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Keywords:

  • fragmentation;
  • gene flow;
  • genetic connectivity;
  • long-distance dispersal;
  • migration rate;
  • Pinus sylvestris (Scots pine);
  • pollination;
  • uniparental markers

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information
  • There is a gap between the order of magnitude of maximum documented distances of airborne tree pollen transport (up to 102–103 km) and effective wind pollination (up to 101 km), which may partly derive from greater difficulties in detecting the latter. This study aims to assess wind pollination over scales closer to the maximum observed physical pollen transport distances.
  • The origin of effective pollen immigrants into a strongly isolated Iberian Pinus sylvestris remnant was investigated using paternally inherited microsatellite markers and maximum-likelihood estimation combined with Monte Carlo assessment of parameter uncertainty.
  • The results revealed significant effective pollen flow (up to 4.4%) from a large population located 100 km away, suggesting that the well-known mesoscale airborne transport of viable pine pollen can result in successful pollination over larger scales than previously reported for wind-pollinated tree species.
  • This study supports the view that the gap between documented potential and effective wind pollen dispersal scales might not accurately reflect biological reality. Expanding the expected range of effective wind pollination has an impact on the assessment of a wide range of ecological and evolutionary processes, including reproductive assurance on fragmentation or colonization, metapopulation connectivity and interactions with local adaptation in heterogeneous habitats.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Propagule movement determines the scale and magnitude of ecological and evolutionary interactions among spatially structured plant populations. Seed dispersal is the vector of demographic connectivity between populations, regulating extinction–colonization processes, source–sink dynamics and species’ coexistence (Nathan & Muller-Landau, 2000); pollen flow defines reproductive assurance, mating patterns and the degree of reproductive isolation between plant demes (Ellstrand, 1992). Both seed and pollen dispersal determine the rate of among-population gene flow, and thus influence genetic population divergence (Wright, 1931), effective metapopulation size, probabilities and times of fixation of new alleles (Whitlock, 2003), and the evolution of local adaptation in heterogeneous environments (Lopez et al., 2008). In the current global warming scenario, the seed dispersal range will place maximum limits on the ability of species to track suitable ecological niches via migration, and both pollen and seed dispersal ranges will establish bounds for the potentially adaptive flow of genotypes from warmer to colder regions (Davis & Shaw, 2001).

Ecological and evolutionary implications of propagule movement, however, depend on the chances of effective pollination and effective seedling establishment, and the scale of potential and effective dispersal need not coincide. For wind-pollinated trees, it has long been known that airborne pollen can flow tens to thousands of kilometres, based on pollen samples collected over the sea, inland beyond the tree line or before local pollen shedding (Sarvas, 1962; Koski, 1970; Nichols et al., 1978; Campbell et al., 1999). It is also recognized that a large proportion of pollen remains viable after such long-distance transport (Lindgren et al., 1995; Varis et al., 2009; Williams, 2010), provided that atmospheric conditions are not very wet or cold (Pulkkinen & Rantio-Lehtimäki, 1995; Bohrerova et al., 2009). Yet, there is a gap between the order of magnitude of maximum documented distances of airborne tree pollen transport (up to 102–103 km) and effective pollination (up to 101 km; see table 2 by Petit & Hampe, 2006; but see Ahmed et al., 2009 for longer distance insect pollination).

An evident discrepancy of this kind is seen for Scots pine (Pinus sylvestris), a monoecious, wind-pollinated, predominantly outcrossing conifer with a wide geographical distribution. Substantial amounts of viable Scots pine pollen have been found to move hundreds of kilometres across northern Europe (Koski, 1970; Lindgren et al., 1995; Varis et al., 2009), and it is presumed that efficient pollen gene flow contributes to the large effective population size of the species (Muona & Harju, 1989). Nonetheless, molecular studies in the species have been unable to identify effective pollen donors beyond a few hundred metres from mother trees (Yazdani et al., 1989; Robledo-Arnuncio & Gil, 2005). Although background pollination from unknown sources into isolated stands is likely to be the result of longer distance dispersal events (e.g. Harju & Muona, 1989; Robledo-Arnuncio & Gil, 2005), experimental constraints have prevented precise measurements of the actual scale of this potentially long-distance pollen immigration process. It is actually unclear whether discrepancies between maximum documented scales of potential and effective pollen dispersal largely derive from obstacles to successful long-distance mating (such as phenological asynchronies, competition with local pollen and genetic incompatibilities) or, rather, from greater difficulties in assessing effective dispersal over broad areas.

