying genetic structure of this species in the region, with increasingly isolated sites being highly differentiated due to founder effects and lack of gene flow between sites. Within the seedling cohort, pollen-mediated gene flow is further restricted between isolated sites leading to a further reduction in their genetic diversity. This effect should be stronger in seedlings in more isolated sites. Given the importance of population density for pollen and propagule abundance, we hypothesize that area-based methods for measuring isolation should prove more sensitive than distance-based methods when assessing genetic impacts of population isolation.

| MATERIAL S AND ME THODS
European beech is a predominantly outcrossing, wind-pollinated tree, with seed dispersed by gravity and animals. It generally lives up to 300 years (Packham, Thomas, Atkinson, & Degen, 2012), flowering at 40-60 years of age (Wagner et al., 2010). Seed dispersal has been described at distances less than 25m (Gregorius & Kownatzki, 2005). To our knowledge the pollen dispersal curve of this mast flowering wind-pollinated tree has yet to be defined but data derived from other wind-pollinated species, such as Quercus macrocarpa, suggest that effective pollen dispersal can reach up to hundreds of kilometres (Craft & Ashley, 2007). Beech covers a 14 million ha range in Europe (see Figure S2.1 in Appendix S2) that is predominantly climatically limited (Packham et al., 2012;Sjölund, González-Díaz, Moreno-Villena, & Jump, 2017). Locally, it is additionally influenced by anthropogenic impacts, such as the historic reduction of deciduous forests (Bradshaw & Lindbladh, 2005), human disturbance and intensive land use (Björkman, 1996;Sjölund et al., 2017). The distribution of beech in Sweden was extensively mapped by Lindquist (1931) using aerial reconnaissance techniques data from 1927 to 1930. Lindquist charted stands of pure/beechdominated forests, mixed stands with beech, and solitary trees. The present-day distribution of beech is substantially unaltered from Lindquist's map and demonstrates a discontinuous migration front with larger more continuous stands in the south of the country and outlying populations further north (Björkman, 1999). The map provided a comprehensive resource to derive both area-and distancebased indices of isolation, which have been shown to differ in their effectiveness as a measure of connectivity (Moilanen & Nieminen, 2002).

| Sample collection, site selection and study sites
Fourteen sites were sampled based on their historic level of isolation according to Lindquist's (1931) map ( Figure 1, see Table S3.1 in Appendix S3). At each plot, we sampled leaf or cambium tissue from 50 adults and 50 seedlings less than 1 year old. Seedlings were sampled towards the centre of the adult plot to improve the probability of capturing the mother tree for parentage analysis. As beech has no persistent seed bank (Packham et al., 2012), seedlings were the result of pollen-mediated gene flow during the previous year (2011), also a mast year. Lindquist's (1931) map was geo-referenced in ArcMAp 10 (ESRI) allowing us to measure the approximate area of beech present in the past, closer to the time when the sampled adult trees were fertilized as seeds. We used two measures of isolation; (i) area-based methods and (ii) distance-based methods. To obtain measures of isolation based on area, circular buffer zones with a radius of 5 km, 10 km and 15 km were created around the centre of the sample plot at each site. Within each buffer zone, polygons were created for all beech stands on Lindquist's (1931) map (see Figure S2.2 in Appendix S2 for examples). Single beech trees were counted and given an arbitrary value of 78.54m 2 , a conservative estimate of the circular crown area of a mature beech tree with a radius of 5m, which was added to the area of polygons, giving a total area of beech forest canopy within each buffer zone. This estimate was derived from unpublished field-derived estimates and was necessary to include single tree counts in area-based estimates. The area of contiguous beech forest within the immediate patch where sampling had taken place (i.e. the site boundary) was also measured as a proxy of population size (e.g. Jump and Peñuelas (2006)).

| Measuring the multiple dimensions of isolation
To obtain measures of isolation based on distance, we used two measurements commonly used to establish isolation levels (e.g. Jump and Peñuelas (2006) and Leonardi et al. (2012)), which includes the F I G U R E 1 Study sites on an interpolated map of the area of beech in 15-km buffer zones. Labelled sampling sites are surrounded by 15-km inclusive buffer boundaries, shown as light circles, with geo-referenced beech forest from Lindquist's (2002) map in dark red. Overlaid basemap (ESRI) of water bodies indicate positioning of the two largest lakes, Vänern (west) and Vättern (east), near sites GUL, GAR and OMB [Colour figure can be viewed at wileyonlinelibrary. com] shortest distance from the centre of the sampled forest to the neighbouring forest boundary (abbreviated CB), and the shortest distance from the boundary of the sampled forest to the neighbouring forest boundary (abbreviated BB). In total, we tested four area-and two distance-based measures of isolation; their explanatory capacity was dependant on the heterogeneity in the distribution and structure of the surrounding forest patches.

