Fertility variation, seed collection and gene diversity in natural stands of Taurus cedar (Cedrus libani)

Seed stand is a natural forest population that is one of the essential seed sources for global seed supply. Individual fertility is an ability to produce progeny to next generation. Prediction of fertility variation is useful for seed quality, ecosystem management and gene conservation. Fertility variation and gene diversity in seed stands of Taurus cedar were estimated based on the difference in strobilus production between female and male parents. A total of 50 trees were randomly chosen from each stand, and female and male strobili were counted for three consecutive years. The mean of female strobili ranged from 31 to 150, and that of male ranged between 77 and 828. The variation in strobilus production was subjected to estimation of female and male fertility variation. The total fertility variation ( $$\Psi$$ Ψ ) was estimated from the female and male fertility variation. The $$\Psi$$ Ψ in a good crop year was smaller than in a poor year. The effective number of parents ( N p ) was calculated based on the $$\Psi$$ Ψ , which varied from 34.7 to 44.2. When strobilus productions were pooled across 3 years or populations, the N p increased. Equal cone harvest could mitigate the fertility variation among individuals but caused loss of seed production. Mixing seeds from different years could also decrease the fertility variation and increase the gene diversity of seeds. However, a balance between the size of N p and the number of pooling years should be carefully considered for maintaining the gene diversity in the natural stands.


Results
Fertility variation and gene diversity were estimated based on the differences of strobilus production in female and male parents from three seed stands of Taurus cedar. A total of 50 trees were randomly chosen from each seed stand, and the female and male strobili were counted for three consecutive years. The coe cients of variation for female and male strobilus production were subjected to estimation female and male fertility variation. The total fertility variation (Ψ) was then estimated from the female and male fertility variation. The effective number of parents (N p ) was calculated based on the Ψ. The mean of female strobili ranged from 31 to 150, and that of male strobili ranged between 77 and 828. The Ψ in a good crop year was smaller than in a poor year and the N p varied from 34.7 to 44.2. The Ψ was improved and the N p was increased when strobilus productions were pooled across three years or populations. The equal cone harvest could mitigate the fertility variation among individuals but caused loss of seed production.

Conclusions
The effective number of parents could estimate gene diversity of seeds from natural stands, which was based on the function of correlated fertility variation between female and male parents. Mixing seeds from different years could improve the fertility variation among individuals and increase the gene diversity of seeds. However, a balancing between the effective number of parents and the number of mixed years or populations should be carefully considered for maintaining the gene diversity.