The characterization of long-distance pollination is, indeed, a great challenge, as it involves not only the sampling of presumably rare mating events, but also ascertaining, among potentially many distant sources, the origin of the corresponding effective male gametes. In addition, it is not simply the detection of effective long-distance dispersal events that should be targeted, but rather the unbiased estimation of long-distance migration rates, the precise magnitude of which strongly influences the expected adaptive outcome of pollen gene flow (Lenormand, 2002). Genetic parentage analysis provides an efficient means of characterizing effective dispersal (e.g. Oddou-Muratorio et al., 2005; Burczyk et al., 2006), but requires exhaustive genotyping of all potential candidate parents, and thus becomes unfeasible over large scales, unless the population density is extremely low (Ahmed et al., 2009). Genetic assignment methods allow the establishment of the population origin of every individual in a sample without exhaustive genotyping of candidate parents (Manel et al., 2005), but suffer low power when genetic differentiation among source populations is modest, and are not efficient for the estimation of unbiased migration rates (Cornuet et al., 1999; Paetkau et al., 2004). Alternative Bayesian methods use gametic disequilibrium information in population samples of multilocus genotypes to jointly estimate contemporary migration rates between populations, the individual origin of every individual, genotypic frequencies before dispersal and population inbreeding coefficients, assuming either low migration (Wilson & Rannala, 2003) or migration–drift equilibrium (Faubet & Gaggiotti, 2008). The latter general procedures are promising for the estimation of long-distance contemporary dispersal rates in different kinds of organism, although their accuracy and convergence properties can be sensitive to model assumption violations (Faubet et al., 2007; Faubet & Gaggiotti, 2008).

Several inferential advantages inherent in plants allow for a more straightforward approach to contemporary long-distance effective dispersal estimation (see Robledo-Arnuncio et al., 2009). First, seed and pollen dispersal typically take place during discrete synchronized periods, before which gene frequencies of candidate source populations can be estimated independently of migration rates. Second, paternally and maternally inherited DNA markers are available for many species, making possible the estimation of male and/or female gametic migration separately, without requiring Hardy–Weinberg equilibrium assumptions or joint estimation of population inbreeding coefficients. It is then possible to estimate contemporary migration rates independently of other parameters, using an analogue of classical mixture analysis for fish stock identification (Milner et al., 1981; Manel et al., 2005), but based on population haplotypic samples of adults and seeds collected before and after dispersal, respectively (Robledo-Arnuncio et al., 2009; see also Broquet et al., 2009).

Based on a multiple population extension of the maximum likelihood approach used in Robledo-Arnuncio et al. (2009) and intensive Monte Carlo significance testing, this study aims to demonstrate the ability of airborne tree pollen for effective pollination over mesoscale distances. The origin of effective pollen immigrants into a small Iberian Pinus sylvestris L. remnant was investigated, revealing significant effective pollen flow (up to 4.4%) from a large conspecific population located c. 100 km away. Results of this study suggest that the well-known mesoscale airborne transport of viable pine pollen clouds can result in successful pollination.

Materials and Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Experimental system

The Northern Meseta is a 60 000-km2 plateau in the central-northwestern Iberian Peninsula. Pinus sylvestris L. (Scots pine) grows in montane isolates over peripheral mountain chains, except for two relict remnants from ancient Holocene forests still surviving in the dry inner plains (Franco-Múgica et al., 2001) (populations A and B in Fig. 1). The smaller relict, population A, consists of 36 isolated adult Scots pine trees. The nearest conspecific population is the other remnant (population B), an 8000-tree fragment located 28 km to the east, and the next nearest (population C) is a widespread dense monospecific woodland growing in the Guadarrama Chain, c. 60 km to the south (Fig. 1 and Table 1). Three other Scots pine populations (D–F) can be delimited on the peripheral mountains in the region at distances ranging from 100 to 150 km from population A. One of these three populations (D) is small and geographically marginal, but the other two extend over hundreds to thousands of hectares each.

image

Figure 1.  Scots pine (Pinus sylvestris): natural distribution and spatial location of the six sampled populations in the Spanish Northern Meseta. Population codes are indicated by capital letters (AF). Numbers in parentheses indicate the size of adult tree samples.

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Table 1.   Pairwise genetic (FST, below diagonal) and geographical (in km, above diagonal) distances between Scots pine (Pinus sylvestris) study populations (AF)
 ABCDEF
A02858111105150
B0.05505613682123
C−0.0040.069011876144
D0.0090.0360.0070193255
E0.0050.0260.0190.032077
F−0.0010.033−0.0020.009−0.0010

Using four chloroplast and two nuclear microsatellites (SSR), Robledo-Arnuncio & Gil (2005) performed a categorical paternity analysis for 813 seeds collected from trees of the small remnant A, finding that 778 could be assigned to local fathers, whereas 35 (4.3%) could not. Putative immigrants most probably originated from long-distance external sources for the following reasons (Robledo-Arnuncio & Gil, 2005): (1) except for remnant B, the dry plains surrounding population A are unsuitable for Scots pine and are either deforested or occupied by exploited monospecific Pinus pinaster stands subject to exhaustive (measuring every tree) 10-yearly inventories since the beginning of the 20th century that have failed to find any other Scots pine; (2) PCR and electrophoresis were repeated for all adult trees and 35 putative immigrants to discard genotyping errors; (3) haplotypes of putative immigrants mismatched those of all local fathers at more than one loci in most cases, and therefore it is very unlikely that they were the result of novel mutations; and (4) 30 of 35 putative immigrants carried unique haplotypes, the kind of diversity expected in a long-distance pollen cloud.