| DNA isolation and microsatellite analysis
Genomic DNA was extracted from dried leaf and cambium samples, total of nine loci were used for parentage analysis, as two further loci, sfc0018 and fs3-04, were removed from parentage analysis, as possible null alleles close to 10% were detected using cervus 3.0.6 (Kalinowski, Taper, & Marshall, 2007) and the accuracy of parentage assignment is particularly sensitive to null alleles. Gametic disequilibrium between locus pairs was tested using FSTAT 2.9.3.2 (Goudet, 1995). Significant associations were tested by random association of genotypes at pairs of loci 1,100 times, using a 5% nominal level after Bonferroni correction.
The mean genotyping error rate was 0.5% for the 11 loci, and 0.6% for the 9 loci used in parentage analysis. We calculated error rate per locus as the number of erroneously assigned alleles over 80 repeated samples.

| Measuring and visualizing genetic diversity and pollen dispersal
We used the inverse distance weight methods available on the spatial analyst interpolation tool on ArcMAp 10 (ESRI) to map multilocus estimates of genetic diversity for the adults and seedlings, and the percentage of seedlings arising from external pollen-mediated gene flow obtained from parentage analysis. Rarefied allelic richness (A R ) and rarefied private allelic richness (A P ) were obtained using ADZE 1.0 (Szpiech, Jakobsson, & Rosenberg, 2008), standardized to a sample size of 47, the smallest number of successfully genotyped individuals per site. Private alleles were defined as those unique to a single site within either the adult or seedling cohort. Estimates of gene diversity (corrected for sample size) (H S ) and the inbreeding coefficient (F IS ) were obtained using spAGeDi 1.4b (Hardy & Vekemans, 2002). The difference between adult and seedling cohorts for each diversity estimator was tested using a Mann-Whitney U-test.
Parentage analysis was performed within each site to quantify the proportion of seedlings arising from trees existing outside the sampled plot using maximum-likelihood based methods in cervus (Kalinowski et al., 2007). We have previously tested three methods for parentage analysis: (a) parent pair analysis, (b) paternity analysis and (c) counts of foreign alleles, to obtain an estimate of pollen flow and present the most sensitive method, parent pair analysis (for further details see Sjölund, 2014). A combined exclusion probability of >99.99% for parent pairs was obtained for nine loci. We followed a method used by Buschbom et al. (2011) to estimate external pollenmediated gene flow. We used a two-step procedure within each site to assign parentage. In the first step, seedlings were primarily assigned a maternal tree based on LOD score at 90% confidence level (Cl). LOD scores are obtained from the natural log of the overall likelihood ratio, which is calculated for candidate parents by dividing the likelihood that they are the true parent by the likelihood that they are not the true parent, with larger ratios indicating that the candidate parent is likely to be the true parent. Individuals with identified parents (single or parent pair) at 90% Cl were assumed to have a maternal tree present, whereas seedlings with no identified parents at 90% Cl were considered as not having a maternal tree present in the adult cohort and therefore excluded from further analysis. For the purpose of maternal tree assignment, seedlings were assumed to be primarily dispersed by gravity (Wagner et al., 2010), which is likely as the seedlings originated from a mast year, known to satiate primary predators, including animals involved in seed dispersal. In the second step, we estimated seedlings originating from external pollen dispersal from parent pair analysis (Figure 2). To avoid potential bias generated by comparing populations of different sizes when estimating pollen immigration, we standardized seedling sample size to 15 per population (i.e. the lowest number of maternal trees assigned for any given site using subsamples by random selection).
Critical LOD scores and Delta (the difference in LOD scores) at 90% confidence between the most likely candidate parent and the second most likely candidate parent were obtained by simulating 100,000 offspring according to the following settings: all adult trees were included as candidate parents and represented 100% of potential parents, the proportion of loci typed varied from 0.998 to 1, the proportion of loci mistyped was set to 1%, as the minimum recommended by the program.

