Long‐distance pollen and seed dispersal and inbreeding depression in Hymenaea stigonocarpa (Fabaceae: Caesalpinioideae) in the Brazilian savannah

Abstract Hymenaea stigonocarpa is a neotropical tree that is economically important due to its high‐quality wood; however, because it has been exploited extensively, it is currently considered threatened. Microsatellite loci were used to investigate the pollen and seed dispersal, mating patterns, spatial genetic structure (SGS), genetic diversity, and inbreeding depression in H. stigonocarpa adults, juveniles, and open‐pollinated seeds, which were sampled from isolated trees in a pasture and trees within a forest fragment in the Brazilian savannah. We found that the species presented a mixed mating system, with population and individual variations in the outcrossing rate (0.53–1.0). The studied populations were not genetically isolated due to pollen and seed flow between the studied populations and between the populations and individuals located outside of the study area. Pollen and seed dispersal occurred over long distances (>8 km); however, the dispersal patterns were isolated by distance, with a high frequency of mating occurring between near‐neighbor trees and seeds dispersed near the parent trees. The correlated mating for individual seed trees was higher within than among fruits, indicating that fruits present a high proportion of full‐sibs. Genetic diversity and SGS were similar among the populations, but offspring showed evidence of inbreeding, mainly originating from mating among related trees, which suggests inbreeding depression between the seed and adult stages. Selfing resulted in a higher inbreeding depression than mating among relatives, as assessed through survival and height. As the populations are not genetically isolated, both are important targets for in situ conservation to maintain their genetic diversity; for ex situ conservation, seeds can be collected from at least 78 trees in both populations separated by at least 250 m.


