Pinus canariensis is an endemic pine to the western Canary Islands (i.e. Tenerife, Gran Canaria, La Palma, La Gomera and El Hierro). Currently, it occupies about 55,000 ha, being much of it planted. In terms of conservation priorities, the natural Canary Island pine formations are Habitats of Community Interest (Habitat Directive 92/43/EEC, 2006/105/EC). It is considered a colonizing species that invades poor soils, that is, salic volcanic substrates with very dry environments that arboreal angiosperms are unable to inhabit (Aboal et al., 2000). As a consequence, P. canariensis occupies a wide range of habitats at varying densities, from semi-desert areas in southern Gran Canaria to humid areas in the slopes of Tenerife or La Palma, usually forming pure stands. Out of its natural range, it is considered an invasive species (Rouget et al., 2004).

Sampling was performed in two sites with contrasting densities. Site 1 (Figure 1) is located in the ravine of Chirigel (28° 25’ N, 16° 23 W, elevation = 1,100 m a.s.l.) and it is representative of the high density forests from the slopes in the south of Tenerife. Diameter at breast height (DBH) was measured for 328 adults and needles were collected from the same trees. In 2007 seeds were collected from 103 seed traps. The seed traps consisted of a cylindrical metallic oil drum transversally cut. The traps had a diameter of 0.55 m and a height of 0.30 m. The open end of the top of the traps was covered with a metallic net that allowed the entrance of seeds, but prevented predation by frugivores. A portion of the collected seeds (324/1354) were germinated to obtain a final sample size of 315 seeds, and for further germination studies (data not shown). Collection of seedlings was done in 120 subplots of 1 m² close to the seed traps (Figure 2). The subplots were located in the nodes of a rectangular grid of 12 x 6 m, with E-W orientation, so the smallest size of the grid was set in line with the direction of the maximum slope. All the seedlings contained within the subplots (540 seedlings) were collected and leaves were stored at –80 ºC for molecular analysis. Seedlings corresponded to at least two regeneration events.

Site 2 is an isolated stand located in the ravine of Arguineguín, 2.5 km inshore from the south coast of Gran Canaria island (27º 47’ N; 15º 40’ W, elevation = 350 m a.s.l.; Figure 1). The nearest P. canariensis population to the study plot is 7 km away in the same ravine. A hundred and twenty five adult pines grow scattered at extremely low density (0.46 trees ha^–1) on two steep hillsides divided by a road. The western hillside supports 80.5% of the population (68.8% of adults and 90.2% of recruits). In the western hillside, a surface of 350 x 1015 m was divided in 290 quadrants of 35 x 35 m containing 125 seedlings (Figure 3). All the 125 adults were used as potential mothers in the parentage analysis (see below). The coordinates of the central points of the quadrants were used to compute the matrix of distances between the mother trees and the seedling-quadrants. Seed-traps were not used in this site because seed production was very low.

DNA extraction was performed with a modification of the protocol by Dellaporta et al. (1983). Five polymorphic nuclear microsatellites (nSSRs): SPAG 7.14, SPAC 11.5, SPAC 11.8 (Soranzo et al., 1998), Pttx3116, Pttx4001 (Auckland et al., 2002); and five chloroplast microsatellites (cpSSRs): Pt15169, Pt26081, Pt30204, Pt87268, and Pt71936 (Vendramin et al., 1996) were amplified under standard PCR conditions. Fluorescence labelled PCR products were analyzed in a 4300 LI-COR automated sequencer (LI-COR biosciences, Lincoln, NE, USA). Allele sizes were determined with SAGA Microsatellite Analysis Software (LI-COR biosciences, Lincoln, NE, USA). Genotyping errors were minimized by genotype double-blind reading, positive and negative controls, and blind duplicate samples. The software MICRO-CHECKER v 2.2.3 (van Oosterhout et al., 2004) was used to test for the presence of null alleles that could bias parentage assignment. Standard diversity statistics were computed with GenAlEx 6.5 (Peakall & Smouse, 2012).