This dataset is exploited here in an attempt to determine the population origin of the 813 four-chloroplast SSR (paternally inherited) embryo haplotypes, based on reference adult haplotypic frequencies from local population A (all 36 individuals genotyped in Robledo-Arnuncio & Gil, 2005) and from external populations B–F, available from a phylogeographical survey (Soto et al., 2010) in which 27–75 randomly collected adult individuals from each population were genotyped at the same four chloroplast SSR loci (Fig. 1). All 813 embryos collected from A were considered, and not only the 35 without a compatible local father, to account for cryptic pollen immigration. Population diversity and differentiation were characterized using Nei’s unbiased haplotypic diversity (Nei, 1987) and FST calculated via analysis of molecular variance (AMOVA) (Excoffier et al., 1992), respectively, with haplotypic identity as the distance metric.

Migration estimation model

A multiple population extension of the maximum-likelihood approach in Robledo-Arnuncio et al. (2009) is introduced here. Let us consider local population A and the = 5 external candidate source populations. Let mi be the proportion of the = 813 seed sample (S) collected from population A that has been sired by individuals from the i-th external population, and inline image the proportion sired by local individuals. That is, we assume that no other external populations send migrants to population A (the violation of this assumption is considered later). Let k be the total number of observed haplotypes, defined as unique combinations of variants at the four chloroplast SSR loci, and let ph,0 and ph,i be the adult population frequencies of the h-th haplotype in the local population and in the external population i, respectively. The probability of observing haplotype h in sample S is then

  • image(Eqn 1)

and the multinomial joint-likelihood function for the whole set of haplotypes carried by the seeds in sample S is

  • image(Eqn 2)

where nh is the number of seeds in the sample carrying haplotype h, with inline image. Migration rate estimates are then obtained conditional on known values for the p frequencies by maximizing the log-likelihood function

  • image(Eqn 3)

A similar formulation has been used to estimate the proportion of fish in a mixed population originating from different stocks at least since Milner et al. (1981), and the method has been found to be well defined, identifiable and to have a unique solution (Millar, 1987). Confidence intervals (CIs) at the 95% level for inline image were obtained with the profile-likelihood method. External adult population haplotype frequencies were estimated following the Bayesian method of Rannala & Mountain (1997) as inline image, where xh,i and ni are the observed count of the h-th haplotype and the sample size for population i, respectively. This method assumes a priori that the total number of haplotypes for each population is identically k, correcting for potential biases arising from undetected haplotypes in small samples. For local population A, however, maximum-likelihood estimates were used, inline image, as all existing adult trees were sampled in this 36-tree isolated stand.

Performance of the estimator

The expected bias, accuracy (root mean square error, RMSE) and CI coverage of pollen migration (inline image) and local pollination (inline image) estimates for the Scots pine system were evaluated via Monte Carlo simulation. The main questions addressed were whether the method might yield inline image significantly different from zero in the absence of pollen immigration, and whether it would be able to estimate accurately small (even or uneven) migration rates, being robust to unsampled sources.

Given the vector of estimated adult haplotypic frequencies for the i-th population, inline image, the actual seed sample size = 813 and the actual adult sample sizes n = {36, 30, 75, 27, 54, 48}, and assuming migration rates m = {1−Σmi, m1, m2, ..., mI}, a first set of stochastic simulations was conducted as follows.

  • 1
    The number of seeds from each population in the simulated seed sample was drawn from a multinomial distribution with class probabilities m and s trials.
  • 2
    The haplotype for every seed originated in population i was drawn from a multinomial distribution with class probabilities inline image.
  • 3
    Adult tree samples were generated for every population i via ni draws from a multinomial with class probabilities inline image, except for local population A, for which the real exhaustive adult sample was kept.
  • 4
    Migration rates m were estimated by applying Eqn 3 to the simulated seed sample, conditioned on haplotypic frequencies estimated from simulated adult samples. These steps were repeated to generate 1000 independent realizations of the process with their corresponding inline image values, which were compared against m to calculate expected estimation errors.

The above Monte Carlo scheme (Scheme 1) assumes good sampling of adult haplotypic frequencies, which might not be valid for the external Scots pine populations. A second set of simulations (Scheme 2) was conducted to assess the effect of adult sampling error, including an initial step to generate parametric adult frequency distributions for the five virtual external populations (BF) corresponding to a level of population differentiation (FST) equal to that observed. Parametric frequencies for population i, inline image, were obtained by sampling from a Dirichlet distribution (Wright, 1931; Faubet et al., 2007)

  • image(Eqn 4)

with λ = 1/FST−1 and qh being the global frequency of the h-th haplotype, assumed to equal the observed global frequency pooling all six sampled populations. After obtaining parametric frequency distributions (inline image) for the five external populations (BF), global FST was calculated for all six populations (including A). If the latter was not within 10% of the target FST value, new parametric frequencies were generated until this condition was satisfied. The next steps in Scheme 2 were the same as the four described above for Scheme 1, but using parametric inline image instead of estimated inline image in steps (2) and (3).