| INTRODUC TI ON
Tropical forests around the world have experienced extensive fragmentation, resulting in tree populations that are spatially isolated in small forest fragments and individuals scattered throughout landscapes interspersed with pastures, agricultural areas, highways, and cities. This is especially true for the Brazilian savannah, where the biome has been significantly deforested (Sano, Rosa, Brito & Ferreira, 2007). As clear-cutting has resulted in the loss of many tree populations and their genetic material, urgent strategies for the in situ and ex situ conservation of remnant tree populations throughout the savannah biome are needed. Information about pollen dispersal patterns is required to identify and understand if populations and individuals that are spatially isolated in this landscape are also genetically isolated.
Habitat fragmentation can result in negative impacts on the remaining tree populations; it disrupts reproductive processes and decreases pollen and seed flow due to spatial isolation, resulting in decreased genetic diversity and effective population size and increased intrapopulation spatial genetic structure (SGS) and inbreeding, affecting subsequent generations (Degen & Sebbenn, 2014;Finger et al., 2012;Ismail et al., 2012). The spatial isolation of trees may decrease the reproductive success because plants may receive fewer visitors to flowers due to a decline in the richness and abundance of pollinator vectors, modifications to species composition, and limitations to movement among populations (Goverde, Schweizer, Baur & Erhardt, 2002). Fragmentation can, thus, modify the activity of pollinators by reducing the density of potential food resources and increasing the distance between those resources (Sih & Baltus, 1987). As plant densities decline, animal pollinators are less likely to shift from one plant to another because of the increased costs of foraging. Furthermore, pollinators foraging on self-compatible plants for longer periods of time can increase the probability of selfing (Karron, Holmquist, Flanagan & Mitchell, 2009). A review of mating systems across 27 plant species in undisturbed versus disturbed populations confirmed the expectation of increased self-fertilization in disturbed plant populations (Eckert et al., 2010).
For a variety of reasons, detecting the effects of forest fragmentation is difficult. Tropical trees are generally long-living species, with many adults in remnants from prefragmentation stages that present overlapping generations, undergo regular long-distance gene flow, and may present adaptive mechanisms for species survival, such as a mixed mating system, thus producing seeds by both outcrossing and self-fertilization (Lower, Cavers, Boshier, Breed & Hollingsworth, 2015). To study the effects of fragmentation, it is important to use samples from different ontogenic stages, including adults, juveniles, and seeds, as the genetic effects of forest fragmentation may be detected only in the new generations.
Advances in molecular genetic markers, statistical analyses, and software development have enabled the detailed investigation and understanding of processes such as mating systems, gene dispersal patterns, and spatial genetic structure and the quantification of genetic diversity, genetic structure, and inbreeding. Parentage analysis (paternity and maternity) has been used extensively to study gene dispersal in tree populations in a wide range of environments, including continuous, fragmented, and logged forests, isolated trees in pastures, and seed orchards (Burczyk, DiFazio & Adams, 2004;Ellstrand, 2014;Smouse & Sork, 2004). In such analyses, it is important to differentiate between the realized and effective gene flow because deterministic factors such as natural selection and stochastic factors such as random mortality, predation, and disease can come into play between the seed and juvenile (regenerant) stages, and many seeds never reach the juvenile and/or adult stages. Paternity and maternity analyses based on samples of established regenerants allow us to assess the realized pollen and seed dispersal, whereas paternity analysis based on open-pollinated seeds represents the effective pollen dispersal or the results of fertilization (Burczyk et al., 2004). Greater realized pollen flow than seed flow in fragmented populations has been reported for animal-pollinated and animal-and wind-dispersed seeds of tropical trees (Baldauf et al., 2014;Gaino et al., 2010;Ismail et al., 2017;Sebbenn et al., 2011).
Due to the high rate of deforestation in the Brazilian savannah biome, studies on the deciduous and monoecious tree Hymenaea stigonocarpa Mart. ex Hayne (Fabaceae: Caesalpinioideae) in the region are needed. In the São Paulo and Mato Grosso do Sul states, H. stigonocarpa is currently only found in forest fragments and as isolated trees in pastures; therefore, plans for its in situ and ex situ conservation are urgent. In Brazil, the species occurs between 3°30′S and 22°40′S, and as such, it is restricted to the savannah habitat in the central and south-east regions of the country (Carvalho, 2006). Hymenaea stigonocarpa trees can reach up to 29 m in height and 50 cm in diameter at breast height (dbh). At least four different bat species pollinate H. stigonocarpa flowers, including Glossophaga soricina, Platyrrhinus lineatus, and Carollia perspicillata (Gibbs, Oliveira & Bianchi, 1999), and both agoutis and birds disperse the fruits and seeds (Ramos, Lemos-Filho & Lovato, 2009). The economic importance of the species is related to its multiple uses; its wood can is used for construction; a yellow dye extracted from its bark is used in various sectors; and its fruits are edible. Hymenaea stigonocarpa is also important for fauna, serving as food for parakeets, parrots, howler monkeys, rodents, small wolves, and insects (Botelho, Ferreira, Malavasi & Davide, 2000), which are also likely seed dispersers. The species is self-compatible, with postzygotic selection in self-pollinated flowers (Gibbs et al., 1999) and a mixed mating system . The species has been indicated for use in the recovery of degraded savannah areas . While the mating system of H. stigonocarpa is relatively well understood, there is limited information about gene flow among trees occurring in pastures and forest fragments . Estimates of outcrossing, correlated mating, inbreeding, and pollen and seed dispersal distance are vital to inform conservation strategies for populations in highly fragmented environments and to calculate the number of seed trees required for seed collection in ex situ conservation and environmental reforestation (Sebbenn, 2006).
Due to the fact that in the São Paulo and Mato Grosso do Sul states, H. stigonocarpa is currently only found in forest fragments and as isolated trees in pastures, we investigated the effects of forest fragmentation on the genetic structure of two of the remaining populations in this region, where the species populations that remain are not continued in natural forests and are only found in fragmented populations. We used microsatellite loci to assess the genetic diversity, inbreeding, intrapopulation SGS, mating system (hierarchically within and among fruits), and seed and pollen dispersal of H. stigonocarpa populations occurring in a forest fragment population and in a pasture. We also sought to determine the number of seed trees needed for seed collection in these sites for ex situ conservation and environmental reforestation. We addressed the following questions: (a) Is there gene flow between the pasture and the forest fragment? (b) What are the distance and patterns of pollen and seed dispersal in the populations? (c) Are there differences in the rates of selfing and mating among relatives, and is there a paternity correlation between trees in the pasture and the forest fragment? (d) Is the paternity correlation lower among fruits than within fruits? (e) Are the levels of effective size variance lower and inbreeding higher in open-pollinated seeds collected from the pasture than in seeds collected from trees in the forest fragment? (f) Do selfing and mating among related trees produce inbreeding depression?

