1. The fixation index, FIS has been a staple measure to detect selection or departures from random mating in populations. However, current Next Generation Sequencing (NGS) cannot easily estimate Fis, in multi-locus gene families, which contain multiple loci having similar or identical arrays of variant sequences of ≥1 kilobase, which differ at multiple positions. In these families, high-quality short-read NGS data typically identify variants, but not the genomic location, which is required to calculate Fis (based on locus-specific observed and expected heterozygosity). Thus, to assess assortative mating, or selection on heterozygotes, from NGS of multi-locus gene families, we need a method that does not require knowledge of which variants are allelic at which locus in the genome. 2. We developed such a method. Like Fis, our novel measure, 1His, is based on the principle that positive assortative mating, or selection against heterozygotes, reduces within-individual variability relative to the population. 3. We demonstrate high accuracy of 1His on a wide-range of simulated scenarios, and two datasets from natural populations of penguins and dolphins. 4. 1His is important because multi-locus gene families are often involved in assortative mating, or selection on heterozygotes. 1His is particularly useful for multi-locus gene families such as toll-like receptors, the major-histocompatibility-complex in animals, homeobox genes in fungi and self-incompatibility genes in plants.

The Australian range of little penguins, Eudyptula minor, extends around southern Australia, with range-edge sites near the large cities of Perth (west) and Sydney (east). Both range-edges are closer to the equator than the range-core, being likely to experience similar heating with climate change. As a result, movement to one range-edge is not an option for little penguins, unlike in many other species. Therefore, adaptation at the range edge might be very important for little penguins. Capacity for future adaptation depends upon the variability each site holds, and the amount of exchange between sites. In peripheral sites, incoming dispersal might either forestall demographic collapse and replenish genetic variation (good), or overcome local adaptation and increase disease transmission (bad). We aimed to establish the genetic variability in each site, and the exchange (dispersal) of individuals between sites. Genetic markers included biparentally-inherited microsatellites, and maternally-inherited mitochondrial DNA sequence. For microsatellites, no site appeared to have critically low variation, including the peripheral sites, however there was a significant but slight trend of increased variation from east to west. In contrast, mitochondrial DNA showed a pattern of significantly reduced variation at the two range-edges, possibly indicating differential dispersal patterns in males and females. There appear to be two main genetically distinct groups, in the west and the east, but analysis of lifetime dispersal patterns across the Australian range also suggests complex dispersal, sometimes with high dispersal or similarity between locations that are not adjacent. Our work suggests that despite some differentiation, little penguin sites are interdependent due to complex dispersal patterns, and all have valuable genetic variation. In particular, the peripheral sites are not depauperate of variation, and are moderately connected to the remainder of the distribution, so possibly may be able to adapt in response to climate warming.

New sequencing technologies have opened the door to many new research opportunities, but these advances in data collection are not always compatible with some important methods for data analysis. Fis has been a staple calculation in the field of population genetics. Fis can be used to measure either a departure from random mating, or measure underlying selective pressures for or against heterozygote genotypes. However, when using Next Generation Sequencing (NGS) technology on multi-locus gene families it is often impossible to discern which allelic variants are present at each locus. Some important multi-locus gene families are: the major histocompatibility complex (MHC) in animals; homeobox genes in fungi; or the self-incompatibility genes in plants. This in turn makes it impossible to calculate either locus-specific expected heterozygosity, or observed heterozygosity, both of which are required to calculate Fis. Without the ability to calculate Fis from NGS of multi-locus gene families, we need a new multi-locus measure that will allow us to detect the underlining mating, and selective patterns present in such multi-locus genes. This paper provides such a novel multi-locus measure, called 1His. We demonstrate the accuracy of the 1His equation using simulated data, and two datasets taken from natural populations of dolphins and penguins. The introduction of this new measure is particularly important because of the great interest in mating patterns and selection of multi-locus gene families, such as MHC.