Effect of unsampled source populations

No other Scots pine populations occur in the plains surrounding A and B, but there are a few unsampled small native stands between populations C and E (Fig. 1), as well as some unsampled scattered mountain plantations growing close to populations C, D, E and F and established from local reproductive material. All unsampled populations are a minimum of 50 km away from A. Although potential pollen migration from these unsampled stands into A would corroborate any evidence of effective pollination over minimum distances of c. 50 km, it might affect migration estimates from sampled populations.

Scheme 2 was used to simulate unknown populations contributing pollen migrants to the seed crop of A. Specifically, a total of I sampled plus U unsampled populations was considered in the initial parametric frequency generation stage, as well as in steps (1) and (2), but only I populations were considered in steps (3) and (4). Estimation errors for pollen migration rates were then calculated by comparing the inline image estimates for sampled populations with their respective assumed values, and errors in local pollination estimates were computed by comparing the estimated inline image with the assumed inline image. C++ programs to conduct this and all other described analyses are available from the author.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Population diversity and differentiation

Seventy-eight different chloroplast haplotypes were found in the total sample of 270 adult trees (Supporting Information Table S1). The observed number of haplotypes roughly increased with population sample size, ranging from a low of 14 in population B to a high of 43 in C. Unbiased haplotypic diversity was similarly high across all six populations (mean inline image; range, 0.931–0.977). Overall differentiation between populations was low (inline image), with pairwise inline image values ranging from 0 to 0.069 (Table 1).

Five of the 813 seeds collected from remnant A had missing data at one or more of the four chloroplast SSR regions and were discarded from the analysis. The remaining 808 seeds showed 37 different chloroplast haplotypes (Table S1) comprising: (1) all 23 present among adult trees of A (cumulative frequency, 0.977), 22 of which were also present in at least one external population sample; (2) seven chloroplast haplotypes present only in the external adult samples (cumulative frequency, 0.010); and (3) seven other chloroplast haplotypes not present in any of the adult samples (cumulative frequency, 0.012).

Pollen migration estimates

Based on estimated adult haplotypic frequencies for all candidate source populations (Table S1), maximum-likelihood pollen immigration estimates from external populations into remnant A ranged from 0% to 4.4%, totalling 6.7% for the whole set of external sources (Table 2). This total was somewhat larger than that (4.3%) reported previously using paternity exclusion (Robledo-Arnuncio & Gil, 2005), consistent with the small external sample (a subset of sample C) used in the latter study to correct for cryptic pollen inflow. Pollen migration estimates were zero or not significantly different from zero for the closest but very small population B, for small population D and for the longest-distant and widespread population F. Estimated migration from the closest (58 km away) large population (C) was 1.6%, although this value was only marginally significantly different from zero (95% CI, 0.003–0.040). The highest estimate (0.044; 95% CI, 0.018–0.109) corresponded to the next-nearest large woodland (population E), growing 105 km away from A.

Table 2.   Maximum-likelihood pollen migration estimates from five long-distant populations (BF) into the standing seed crop of an isolated Scots pine (Pinus sylvestris) stand (A)
SourceABCDEF
Migration (95% CI)0.933 (0.865–0.944)0.000 (0–0.012)0.016 (0.003–0.040)0.007 (0–0.023)0.044 (0.018–0.109)0.000 (0–0.011)

Expected errors and uncertainty estimation

Assuming that there are no pollen sources other than the six sampled populations, the first question was whether the method would yield false positives in the absence of pollen migration into population A (i.e. inline image when Σmi = 0). Simulations clearly rejected this possibility (Table 3), when using estimated frequencies (Scheme 1) or simulated parametric frequencies (Scheme 2 with FST = 0.016) to generate virtual adult samples. In both cases, none of the 1000 independent replicates yielded inline image for any of the five external populations, translating into null bias and RMSE, and 100% profile-likelihood CI coverage.

Table 3.   Expected absolute bias, accuracy and confidence interval coverage of pollen migration rate and local pollination rate estimates
Population frequenciesmiMigration estimates inline imageLocal pollination estimate inline image
BiasRMSELLTHULTLBiasRMSELLTHULTL
  1. Based on 1000 independent Monte Carlo simulations assuming: five source populations of Scots pine (Pinus sylvestris) with equal migration rates (mi); adult and seed sample sizes equal to real sizes; population haplotypic frequencies equal to the observed frequencies (Scheme 1) or simulated parametrically (Scheme 2 with FST = 0.016).