Parentage analysis based on nSSRs was used to generate the most likely parent pairs. Parentage analysis is based on exclusion probabilities for single parent and parent pair assignment as implemented in software Famoz (Gerber et al., 2003). Statistical confidence in parentage assignment was based on offspring simulations from allele frequencies and genotyped parents. To account for possible genotyping errors, we considered a relaxed error level of 0.05 as input in Famoz. Then, we compared cpSSR haplotypes of possible parent pairs with those of the offspring assigned by nSSRs. If the pollen donor had the same cpSSR haplotype as the offspring, and the seed donor had a different cpSSR haplotype, these two adults were the presumed parent pair. If both adults had different cpSSR haplotypes from the offspring, none of them was considered the pollen donor. If both adults had the same cpSSR haplotype as offspring, the gender of each parent could not be identified. Second, we compared cpSSR haplotypes of the offspring when nSSR markers had identified a single possible parent. If the cpSSR haplotype of the candidate was not identical to that of the offspring, the candidate was considered the seed donor. If the cpSSR haplotype was identical, seed donors could not be identified and were considered as coming from outside the plot.

Both basic and effective seed dispersals were assessed using the ‘gene shadow model’ (GSM) (Jones & Müller-Landau, 2008). While the primary seed dispersal was estimated from seeds collected in traps from site 1, effective seed dispersal was modeled using data from the seedlings genotyped in site 1 and site 2. Unlike the classical inverse modeling approach that is applied to the numbers of offspring in each seed-trap/seedling-quadrant (Ribbens et al., 1994), the GSM extends the model to the numbers of offspring of each genotype in a sample from each trap/seedling-quadrant.

The fecundity of the tree i as the seeds produced per year (Q_i) is estimated as:

Model fitting was performed under a Bayesian framework using modified programs run in R (R Development Core Team 2010), kindly provided by Drs. H. Müller-Landau and A. Jones (Jones & Müller-Landau, 2008). We fitted the parameters for lognormal, Weibull, Clark’s 2Dt and generalized exponential distributions (see Suppl. File S1 [pdf on line] for an explanation of the different dispersal kernels).

We ran 10 independent Markov chains of 100,000 iterations to estimate the posterior probabilities. We used non-informative priors for all fitted parameter estimates, because priors have a strong influence in dispersal parameter estimation (Kass & Wasserman, 1996), and we had no previous information about seed dispersal in P. canariensis. A re-parameterization of the models was used by which the fitted parameters were log-transforms of the original parameters. We used the Poisson error distribution as it performs better for wind-dispersed species with medium to large dispersal means (Greene et al., 2004). We used the median of the posterior distributions of each parameter as our best estimates, and computed 95% symmetric credible intervals. Convergence of the models was evaluated using the potential scale reduction factor –PSRF– (Brooks & Gelman, 1998). A model was assumed to have converged when the PSRF was close to 1 (PSRF < 1.1). Mean and median dispersal distances were estimated for each model’s parameters when convergence was achieved. Due to the high proportion of offspring with no parents assigned within the plots (see below), we used the version of the model that considers immigrant seed flow (equations [4] and [5]). After several preliminary runs, and due to the distance at which other adult trees are found in site 1, we considered a radius of 1 km around the plot.

The Deviance Information Criterion (DIC) (Spiegelhalter et al., 2002) was computed to perform model comparisons and choose the optimal distribution fitting to our data. We compared the ranges of the 95 % credible intervals between site 1 and site 2, and between dispersal estimated from seeds and seedlings, in order to test for discordance between primary and effective dispersals. In Bayesian inference, a probability interval is a probabilistic region around a posterior moment, and is similar in use to a frequentist confidence interval. We specifically tested the following hypotheses: 1) Hypothesis I: patterns are not discordant between the primary and the effective dispersal kernels in site 1 (H₀: δ_p1 = δ_e1; H_a: δ_p1 ≠ δ_e1); 2) Hypothesis II: the mean effective dispersal distances were significantly higher in site 2 (low density) than in site 1 (high density) (H₀: δ_e1 = δ_e2; H_a: δ_e1 < δ_e2).