Background
Taurus cedar (Cedrus libani A. Rich), also called as Lebanon cedar, is a valuable timber species and quite striking specimen plants in the landscape. It is endemic to elevated mountains around the Eastern Mediterranean in Lebanon, Syria, and Turkey. Taurus cedar is classi ed as one of the economically important species for Turkish forestry and the 'National Tree Breeding and Seed Production Programme' (Koski and Antola 1993) because of its valuable wood product and the largest natural distribution on the Taurus Mountains in southern Turkey (Boydak 2003).
Taurus cedar forests cover about 463,000 ha according to Turkish forest inventory, while Boydak (2003) reported that the suitable plantation area for the species was 600,000 ha. Annual seed production is about 139 tones based on forestry inventory between 2012 and 2018 from the seed stands of Taurus cedar (General Directorated of Forestry 2015). The seeds are produced from 21 seed stands selected at 1,313.5 ha core area and 2,791.9 total area included protection zones. A total of 8 seed orchards (54.1 ha) were established but they are not productive yet because of young age (General Directorated of Forestry 2020).
Seed stands are one of the important seed sources and they are essential for global seed production programs. The primary objective of seed stands is to produce seeds as fast and urgent as possible, but they can also act as breeding and conservation populations. Seed stands have been designated and utilized to produce seeds for reforestation in many countries, and become an important global seed source (Zobel and Talbert 2003). The seed stands are one of the most common and cost-effective means of making available a stable supply of seeds for arti cial planation.
Genetic quality of seed stands and the vitality and performance of the resulting seeds depend on many factors, including individual fertility, owering synchronization, mating system, and gene ow (Muller-Starck and Ziehe, 1984; Zobel and Talbert 2003; Bilir 2011). In any seed stands, some trees produce more owers, pollen or seeds than others. The seeds from seed stands are often derived from a limited number of parents. It is reasonable to assume that the seed lot from one crop year does not represent the total gene pool of the respective seed stand. It is common that a small portion of the seed parents contribute a disproportionately large amount to the progeny. This unequal contribution leads to an increase in genetic relatedness and gene diversity loss in the resultant seeds.
Estimation of fertility variation is one of the important procedures of breeding and conservation programs, which is de ned as a difference of the ability to give progeny (i.e. reproductive success) among individuals (Bila 2000;Kang 2001). It is a useful tool for different purposes such as gene conservation, seed production programs, managing forest genetic resources, and evolutional and physiological study. reproductive characters is getting importance because of its easy, cheap and light survey. The fertility variation should be quanti ed and its impacts on the population should also be evaluated and mitigated for maintaining gene diversity (Kang et al. 2003). However, theoretical development on fertility variation and its related genetic parameters has been limited in natural forest populations.
A census (minimum) number of adult trees should be required to form approved seed stands in the category "Selected" for wind-pollinated tree species in the scheme of forest reproductive materials (OECD 1974). In German, for example, a number of 40 adult trees, an age of 40 years and an area of 0.25 ha are required as the minimum for Douglas-r while a minimum area of 2.5 ha is required for Norway spruce and Scots pine (Wojacki et al. 2019). The census number does not give su cient genetic information while the effective number size would give better information for the characteristics of reproductive materials (Wright, 1931;Falconer and Mackay, 1996;Lindgren and Mullin, 1998).
An effective population size is one of the key parameters in conservation and population genetics (Allendorf et al. 2013). The concept of effective population size is central to ecological, quantitative and evolutionary genetics (Charlesworth and Charlesworth 2010) and plant breeding (Falconer and Mackay 1996). It quanti es the magnitude of genetic drift and inbreeding in real populations. A substantial number of extensions to the basic theory and predictions have been made such as the inbreeding effective population size, the variance effective population size (Wright 1931), the selection effective population size (Lynch 2007) and the status number (Lindgren and Mullin 1998).
The main purposes of the present study are 1) to survey the female and male strobilus production for three consecutive years in three seed stand populations of Taurus cedar, 2) to estimate the female and male fertility variation among individuals based on the owering survey, 3) to estimate the effective number of parents in order to monitor gene diversity of seeds harvested from the seed stands, and 4) to discuss its effect on forest management practices (i.e. gene diversity manipulation) for supplying reproductive materials in the natural seed stands of Taurus cedar.

Flowering survey
Three seed stands were set to be surveyed owering at three different locations where the species have optimal natural distributions from southern part of Mediterranean region in Turkey ( Table 1). The fty healthy individual trees were randomly chosen from each seed stands. The numbers of female (N ) and male (N ) strobili were surveyed for three consecutive years (2016-2018) in three seed stand populations.
The production of female strobilus was counted entirely from the individuals. The production of male strobilus was estimated by using number of male strobili in a branch sampled from each direction and multiplying the branch number of each individual. We did not collect data of owering time or female receptivity to describe the overlapping of owering periods. Pollen contamination was ignored in the study. The coe cients of variation (CV) for female and male fertility were calculated and applied to estimate the fertility variation as female and male parents, respectively (see the Eq. 2-a and 2-b). The individual contribution (fertility) to strobilus production was proportionally calculated from the surveyed owering data in each population.

Genetic variation and parental balance
The following ANOVA model was used to analyses the difference of strobilus production among populations and years by the SAS software (SAS Inst. Inc. 1988) in the present study.
where Y ijk is the observation from the k th tree of the j th population in the i th year, µ is the overall mean of strobilus production, F i is the effect of i th year, B j is the effect of the j th population in the i th year, FB (ij) is the effect of the interaction between i th year and j th population, and e ijk is the random error.
The correlation between female and male strobilus production was analyzed by the Pearson's product moment correlation coe cients. The correlation coe cients (r) were implemented to estimate the total fertility variation (see below Eq. (4)).
The parental balance curve was used to characterize high or low productive individuals for female and male strobili. Individual trees were ranked from high to low for the production of female and male strobilus production, and then cumulative percentage calculations are plotted against the total number of individuals in the studied population (Chaisurisri and El-Kassaby 1993). Female and male genetic contributions can be explained by the parental balance curves, and the cumulative percentage curve is often used to quantify fertility variation in forest populations (Gri n 1982; Kang, 2001).
Theoretical frameworks on fertility variation and effective number

