Mating system parameters in a high density population of andirobas in the Amazon forest

The objective of this work was to estimate the mating system parameters of a andiroba (Carapa guianensis) population using microsatellite markers and the mixed and correlated mating models. Twelve open‐pollinated progeny arrays of 15 individuals were sampled in an area with C. guianensis estimated density of 25.7 trees per hectare. Overall, the species has a mixed reproductive system, with a predominance of outcrossing. The multilocus outcrossing rate (tm = 0.862) was significantly lower than the unity, indicating that self‐pollination occurred. The rate of biparental inbreeding was substantial (tm ‐ ts = 0.134) and significantly different from zero. The correlation of selfing within progenies was high (rs = 0.635), indicating variation in the individual outcrossing rate. Consistent with this result, the estimate of the individual outcrossing rate ranged from 0.598 to 0.978. The multilocus correlation of paternity was low (rp(m) = 0.081), but significantly different from  zero,  suggesting  that  the  progenies  contain  full‐sibs.  The  coancestry  within  progenies  (Θ = 0.185) was higher and the variance effective size (Ne(v) = 2.7) was lower than expected for true half‐sib progenies (Θ = 0.125; Ne(v) = 4). These results suggest that, in order to maintain a minimum effective size of 150 individuals for breeding, genetic conservation, and environmental reforestation programs, seeds from at least 56 trees must be collected.


Introduction
Andiroba (Carapa guianensis Aubl.) is a deciduous tree from the Meliaceae family commonly found in the Neotropics (Dayanandan et al., 1999;Cloutier et al., 2007b).The species inhabits the upland and floodplain forests of the Amazon basin (Cloutier et al., 2007b).It is economically important as a source of timber and oil (Cloutier et al., 2007a(Cloutier et al., , 2007b)).The seeds consist of a large kernel containing a high proportion of lipids, and the oil is widely used for medicines, cosmetics, and insect repellency (Revilla, 2001).In the Brazilian Amazon forest, individuals can reach up to 65 cm of stem diameter at breast height (DBH) (Martins et al., 2012).The population density of reproductive individuals is relatively high in natural forest (>5 trees per hectare), but variable among populations (Dayanandan et al., 1999;Cloutier et al., 2007a;Martins et al., 2012).
Despite the economic potential of andiroba, there is still little information about its botanics, ecological, and genetics.In general, due to the intensive logging of the species in the Amazon forest, genetic studies have been focusing on the effects of this practice on mating systems and gene flow (Hall et al., 1994;Cloutier et al., 2007b;Klimas et al., 2007;Raposo et al., 2007;Martins et al., 2012).However, no studies have been carried out to investigate coancestry levels, effective size, and sample size for purposes of genetic breeding, conservation, and environmental reforestation plans.Reproductive biology, mating systems, pollen and seed dispersal (gene flow), and intra-population spatial genetic structure (SGS) have a strong effect on the genetic composition of natural populations.The mating system patterns of a species determine the levels of relatedness and inbreeding within open-pollinated progenies, and such information is essential to estimate sample size for genetic breeding and conservation, as well as for collecting seeds to be used in environmental reforestation plans (Sebbenn, 2006).
Carapa guianensis is an insect pollinated monoecious tree, predominantly outcrossed (Hall et al., 1994;Cloutier et al., 2007b).Hall et al. (1994) found outcrossing rates that were not significant and different from 1.0 in unlogged (t m = 0.967) and in logged (t m = 0.989) populations, in Costa Rica.However, Cloutier et al. (2007b) observed outcrossing rates significantly different from 1.0 (0.939 before logging and 0.927 after logging), in a population from the Brazilian Amazon forest (state of Pará), which suggests the occurrence of some selfing.Furthermore, both pollen and seeds can be long-distance dispersed (>430 m for pollen and >397 m for seeds) (Martins et al., 2012), and this may explain the observed weak SGS in natural and logged populations (Cloutier et al., 2007b;Martins et al., 2012), and the absence of biparental inbreeding found in logged and unlogged populations (Cloutier et al., 2007b).However, mating system patterns may vary among populations, individuals within a population, flowers within individuals, and within different reproductive events (Sebbenn, 2006;Feres et al., 2012), since they are affected by both biotic and abiotic factors (Sebbenn, 2006).Therefore, it is necessary to study the mating system of a species in more than one population, with several individuals and reproductive events (Sebbenn, 2006;Feres et al., 2012).For genetic breeding, conservation, and reforestation purposes, it is also important to know inbreeding levels, coancestry coefficient, and effective size within open-pollinated progenies because these genetic parameters allow to estimate the required sample size in order to retain a specific effective population size (Sebbenn, 2006;Feres et al., 2012).