| Modelling the effects of isolation on genetic diversity and pollen-mediated gene flow
We performed a partial least squares regression (PLSR) using the R package plsDepot 0.1.17 to determine the effects of isolation on each of the genetic diversity estimators and the measures of external pollen-mediated gene flow. PLSR is relatively robust to small sample sizes compared to multiple regression and has the added benefit of allowing easy visualization of data consisting of correlated predictor variables (Carrascal, Galva, & Gordo, 2009). PLSR deals with the lack of independence among predictor variables by grouping them into one or more orthogonal, linear gradients of covariation while maximizing the explained variance in the response variable (Palomino & Carrascal, 2007).
We tested three variables describing genetic diversity in adults and seedlings: allelic richness (A R ); private allelic richness (A P ) and gene diversity (H S ). We did not perform tests on F IS as patterns are confounded by the significance of the F IS values. For measures of pollen-mediated gene flow, we tested the number of seedlings with no local parent pairs (LPP) at 95% Cl, that is, seedlings that could not be assigned to two local adult trees. The predictor variables used were the six measures of isolation derived from Lindquist's (1931) map, comprising the four area-based (5-km buffer, 10-km buffer, 15-km buffer, site boundary) and two distance-based (CB, BB) measurements. Latitude and longitude were also included as predictors to account for geographical variation. Predictor variables were log(x + 1) transformed to standardize the scale of predictors. In models with two significant components, the secondary components were found to be redundant, revealing similar trends as the main component and are therefore not presented. We present weights of significant predictor variables, which indicate the trend and the importance of the relationship with the component.
We used the program Bottleneck 1.2.02 (Cornuet & Luikart, 1996) to test for recent bottlenecks in the adult and seedling cohort using 11 loci. Populations were tested under the Two-phase model (TPM), allowing 95% single-step mutations and 5% multi-step mutations with a variance of 12 among multi-step mutations under 1,000 simulation iterations, as recommended for microsatellites by Piry & Luikart (1999). Significance tests for H S > H eq (where, H s is gene diversity and H eq is the heterozygosity expected under mutation-drift equilibrium) were performed using Wilcoxon's test implemented in the program. A recent reduction in population effective size that causes bottlenecks, can be detected as a reduction in allelic richness and gene diversity H S , where allelic richness is reduced faster than H S leading to a larger heterozygosity than expected under mutation-drift equilibrium.
2.6 | Identifying regional population structure at the leading edge To characterize regional genepools and identify potential barriers to dispersal, individual-based assignment methods were performed on the adult cohort using GenelAnD 4.0.4 (Guillot, Estoup, Mortier, & Cosson, 2005) a spatially explicit Bayesian clustering model.

| Isolation indices
The level of isolation obtained by area-based measurements ranged from 32.94 ha to 8,396.37 ha of surrounding forest. Distance measures of isolation ranged from 0.065 km to 50.429 km (see Table S3.1 F I G U R E 2 Percentage of seedlings resulting from external pollen dispersal. Interpolated maps of parentage analysis using nine loci depicting the percentage of seedlings (%) with no local parent pair at 95% Cl (No LPP 95% Cl) [Colour figure can be viewed at wileyonlinelibrary.com] in Appendix S3). Mapping the total area of beech within a 15-km buffer zone around each site revealed a north-easterly trend of increasing isolation (Figure 1), reflecting the reduction of population density visible in Linquist's (1931) map.

| Estimates of genetic diversity and external pollen-mediated gene flow
The 11 loci used in this study were found to be in gametic equilibrium. The maximum number of alleles for all samples had a multilocus average of 13.36, ranging from 4 to 28 alleles per locus. Rarefied allelic richness (A R ) in adults ranged from 5.06 to 7.17, and 4.50 to 6.17 in seedlings, with adults having a significantly higher level of allelic richness compared to seedlings (U(12) = 147, Z = 2.25, p < .05) (Table 1, Figure 3). Adult rarefied private allelic richness (A P ) ranged from 0.02 ± 0.02 to 0.39 ± 0.22, while in seedlings A P ranged from 0.00 to 0.53 ± 0.36. There were no significant differences between levels of private allelic richness in adults and seedlings (U (12)