Fertility variation estimation
Female and male fertilities of the i th individual were de ned as the ability to produce female and male strobili, respectively and estimated as the relative proportion of female and male strobilus production to the entire population (Muller-Starck and Ziehe 1984). The variations of female and male fertility (ψ f and ψ m ) among individuals, also called female and male gametic fertility variations, were estimated by the coe cient of variation (CV) for female and male strobilus production suggested by Kang and Lindgren (1998) as: where N is the census number, f i is the fertility as female of the i th individual, m i is the fertility as male of the i th individual, and CV f and CV m are the coe cients of variation in female and male strobilus production among individuals in the studied population, respectively.
Combined fertility variation both female and male leads to the total fertility variation, designated as a symbol of Ψ and called as a sibling coe cient. The total fertility variation (Ψ) can be calculated by Kang (2001) as: where N is the census number; p i is the total fertility as an whole parent of i th individual; f i and m i are the fertilities as female and male parents of the i th individual, respectively.
Sibling coe cient (Ψ) expresses the probability that two alleles drawn randomly from the gamete gene pool originate from the same parent compared to the probability when the parents have equal representation (Kang and Lindgren 1998;Kang et al. 2003). Fertility variation (sibling coe cient) is a standardized measure that does not depend on the census number (N) of parents, but only on how variable their fertility is. Thus, the fertility of each parent is given as a fraction of all gametes.
The Eq. (3) was improved under the correlation (last term of the equation) between female and male fertility. The new equation was implemented for the estimation of total fertility variation (Ψ) as a whole parent in the present study as; where N is the census number; p i is the total fertility as an whole parent of i th individual; f i and m i are the fertilities as female and male parents of the i th individual; ψ f and ψ m are the fertility variations of female and male parents; r is the correlation coe cient between female and male strobilus production in the population, respectively.
If there is no correlation between female and male fertility, the Eq. (4) is simpli ed as: An equal seed harvesting among individuals is imposed in a seed stand population, the Eq. (5) is then described, Ψ = 0.25ψ m + 0.5, as the female fertility does not have variation. However, note that the equalizing female fertility should be given to the most productive parents.

Effective number of parents
The effective number of parents (N p ) is the number of individuals in which an idealized population would produce the same number of sibs (offspring) as the real population (Kang 2001). The effective number of parents is one of the concepts of effective population size that comes from the fertility variation among population members. It can estimate loss of gene diversity at the state rather than generation transition (Kang 2001).
The effective number of parents (N p ), the effective number of female (N p  The coe cient of variation (CV) of strobili production changed over years and varied among populations, and the CV values between female and male were not much larger than expected in natural seed stands ( Table 2). When pooled, the CVs were improved for female and male fertility, compared to a single year or population. The value of CV ranged from 0.288 in 2017 (male) to 0.651 in 2018 (male) when crossed populations in a year, and varied from 0.353 in P 3 (female) to 0.662 in P 1 (male) for pooled three years in a population (Table 2). However, the CV values were increased (0.887 and 1.407) for grand mean of three years and three populations, implying that female and male fertility variation among individuals could worsen when the entire strobilus production were completely pooled.
There was uctuation of female and male strobilus production among years and populations (Fig. 1). In seed stands of Taurus cedar, the production of female (seed) and male (pollen) strobili seemed to be low, especially in the poor owering year. The observed parental balance curves for female and male strobili production were deviated signi cantly from the ideal situation (equal production among individuals) in all seed stands (Fig. 2). It was clearly showed that the female and male parents contributed unequally to the gamete gene pool. Thus, speci c individuals may consistently produce high-or low-strobili based on genetic tendencies. The most abundant ve individual trees (10% of total) produced 29.9% and 21.3% of female and male strobili in 2016, 23.3% and 23.2% in 2017, and 22.0% and 25.0% in 2018 in the P 1 population. These were the similar trend as in the P 2 and P 3 populations (Fig. 2). The signi cant difference of female and male strobilus production among populations and years were supported by the analysis of variance (ANOVA). The ANOVA for female and male strobilus production showed highly signi cant differences (p < 0.01) among populations and years ( Table 3).
The Pearson's correlation coe cients showed positive and signi cant relationships between female and male strobilus production for all populations within a year (r = 0.491, 0.454 and 0.581) ( Table 4). The correlation coe cients (r) between female and male strobilus production were applied to estimate the total fertility variation (Ψ) and the effective number of parent (N p ) (see Eq. (4)).   Table 5).
The ψ f ranged from 1.23 (P 3 in 2018) to 1.55 (P 1 in 2016) and the ψ m ranged 1.13 (P 1 in 2017) to 1.73 (P 1 in 2018), showing that the difference of fertility between female and male was not so large. The variation also indicated that the fertility variation among individuals in a good crop year was smaller than in a poor year (Table 5). Table 5 Female (ψ f ) and male (ψ m ) fertility variation and the female (N p (f) ) and male (N p (m) ) effective number in the seed stand populations for the three consecutive years  *: note that the census number (N) increased when populations were pooled across a year.
The total fertility variation (Ψ) ranged from 1.13 to 1.44 across populations and years ( Table 6). The Ψ was smallest in the population P 3 in 2017 and largest in the population P 2 in 2018. This was inversely mirrored to the effective number of parents (N p ), and thus the N p was smallest (69% of census) in the population P 2 in 2018 and largest (88%) in the population P3 in 2017 (Table 6).