| Study site and sampling
The studied savannah landscape is characterized by high levels of anthropogenic disturbances. It consists of large (approximately 2,523 ha), extended pastures and sugarcane and eucalyptus plantations, interspersed with small forest fragments and isolated H. stigonocarpa trees in the pastures. The area (20°07′S, 51°44′W, altitude of 373 m) is located near highway MS444, in the municipality of Inocência, Mato Grosso do Sul State, Brazil. The climate is tropical with a dry winter, a humid summer, an average annual rainfall of 1,232 mm, and an average temperature of 24.5°C. In this region, much of the savannah was cut down between 1970 and 1980 for livestock production. The study was carried out in two populations (PA and PF) located approximately 5 km apart (Figure 1) distance ranging from 1 to 2,641 m, mean of 1,282 m), representing nonreproductive plants. We also collected and genotyped openpollinated seeds from 20 seed trees in the PA population and 15 seed trees in the PF population; 30 seeds per tree from different fruits were included the sample, resulting in a total of 600 PA seeds and 450 PF seeds. Seeds were identified by mother (family) and fruit origin for the hierarchical paternity analysis within and among fruits.
To support the ex situ conservation of the populations and to investigate the inbreeding depression, we germinated seeds and used the resulting offspring to establish a provenance and progeny test in the Fazenda de Ensino, Pesquisa e Extensão, UNESP Ilha Solteira Campus (FEIS/UNESP), located in Selvíria, Mato Grosso do Sul State, F I G U R E 1 Spatial distribution of Hymenaea stigonocarpa trees in the pasture (PA) and forest fragment (PF) using an unbalanced random block design comprising two provenances (PF and PA populations), 35 families (family was defined as seeds sampled of individuals seed trees), 17-69 replicates, one plant per plot, and tree spacing of 6 × 1.5 m. At 18 months after planting, we measured the percent of family survival (SUR) and individual offspring height (H). The percent rate of SUR offspring per family was calculated as SUR = (n surv /n)100%, where n surv is the number of surviving offspring per family, and n is the number of planted offspring per family. The individual offspring height was measured using a ruler (cm).

| Analysis of genetic diversity
The genetic diversity for adults, juveniles, and the offspring of each population was quantified by the total number of alleles across all loci (k), allelic richness (R), and observed (H o ) and expected (H e ) heterozygosity. We estimated the fixation index (F), and its statistical significance was calculated by the permutation of alleles among individuals (600 randomizations). These analyses were carried out using FSTAT software (Goudet, 2002). However, as the F estimated for offspring can be biased due to the overestimation of gene frequencies of maternal alleles (each plant within a family receives at least one maternal allele), this index was estimated as described in Manoel et al. (2015). To test if the estimated indices were significantly different between samples, we used the unpaired t test.

| Analysis of spatial genetic structure and effective population size
The analysis of SGS was carried out for adults and juveniles based on the estimate of the coancestry coefficient (θ xy ), as described in Loiselle, Sork, Nason and Graham (1995), using SPAGEDI (Hardy & Vekemans, 2002). To compare the SGS of PA and PF adults and PF juveniles, we arbitrarily chose to use the same 11 distance classes between samples (25-1,000 m). We obtained the statistical significance of θ xy by comparing the confidence interval limits at a 95% probability of the average estimate θ xy for each distance class, as calculated by the permutation of individuals among distance classes.
To compare the extent of SGS between PA and PF adults and PF juveniles, the S p statistic (Vekemans & Hardy, 2004) was calculated.
To test for the statistical significance of SGS, the spatial positions of the individuals were permuted 1,000 times. The group coancestry (Θ) for the adults and juveniles was estimated following Lindgren and Mullin (1998), and effective population size was calculated as described in Sebbenn et al. (2011).

