Paternity

Two pedigrees (1 and 2) and a genomic relatedness matrix (GRM) were used in our analyses.
Pedigree 1: This pedigree was the most complete and accurate Soay sheep pedigree constructed using microsatellites to infer parentage. Maternities were assigned by field observation, and molecular parentage analysis was used to infer paternities (detailed description of methods in Morrissey et al. 2007 (link)). Individuals were genotyped at 14–18 microsatellite loci (Overall et al. 2005 (link)), and mean individual-level posterior support for paternity assignments was 98%. Parentage was assigned for all cohorts born between 1985 and 2009.
Pedigree 2: This pedigree was primarily built using molecular parentage analysis (for maternity and paternity) for all cohorts between 1980 and 2012. For each cohort maternity and paternity were inferred simultaneously using 315 high MAF, unlinked SNPs in the R package masterbayes (Hadfield et al. 2006 (link)) and all assignments were inferred with 100% confidence [see Table S1, Supporting information for a list of SNP names and map positions, more detailed information on how loci were selected can be found in (Johnston et al. 2013 (link))]. For 96 of 3515 sheep with a mother previously assigned through observation, a different mother was found using SNP-based assignments (2.7%). Among these, about half were lambs found as dead neonates, indicating that in these cases, maternity is difficult to assign accurately in the field. For 2113 sheep with paternity assignments obtained from both Pedigree 1 and SNP-based inference, only 91 assignments differed (4.4%).
During the construction of Pedigree 2, not all parentage inferences could be made based on SNP genotypes alone, as we have not genotyped all offspring and their candidate parents (particularly for individuals alive prior to 1990). We used observations or assignments inferred using microsatellites to fill in the gaps. In 1257 cases where no maternity was assigned using molecular markers, field observational data were used. For 222 lambs without assigned fathers, paternity data from Pedigree 1 were used if confidence of assignment was >95%. For Pedigrees 1 and 2, pairwise relatedness between all individuals was estimated using the R package pedantics (Morrissey & Wilson 2010 (link)).
Genomic relatedness: The genomic relatedness between all pairs of SNP genotyped individuals was estimated in gcta v1.04 which estimates the proportion of the genome identity-by-state (IBS) between individuals. At each locus, relatedness was scaled by the expected heterozygosity 2pq (Yang et al. 2010 (link), 2011a ). No adjustments for sampling error or difference in allelic spectrum between genotyped SNPs and causal variants were made.

We used the descriptive data obtained from the August 2019 survey to determine the number of additional new anesthesiologists needed to replace the on-call anesthesiologists who would no longer be available for the morning weekday shift prior to call, following the new 18-h on-call shift policy. The number of vacant spaces that need to be filled is equal to the number of anesthesiologists currently on-call in Israel during weekdays, as determined directly from the August 2019 survey data, multiplied by productive work coefficients. Therefore, the actual number of new full-time hires required to provide this number of replacement anesthesiologists was calculated using locally accepted productive work coefficients: 1.22 for attending anesthesiologists and 1.45 for anesthesiology residents. These productive work coefficients were based on the provisions of the physicians’ union contract between the Israel Medical Association and the Israeli Government in 2011. For residents, the productive work coefficients were also based on the Anesthesiology Residency Curriculum of the Scientific Council of the Israel Medical Association. For both attendings and residents, vacations, radiation vacation days, sick leave, maternity/paternity leave and military reserve duty were contributing factors. For residents, additional contributing factors were the mandatory study leave prior to the two specialty certification examinations, and non-operating room rotations (e.g. ICU, pain management, research, rotations in other clinical departments).
The total shortage following the 18-h shift policy of anesthesiologists was calculated as the number needed to replace those on-call plus the number of unfilled positions and non-authorized positions reported by the department chairs.

The 206 progeny individuals from five different F₁ mandarin populations growing at the University of Florida-IFAS Citrus Research and Education Center (Lake Alfred, FL) were used in this study (Figure 1). Mukaku Kishu (Citrus reticulata Blanco) (‘MK’), a completely seedless mandarin cultivar, was the common male parent in all the populations. All five maternal mandarin parents, ‘SB’ (Clementine mandarin × Minneola tangelo), ‘D’ [(Clementine mandarin × Orlando tangelo) × (Clementine mandarin × Ponkan mandarin)], Temple (‘T’) (a natural mandarin × sweet orange hybrid), Lee (‘L’) (Clementine mandarin × Orlando tangelo), and Clementine × Valencia orange (‘CVO’) produce fruit containing monoembryonic seeds. All of these, except ‘CVO’ are released commercial cultivars. To preclude any inadvertent inclusion of off types/nucellars in the mapping population, the hybridity of the population individuals (for ‘MK’ paternity) was verified through few homozygous SNPs polymorphic between the maternal parents and ‘MK’. The individuals with doubtful identity were not used in this study. All the populations were fruiting in the 2017-18 season.