Equal cone harvest simulation
The census number (N) to collect cones could be taken to achieve satisfactory gene diversity of seeds when the fertility variation among individuals is quali ed in a population (Kang et al. 2003). The practice of equal cone harvest was simulated for a good crop year (2018) in Kizildag population (P3). The equalizing of female fertility was preferentially applied to the most fertile female parents. When the equal cone harvest was proportionally increased, the effective number of parents was also increased (Fig. 3).
The simulation of equal cone harvest, however, resulted in loss of seed-cone production. Thus, a balancing among proportion of cone harvest (census number), production of cone (seeds) and effective number of parents (gene diversity) should be considered for the implementation of equal cone harvest. In the simulation, the over-represented female parents were the rst concern for the equalizing of female fertility in the seed stand of Taurus cedar.

Strobilus production variation
The quantity of strobilus and coe cient of variation (CV) showed a large difference among populations and years, and also between individuals within a population (Table 2). This was supported by yearly uctuation of strobilus production (Fig. 1) and ANOVA results (Table 3). These results were consistent with the previous reports that a large difference of strobilus production was found among individuals and  Boydak (2003) reported that a good crop year in natural stands of the same species was once in two or three years. It should be emphasized that selecting populations and harvesting years are import for collecting seeds and managing seed stand populations. There could be genetical (Eriksson et al. 1973) and environmental factors such as tree form, growth, resistance, slope, aspect, altitude and age (Bilir 2011; Yazici and Bilir 2017) for selecting and managing the seed stands.
The production of cones, owers, pollen, fruits and seeds have been used to estimate fertility variation among individuals in many plant species (Savolainen et al. 1993; Yazici and Bilir 2017). We did not consider the gene ow from outside populations and owering synchronization that are certainly contributing to gene diversity of seeds from the seed stand populations. The progress of a seed production program depends on a plentiful delivery of viable seed. The nal seed yields may be in uenced by breakdown of any one of the processes of pollination, pollen grain germination, pollen tube growth, fertilization and embryo development (Brown 1971;Sarvas 1962). For maximum yield of seed, the female strobili must be pollinated when they are fully receptive to pollen. Empty seeds and low viability may result from a breakdown in embryogeny, and a further loss of seeds is occasioned by premature abscission of seed cones.
Positive and signi cant correlations were found between female and male strobilus production (Table 4).
This result was also reported in the same species (Yazici and Bilir 2017) and in the similar conifer species Fertility variation and effective number of parents Female and male fertility variations varied among populations and years (Table 5, Fig. 1). When pooled across years in a population, the female and male gametic fertility variations (ψ f and ψ m ) were improved (Table 5). When pooled years or populations, the total fertility variation (Ψ) and the effective number (N p ) were improved, respectively ( Table 6), indicating that pooling seeds from three years could increase the gene diversity of seeds from the Taurus cedar seed stands.
On the other hand, the mixing all populations and years increased the Ψ value, meaning that fertility variation got worse compared to a single population (Table 6). When pooling three populations, it should be noted that the census number (N) increased as 150 and thus the N p was larger than a single population. However, the relative effective number of parents (N r ) decreased. Therefore, a balancing between the effective number of parents (gene diversity) and the number of populations and years should be carefully considered for management the seed stands of Taurus cedar. This result might be due to the boosted strong positive correlation (covariation) among populations and years by pooling strobilus productions (see Eq. 4 and Fig. 3).
Sibling coe cient (Ψ) expresses how fertility varies among parents as the increase in the probability that sibs occur compared to the situation where parents have equal fertility (Kang 2001). The Ψ cannot be smaller than one. If Ψ = 1, all individuals have the equal fertility, and Ψ = 2 means that the probability that two individuals share a parent is twice as high, compared to when the parental fertility is equal across the population. As a heuristic rule of thumb, Kang et al. (2003) suggested that the Ψ equals 3 in natural seed stands and 2 in managed populations as seed orchards. Total fertility variation (Ψ) was 2.03 in totally pooled populations and years, which was smaller than the thumb rule (Table 6).
Effective population size theory has been based on the rate of change in gene frequency variance regeneration and sustainability of a species, and for adaptation to climate change and to resistance to biotic factors. The loss of gene diversity in the seeds from the populations could be estimated to be less than 2% which was not alarming.