| Parentage analysis
Pollen flow, seed flow, dispersal distance, the combined exclusion probability of the first (P 1 ) and second (P 2 ) parent, and the combined exclusion probability of identity (Q i ) were calculated using CERVUS 3.0 software (Kalinowski, Taper & Marshall, 2007). The cryptic pollen and seed flow (C gf ) values were estimated as described in Dow and Ashley (1996). Parentage (maternity and paternity) analyses were based on the single exclusion method, assuming no mismatching among the offspring-(or juvenile)-mother-father trio. Due to the fact that our parentage (maternity and paternity) analyses were based on only six microsatellite loci, and the number of candidate putative parents was high (359 + 111 = 470 adults), which may have resulted in a high probability of cryptic gene flow (see Section 3), we chose to be conservative, and we only accepted the positive assignment of seeds and juveniles to parents, assuming no mismatching among the offspring-(or juvenile)-mother-father trio. Offspring and juveniles that were not assigned any parent in the populations were determined to originate from gene immigration. Individuals that received the same parent individual for both the maternal and paternal assignment were identified as resulting from self-fertilization. We estimated the effective (for offspring) or realized (for juveniles) selfing rate (s) and the outcrossing rate from nonrelated individuals (t u ) and from related parents (t r ) based on the genotyped offspring of the provenance and progeny test. The selfing rate (s) was estimated as s = n s /n 1 , where n s is the number of individuals originating from self-fertilization, and n 1 is the total number of sampled seeds or juveniles of each population. The outcrossing rate was estimated as t = 1 − s. Outcrossed individuals were classified as originating from mating among nonrelated (t u ) or related (t r ) parents.
Offspring and juveniles from t r were determined using the estimate of the coancestry coefficient (θ xy ) between assigned parents in SPAGEDI 1.3 (Hardy & Vekemans, 2002). Following Ismail et al. (2014), if θ xy ≥ 0.1 between the assigned parents, we assumed that the offspring or juvenile was inbred due to mating between related parents. The t u value was calculated as t u = n u /n 1 , and for related parents, t r = n r /n 1 , where n u and n r are the number of individuals originating from nonrelated parents and related parents, respectively. To confirm the results of the parentage analysis, we estimated the mean θ xy between offspring or juveniles and their assigned parents. We estimated the mean, standard deviation, and minimum and maximum for θ xy within families. The spatial positions of adults and juveniles (x and y coordinates) were used to estimate the mean, standard deviation (SD), median, minimum and maximum pollen and seed dispersal distances, based on the Euclidian distance between two points. To investigate if reproductive success was a function of the distance between trees, we compared the frequency distribution of pollen dispersal to the frequency distribution of the distance between all trees of both populations using the Kolmogorov-Smirnov test. The effective pollination neighbor area (A ep ) was calculated as described in Levin (1998), and the effective radius of pollen dispersal was based on Austerlitz and Smouse (2002). To investigate male and female fertility and whether trees with the greatest dbh produced more offspring and juveniles as pollen donor parents (male fertility) or maternal parents (female fertility), we used the Spearman correlation coefficient (ρ).

| Analysis of mating system by MLTR
We assessed the mating system at the population and individual levels based on the Expectation-Maximization numerical method (EM) using MLTR 3.1 software (Ritland, 2002). The estimated indices were the maternal fixation index (F m ); multilocus (t m ) and single-locus (t s ) outcrossing rates; mating among related individuals (t m − t s ); correlation of selfing (r s ); correlation of selfing among loci (r s(l) ); paternity correlation within and among fruits (r p ), within fruits (r p(w) ), and among fruits (r p(a) ); and gene frequencies of pollen and ovules. The standard deviations of these indices were estimated by 1,000 bootstraps, using individuals within families as candidate he units of resampling. The effective number of pollen donors within and among fruits (N ep = 1/r p ), within fruits (N ep(w) = 1/r p(w) ), and among fruits (N ep(a) = 1/r p(a) ) was calculated following Ritland (1989). The mean coancestry coefficient (Θ) and variance effective size (N e ) within families was estimated based on Sebbenn (2006), and the number of seed trees for seed collection (m) was calculated to retain an effective reference size of 150 in the total sampled progeny array (Sebbenn, 2006). The 95% confidence interval of the indices was estimated as described in Wadt et al. (2015).
To determine the associations among the sample size (n), R, H o , F, s + (t m − t s ), N ep , and N e within families, we used Spearman's rank correlation coefficient (ρ).

| Analysis of inbreeding depression
Inbreeding depression for offspring of the provenance-progeny test was assessed in terms of selfing (δ s ) and mating among relatives (δ r ) as: and where x t u , x t r , and x s are the means of the traits (survival and height) for offspring originating from outcrossing between unrelated individuals, outcrossing between related individuals, and self-fertilization, respectively, based on paternity analysis and the coancestry coefficient between the assigned parents.

| Genetic diversity
For all adults, juveniles, and offspring of both populations (1,565), we found 99 alleles across the six loci (Table 1). Based on an unpaired t test, the mean allelic richness (R) was significantly higher in the PA adults and offspring than the PF adults, offspring, and juveniles; the observed heterozygosity (H o ) was significantly higher in adults than offspring for both populations; and, for the PF population, the expected heterozygosity (H e ) was significantly higher in adults than in offspring. For both populations, the fixation index (F) was significantly lower than zero in adults and juveniles, significantly higher than zero in offspring, and significantly lower in adults than offspring.

