Approximations from Anywhere and General Rough Sets

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical perspective, a few (as opposed to one) theoretical frameworks may be suitable for formulating the problem itself. \emph{Granular operator spaces} have been recently introduced and investigated by the present author in her recent work in the context of antichain based and dialectical semantics for general rough sets. The nature of the inverse problem is examined from number-theoretic and combinatorial perspectives in a higher order variant of granular operator spaces and some necessary conditions are proved. The results and the novel approach would be useful in a number of unsupervised and semi supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings, Springe

Genomic data of different resolutions reveal consistent inbreeding estimates but contrasting homozygosity landscapes for the threatened Aotearoa New Zealand hihi

Inbreeding can lead to a loss of heterozygosity in a population and when combined with genetic drift may reduce the adaptive potential of a species. However, there is uncertainty about whether resequencing data can provide accurate and consistent inbreeding estimates. Here, we performed an in-depth inbreeding analysis for hihi (Notiomystis cincta), an endemic and nationally vulnerable passerine bird of Aotearoa New Zealand. We first focused on subsampling variants from a reference genome male, and found that low-density data sets tend to miss runs of homozygosity (ROH) in some places and overestimate ROH length in others, resulting in contrasting homozygosity landscapes. Low-coverage resequencing and 50 K SNP array densities can yield comparable inbreeding results to high-coverage resequencing approaches, but the results for all data sets are highly dependent on the software settings employed. Second, we extended our analysis to 10 hihi where low-coverage whole genome resequencing, RAD-seq and SNP array genotypes are available. We inferred ROH and individual inbreeding to evaluate the relative effects of sequencing depth versus SNP density on estimating inbreeding coefficients and found that high rates of missingness downwardly bias both the number and length of ROH. In summary, when using genomic data to evaluate inbreeding, studies must consider that ROH estimates are heavily dependent on analysis parameters, data set density and individual sequencing depth

Polygenic basis for adaptive morphological variation in a threatened Aotearoa | New Zealand bird, the hihi (Notiomystis cincta)

To predict if a threatened species can adapt to changing selective pressures, it is crucial to understand the genetic basis of adaptive traits, especially in species historically affected by severe bottlenecks. We estimated the heritability of three hihi (Notiomystis cincta) morphological traits known to be under selection: nestling tarsus length, body mass and head-bill length, using 523 individuals and 39,699 single nucleotide polymorphisms (SNPs) from a 50K Affymetrix SNP chip. We then examined the genetic architecture of the traits via chromosome partitioning analyses and genome-wide association scans (GWAS). Heritabilities estimated using pedigree relatedness or genomic relatedness were low. For tarsus length, the proportion of genetic variance explained by each chromosome was positively correlated with its size, and more than one chromosome explained significant variation for body mass and head-bill length. Finally, GWAS analyses suggested many loci of small effect contributing to trait variation for all three traits, although one locus (a SNP within an intron of the transcription factor HEY2) was tentatively associated with tarsus length. Our findings suggest a polygenic nature for the morphological traits, with many small effect size loci contributing to the majority of the variation, similar to results from many other wild populations. However, the small effective population size, polygenic architecture and already low heritabilities suggest that both the total response and rate of response to selection are likely to be limited in hihi

Who are you? A framework to identify and report genetic sample mix‐ups

Sample mix-ups occur when samples have accidentally been duplicated, mislabelled or swapped. When samples are subsequently genotyped or sequenced, this can lead to individual IDs being incorrectly linked to genetic data, resulting in incorrect or biased research results, or reduced power to detect true biological patterns. We surveyed the community and found that almost 80% of responding researchers have encountered sample mix-ups. However, many recent studies in the field of molecular ecology do not appear to systematically report individual assignment checks as part of their publications. Although checks may be done, lack of consistent reporting means that it is difficult to assess whether sample mix-ups have occurred or been detected. Here, we present an easy-to-follow sample verification framework that can utilise existing metadata, including species, population structure, sex and pedigree information. We demonstrate its application to a data set representing individuals of a threatened Aotearoa New Zealand bird species, the hihi, genotyped on a 50K SNP array. We detected numerous incorrect genotype-ID associations when comparing observed and genetic sex or comparing to relationships in a verified microsatellite pedigree. The framework proposed here helped to confirm 488 individuals (39%), correct another 20 bird-genotype links, and detect hundreds of incorrect sample IDs, emphasizing the value of routinely checking genetic and genomic data sets for their accuracy. We therefore promote the implementation and reporting of this simple yet effective sample verification framework as a standardized quality control step for studies in the field of molecular ecology