The objective of this work was to estimate the mating system parameters of a andiroba (C.guianensis) population, using microsatellite markers and the mixed and correlated mating models.

Materials and Methods
The study was carried out in the 1,200 ha experimental forest of the Brazilian Agricultural Research Corporation (Embrapa), in the southwestern portion of the state of Acre, Brazil (10°01'28"S, 67°42'19"W).The experimental region has a lightly undulating topography, with a dominant vegetation classified as humid.The region has a pronounced three-month dry season, from June to August, and the annual mean temperature is 24.5°C.The evaluated forest is an occasionally inundated primary forest.The peak of the flooding events occurs from November to February.Fluctuations in yearly rainfall influence the range and duration of these events (from a few days to a month).Therefore, these forests cannot be considered floodplain forests, and they do not have consistent yearly flooding.
Carapa guianensis density was estimated at 25.7 trees per hectare (Klimas et al., 2007).Four 400x400 m plots (16-ha) were established within the reserve, as described by Klimas et al. (2007); two of them comprised the studied seed trees.In 2009, seeds were randomly collected from 15 seed trees present in the occasionally inundated forest: six in plot 1 and nine in plot 3.In plot 1, the average distance between trees was 164.6 m, with minimum distance of 111.7 m and maximum of 229.4 m.In plot 3, the average distance was 93.7, with minimum of 21.9 m and maximum of 227.7 m.Approximately 20 open-pollinated seeds were germinated from each seed tree (progenies).Twelve plants per progeny were evaluated by SSRs, totaling 180 individuals.
The software Genetic Data Analysis (GDA) (Lewis & Zaykin, 2002) was used to estimate the average number of alleles per locus, observed (H o ) and expected heterozygosities (H e ), and the fixation index (F) in the progeny array.To test if the average F was significantly different from zero, 1,000 bootstrap replicates were used, with the GDA program.
The mating system at the levels of population and individual was analyzed according to the mixed mating (Ritland & Jain, 1981) and correlated mating (Ritland, 1989) models, using the mLTR software, version 3.1 (Ritland, 2002).The mixed mating model assumes that: each mating represents a random event of an outcross or a self-fertilization, with probabilities equal to t and s (1-t), respectively; no mutation and selection following fertilization may occur between fertilization and DNA analysis; and that there is no assortative mating (the probability of an outcross is independent of the maternal or paternal genotypes) (Ritland & Jain, 1981).The following parameters were estimated within progeny arrays: maximum-likelihood (ME) of single-locus (t s ) and multilocus (t m ) outcrossing rates, biparental inbreeding (t m -t s ), and correlation of paternity (r p(m) ) and of selfing (r s ).The average frequency of pairwise of self-sibs (P ss ), half-sibs (P hs ), full-sibs (P fs ), and self-half-sibs (P shs ) within progenies was respectively estimated as (Sebbenn, 2006): P ss = s 2 ; P hs = t m 2 (1 -r p(m) ); P fs = t m 2 x r p(m) ; and P shs = 2st m .The effective number of pollen donors was estimated by N ep = 1/r p(m) (Ritland, 1989).The 95% confidence interval of the parameters was calculated based on 1,000 bootstraps between individuals within progeny array.The average coancestry coefficient within progenies was estimated from the mating system parameter by Θ = 0.125(1 + F p )│4s + (t m 2 + t m x sr s )(1 + r p(m) )│, in which F p is the inbreeding in the parental population.This estimator corresponds to half of the relatedness coefficient within families (Θ = r/2), as derived by Ritland (1989).The variance effective size (N e(v) ) was estimated by N e(v) = 0.5/{Θ [(n -1)/n] + (1 + F s )/2n} (Cockerham, 1969), in which F s is the inbreeding coefficient of the seeds and n is the sample size (n = 100 was assumed to exclude the effect of sample size on the estimation of N e(v) ).The minimum number of seed trees required for harvesting, for conservation purposes, was calculated by m = N e(reference) /N e(v) (Sebbenn, 2006), in which N e(reference) is the required effective population size for conservation purposes, which, according to Lacerda et al. (2008), means 150 individuals.