| Spatial genetic structure and effective population size
For the adults of both populations, the spatial distribution of genotypes (SGS) was significantly structured up to 250 m, and for PF TA B L E 1 Genetic diversity and fixation index (F) for adults, offspring, and juveniles in a pasture (PA) and a forest fragment (PF) Notes. Different letters mean significant differences at the 5% probability level of the unpaired t test. H e is the expected heterozygosity; H o is the observed heterozygosity; k is the total number of alleles; n is the sample size; N e is the effective population size; R is the allelic richness for 111 individuals genotyped for six loci; SD is the standard deviation; Θ is the group coancestry coefficient. *p < 0.05.
juveniles, it was significantly structured up to 125 m ( Figure 2). The strength of SGS was similar among the adults of PA (S p = 0.014) and PF (S p = 0.009) and the juveniles of PF (S p = 0.015). The group coancestry (Θ) for adults and juveniles was low (Θ < 0.003), indicating that during random mating, a low level of inbreeding should be expected (<1%). The effective population size (N e ) was lower than the sample size of adults and juveniles (N e /n < 1), especially for PF juveniles and PA adults.  were from outside PF, with 2.6% originating from PA. Assuming that a single assigned parent represents the mother, at least one putative mother was assigned for 96.8% of the juveniles, with 3.2% not from within the two populations (realized seed immigration), 83.6% originating from mothers located within PF and 16.4% from mothers outside of PF, with 13.2% of mother trees from the PA population. The mean pairwise coancestry between juveniles and the first (assumed as the mother: θ 1 = 0.19) and second (assumed as the father: θ 2 = 0.19) parent were lower than expected (0.25).

| Parentage analysis
The mean pairwise coancestry between offspring and the mother  Table S1). For offspring assigned a father, the mean and maximum pollen dispersal distances F I G U R E 2 Spatial genetic structure in the adults of PA (a) and PF (b) and the juveniles of PF (c). The continuous line represents the average estimated coancestry coefficient described in Loiselle et al. (1995), and the dashed lines represent the confidence interval at the 95% probability of the hypothesis of no spatial genetic structure (H0: θ xy = 0)  was higher than expected (0.5), and the mean fixation index for offspring produced through t r (F r ) in PA (0.36) and PF (0.36) was higher than θ r . All juveniles were the result of outcrossing, with 4.1% from t r , a mean distance between related parents (D r ) of 310 m, and a F r of 0.08, which was lower than θ r (0.17).

| Mixed mating system hierarchy within and among fruits by MLTR
The mean population fixation index of seed trees (F m ) was not significantly different from zero (Table 3), but the individual F m was lower than F o for 51.7% of the families. These results suggest selection against inbred individuals between seed and adult stages (Supporting Information Table S2). The multilocus outcrossing rate (t m ) was significantly lower than the unity (PA = 0.77, PF = 0.81) and variable among seed trees (0.53-1.0), indicating that some offspring were produced through self-fertilization. The selfing correlation (r s ) was significantly higher than zero, confirming the individual variation for t m . Mating among related individuals (t m − t s ) was significantly higher than zero in 19 families of PA and 12 families of PF.
The rate of mating among relatives was also significantly higher in PA than in PF. The correlation of selfing among loci (r s(l) ) was low (<0.12), indicating that inbreeding within the populations was mainly the result of selfing. The paternity correlations within and among (r p ), within (r p(w) ), and among (r p(a) ) fruits were not significantly different between populations, indicating that seed trees were fertilized by a limited number of pollen donors (maximum N ep = 2). However, all estimates of the paternity correlation and effective number of pollen donors were variable among seed trees, with r p(w) higher than  Table   S2). The Spearman rank correlation (ρ) (Supporting Information Table   S3) was positively significant between the indices N ep vs. R, N e vs.

| Inbreeding depression
The rate of survival (SUR) of the offspring at 18 months after establishing the provenance and progeny test (  TA B L E 4 Survival (SUR), mean height (H), and inbreeding depression for selfing (δ s ) and mating among related trees (δ r ) at 18 months for offspring of the PA and PF populations sizes of adult trees and seeds sampled from the forest fragment (28 adults and 137 seeds) and isolated trees and seeds sampled from the pasture (six adults and 34 seeds); furthermore, the realized pollen and seed dispersal in juvenile trees were never investigated. Due to that, we carried out the present study using higher sample sizes of adults and seeds from a forest fragment (111 adults and 450 seeds) and isolated trees and seeds from a pasture (359 adults and 600 seeds), and we also sampled juvenile trees (219)