  2. RMSE, root mean square error; LLTH and ULTL, the proportion of times that the 95% confidence interval (CI) lower limit was higher, or the CI upper limit was lower, respectively, than the assumed value.

Estimated (Scheme 1)00.0000.0000.0000.0000.0000.0000.0000.000
0.0100.0000.0070.0320.048−0.0010.0130.0350.120
0.0500.0000.0180.0570.0690.0020.0270.0590.041
Simulated (Scheme 2)00.0000.0000.0000.0000.0000.0000.0000.000
0.0100.0000.0090.0330.043−0.0010.0140.0260.140
0.050−0.0010.0220.0580.0810.0050.0300.0940.049

Assuming equal non-null migration rates (mi = 0.01 or 0.05) from all five external populations (Σmi = 0.05 or 0.25, respectively), both migration (inline image) and local pollination (inline image) estimates remained virtually unbiased in the simulations, whereas their variance (and thus RMSE) increased somewhat with increasing migration (Table 3). Coverage of nominally 95% CI for inline image and inline image ranged from c. 85% to 92%, decreasing with increasing parametric values of mi and LP, respectively, and generally exhibiting too-low upper limits more frequently than too-high lower limits. Results were largely similar for Schemes 1 and 2, even though, as expected, estimation errors and CI coverage worsened when introducing adult sampling error (Scheme 2; Table 3).

Simulations indicated that the method is able to estimate unequal migration rates fairly accurately as well, with a tendency to underestimate higher rates and overestimate lower ones (Fig. 2 and Table 4). This tendency suggests that the estimated null value of pollen migration rates from populations B, D and F, and the non-null value of pollen migration rates from populations C and E (Table 2), are not the result of systematic biases. Considering a simulated migration rate distribution similar to that estimated from the real samples, with = {0, 0.016, 0, 0.044, 0}, and assuming good adult sampling (Scheme 1), estimates of the three null migration rates exhibited similarly low positive biases, with CI matching closely the nominal coverage, whereas estimates of the two non-null migration rates showed low negative biases, larger variances and CI coverage slightly below 90% (Table 4 and Fig. 2a). Introducing adult sampling error (Scheme 2) did not alter the ranking of migration estimates across populations (Fig. 2c), but enlarged the bias and variance of all migration estimates, and yielded generally poorer CI coverage, down to a low of 73% for the estimator of the highest migration rate (mE = 0.044), as a consequence of its stronger bias (Table 4). Permuting the assumed migration rates between populations yielded similar results under both Schemes 1 and 2 (examples in Fig. 2b,d, respectively), suggesting that neither adult population genetic structure nor unequal adult sample sizes tended to produce spurious asymmetries in the estimated migration rate distribution.

image

Figure 2.  Distribution of estimated unequal pollen migration rates from five simulated source populations into a small recipient population. The assumed migration rate distribution was either equal to that estimated into the Scots pine (Pinus sylvestris) remnant (a, c) or a random permutation of the latter (b, d). Assumed adult and seed sample sizes were equal to real sizes. Adult haplotypic frequencies of source populations were independently generated for each replicate either from the real estimated frequencies (a, b) or from simulated parametric distributions (c, d). Assumed haplotypic frequencies for the small recipient population were equal to those of the exhaustively sampled Scots pine remnant. Results correspond to 1000 independent replicates. Boxes indicate the 25%, 50% and 75% percentiles and whiskers the 5% and 95% percentiles. Points indicate outlier estimates and small squares assumed migration rates.

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Table 4.   Expected bias, accuracy and confidence interval coverage of unequal pollen migration rate estimates
Population frequenciesAssumed parameter valueEstimation error
BiasRMSELLTHULTL
  1. Based on 1000 independent Monte Carlo simulations assuming: five source populations of Scots pine (Pinus sylvestris) (B–F) with migration rates mi; adult and seed sample sizes equal to real sizes; population haplotypic frequencies equal to the observed frequencies (Scheme 1) or simulated parametrically (Scheme 2 with FST = 0.016).

  2. RMSE, root mean square error; LLTH and ULTL, the proportion of times that the 95% confidence interval (CI) lower limit was higher, or the CI upper limit was lower, respectively, than the assumed value.

