Fertility covariation and effective number of parents
Under various scenarios of female and male fertility covariation (i.e., joint variability of female and male fertility related to correlation), the effective number of parents was stochastically simulated under a range of correlation coefficients (-1.0 ≤ r ≤ 1.0) (Fig. 1). Generally, under no or limited female and male parents reproductive output fertility covariation, the effective number of parents (Np) was always equivalent to the census number (N) as the seed orchard parents are unrelated and assumed to be non-inbred (Fig. 1).
Positive female and male parents reproductive output fertility covariation increased the sibling coefficient (Y; parental fertility variation) as Y is affected by variation in both female (yf) and male (ym), causing the effective number of parents (Np) declined (Fig. 1.a – 1.d), compared to equal fertility with no correlation. On the other hand, negative female and male parents reproductive output fertility covariation mitigated the asymmetrical variation between yf and ym (fertility variation imbalance), resulting the incremental increase of the effective number of parents (Fig. 1.e – 1.i).
Knowledge regarding the extent of gene diversity loss (GD) when genes are transmitted from orchard parents to their progeny is valuable. The GD is estimated using Eq. (8) for new seed orchard establishment plans. If 5% loss of gene diversity is tolerable, then the effective number of parents Np of 10 would be sufficient in providing the desired seed crop’s gene diversity (Fig. 2). However, striving to reach higher effective number of parents is preferable to ensure capturing reasonable level of gene diversity.
Case study: Pinus koraiensis seed orchard
The average number of female strobili per ramet (a member of a clone) fluctuated across the studied years, with 2015 and 2016 representing the highest and lowest production with clone averages of 2.99 and 0.33, respectively (Table 1). The clonal average number of male strobili over years produced striking differences with 2017 and 2014, showing the highest and lowest production with averages of 1,912.2 and 1.82, respectively (Table 1). The female and male strobili production over the studied years was low and negating panmixia expectations in the 1.5 generation clonal seed orchard of P.koraiensis. This was similar situation with previous observation in the first-generation clonal seed orchards of the same species.
The effective number of female parents (Np(f)) was higher than that of male parents (Np(m)) except in the year 2017 (Table 2, Fig. 3). The relative effective number of female parents ranged 45.9% in 2016 (poor year) to 85.5% in 2014 (good year), and the expected loss of gene diversity (GD) for female and male parents were 1.1% and 1.6%, respectively, which was not so alarming for a 52 clonal seed orchard (Table 2). The clonal effective number of parents (Np) under female and male strobili production covariation varied between 14.8 and 36.8 for 2014 and 2017 across the four studied years (Table 3) where Np was calculated using the CV and r of female and male strobili production (see Equation 6). The seed crops’ loss of gene diversity (GD) varied between 3.4% and 1.4% for 2014 and 2017, presenting higher than expected values for female and male parents and indicating the effect of covariation (correlation) between female and male fertility.
The parental balance curves showed that clonal cumulative gamete contribution was far from expectation (i.e., equal contribution) specifically for 2016 female and 2014 male (Fig. 4). The male strobili production cumulative curves showed greater distortion than that for female. The top 20% of clone contributed 59.6% of female strobili production (2016) while 86.4% of male production (2015). On the other hand, male strobili production was limited to extremely limited clones as only two clones contributed 50% of total production (Fig. 4).
Parental contribution as males, females or both sexes should influence the seed crop’s genetic composition, and this can be determined with assessment of the orchard’s initial reproduction and throughout the cone crop development. The current study indicated that there were 8 clones (15.4%) consistently ranked high on the gametic contribution. On the other hand, 8 clones were persistently ranked low across the orchard reproduction years, which could contribute to the needed reproductive output assessment. The genetic worth of orchards’ seed crops is a function of parental gametic contribution and their respective breeding value, thus sibling coefficient could be one of the criteria needed for evaluating the genetic composition as it determines parental gametic contribution (Kang 2000). Large variation among orchard parents’ gametic contribution is common and widely reported in many seed orchards (Funda and El-Kassaby 2012). Thus, an evaluation of seed crops’ genetic composition should consider the entire parental population as an analytical unit of gametic and genetic contribution.
By knowing the magnitude of fertility variation among individuals in a seed orchard, the census number to collect seed-cones could be chosen to achieve satisfactory gene diversity of seed crops (Kang et al. 2003). We exposed the practice of equal seed-cone harvest for a good crop year (2015) in the P. koraiensis seed orchard. The equalizing of female fertility should be preferentially set to the most-fertile female parents, and the male fertilities were not changed. When the proportion of equal seed-cone harvest increased, the effective number of parents increased, but the relative seed-cone production was decreased when compared to the commercial harvest (Fig. 5).