| Genetic diversity
The mean allelic richness (R) was higher in adults and offspring from PA than those from PF. Adult individuals in these populations are remnants of prefragmentation phases (which occurred approximately 50 years ago), which may explain the differences in the genetic diversity levels between the populations. The PA adults, although in a highly modified habitat, retain levels of genetic diversity from the prefragmentation period, which may have been higher than that of the near-neighbor PF population. This result indicates that the PA population is important for the maintenance of the species in the landscape.
The mean observed heterozygosity (H o ) was higher and the fixation index (F) and was lower in adults than in offspring of both

| Spatial genetic structure and seed dispersal
Adults of both populations and PF juveniles present a SGS. Thus, there is a high probability that near-neighbor adults located within 280 m (PA) or 350 m (PF) and PF juveniles within 125 m are related.
SGS is mainly determined by short-distance seed dispersal, although short-distance pollen dispersal can also contribute to SGS (Collevatti, Lima, Soares & Telles, 2010;Hardy et al., 2006). For H. stigonocarpa, SGS is likely the result of short-distance seed dispersal near the mother trees, with pollen dispersal contributing minimally to the creation of SGS. Seed dispersal reached long distances (up to 8,091 m), but the dispersal pattern was IBD, with a high frequency of juveniles established near parent trees, which can explain the SGS. The seed and pollen dispersal vectors of the species have the potential for long-distance dispersal. Hymenaea stigonocarpa seeds are dispersed by large mammals (Agoutis agoutis) and birds (Ramos et al., 2009), and, as discussed above, pollen is dispersed by bats (Gribel & Lemos, 1999;Lacerda, Kanashiro & Sebbenn, 2008) that frequently travel more than 200 m between trees (Dunphy, Hamrick & Schwagerl, 2004). In the present study, the sampled populations are surrounded by sugar cane and Eucalyptus plantations, resulting in a limited presence of animals, such as large mammals, to disperse seeds. This lack of seed dispersers results in seedling establishment near the mothertree, thus increasing the probabilities of mating among relatives and inbreeding in subsequent generations. Our results confirm these expectations, as mating among related individuals (t r and t m − t s ) was detected by the parentage analysis for seeds (t r : 24.3%-31.9%) and juveniles (t r = 4.1%), by the MLTR mixed mating system analysis for both seeds (t m − t s : 30%-46%) and by the inbreeding in seeds (

| Effective population size
The effective population size (N e ) was lower than the sample size (n) for the adults and juveniles (N e /n < 1) of the populations due to the occurrence of SGS. Related individuals present identical-by-descent alleles, which decreases the effective population size (N e ) in populations. The effective population size (N e ) is a key variable for conservation genetics, as populations with a low effective population size (N e ) can lose genetic diversity and increase inbreeding, resulting in inbreeding depression and reduced population fitness (Kalinowski & Waples, 2002). Therefore, for in situ conservation, a minimum effective population size (N e ) of 70 has recently been suggested for random mating populations to avoid inbreeding depression (Caballero, Bravo & Wang, 2016). Although they occur in a significantly fragmented landscape, the adults and juveniles of our studied populations presented effective population size (N e ) values  greater than 70, indicating that both the PA and PF populations have an effective population size (N e ) sufficient for in situ conservation.
However, as the populations present deviation of random mating due to selfing, mating among related trees and correlated mating, we must consider using a reference effective population size of 150, as suggested by Sebbenn (2006), for in situ conservation. This indicates that the effective population size (N e ) of the PF population must be increased by, for example, the plantation of 80 individuals that are neither inbred nor related.

| Gene flow
Our results show that the two studied populations are not genetically isolated due to pollen and seed flow between the PA and PF populations and from individuals not included in the analysis located outside of the study area. Pollen immigration levels in PA (20.6%) and PF (21.5%-23.9%) were similar, but pollen flow into PF from PA was greater (2.6%-7.3%) than pollen flow from PF into PA (0.7%), suggesting that bats tend to move from pastures to forests. Furthermore, in PF, the realized pollen flow (m p ) was 1.3 times higher (m p /m s = 21.5%/16.4%) than the seed flow (m s ), with pollen immigration mainly coming from outside both populations (m p /m s = 14.2%/3.2% = 4.4) and seed immigration mostly coming from PA (m p /m s = 7.3%/13.2% = 0.55). Although the inbreeding depression and stochastic factors, such as random mortality, predation, and diseases, may change the effective to realized pollen and seed dispersal stages, these results suggest that bats are more efficient gene dispersers than large mammals and birds. To understand the pollen flow of a species, we must first consider the behavior of its pollinators. Bats need to consume 1 mg of sugar or approximately 5 μl of nectar, and flower nectar has a sugar concentration of 20% (Nassar, Ramirez & Linares, 1997). In the savannah region of Brazil, Bobrowiec and Oliveira (2012)