Estimated (Scheme 1)mB = 00.0020.0030.0470.000
mC = 0.016−0.0050.0090.0050.119
mD = 00.0020.0030.0580.000
mE = 0.044−0.0060.0170.0120.097
mF = 00.0020.0040.0510.000
inline image0.0050.0170.0470.154
Simulated (Scheme 2)mB = 00.0050.0090.1400.000
mC = 0.016−0.0010.0100.0270.048
mD = 00.0060.0100.1320.000
mE = 0.044−0.0140.0200.0030.263
mF = 00.0050.0080.1210.000
inline image0.0000.0150.0260.137

Expected effect of unsampled source populations

Simulated pollen immigration from unsampled populations resulted in overestimated migration from sampled populations, as LP estimates remained virtually unbiased (Table 5). The positive bias was approximately inline image in all scenarios considered (U and I being the number of unsampled and sampled populations, respectively). Total pollen immigration was thus accurately estimated, but the portion originating from unsampled sources was wrongly allocated among sampled ones. This result held for different total immigration levels, numbers of unsampled populations and for either the presence or absence of migration from sampled sources (Table 5). Increasing amounts of total migration increased the bias of migration estimates from sampled sources (as = 5 in all cases), as well as its variance and that of LP estimates. For a fixed level of immigration, more unsampled populations resulted in lower estimation variance. CI coverage was inversely related to estimation bias; assuming a total immigration equal to the estimated value (Σmi = 0.067), 95% CI contained the true migration rate as infrequently as 66% of the time assuming no migration from sampled sources, and c. 90% assuming equal migration rates from both sampled and unsampled sources (Table 5).

Table 5.   Expected absolute bias, accuracy and confidence interval coverage of pollen migration rate and local pollination rate estimates with unsampled populations
Total immigration (Σmi)n unsampled populationsmi unsampledmi sampledMigration estimates inline imageLocal pollination estimate inline image
BiasRMSELLTHULTLBiasRMSELLTHULTL
  1. Based on 1000 independent Monte Carlo simulations assuming: five sampled and n unsampled source populations of Scots pine (Pinus sylvestris) each with migration rate mi; adult and seed sample sizes equal to real sizes; parametric adult population frequencies with overall population differentiation FST = 0.016.

  2. RMSE, root mean square error; LLTH and ULTL, the proportion of times that the 95% confidence interval (CI) lower limit was higher, or the CI upper limit was lower, respectively, than the assumed value.

0.02010.0030.0030.0010.0050.0300.000−0.0010.0080.0140.114
10.02000.0040.0070.1150.0000.0000.0090.0230.081
30.00700.0040.0070.1150.000−0.0010.0090.0150.113
0.06710.0110.0110.0020.0110.0560.0310.0000.0160.0290.109
30.0080.0080.0050.0120.1050.007−0.0010.0170.0320.121
10.06700.0140.0190.4080.000−0.0010.0210.0630.144
30.02200.0140.0180.4300.000−0.0010.0180.0500.137
60.01100.0140.0180.4380.000−0.0010.0190.0440.135
0.10010.0170.0170.0030.0130.0760.0330.0000.0190.0380.083
30.0120.0120.0070.0150.1370.0140.0000.0200.0450.095
60.0090.0090.0110.0180.2390.004−0.0010.0200.0450.109
10.10000.0200.0270.5150.0000.0000.0250.0820.142
30.03300.0200.0260.5660.000−0.0010.0240.0630.121
60.01700.0200.0180.4290.000−0.0010.0180.0500.137

Hence, simulations suggest that the total pollen immigration estimate into lowland population A (6.7%) would not be biased by (as it would actually incorporate) potential pollen flow from unsampled sources in peripheral mountains, supporting effective pollination distances over 50 km. To test whether migration estimates from populations C and E (0.016 and 0.044; Table 2) could be an artefact of potential incoming pollen from unsampled populations, the proportion P of independent replicates in the simulations yielding migration estimates inline image (or inline image) was evaluated, under the assumptions that mC = mE = 0 and thus that pollen immigration from unsampled sources amounts to the observed 6.7% total immigration value. If P is sufficiently small, it would be possible to reject the hypothesis that mC = mE = 0 under the simulation and model assumptions.

Applying this test in the three relevant scenarios of Table 5 (rows 6–8), corresponding to one, three and six unsampled populations, respectively, a small proportion (< 0.05) of replicates yielded inline image, whereas many (> 0.4) yielded inline image. Similar results were obtained in three additional simulation scenarios reflecting potentially more confounding situations. Specifically, haplotypic frequencies of the six sampled populations were kept equal to those estimated from real adult samples (as in Scheme 1, see Materials and Methods), whereas those of a single unsampled population, assumed to be the sole origin of the total = 0.067 pollen migration into population A, were simulated using Eqn 4 to satisfy any of the following conditions: overall genetic differentiation among the seven populations was FST = 0.016 (Fig. 3a); pairwise differentiation between the unsampled population and recipient population A was as low (FST = 0.005) as that observed between A and E (Fig. 3b); or pairwise differentiation between the unsampled population and population E was as low as FST = 0.005 (Fig. 3c). In all three cases, few (< 0.05) replicates yielded inline image (Fig. 3), suggesting that the actual migration estimate from population E was not (whereas that of C could be) a spurious outcome of potential pollen flow from unsampled sources.

image

Figure 3.  Distribution of estimated pollen migration rates from five simulated sampled source populations into a small recipient population in the presence of an unsampled source. The assumed migration rate from the unsampled source was 0.067, whereas those from sampled populations were null. Assumed adult and seed sample sizes for sampled populations were equal to real sizes. Adult haplotypic frequencies of sampled populations were kept equal to the real estimated frequencies. Simulated parametric frequencies of the unsampled population satisfied one of the following conditions: (a) the overall genetic differentiation among the seven populations was FST = 0.016; (b) the pairwise differentiation between the unsampled source and the recipient population was FST = 0.005 (b); or (c) the pairwise differentiation between the unsampled source and population E was FST = 0.005. Boxes indicate the 25%, 50% and 75% percentiles and whiskers the 5% and 95% percentiles. Small triangles indicate real estimates in the Scots pine (Pinus sylvestris) study. Histograms on the right show in more detail the distribution of migration estimates from population E.

