Power analyses to inform clutch sampling design to determine the breeding sex ratio in populations with multiple paternity

In many species, demographic assessments of population viability require an estimate of the number or proportion of breeding adults in a population that are male (the breeding sex ratio). However, this estimate is often difficult to obtain directly in species with multiple paternity when males are difficult to sample. Parentage analysis of breeding females and offspring can produce this estimate by identifying the number of unique males that contribute genetic information to (<i>i.e.</i>, sired) a given cohort. There is an added challenge of choosing a sample design with the desired level of confidence to identify all the fathers contributing to a cohort, either at the scale of individual clutches or an entire nesting season, given limited resources. Sampling effort can be defined as the number of offspring sampled per clutch, or the number of clutches sampled per breeding season, depending on the analysis. The minimum number of samples required may depend on the proportions of eggs that different fathers fertilize in a clutch (the paternal contribution mode), the total number of fathers fertilizing a clutch, the proportion of adults available for breeding that are male (the operational sex ratio), and population size. We conducted power analyses to quantify the confidence in identifying all fathers in animal populations with multiple paternity. We simulated sampling a theoretical sea turtle population with a range of population demographics, mating systems, and sampling effort, and used the proportion of 10,000 simulations in which all fathers were identified as a proxy for confidence. At the clutch level, confidence was strongly dependent on the paternal contribution mode, and when it was skewed, it also depended on the total number of fathers contributing and the number of offspring sampled. However, sampling about one third of a clutch was sufficient to identify all fathers with high confidence for most scenarios, unless the paternal contribution mode was extremely skewed and there were many contributing fathers, such that some fathers fertilized very few eggs and were difficult to detect. At the scale of an entire nesting season, confidence was more strongly affected by the operational sex ratio, the proportion of clutches sampled, and the presence or absence of polygyny than by the lesser effects of paternal contribution mode and within-clutch sample size. Sampling fewer offspring from more clutches increased confidence compared to sampling more offspring from fewer clutches. Relaxing the minimum required proportion of fathers identified from 100% to 90% led to high confidence while sampling 50% to a maximum of 75% of clutches, depending on the mating system, even as the population size increased by an order of magnitude. Our approach and results can be widely informative for sample design as well as quantifying uncertainty in existing and future estimates of the number of breeding males in populations with multiple paternity.