The algorithm evaluates the compatibility of each maternal cell-free fetal DNA sample against each alleged father. The fetal genotypes for each SNV included in the analysis are inferred from the maternal samples. Furthermore, the algorithm robustness has been validated using a set of mock samples generated by simulating 100 biological brothers for each biological father.
The algorithm utilizes the BAM files obtained from the next-generation sequencing process, and it produces some intermediate reports (one for each mother vs. alleged father comparison) and a final overall report including the paternity probability (W) for each comparison. The evaluation is straightforward from the Combined Paternity Index (CPI likelihood statistic) adapted to be used in the context of an SNV-based prenatal test.
A kinship relationship is universally evaluated by comparing the likelihoods of observing the obtained genotypes given two alternative hypotheses (i.e., the Likelihood Ratio, LR). In the case of paternity testing, it is evaluated whether an individual is related to another individual with a father–son relationship versus the hypothesis that the two individuals are not related. The higher the LR, the more supported is the first hypothesis (paternity). The lower the LR (i.e., <1), the more supported is the second hypothesis (unrelated individuals). For each SNV, the Paternity Index (PI) is classically calculated as a likelihood ratio according to the Bayesian theorem [22 ]. PI is defined as the ratio between the probability of the fetal genotype to be the observed one (event E) conditioned to the alleged father being the biological father (hypothesis H₁) and the same probability where the father is a random individual extracted from the population (hypothesis H₂) (PI = Pr(E | H₁)/Pr(E | H₂) [22 ]. When multiple loci are used to determine paternity, the product of all the individual PI values for each locus is the combined paternity index. PI formulas are adapted to the cases of prenatal tests where fetal genotypes need to be inferred from the maternal cffDNA samples [16 (link),23 (link),24 (link)]. In particular, this was undertaken by also taking into account technical errors and natural effects (e.g., sequencing errors or ex novo mutations) that could lead to fetal genotype misinterpretation and eventually to a biased PI calculation. The CPI for a couple is then the product of all the PIs—one for each SNV included in the analysis—and paternity probability (W) is calculated as (CPI/CPI + 1)*100.
Only SNVs where the mother genotype is homozygous have been included in CPI calculation because for heterozygous maternal positions it is statistically inaccurate to infer the fetal genotype from the maternal cell-free fetal DNA sample only [24 (link),25 (link)].
The algorithm defines the fetal genotype from the maternal cffDNA sample using a set of fetal base thresholds. In fact, for each SNV, if a low-frequency base is detected on the maternal sample, and it is different from the maternal homozygous genotype, the fetal genotype is inferred as heterozygous. In particular, a minimal coverage of 1000 reads for the maternal sample and 100 reads for the alleged father are required for the inclusion in the Paternity Index calculations. A base coverage of at least 100 reads is required to be assigned as fetal for allele characterized by frequency ranging from 1.5% to 15%.
In the case of variants located on chromosome Y, the maternal zygosity filter is obviously inapplicable; however, for a coverage > 100 reads, the filter is still applied. In the end, the number of SNVs reporting a low-frequency allele varies among different meiosis samples, ranging from 131 to 173 with an average of 145 SNVs.
Multiple checks and features are included in the algorithm to improve the robustness against both human and technological errors. The algorithm performs an assessment of relatedness indexes among all different sample pairs [24 (link),26 (link)]. Some thresholds are set in the algorithm to deal with noise and low coverage. In particular, the algorithm includes a noise reduction method to ensure a more robust call for the fetal base, starting from the mother’s genotype. Fetal genotype calling implements a SNV-specific threshold for the low-frequency alleles which relies on previously collected data of low-frequency alleles on samples without cffDNA. As a support, CPI is also calculated using a different set of thresholds optimized for low-fetal-fraction samples. Robustness of the CPI calculation is also assured by the usage of no less than 30 SNVs reporting a low-frequency allele (1.5–15%).