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

The results of this study indicate that airborne tree pollen transport can result in effective pollination over a larger scale than documented to date for wind-pollinated species, as shown by the 6.7% of effective male gamete migrants into a strongly isolated Scots pine remnant. Notably, effective pollen migration from a large population 100 km away from the remnant was estimated at 4.4%. Extensive numerical analysis showed that the latter estimate remains significant even after controlling for small adult reference samples, unequal migration rates and the presence of unsampled populations, all of which were a minimum of 50 km away from the recipient population in the study system. Pollen migration from a more nearby (c. 30 km away), but small, woodland was null (Fig. 1; Table 2), consistent with mass-action models, which predict increasing immigration for larger source to sink population size ratios (Holsinger, 1991; Ellstrand & Elam, 1993). Moreover, the proximity advantage of discrete source populations is expected to diminish under leptokurtic propagule movement (Klein et al., 2006), and the pattern of pollen dispersal has been shown to be markedly fat-tailed in Scots pine (Robledo-Arnuncio & Gil, 2005).

Pollen migration from the largest sampled population (F) appeared, however, to be null, and that from population C was nonsignificant and lower than that from the smaller population E. Two additional factors could explain the variation in migration rates: atmospheric conditions and flowering phenology. Turbulent updrafts within and above the canopy during pollen release, wind conditions during transport, stability during deposition, and other microscale and synoptic atmospheric processes driving long-distance dispersal are highly stochastic (Kuparinen et al., 2007; Nathan et al., 2008), and we lack related information in the study region that might help to approximate the expected migration rate distribution. It seems clear, however, that the sole effects of interpopulation distance and relative population size are unlikely to explain long-distance pollen movement across broad heterogeneous regions. With regard to phenology, it is well known that Scots pine flowering overlaps over large climatic gradients, even over 500–1000-km latitudinal clines with strong temperature differences, but also that earlier pollen is expected to have a competitive advantage (Sarvas, 1962; Pessi & Pulkkinen, 1994; Lindgren et al., 1995; Pulkkinen & Rantio-Lehtimäki, 1995). This advantage could have favoured effective pollen dispersal from population E, which is c. 1400 m in elevation, an intermediate altitude between recipient population A (800 m) and population C, which grows up to the treeline (1500–1800 m) and thus presumably starts to shed pollen later.

This study establishes the possibility of effective wind pollination over mesoscale distances for Scots pine, but the observed distribution of pollen migration rates should not be generalized directly to other species or to different demographic settings. For comparatively larger recipient populations, the dilution effect associated with more abundant local pollen shedding might reduce the proportion of long-distance pollination. For species with pollen grains not as buoyant as those of Pinus (Williams, 2008), as another example, mechanistic models would predict relatively shorter range dispersal. The present findings represent, however, a benchmark for future studies of different biological and demographic systems.

Ecological and evolutionary implications

An order of magnitude increase in the expected range of effective pollen dispersal would have an impact on the assessment of many ecological and evolutionary processes. Strongly geographically isolated tree fragments, either remnants or founders, may be within mating distance of central populations more often than presumed. A yearly pollen immigration rate of c. 5% might translate into an even larger per generation rate, as opportunities for long-distance dispersal accumulate over many decades of tree maturity. Indeed, in the same way that the reproductive assurance brought by longevity is considered to be a potential ultimate cause of the predominantly outcrossed mating system of trees (Ashman et al., 2004; Petit & Hampe, 2006), the large mating neighbourhood granted by long-distance pollination may represent a spatial component of reproductive assurance as important as the temporal one conferred by longevity.

