Uncertainty in variance effective population size for dioecious crop species: propagation of sex ratio estimation error and implications for germplasm conservation and breeding

Abstract The variance effective population size ( $$N_{e}$$ N e ) framework for dioecious crop species links $$N_{e}$$ N e to the offspring sex ratio ( $$r$$ r ), total offspring sampled ( $$t$$ t ), and the gametic-control regime applied during seed collection or regeneration (Vencovsky et al. 2012). These equations treat $$r$$ r as a known constant, yet in practice $$r$$ r is estimated from finite samples and therefore carries sampling uncertainty. Here, closed-form first-order expressions for the sampling standard deviation, $$SD\\left( {N_{e} } \\right)$$ S D N e , and coefficient of variation, $$CV\\left( {N_{e} } \\right)$$ C V N e , are derived using the delta method for random sampling (RS), female gametic control (FGC), and female plus male gametic control (FGC + MGC), and evaluated by Monte Carlo simulation. Under RS, $$CV\\left( {N_{e} } \\right)$$ C V N e reaches 21.2% at $$r = 0.2$$ r = 0.2 and $$t = 50$$ t = 50 and decreases as $$t$$ t increases. Gametic control increases $$N_{e}$$ N e point estimates but also increases relative uncertainty attributable to estimation of $$r$$ r , with FGC+MGC having the largest CV among the three regimes. Because the first-order delta method degenerates at $$r = 0.5$$ r = 0.5 , a second-order approximation is used near balanced sex ratios. Illustrative scenarios are presented using published adult sex ratios for Araucaria angustifolia (Bertol.) Steud., explicitly treated as numerical values for $$r$$ r