| PLSR models of genetic diversity and external pollen-mediated gene flow
Significant PLSR components were found for rarefied allelic richness (A R ) and gene diversity (H S ) in adults and seedlings, and for measures of external pollen-mediated gene flow (Table 2) The number of seedlings with no local parent pairs at 95% Cl increased in sites with lower distances between forests and higher areas of surrounding beech, following a north to south gradient (R 2 = 58.2%; p < .01). This pattern is visible in Figure 2. The contribution of significant isolation variables and geographical variables were similar, with the distance-based variable, CB, explaining 10.2% (p < .05) of the variation within the response, the area of beech within the 5-km buffer zone explaining 10.1% (p < .001), and latitude explaining 6.5% (p < .001). Overall, isolation indices and latitude explained more variation in pollen-mediated gene flow, with an R 2 ranging from 5.7% to 10.2%, compared to the adult and seedling measured of genetic diversity ( Table 2). Measures that were taken closest to the sampling area, for example, 5-km buffer and CB, explained the largest amount of variation 10.1% and 10.2%, respectively, reflecting the sensitivity of measures of pollen-mediated gene flow to local measures of isolation.
There was no evidence for recent genetic bottlenecks in any of the 14 sites in the adult or seedling cohort (see Table S3.2 in Appendix S3). For genetic diversity estimators, the strongest relationship between predictor variables and response was found in seedling A R (R 2 = 58.3%, p < .05), which was significantly negatively related to isolation. The remaining genetic diversity response variables in order of the original variance explained were seedling H S (R 2 = 33.8%, p < .05), seedling A R (R 2 = 30.1%, p < .05) and adult H S (R 2 = 26.2%, p < .05).
An increase in A R in adults was associated with southern sites, with a high area of surrounding beech forest (Table 2, Figure 3). Latitude explained the largest variation in adult A R (R 2 = 7.3%, p < .001), with site boundary explaining the most variation out of the area-based measurements (R 2 = 5.8%, p < .001). There was an unexpected significant, positive relationship of increasing distance and increasing adult A R . However, this explained <0.1% of R 2 (p < .05) and therefore was not considered biologically relevant. Seedling A R revealed a similar trend to that found in adults, although isolation was the primary driver of variation in the response, instead of latitude. Increased A R in seedlings was associated with a high area of surrounding forests and low distances between forests in southern latitudes. The areabased measure of beech in the 15-km buffer zone was the primary contributor to variation in the response (R 2 = 8.3%, p < .001) with a comparable amount of variance explained by the distance measure, boundary to boundary (BB) (R 2 = 8.2%, p < .001). Latitude only explained 0.4% of the total variation in the response (p < .001).
Adult H S was primarily related to increased area of surrounding beech, specifically associated with the 15-km buffer zone (R 2 = 14.9%, p < .001). As with adult allelic richness, southern sites also displayed higher levels of H S . However, in the maps of genetic diversity (Figure 3), the trend for adult H S was not as clear as that displayed by adult A R . Seedling H S was the only response significantly influenced by longitude, with H S increasing on a west to east gradient, explaining the largest amount of variation in the response (R 2 = 14.7%, p < .001) (Table 2, Figure 3). The relationship with isolation was contradictory to that found in the other genetic diversity response variables, as higher levels of seedling H S were associated with a decrease in surrounding beech area (10 km: R 2 = 4.3%, p < .01) and lower distances between forests (CB: R 2 = 2.7%, p < .05).
When considering all models for both genetic diversity and  (Petit, El Mousadik, & Pons, 1998); A P , private allelic richness (Szpiech et al., 2008); H S , gene diversity corrected for sample size (Nei, 1978); F IS , inbreeding coefficient (Weir & Cockerham, 1984). The minimum number of gene copies (k) used for rarefication analysis of A R and A P is 94 with standard errors of the rarefaction procedure provided. p-values for F IS are obtained after 10,000 permutations of gene copies within adult or seedling individuals of each site. p-values for mean genetic diversity estimates indicate significant differences between adults and seedlings. Significant two-sided p-values are indicated as *p < .05, **p < .01 and ***p < .001. The sites are ordered in terms of total area of beech within the 15 km inclusive buffer zone. Multilocus estimates of genetic diversity were attained from 11 loci.
were made by the addition of each buffer zone in all response variables except for H S , which in adults only related to the 15-km buffer, and in seedlings, the 10-km buffer. The boundary-based distance measure, BB, which was significant in most models, did not significantly explain variation in adult or seedling H S.

