Pedigree accumulation analysis: Combining methods from community ecology and population genetics for breeding adult estimation

Abstract

1. Estimates of the number of successfully breeding adults (N S ) in a population can predict levels of recruitment. However, assessments of N S are often difficult to obtain because encounters with adults are limited due to life-history characteristics, low abundance or other constraints associated with access to critical habitats. Alternatively, efforts to sample individuals at earlier ontogenetic stages can be more tractable, resulting in more comprehensive samples. 2. To estimate N S , we describe, evaluate and apply two nonparametric species richness estimators to information associated with genetic pedigree reconstruction.Simulations compared bias and precision associated with Chao and Jackknife methods when estimating N S . We also evaluated N S estimation sensitivity to two sources of variation associated with species reproductive ecology (variance in reproductive success and sex ratio skew) and genetic pedigree assignment error.Finally, the application of our novel method was demonstrated in two different species and systems (Chinook Salmon in Oregon, USA and Lake Sturgeon in Michigan, USA).3. We found unbiased N S estimates were generated across a broad range of offspring sample sizes using the Chao method. Empirical results corroborated simulationbased expectations and highlighted applications where parents and offspring are sampled, and when only offspring are sampled.4. When offspring sample sizes are adequate and pedigree reconstruction errors are low, the combination of established methods from community ecology and genetic pedigree reconstruction provides an accurate alternative method to estimate N S that can facilitate population assessments.

Evaluating sources of bias in pedigree‐based estimates of breeding population size

“…To accomplish this, once the breeding matrix structure was established (i.e., actual N S was defined, please refer to subsequent paragraphs), the numbers of males and females were separated by a 5:1 sex ratio to determine the number of rows (males) and columns (females) in the matrix. Next, mates for each adult were randomly identified per λ (following Sard et al, 2021) and N Off _f per female was drawn randomly. We then allocated each female's N Off_f non‐randomly across her mates to represent male–male fertilization competition.…”

“…Sard et al (2021) evaluated bias in $$$ \hat{N} $$$ S from Chao and Jackknife estimators; however, they did not assess how bias in $$$ {\hat{N}}_{det} $$$ from errors in pedigree reconstruction affected $$$ \hat{N} $$$ S . Therefore, we used Chao, Jackknife, and bootstrapping methods to estimate N S under two scenarios.…”

“…We then allocated each female's N Off_f non‐randomly across her mates to represent male–male fertilization competition. This was accomplished using the equation $$$ {N}_{Off\_f}={\sum}_{m=1}^{t_m}{O}_m={\sum}_{m=1}^{t_m}\frac{m}{\frac{t_m\left({t}_m+1\right)}{2}}\times {N}_{Off\_f} $$$ adapted from Sard et al (2021) that allocates a subset ($$$ {O}_m $$$) of a female's N Off_f to each of her mates ( m ). As the female's total number of mates ($$$ {t}_m $$$) increases, some mates receive a larger proportion of her $$$ {N}_{off\_f} $$$ relative to other mates.…”

“…Sard et al (2021) determined that $$$ \hat{N} $$$ S obtained with the Chao method was unbiased, even when N Off_s is small. However, their simulations assumed an equal sex ratio and low variance in fecundity.…”

“…We estimated N S using three rarefaction approaches. The first two estimated N S using the non-parametric Chao (1984) and first-order Jackknife (Quenouille, 1949;Tukey, 1958) methods (Sard et al, 2021). Both estimators have been traditionally applied to estimate species richness; however, Chao (Equation 1) and Jackknife (Equation 2) methods can be applied to estimate N S using total N det from a pedigree using the number of parents detected once (singletons; α 1 ) or twice (doubletons; α 2 ), and N Off_s :…”