The standard diversity statistics for nuclear (Table 1) and chloroplast microsatellites (Table 2) showed polymorphism enough to perform parentage analysis. The theoretical multilocus exclusion probabilities (Jamieson & Taylor, 1997) exceeded 0.999 for the combination of nuclear and chloroplast microsatellite loci for both seeds and seedlings in the two sites (Table 3). Under this approach, the chloroplast DNA is considered as a single independent locus and each haplotype as an allele. In site 1, seeds showed a critical LOD-score of 3.62 for a single parent, and 9.01 for a parent pair, at a confidence level of 95 %. For seedlings, the critical LOD-scores were 3.62 for a single parent, and 8.92 for a parent pair, at the same confidence level than for seeds. The mother was assigned to 90 seeds (28.6 % of genotyped seeds) and to 151 seedlings (28.0 % of genotyped seedlings). Interestingly, the same percentage of immigrants was scored for seeds (71.4 %) and seedlings (72.0 %).

In site 2, the LOD-scores for single parent and parent-pair assignments were, respectively, 3.82 and 9.94 (Table 3). The mother was unambiguously assigned to 59 seedlings (38.8% of the data) when only the highly reliable parent-offspring matches were analysed.

Convergence was achieved for fecundity and scale parameters of the lognormal, Weibull and Clark’s 2Dt distribution in all three models (PSRF < 1.001). The model for the generalized exponential dispersal kernel did not converge in site 2. The models using the lognormal kernel showed the smallest DIC values and largest estimates for mean and median dispersal distances (Table 4). The DIC values scored for the Weibull, Clark’s 2Dt and generalized exponential kernels were higher than for the lognormal, but the mean and median dispersal distance estimates were more consistent across these models.

Both primary and effective dispersal estimates showed a remarkable dispersal ability for P. canariensis in sites 1 and 2 (Table 4; Figure 4). Using the Weibull dispersal kernel, the average mean and median dispersal distances were c. 60 m in site 1, but over 800 m in site 2 (Table 4). The fecundity parameters were consistent with ‘de visu’ predictions about seed production made at the sampling time showing large differences between sites: site 1 had much higher fecundity parameter for both seeds (2242 seeds m^–2) and seedlings (448 seedlings m^–2) than site 2 (2.3 seedlings m^–2).

For Hypothesis I, there was no apparent discordance between primary and effective dispersals, as the 95 % credible intervals for seed and seedling dispersal distance overlapped irrespective of the kernel of choice (Table 4). That is, the GSM for seeds and seedlings converged to very similar dispersal parameters and we cannot reject the null hypothesis of equal primary and effective dispersals. For Hypothesis II, the 95% credible intervals for seedling dispersal parameters showed remarkable differences between sites. The sparse stand (site 2) showed higher mean effective dispersal distance than the dense stand (site 1). Therefore, we rejected the null hypothesis of equal effective dispersal distances in dense and sparse stands.

The hypotheses tested in the present study were validated for any dispersal kernel we used. However, there were differences in the intensity of the dispersal process depending on the kernel of choice. According to DIC, the best models were the ones with lognormal dispersal kernel. The median dispersal distance characterizes better the dispersal process than the mean for estimations based on the lognormal kernel. However, median dispersal distances for these models were excessively large: four times the median using the Weibull kernel for site 1, and more than 20 times the median obtained with the Weibull kernel for site 2. When using Clark’s 2Dt, Weibull, and generalized exponential kernels the mean dispersal values were similar for both sites. When using Clark’s 2Dt, Weibull, and generalized exponential kernels the mean dispersal values were very similar for both sites and cohorts. Therefore, we will discuss the results in terms of the models fitted with the Weibull dispersal kernel.