Assuming that all 6.7% of seeds sired by long-distance pollen were able to germinate and establish in recipient population A, and that this yearly pollen migration rate translated into an equal per generation rate, without seed immigration, the resulting gene flow rate for autosomal loci would be = 0.067/2 = 0.033, yielding Nm = 36 × 0.033 = 1.2 migrants per generation, further assuming equal effective and census sizes. Under an island migration model (Wright, 1931), this estimate suggests that long-distance pollen flow would largely counterbalance the strong rate of drift-induced neutral genetic differentiation expected in such a small population. The consequences for local adaptation are more uncertain, as long-distance pollen movement across heterogeneous habitats may bring in gametes adapted to very different environments. It could therefore counteract divergent natural selection, hampering local adaptation and increasing genetic load (Garcia-Ramos & Kirkpatrick, 1997; Lenormand, 2002). For a given gene flow rate, selection is in fact expected to oppose maladaptive effects of pollen dispersal less efficiently than those of seed dispersal in strongly heterogeneous habitats (Lopez et al., 2008). However, long-distance pollen gene flow is also expected to increase additive genetic variance within tree populations (e.g. Yeaman & Jarvis, 2006 for Pinus), providing the necessary basis for adaptive divergence (Lenormand, 2002), especially in small populations (Alleaume-Benharira et al., 2006).

Predicting the net effect of long-distance pollen migration on adaptation is thus difficult. A critical question for the Scots pine remnant in its dry environment will be whether, in the face of climate warming, selection will overcome the gametic inflow from mountain populations that are locally adapted to colder and wetter conditions (Alía et al., 2001). Although long-distance pollen immigration might have an ultimately maladaptive effect in this southern relict, it might not be the case in populations such as northern woodlands distributed along steep latitudinal climatic gradients. South to north pollen flow has been considered to hamper local adaptation through frost tolerance disruption in northern Finnish Scots pine populations (Aho, 1994; cited in Savolainen et al., 2007). This situation might be reversed soon, however, as previously maladaptive southern gene flow could favour local adaptation of northern populations to climate warming (Davis & Shaw, 2001), presumably in a more pervasive and rapid way than migration via seed dispersal.

Methodological considerations

Two key experimental advantages in this study were the small size of the recipient stand, which allowed an accurate determination of total pollen immigration, and its strong geographical isolation from peripheral discrete populations, which facilitated the estimation of immigrant proportions from long-distance sources. The approach used can only be applied to discrete populations, relying on a good characterization of their haplotypic frequencies before dispersal at paternally inherited loci. The sampling intensity required to achieve the latter condition is a function of marker polymorphism. Scots pine chloroplast SSR haplotypes have moderate levels of variation, yielding acceptable estimation error for relatively small sample sizes, but the bias and variance may increase, and the CI coverage decrease, for higher or lower haplotypic diversity levels, especially with low levels of differentiation between populations and/or larger recipient populations (JJ Robledo-Arnuncio, unpublished data).

Given the spatial scale involved in long-distance dispersal studies, additional concerns in abundant species are unsampled populations, which will result in overestimates of migration from sampled sources (see Slatkin, 2005 in the context of historical migration), in turn yielding overestimates of dispersal range if missing sources are closer to the recipient population than sampled sources, or underestimates otherwise. Researchers should consider the minimum estimated dispersal distance with caution when unsampled sources are likely to occur within this distance, and should be advised to conduct significance tests under the assumption of incoming pollen from missing sources. If the amount of migrants is large, which will rarely be the case in long-distance plant dispersal, it might be possible to recover genotypic frequency information about unsampled sources from the seed sample, as in fish stock identification problems (Smouse et al., 1990). However, even when all individuals in a large sample are migrants (as in fish stocks), the presence of entire unsampled populations seems difficult to overcome (Smouse et al., 1990).

Finally, contemporary seed migration estimation could be undertaken in a similar way, using either maternally inherited DNA markers or biparentally inherited markers, such as nuclear microsatellites, assessed at maternal origin seed tissue (Godoy & Jordano, 2001). In the latter case, the potentially enormous number of different genotypes would enforce intensive population sampling, and Bayesian procedures jointly estimating genotypic distributions could help in tackling the problem (Pella & Masuda, 2001). A drawback of time-consuming Bayesian computations, however, is the difficulty in conducting sufficiently replicated numerical uncertainty analysis of low migration estimates. In general, if no polymorphic uniparentally inherited markers were available, or maternal origin seed tissue for analysis dealing with seed dispersal, less specific methods for multilocus diploid markers would become necessary to estimate contemporary migration rates, at the cost of additional assumptions and higher parameter dimensionality (Wilson & Rannala, 2003; Faubet & Gaggiotti, 2008; Broquet et al., 2009).

The apparent gap between the scale of airborne propagule transport and effective dispersal might be bound to disappear for many plant species as more comprehensive datasets and ad hoc statistical methods become available to unravel previously cryptic long-distance ecological processes. The present study supports the view that this gap may not reflect a biological reality for Scots pine, extending the scale of documented effective pollen dispersal range for wind-pollinated trees.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

I thank Ricardo Alía, Luis Gil and colleagues at the Centro de Investigación Forestal of the Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria and the Universidad Politécnica de Madrid for their support and feedback, and two anonymous reviewers for constructive criticism. JJRA was supported by a Ramón y Cajal research fellowship and CGL2009-09428 project from the Spanish Ministry of Science and Innovation.

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  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information
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Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Table S1 Haplotypic frequencies in the six Scots pine populations

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