Results and Discussion
Of the seven microsatellite tested, four were polymorphic: Cg05, Cg06, Cg07, and Cg16.They were used to genotype the seeds.The remaining three loci were monomorphic (Cg12) or had stutter bands (Cg17 and Cg01).In this last case, the genotyping profile was not clear and, therefore, these loci were not included.The number of alleles per locus ranged from four to eight, with an average of 5.75 alleles per locus.The expected heterozygosity varied from 0.628 to 0.770 (average of 0.724), and the observed heterozygosity ranged from 0.326 to 0.756 (average of 0.570).The expected heterozygosity was similar to the one estimated by Cloutier et al. (2007b), using six microsatellite loci in a C. guianensis population from the Brazilian Amazon forest, with seeds collected before and after logging (0.69 and 0.70, respectively).However, Cloutier et al. (2007b) estimated higher values of observed heterozygosity, before and after logging (0.68 and 0.67, respectively).
The multilocus outcrossing rate (t m = 0.862) was significantly lower than the unity (1.0), indicating that some selfing occurred (Table 1).Even with the few microsatellite markers used, the estimated multilocus outcrossing rate, in general, was not significantly different from those reported in other populations, in previous studies with allozymes [t m = 0.967 before and t m = 0.986 after logging (Hall et al., 1994)] and with microsatellite loci [t m = 0.939 before and t m = 0.927 after logging (Cloutier et al., 2007b); and t m = 0.918 (Cloutier et al., 2007a)].This significantly lower rate reflects the stability of crossing rates in C. guianensis, even in different populations, years, environmental conditions, and samples.Therefore, the present study and the ones reported above show that outcrossing is predominant in the species, which is favorable to maintain the genetic diversity and the effective population size of populations.However, the correlation of selfing was high (r s = 0.635), indicating high variation in individual outcrossing rates (Table 2), ranging among progenies from 0.598 to 0.978.This result contrasts to some extent with the ones reported by Maués (2006), who observed the presence of a partial pre-zygotic incompatibility system in the species.According to the results obtained in the present study, the species is not self-incompatible.
The average single-locus outcrossing rate (t s = 0.726) was also significantly lower than the unity (1.0), and the average difference (t m -t s = 0.134) was significantly different from zero (Table 1).This result was also observed in the progeny level (Table 2), indicating that biparental inbreeding may have occurred.Biparental inbreeding can be explained by the presence of some related individuals within the population.Martins et al. (2012), studying the same population, did not find significant SGS.However, it is important to note that the absence of significant SGS does not mean the absence of relatives within the population, only that they are not spatially structured.The estimates of biparental inbreeding were also higher than those detected by Cloutier et al. (2007b) before (t m -t s = 0.015) and after logging (t m -t s = 0.028).One possible explanation for this may be the presence of different levels of genetic load, in which the present population may have lower levels than the population studied by Cloutier et al. (2007b).In this case, it would have resulted in low inbreeding depression in the studied population.A study with inbreeding depression estimated in seeds collected from both populations could precisely explain these contrasting results.
The average multilocus correlation of paternity was low (r p(m) = 0.081), but significantly different from zero (Table 1).At individual level, this parameter ranged from 0.049 to 0.240 (Table 2), and generally it was
(1) t m , multilocus outcrossing rate; t m -t s , biparental inbreeding; r p(m), multilocus correlation of paternity; N ep , effective number of pollen donors; Θ, coancestry within families; N e(v) , variance effective size.SD, the standard deviation based on 1,000 bootstrap replicates.