Both basic and effective mean dispersal estimates suggest high dispersal ability for P. canariensis, even in dense stands. The mean primary dispersal distance estimated for other species using inverse modeling on seeds collected in traps was lower than the mean primary dispersal distance for P. canariensis (δ_p1 = 61.9 m): P. rigida (δ_p = 15.1 m) (Clark, 1998), P. strobus (δ_p = 13-30 m) (Greene et al., 2004) or P. pinaster (δ_p = 8.8-21.24 m) (González-Martínez et al., 2006). Considering only studies that used molecular data and parentage analysis on seedlings and saplings, P. canariensis showed higher effective dispersal ability than other pine species (δ_e1 = 60 m; δ_e2 = 817.2 m), such as P. pinaster (δ_e = 26.5 m) (González-Martínez et al., 2006), P. halepensis (δ_e = 41.6 m) (Steinitz et al., 2011) or P. sylvestris (δ_e = 53 m) (Burczyk et al., 2006). These studies used different sampling schemes, and therefore may not serve as adequate comparisons to P. canariensis. We cannot rule out that models based on genetic information may overestimate the dispersal distances when sampling is biased in areas with high seed density, because they only use a small proportion of the total amount of seeds collected in traps (Jones & Muller-Landau, 2008). There is also a source of error associated to microsatellite mistyping and mother assignment that could inflate the percentage of immigrant seeds, thus increasing the mean dispersal estimates for P. canariensis. Furthermore, the miss-specification of the fecundity term in the dispersal model may also lead to overestimation of the dispersal distances (Nanos et al., 2010), because very often fecundity does not have a straightforward relation with the basal area of the parent trees.

Despite the limitations of the genetic models, the high dispersal ability of P. canariensis is not surprising in a > 35 m tall species that inhabits steep slopes subjected to strong winds. In fact, one of the factors that may explain the efficiency in seed dispersal is that the wing of the Canary Island pine seeds is adnate, which is a rare trait in the species of subgenus Pinus (Diploxylon). Pines with adnate seed-wings disperse by wind after seeds are released from the cone. The persistence of this trait, which is also present in some island pine species (Eckenwalder, 2009), could be related to the ability for long distance dispersal that allows the colonization of bare soils. Together with Pinus caribaea, P. canariensis is acknowledged as an “island-jumper” (Klaus, 1989).

The high percentage of immigrant seeds scored for P. canariensis in both sampling sites is consistent with the invasive character of the species. A previous study conducted in site 1, evaluating the seed rain along one year (García-del-Rey et al., 2011) showed a remarkable variation in seed deposition between the upper and the lower parts of the plot. However, all seed-traps received more than 25 seeds m^–2. Our results based on parentage analysis suggest that a large part of this seed rain came from outside the plot. Moreover, even in the apparently isolated site 2, the percentage of immigrant seeds was very high. Such as other pine species, P. canariensis undergoes an outcrossing mating system. Seeds are wind-dispersed and they can potentially travel long distances providing the species with a very efficient mechanism of gene flow. Consistently with this, molecular studies have shown effective gene flow among islands (Vaxevanidou et al., 2006) and evidence of recent range expansions (López de Heredia et al., 2014).

The dispersal ability of P. canariensis has important implications for landscape dynamics. Pines are the first plant species colonizing salic outcrops after volcanic disturbance. In line with this, pines will show a high potential for the colonization of new ecological niches above the tree-line that will become abundant in a global change scenario (VVAA, 2011). High dispersal ability may have aided in the substitution of the thermophilous forests that occurred in the Canary Islands in the last 2,000 years (de Nascimento et al., 2009), promoting the colonization of degraded areas by pines. Out of its natural range, P. canariensis is a potential invasive species (Rouget et al., 2004). Invasiveness is enhanced by the high dispersal efficiency and by the resilient character of the species, which is one of the few pines able to re-sprout (Climent et al., 2004). Due to the dispersal characteristics of the species, P. canariensis is highly competitive with other species of pines (Arévalo et al., 2005) and angiosperms (Aboal et al., 2000).

Spatial patterns of recruitment largely depend on the initial template established by primary seed dispersal, but are also influenced by successive post-dispersal factors such as seed predation, germination and seed mortality (Nathan & Muller-Landau, 2000). The spatial concordance of primary and effective dispersals indicates a positive relationship between seed rain and recruitment. Conversely, if there is spatial discordance between primary and effective dispersal, negative relationship between seed rain and recruitment is inferred (Houle, 1995).