| Regional genetic structure at the leading range edge
Three clusters were identified using individual-based assignment  Figure S2.4 in Appendix S2 for maps of cluster posterior probabilities). No further substructuring was found in the western cluster 1. All inferred clusters using 13 sites were found to be significantly differentiated and in gametic equilibrium, except for site OMB, which showed significant disequilibrium at one pair of loci (data not shown).
Analysis with structure was in agreement with GenelAnD and indicated a presence of three clusters in the data (see Figure S2.5 in Appendix S2 for the log probability of the data and ΔK). The levels of admixture were higher according to structure as opposed to GenelAnD, with a trend of decreasing admixture as isolation (i.e. area of beech forest in the 15-km buffer zone) increased ( Figure 5).

| Founder events and isolation shape genetic diversity
We found evidence of reduced allelic richness (A R ) in both adults and seedlings in isolated sites, with latitude also significantly explaining a large proportion of variation in adults (Table 2). Adult gene diversity (H S ) revealed a similar trend to that found in allelic F I G U R E 3 Distribution of genetic diversity in adults and seedlings. Multilocus genetic diversity estimators using 11 loci are abbreviated as follows: rarefied allelic richness (A R ); rarefied private allelic richness (A P ); gene diversity corrected for sample size (H S ) and the inbreeding coefficient (F IS ). p-values for F IS are obtained after 10,000 permutations of gene copies within adult or seedling individuals of each site. Significant two-sided p-values less than .05 are indicated by yellow circle [Colour figure can be viewed at wileyonlinelibrary.com] richness. The observed pattern in genetic diversity also resembled the southern richness and northern purity paradigm, coined by Hewitt (1999), and was based on the observed reduction in population size through founder events at the leading edge, resulting in a loss of alleles through genetic drift (Excoffier, Foll, & Petit, 2009;Lande, 1988;Nei et al., 1975). Low migration between isolated populations contributes to this trend (Vucetich & Waite, 2003). As rare alleles are at risk of disappearing first, a reduction in population size can affect A R disproportionally more than H S (Comps et al., 2001;Jump & Peñuelas, 2006;Piry & Luikart, 1999). This pattern was reflected in both adults and seedlings, which displayed a higher amount of variation explained by predictor variables for A R compared to H S .
Additionally, the most southerly site, HAC displayed the highest level of rarefied private allelic richness (A P ) in adults and seedlings ( Figure 3), although PLSR models for A P were not significant.
The interacting effects of latitude and isolation on A R in adults suggest that marginal, isolated populations are subject to strong genetic drift, possibly due to the combination of founder events and persistent small population sizes that lead to the loss of alleles over time. The relatively weaker effect of isolation on A R in adults, compared to latitude, may also be influenced by an outlier, site OMB, which displayed relatively high levels of allelic richness (Figure 3).
Although OMB is not the most northerly site, it is the most isolated in terms of surrounding area and the distance to the nearest neighbouring forest (see Table S3.1 in Appendix S3), influencing the trend found with isolation indices. Seedling A R was strongly affected by isolation, with very little contribution of latitude. This stronger negative impact of isolation on seedlings compared to adults (Table 1, Figure 3) reflects temporal effects of genetic drift on small populations, which intensify over time (Aguilar et al., 2008;Ellstrand & Elam, 1993). This pattern is in agreement with the observed adult to seedling relative reduction of A R in site OMB, compared to remaining sites ( Figure 3). As the life span of beech is between 150 and 300 years, the oldest populations, having established approximately at 3,000 BP (Bradshaw & Lindbladh, 2005), have experienced at least 10 to 20 generations. Even without considering overlapping generations, this is in agreement with the values obtained from a simulation study on habitat fragmentation by Mona et al. (2014) who recommend at least 10 generations, ideally more than 100 generation needed for isolation to affect genetic diversity at the leading range edge. Overall, these patterns are indicative of a relatively strong effect of isolation on genetic diversity in these range-edge populations.