| Pollen dispersal distance
The pollen dispersal across the studied landscape reached long dis-  (Lacerda et al., 2008) and a distance of 18 km reported for Ceiba pentandra (Gribel & Lemos, 1999). However, the observed pollen dispersal pattern for H. stigonocarpa was isolation by distance, with most pollination events occurring at distances less than 2,000 m; in PA, 89.4% occurred within 600 m, and in PF, 68.9% occurred within 2,000 m. We can attribute this pattern to the fact that bats feed less than two minutes per tree and often travel more than 200 m between trees (Dunphy et al., 2004). Although bats can travel long distances, they tend to forage at high frequencies between near-neighbor trees. The curve of the pollen dispersal distance pattern was also different between PA and PF, which can be explained by the distribution of trees across the landscape or the tree population density, with the trees in PA having a lower range of distance (1-1,528 m) and population density (3.29 trees/ha) than the trees in PF (3-2,727 m; 0.17 trees/ha). The low population density, associated with other factors, such as variations in flower phonology, may increase the pollen dispersal distance since pollinator vectors must fly longer distances to collect nectar than they do in regions with higher tree population densities (Degen & Sebbenn, 2014;Dick et al., 2008;Tambarussi, Boshier, Vencovsky, Freitas & Sebbenn, 2015).

| Parent fertility success
Female and male fertility in PF increased with tree dbh. Our results show that in PF, offspring, and juveniles were fathered by pollen donor trees with a high dbh, and juveniles were produced from mother trees with a high dbh. Thus, the observed IBD effective pollen dispersal and realized pollen and seed dispersal were determined in part by the size of the trees. Male fertility successes for trees with high dbh values and IBD pollen dispersal patterns have also been reported in other studies (Castilla, Pope & Jha, 2016;Klein, Desassis & Oddou-Muratorio, 2008;Setsuko, Nagamitsu & Tomaru, 2013;Tambarussi et al., 2015), but see also Tarazi, Sebbenn, Kageyama and Vencovsky (2013). The high fertility of trees associated with greater dbh values may be related to the large size of the crowns and the high flower production level, which are favored by foraging pollinators (Setsuko et al., 2013).

| Outcrossing and inbreeding
Our results show that the species presents a mixed mating system, with a predominance of outcrossing (>75%) and individual variation among trees (0.53-1.0). Hymenaea stignocarpa is monoecious and self-compatible, and seeds can be produced through mixtures of outcrossing and selfing (Gibbs et al., 1999;.
Plants with a mixed mating system have evolutionary advantages over strictly selfing or outcrossing species due to the possibilities for gene recombination through both seed production mechanisms.
These processes may guarantee reproduction in specific situations, such as the spatial isolation of trees . For H. stignocarpa, self-fertilization occurs due to the mobility and food foraging habits of bats as they move between flowers of the same tree before flying to other trees (Collevatti, Estolano, Garcia & Hay, 2009). The outcrossing (or selfing) variations among trees can be explained by individual variations in inbreeding depression for inbred seeds produced through selfing and mating among relatives.
For selfing, this variation depends on the genetic load (deleterious alleles) of the mother; for mating among related trees (t r ), it depends on the mother and father and the probability that ovules and pollen gametes carrying deleterious alleles are combined in homozygosis during fertilization. Inbreeding from both selfing and mating among relatives will not produce inbreeding depression if the parents do not present deleterious alleles or if the alleles are combined in a heterozygous state. In contrast, inbreeding depression will be high for parent trees with an increased number of deleterious alleles, and many inbred seeds will not germinate (and, as such, will not be included in genetic analyses). Thus, variations in the genetic load of trees can result in individual variations in the outcrossing rate due to inbreeding depression, which may result in the mortality of some offspring.
Our estimate of group coancestry (Θ) indicates that under conditions of random mating in PA and PF, low levels of inbreeding should be expected in the descendant populations (<1%). This result is supported by the results for PF juveniles, which detected no inbreeding, although we did detect a 4.1% rate of realized mating among related individuals (t r ). In contrast, the offspring of both populations presented inbreeding due to selfing and mating among relatives. Both paternity and mixed mating system (MLTR) analyses showed that mating among related trees was higher in PA than PF.
The SGS in adults and the IBD pollen dispersal pattern of the populations can explain the results for mating among related trees (t r ) and the differences between populations. The mean distance at which mating among related trees (t r ) was detected in PA (272 m

