Haplotype tagging reveals parallel formation of hybrid races in two butterfly species.

Genetic variation segregates as linked sets of variants or haplotypes. Haplotypes and linkage are central to genetics and underpin virtually all genetic and selection analysis. Yet, genomic data often omit haplotype information due to constraints in sequencing technologies. Here, we present "haplotagging," a simple, low-cost linked-read sequencing technique that allows sequencing of hundreds of individuals while retaining linkage information. We apply haplotagging to construct megabase-size haplotypes for over 600 individual butterflies (Heliconius erato and H. melpomene), which form overlapping hybrid zones across an elevational gradient in Ecuador. Haplotagging identifies loci controlling distinctive high- and lowland wing color patterns. Divergent haplotypes are found at the same major loci in both species, while chromosome rearrangements show no parallelism. Remarkably, in both species, the geographic clines for the major wing-pattern loci are displaced by 18 km, leading to the rise of a novel hybrid morph in the center of the hybrid zone. We propose that shared warning signaling (Müllerian mimicry) may couple the cline shifts seen in both species and facilitate the parallel coemergence of a novel hybrid morph in both comimetic species. Our results show the power of efficient haplotyping methods when combined with large-scale sequencing data from natural populations.

Private Genomes and Public SNPs: Homomorphic Encryption of Genotypes and Phenotypes for Shared Quantitative Genetics.

Sharing human genotype and phenotype data is essential to discover otherwise inaccessible genetic associations, but is a challenge because of privacy concerns. Here, we present a method of homomorphic encryption that obscures individuals' genotypes and phenotypes, and is suited to quantitative genetic association analysis. Encrypted ciphertext and unencrypted plaintext are analytically interchangeable. The encryption uses a high-dimensional random linear orthogonal transformation key that leaves the likelihood of quantitative trait data unchanged under a linear model with normally distributed errors. It also preserves linkage disequilibrium between genetic variants and associations between variants and phenotypes. It scrambles relationships between individuals: encrypted genotype dosages closely resemble Gaussian deviates, and can be replaced by quantiles from a Gaussian with negligible effects on accuracy. Likelihood-based inferences are unaffected by orthogonal encryption. These include linear mixed models to control for unequal relatedness between individuals, heritability estimation, and including covariates when testing association. Orthogonal transformations can be applied in a modular fashion for multiparty federated mega-analyses where the parties first agree to share a common set of genotype sites and covariates prior to encryption. Each then privately encrypts and shares their own ciphertext, and analyses all parties' ciphertexts. In the absence of private variants, or knowledge of the key, we show that it is infeasible to decrypt ciphertext using existing brute-force or noise-reduction attacks. We present the method as a challenge to the community to determine its security.