| Isolation shapes regional genetic structure
Isolation appears to be acting as a barrier to gene flow at the range edge in Sweden, indicated by the reduction in external pollen-mediated gene flow with increased isolation (Figure 2). Although we found isolation-by-distance in the adult cohort, it appears that paired sites  Figure S2.6 in Appendix S2 for plot of geographical and genetic distance within and between clusters). In terms of geographical barriers, the southern area of Sweden sampled in this study is quite flat with the highest peak, Tomtabacken, being 361m in elevation. The sampling area does enclose Vättern, Sweden's second largest lake, which may have been a barrier to gene flow between GAR and OMB northerly sites that lie on either side of the lake.
Clustering results using STRUCTURE revealed a trend of increased admixture in south-westerly sites with increased homogeneity among individuals between north-eastern clusters ( Figure 5). A similar trend has been found in leading-edge populations of Acer campestre in Poland, which also display further genetic structuring and less admixture with latitude (Chybicki, Waldon-rudzionek, & Meyza, 2014). The large western cluster 1 identified by GenelAnD in the adult cohort (Figure 4), contains sites displaying a range of isolation levels.
Although our markers are unable to confirm phylogeographical patterns, the pattern is in agreement with palynological evidence on the initial colonization of beech in Sweden around 3,000 BP (Bradshaw & Lindbladh, 2005). Further population substructure observed for clusters 2 and 3 (Figures 4 and 5) is likely to have arisen from genetic drift in marginal isolated populations (Excoffier et al., 2009).

| Pollen dispersal and its relation to forest patch density
The directional relationships observed for pollen dispersal with isolation and latitude were consistent between models, although the amount of variation explained varied. As our study plots exist within forest fragments, measures of external-mediated pollen dispersal reflect the density of the pollen cloud produced by surrounding forest as opposed to strict long-distance pollen flow. As pollen production is related to the number of reproductive trees, it is likely that pollen production is higher in continuous populations compared to fragmented isolated populations. Therefore, the probability of fertilization by pollen grains from external trees decreases along with isolation. This pattern is in agreement with previous studies that have found an increase in pollen dispersal with tree density (Vranckx et al., 2014;Wang et al., 2010). Although the isolation indices used in our study do not incorporate density in terms of tree numbers, the buffer measures do incorporate the density of forest fragments.
The reduction in allelic richness between adult and seedling cohorts suggests that the pollen donor diversity is not large enough to safeguard against the effects of genetic drift under small population sizes (Table 1, Figure 3). As seedlings were the result of pollen dispersal during a mast year, we would expect a stronger negative impact of isolation on pollen dispersal during non-mast years when flowering and pollination success are significantly lower (Hilton & Packham, 1997;Linquist, 1931;Nilsson & Wästljung, 1987).

| Effective measurements of isolation
A combination of isolation variables was effective at explaining variation in genetic diversity and pollen dispersal. Area-based measurements using buffer zones present a standardized measure for the surrounding area of forest. We found a general additive effect of increasing buffer zone size, implying a sensitivity to buffer size and also the importance of local and regional isolation levels on F I G U R E 4 Inference of genetic clusters in the adult cohort over 13 sites. Sites are displayed as small black circles, with large open ellipses indicating the grouping of the three inferred population clusters: the western cluster 1 (grey); the south-eastern cluster 2 (green) and the north-eastern cluster 3 (orange). The dotted lines indicate further substructuring found in further analysis of the subset of sites in cluster 2 and 3. A total of 11 loci were used in analysis [Colour figure can be viewed at wileyonlinelibrary.com] F I G U R E 5 Individual assignment to each cluster using structure. The Q-matrix presents the average assignment probabilities over 10 consecutive runs for K = 3. Site codes are indicated below, and are ordered by increasing isolation from left to right obtained from estimates for the area of beech (ha) in the 15-km inclusive buffer zone. A total of 11 loci were used in analysis [Colour figure can be viewed at wileyonlinelibrary.com] genetic diversity and pollen dispersal of beech. In a meta-analysis by Moilanen and Nieminen (2002), buffer-based measurements were found to be superior to distance-based measurements when quantifying isolation. Our findings emphasize the utility of such area-based measurements to provide a relatively easy and quick way of measuring isolation that, in our study, outperforms commonly used site boundary and distance measures.

| CON CLUS ION
The gradient of isolation at the leading range edge of beech in Sweden has shaped contemporary gene flow in adult and seedling cohorts of the species. Isolation has a negative impact on allelic richness, which is exacerbated over time, further affecting progeny. In