This work has one supplementary file.

The authors have declared that no competing interests exist.

Seed dispersal strongly influences the demographic cycle of plants (

The integration of methods based on seed or seedling counts in either seed traps or regeneration quadrants, and genetic methods, based on parentage analysis, has been used to model the different components of dispersal (

Other genetic methods that utilize frequencies of offspring genotypes, and that rely on a spatially explicit model for the mating event resulting in that offspring can be used to model the ‘basic’ dispersal: 1) the

Disentangling the different components of seed dispersal, by comparing the mean primary and effective dispersal distances (δ_{p}
_{e}), assists in evaluating the relative contributions to the whole dispersal process of the main factors affecting the spatial patterns of recruitment: 1) density dependent mortality (i.e. the Janzen-Connell effect); and 2) secondary dispersal vectors. The Janzen-Connell hypothesis predicts a lower survival rate in the proximity of the mother plant owing to higher frequency of pathogens, seed predators or herbivorous animals (_{e} ≠ δ_{p}). If there is discordance between primary and effective dispersal, some methodologies that compare the ‘basic’ and effective dispersals have been recently developed to disentangle the effects of secondary dispersal and the Janzen-Connell effect (

The parent tree density is determinant to seed dispersal, affecting the shape and scale of the dispersal kernels, and fecundity. Trees in dense forests produce and disseminate fewer seeds per year and unit of basal area than trees in sparser locations (

In the present study we applied a model that integrates genetic and spatial information (GSM) to estimate the primary and the effective dispersal kernels in two stands of high (site 1) and low (site 2) stand density, respectively, of the endemic insular tree _{p1} ≈ δ_{e1}), therefore, primary dispersal can be considered the template for recruitment; 2) the mean effective dispersal distances are significantly higher in the sparse than in the dense pinewood (δ_{e1} < δ_{e2}).

Sampling was performed in two sites with contrasting densities. Site 1 (^{2} close to the seed traps (

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.; ^{–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 (

DNA extraction was performed with a modification of the protocol by

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

Both basic and effective seed dispersals were assessed using the

The fecundity_{i}) is estimated as:

where β_{i} is the fecundity parameter of tree ^{2} and _{i} the basal area of tree ^{2}.

The expected number of offspring of genotype _{k }

where _{j} is the proportion of all offspring in trap/quadrant _{i} is the fecundity of tree _{ij}

In equation

where _{ij} is the observed number of offspring of genotype

The expected number of offspring whose genotype does not match that of any parent on the plot, i.e. immigrant seeds, can be calculated as (

where _{j} and _{j} are the coordinates of the trap

where ŝ_{*j} is the observed number of offspring whose genotype does not match that of any parent.

Model fitting was performed under a Bayesian framework using modified programs run in R (

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 (

The Deviance Information Criterion (DIC) (_{0}: 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) (H_{0}: δ_{e1 }= δ_{e2}; H_{a}: δ_{e1 }< δ_{e2}).

The standard diversity statistics for nuclear (

In site 2, the LOD-scores for single parent and parent-pair assignments were, respectively, 3.82 and 9.94 (

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 (

Both primary and effective dispersal estimates showed a remarkable dispersal ability for ^{–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 (

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 _{p1} = 61.9 m): _{p} = 15.1 m) (_{p} = 13-30 m) (_{p} = 8.8-21.24 m) (_{e1} = 60 m; δ_{e2} = 817.2 m), such as _{e} = 26.5 m) (_{e} = 41.6 m) (_{e} = 53 m) (

Despite the limitations of the genetic models, the high dispersal ability of

The high percentage of immigrant seeds scored for ^{–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,

The dispersal ability of

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 (

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 (

Second, it seems that animal mediated secondary dispersal of

The landscapes dominated by

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 (

Models that combine genotypic and spatial information, such as the GSM, have proven valuable to infer seed dispersal parameters in stands of

We wish to thank G. González-Gordaliza for field assistance.