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Whole genome duplications have occurred in the recent ancestors of many plants, fish, and amphibians, resulting in a pervasiveness of paralogous loci and the potential for both disomic and tetrasomic inheritance in the same genome. Paralogs can be difficult to reliably genotype and are often excluded from genotyping-by-sequencing (GBS) analyses; however, removal requires paralogs to be identified which is difficult without a reference genome. We present a method for identifying paralogs in natural populations by combining two properties of duplicated loci: 1) the expected frequency of heterozygotes exceeds that for singleton loci, and 2) within heterozygotes, observed read ratios for each allele in GBS data will deviate from the 1:1 expected for singleton (diploid) loci. These deviations are often not apparent within individuals, particularly when sequence coverage is low; but, we postulated that summing allele reads for each locus over all heterozygous individuals in a population would provide sufficient power to detect deviations at those loci. We identified paralogous loci in three species: Chinook salmon (Oncorhynchus tshawytscha) which retains regions with ongoing residual tetrasomy on eight chromosome arms following a recent whole genome duplication, mountain barberry (Berberis alpina) which has a large proportion of paralogs that arose through an unknown mechanism, and dusky parrotfish (Scarus niger) which has largely re-diploidized following an ancient whole genome duplication. Importantly, this approach only requires the genotype and allele-specific read counts for each individual, information which is readily obtained from most GBS analysis pipelines. This article is protected by copyright. All rights reserved.

Whole-genome duplications have occurred in the recent ancestors of many plants, fish and amphibians. Signals of these whole-genome duplications still exist in the form of paralogous loci. Recent advances have allowed reliable identification of paralogs in genotyping-by-sequencing (GBS) data such as that generated from restriction-site-associated DNA sequencing (RADSeq); however, excluding paralogs from analyses is still routine due to difficulties in genotyping. This exclusion of paralogs may filter a large fraction of loci, including loci that may be adaptively important or informative for population genetic analyses. We present a maximum-likelihood method for inferring allele dosage in paralogs and assess its accuracy using simulated GBS, empirical RADSeq and amplicon sequencing data from Chinook salmon. We accurately infer allele dosage for some paralogs from a RADSeq data set and show how accuracy is dependent upon both read depth and allele frequency. The amplicon sequencing data set, using RADSeq-derived markers, achieved sufficient depth to infer allele dosage for all paralogs. This study demonstrates that RADSeq locus discovery combined with amplicon sequencing of targeted loci is an effective method for incorporating paralogs into population genetic analyses.

An important use of genetic parentage analysis is the ability to directly calculate the number of offspring produced by each parent (ki) and hence effective population size, Ne. But what if parental genotypes are not available? In theory, given enough markers, it should be possible to reconstruct parental genotypes based entirely on a sample of progeny, and if so the vector of parental ki values. However, this would provide information only about parents that actually contributed offspring to the sample. How would ignoring the ‘null’ parents (those that produced no offspring) affect an estimate of Ne? The surprising answer is that null parents have no effect at all. We show that: (i) The standard formula for inbreeding Ne can be rewritten so that it is a function only of sample size and P k 2 �� ; it is not necessary to know the total number of parents (N). This same relationship does not hold for variance Ne. (ii) This novel formula provides an unbiased estimate of Ne even if only a subset of progeny is available, provided the parental contributions are accurately determined, in which case precision is also high compared to other single-sample estimators of Ne. (iii) It is not necessary to actually reconstruct parental genotypes; from a matrix of pairwise relationships (as can be estimated by some current software programs), it is possible to construct the vector of ki values and estimate Ne. The new method based on parentage analysis without parents (PwoP) can potentially be useful as a single-sample estimator of contemporary Ne, provided that either (i) relationships can be accurately determined, or (ii) P k 2 �� can be estimated directly.

An important use of genetic parentage analysis is the ability to directly calculate the number of offspring produced by each parent (k(i)) and hence effective population size, N(e). But what if parental genotypes are not available? In theory, given enough markers, it should be possible to reconstruct parental genotypes based entirely on a sample of progeny, and if so the vector of parental k(i) values. However, this would provide information only about parents that actually contributed offspring to the sample. How would ignoring the 'null' parents (those that produced no offspring) affect an estimate of N(e)? The surprising answer is that null parents have no effect at all. We show that: (i) The standard formula for inbreeding N(e) can be rewritten so that it is a function only of sample size and ∑(k(2)(i)); it is not necessary to know the total number of parents (N). This same relationship does not hold for variance N(e). (ii) This novel formula provides an unbiased estimate of N(e) even if only a subset of progeny is available, provided the parental contributions are accurately determined, in which case precision is also high compared to other single-sample estimators of N(e). (iii) It is not necessary to actually reconstruct parental genotypes; from a matrix of pairwise relationships (as can be estimated by some current software programs), it is possible to construct the vector of k(i) values and estimate N(e). The new method based on parentage analysis without parents (PwoP) can potentially be useful as a single-sample estimator of contemporary N(e), provided that either (i) relationships can be accurately determined, or (ii) ∑(k(2)(i)) can be estimated directly.