| Correlated mating
The paternity correlation was high and similar between populations (r p > 0.5), but it was variable among seed trees. This can be explained by pollen being deposited within trees, which is associated with individual variations in flowering phenology . Paternity correlation was similar within (r p(w) ) and among (r p(a) ) fruits, which indicates the probability of finding full-sibs within and among fruits; however, at the level of individual trees, the r p(w) values were generally lower than the r p(a) values. Higher r p(w) values than r p(a) values have been reported for other tropical tree species (Giustina et al., 2018;Manoel et al., 2015;Quesada et al., 2001;Silva et al., 2011;Tambarussi et al., 2016;Wadt et al., 2015). Thus, as we also found self-fertilization in both populations, and families presented mixtures of self-sibs, half-sibs, full-sibs, and self-half-sibs, with inbred selfed offspring and substantial proportions of half-sibs and full-sibs presenting inbreeding due to the detected mating among related individuals. Therefore, the coancestry coefficient (Θ) was higher and the effective size (N e ) within families was lower than the corresponding values expected for panmictic populations (Θ = 0.125; N e = 4).

| Inbreeding depression
Our study shows strong evidence of inbreeding depression (ID) for H. stigonocarpa. Inbreeding was detected only in offspring, which we can attribute to selfing and mating among relatives. However, for juveniles, no selfed individuals were detected, mating among related trees (t r ) was low (4.1%), and no inbreeding was detected. Again, these results suggest selection against inbred individuals between the seed and juvenile stages. In the provenance and progeny test, we observed a high rate of aborted seeds and a high mortality. Progeny from PA showed lower levels of survival (54%) than those from PF (64%), and the levels of inbreeding in PA were also higher. Survival and mean height (H) were greater for offspring originating from mating among unrelated individuals (t u ) than those originating from selfing (s) and mating among relatives (t r ). The ID for survival and H were higher for offspring produced from selfing (s) than offspring produced from mating among related trees (t r ) in both populations. These results confirm the expectation that selfing results in more ID than mating among relatives due to a greater probability that identical-by-descent alleles are combined in a homozygous state in the selfed offspring.
Nevertheless, H was less affected by inbreeding than survival.

| Implications for conservation genetics
The two investigated populations are inserted within a large savannah landscape (approximately 2,523 ha) composed of a mix of pastures and sugarcane and eucalyptus plantations and interspersed with small forest fragments and isolated H. stigonocarpa trees in pastures. The PA population consists of an area of 109.12 ha of isolated trees in a pasture located approximately 5 km from the PF population, which is within a large forest fragment (666.7 ha). Our results show that these two populations are not reproductively and genetically isolated, as there is pollen and seed flow between both populations and immigration from outside the study area. As the isolated trees of the PA population presented higher allelic richness than the trees of the fragmented PF population, for in situ conservation, it is important to conserve both areas to maintain the genetic diversity of the neighboring populations. Our results also indicate that populations of H. stigonocarpa must be preserved at distances of at least 5 km to maintain genetic connectivity through gene flow, which is carried out by both pollen and seed dispersal.
For ex situ conservation, our results indicate that (a) as there are no strong genetic differences between populations, seeds can be collected from just one or both populations; (b) due to the presence of similar levels of SGS in both populations and to avoid the collection of seeds from related trees, we recommend harvesting seeds from trees at least 250 m apart; (c) as the paternity correlation among and within fruits was similar and high, indicating a low number of effective pollen donors fertilizing the trees and their fruits, seed collection should include many fruits from each tree to increase the probability of more pollen donors contributing to the seed samples. Furthermore, we suggest mixing seeds from different seed trees in equal proportions (maternal gamete control) to decrease the variation in the maternal genetic contribution of seeds used in conservation and reforestation plans; (d) to retain an effective size of 150 in progeny array samples, seed collection must include at least 83 trees from PA and 78 from PF. However, because we detected inbreeding depression for survival due to a high number of inbred seeds, we suggest collecting a greater number of seeds from each tree and selecting seedlings that show greater vigor and growth at the nursery stage for ex situ conservation, tree improvement, and environmental reforestation to maximize the survival rates. Finally, the species presents a mixed mating system combined with high levels of correlated mating, resulting in a coancestry within families (Θ) similar to that expected for full-sibs (Θ = 0.25); thus, for tree improvement programmes, we suggest estimating the additive genetic variance ( 2 A ) as 2 A = 2 f ∕2Θ = 3 f ∕0.504 ( 2 f is the genetic variance among families), instead of using the general formula for half-sib families ( 2 A = 3 f ∕0.25).