The comparison of dispersal estimates in site 1 shows that effective dispersal does not differ from primary dispersal; therefore, primary dispersal can be considered the ‘basic’ seed dispersal (sensu Bontemps et al., 2013), i.e. the template for recruitment. Two main conclusions derive from this result. First, there is no evidence for a Janzen-Connell effect for P. canariensis. The Janzen-Connell hypothesis predicts that a lower survival rate in the proximity of the mother plant owing to pathogens, seed predators or herbivorous, which can occur directly under it (Janzen, 1970; Connell, 1971). The Janzen-Connell effect was originally described for tropical forests, but recently it was empirically shown for P. halepensis (Steinitz et al., 2011). However, at least at the scale of our study, such density dependent mortality effects seem not to be operating in P. canariensis.

Second, it seems that animal mediated secondary dispersal of P. canariensis’ seeds has no effect on the spatial arrangement of recruits. Animal mediated dispersal of pine-nuts has been addressed for Mediterranean pines (Rost et al., 2010), as well as for other American and European pines (Briggs et al., 2009). The number of potential predators/dispersers on islands is much more reduced than in the mainland, but they can compensate this effect by increasing population densities (MacArthur et al., 1972). Traditionally, only two avian species are considered as pine-wood specialists in the Canary Islands (Volsoe et al., 1955): the blue chaffinch (Fryngilla teidea) (Bannerman & Bannerman, 1963; García-del-Rey et al., 2009) and the great spotted woodpecker (Dendrocopos major canariensis) (García-del-Rey et al., 2007). While the blue chaffinch is mainly a predator of post-dispersed seeds, the great spotted woodpecker is not considered a real pine-nut predator. According to our results, none of both bird species can be considered a true disperser, and therefore, a landscape modeler. Other factors, such as shade tolerance or competition with the understory (Otto et al., 2010) may be more important in dense humid pinewoods in order to explain the patterns of recruitment. In low density forests from arid environments, such as site 2, where evidence of local adaptation to drought was found (López et al., 2013), López de Heredia et al. (2010) showed strong evidence for clustering of recruits on hygrophilous stream beds.

The landscapes dominated by P. canariensis have a varying stand structure (del Arco et al., 1992; Pérez de Paz, 1994), from low density pine-woods in the south of Gran Canaria to dense forests on the humid slopes of La Palma and Tenerife. In the present study we compared the effective dispersal distributions from two pure stands that lack sub-canopy vegetation. As was hypothesized, the open pine-wood from site 2 showed much higher mean effective dispersal distance than the dense forest from site 1. This result was expected, because standing vegetation probably acts as a physical barrier to wind dispersed seeds across the landscapes (Pounden et al., 2008), and wind speed increases in open canopies (Katul et al., 2005) promoting long distance dispersal. The trunks and canopies of dense stands intercept seeds, which fall to the ground and are rapidly covered by litter that confers protection against predators, and a favourable microclimate for germination. Changes in vegetation density also induce changes in abundance and behaviour of predators and dispersers (Bannerman & Bannerman, 1963; Jordano et al., 2007), but, as we have shown above, it does not seem that birds have a significant incidence in the seed dispersal process of P. canariensis.

Despite interception of seeds by the overstory seems the most plausible scenario to explain the decrease of dispersal distances in dense pine-woods, we cannot discard that other factors associated to density may have an effect on the extent of seed dispersal. For instance, under the canopy of a dense pine-wood the optimal conditions for regeneration are created (Otto et al., 2010). Therefore, a higher percentage of the seeds dispersed at shorter distances are able to establish. Conversely, in open landscapes subjected to high irradiance, the seedlings will install depending on edaphic factors and, mainly, water availability. In line with this, López de Heredia et al. (2010) found that establishment in site 2 was strongly related to the presence of hygrophilous bed-streams where seedlings could develop. The spatial arrangement of these optimal niches for seedling occurrence relative to the mother trees (i.e. directional bias due to the anisotropy of the habitat) may strongly bias the effective seed dispersal inference (Schurr et al., 2008). In dense pine-woods, however, the habitat is less heterogeneous and, therefore, we expect less bias of seed dispersal inference.