Implication on management of seed stands
The use of bulked seeds derived from commercial harvests can in uence the estimate of effective number and gene diversity. Adult trees with insu cient yield of seed cones are generally not climbed during the commercial harvest. Therefore, these adults could only contribute to the seeds as male parents. The variation in reproductive success of individual trees is ampli ed by this harvesting procedure (Wojacki et al. 2019). In contrast, the equal seed collection per mother tree may have an arti cial balancing in uence.
Seeds from seed stands must re ect the gene diversity of their parents and keep gene diversity su ciently for future generations. One of the management options to reduce loss of gene diversity due to fertility variation is to restrict the parental contribution to the next generation (Bila 2000;Kang et al. 2003).
This restriction is more likely to be applied to the maternal contribution (e.g., equal cone harvest). The equal utilization of seeds among trees is often proposed to mitigate the effect of unbalanced contribution among parents in seed stands and orchards (Kang and Lindgren 1998;Bila 2000). By keeping the female contribution equal among individuals, the gene diversity is optimized in the seeds from seed stands. The balancing between gene diversity and seed collection would be more important in genetic resource conservation of Taurus cedar Mixing of seeds from a few seed stands or different years was suggested as a means to mitigate the When seeds were mixed for three years, the fertility variation (Ψ) was improved and the effective number of parents (N p ) was increased (Table 6). However, a certain loss of gene diversity during cone harvest seems inevitable (Fig. 3), and mixing seeds from too many populations or years might be deteriorate fertility variation and gene diversity. Thus, choice of population numbers, structural characteristics of seed stands, and spatial distribution of seed trees need to be optimized in a way that keeps the gene diversity loss to a minimum.
Stimulation of strobilus production would be necessary to increase the seed and pollen production in seed stands of Taurus cedar. Silvicultural thinning based on the survey of strobilus production would be proposed for spacing, aeration and pollen ow. Organic fertilizing may also be effective to produce more female strobili in the seed stands of Taurus cedar.

Conclusions
The effective number of parents estimates gene diversity of seeds from natural stands, which is based on the function of fertility variation between female and male parents. The fertility variation, called as a sibling coe cient (Ψ), expresses how fertility varies among parents as the increase in the probability that sibs occur compared to the situation where parents have equal fertility. The gene diversity of seeds could be estimated by the effective number of parents (N p ) that is the number of individuals in which an idealized population would give the same number of sibs (relatives) as the real population. The equal cone harvest improved fertility variation and effective number but resulted in loss of seed production in natural stands of Taurus cedar. The mixing seeds from different years also improved the fertility variation among individuals and increased the gene diversity of seeds. However, a balancing between the effective number of parents and the number of mixed years or populations should be carefully considered for maintaining the gene diversity.

Consent for publication
Not applicable.

Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Competing interests
The authors declare that they have no competing interests.

Funding
This work was supported by the R&D program of Korea Forest Service (Korea Forestry Promotion Institute, project No. 2020185A00-2022-AA02), and partly carried out when Prof. Kang was a visiting faculty to UBC, Canada.
Author contributions NB conducted eldwork and data analyses with assistance from K-S and regional forest directorate in Turkey. The manuscript was written by K-S and NB. K-S also developed new equations.  Parental-balance curve of female and male strobilus productions in the seed stand populations for 2016 to 2018