Checking Consistency of Pedigree Information is NP-complete (Preliminary Report)

Consistency checking is a fundamental computational problem in genetics. Given a pedigree and information on the genotypes of some of the individuals in it, the aim of consistency checking is to determine whether these data are consistent with the classic Mendelian laws of inheritance. This problem arose originally from the geneticists' need to filter their input data from erroneous information, and is well motivated from both a biological and a sociological viewpoint. This paper shows that consistency checking is NP-complete, even in the presence of three alleles. Several other results on the computational complexity of problems from genetics that are related to consistency checking are also offered. In particular, it is shown that checking the consistency of pedigrees over two alleles can be done in polynomial time

On Counting the Number of Consistent Genotype Assignments for Pedigrees

Consistency checking of genotype information in pedigrees plays an important role in genetic analysis and for complex pedigrees the computational complexity is critical. We present here a detailed complexity analysis for the problem of counting the number of complete consistent genotype assignments. Our main result is a polynomial time algorithm for counting the number of complete consistent assignments for non-looping pedigrees. We further classify pedigrees according to a number of natural parameters like the number of generations, the number of children per individual and the cardinality of the set of alleles. We show that even if we assume all these parameters as bounded by reasonably small constants, the counting problem becomes computationally hard (#P-complete) for looping pedigrees. The border line for counting problems computable in polynomial time (i.e. belonging to the class FP) and #P-hard problems is completed by showing that even for general pedigrees with unlimited number of generations and alleles but with at most one child per individual and for pedigrees with at most two generations and two children per individual the counting problem is in FP

On Counting the Number of Consistent Genotype Assignments for Pedigrees

Consistency checking of genotype information in pedigrees plays an important role in genetic analysis and for complex pedigrees the computational complexity is critical. We present here a detailed complexity analysis for the problem of counting the number of complete consistent genotype assignments. Our main result is a polynomial time algorithm for counting the number of complete consistent assignments for non-looping pedigrees. We further classify pedigrees according to a number of natural parameters like the number of generations, the number of children per individual and the cardinality of the set of alleles. We show that even if we assume all these parameters as bounded by reasonably small constants, the counting problem becomes computationally hard (#P-complete) for looping pedigrees. The border line for counting problems computable in polynomial time (i.e. belonging to the class FP) and #P-hard problems is completed by showing that even for general pedigrees with unlimited number of generations and alleles but with at most one child per individual and for pedigrees with at most two generations and two children per individual the counting problem is in FP

An Abstract Interpretation framework for genotype elimination algorithms

We apply Abstract Interpretation to the problem of genotype elimination in pedigrees. First, we give a formalization of some existing algorithms that try to remove from pedigrees all genotypes that violate the Mendelian rules of inheritance. The formalization enables the application of the Abstract Interpretation technique to the problem. We then introduce a particular abstraction, parameterized on given partitions of the set of genotypes. We instantiate this abstraction in order to obtain two existing algorithms for Allele Consolidation, thus giving a formal proof of their correctness. Moreover, the second of these two algorithms is shown to be an example of a forward complete abstraction

Identification of Mendelian inconsistencies between SNP and pedigree information of sibs

Background Using SNP genotypes to apply genomic selection in breeding programs is becoming common practice. Tools to edit and check the quality of genotype data are required. Checking for Mendelian inconsistencies makes it possible to identify animals for which pedigree information and genotype information are not in agreement. Methods Straightforward tests to detect Mendelian inconsistencies exist that count the number of opposing homozygous marker (e.g. SNP) genotypes between parent and offspring (PAR-OFF). Here, we develop two tests to identify Mendelian inconsistencies between sibs. The first test counts SNP with opposing homozygous genotypes between sib pairs (SIBCOUNT). The second test compares pedigree and SNP-based relationships (SIBREL). All tests iteratively remove animals based on decreasing numbers of inconsistent parents and offspring or sibs. The PAR-OFF test, followed by either SIB test, was applied to a dataset comprising 2,078 genotyped cows and 211 genotyped sires. Theoretical expectations for distributions of test statistics of all three tests were calculated and compared to empirically derived values. Type I and II error rates were calculated after applying the tests to the edited data, while Mendelian inconsistencies were introduced by permuting pedigree against genotype data for various proportions of animals. Results Both SIB tests identified animal pairs for which pedigree and genomic relationships could be considered as inconsistent by visual inspection of a scatter plot of pairwise pedigree and SNP-based relationships. After removal of 235 animals with the PAR-OFF test, SIBCOUNT (SIBREL) identified 18 (22) additional inconsistent animals. Seventeen animals were identified by both methods. The numbers of incorrectly deleted animals (Type I error), were equally low for both methods, while the numbers of incorrectly non-deleted animals (Type II error), were considerably higher for SIBREL compared to SIBCOUNT. Conclusions Tests to remove Mendelian inconsistencies between sibs should be preceded by a test for parent-offspring inconsistencies. This parent-offspring test should not only consider parent-offspring pairs based on pedigree data, but also those based on SNP information. Both SIB tests could identify pairs of sibs with Mendelian inconsistencies. Based on type I and II error rates, counting opposing homozygotes between sibs (SIBCOUNT) appears slightly more precise than comparing genomic and pedigree relationships (SIBREL) to detect Mendelian inconsistencies between sib

Improved IBD Detection Using Incomplete Haplotype Information

The availability of high density genetic maps and genotyping platforms has transformed human genetic studies. The use of these platforms has enabled population-based genome-wide association studies. However, in inheritance-based studies, current methods do not take full advantage of the information present in such genotyping analyses. In this paper we describe an improved method for identifying genetic regions shared identical-by-descent (IBD) from recent common ancestors. This method improves existing methods by taking advantage of phase information even if it is less than fully accurate or missing. We present an analysis of how using phase information increases the accuracy of IBD detection compared to using only genotype information

A research review of quality assessment for software

Measures were recommended to assess the quality of software submitted to the AdaNet program. The quality factors that are important to software reuse are explored and methods of evaluating those factors are discussed. Quality factors important to software reuse are: correctness, reliability, verifiability, understandability, modifiability, and certifiability. Certifiability is included because the documentation of many factors about a software component such as its efficiency, portability, and development history, constitute a class for factors important to some users, not important at all to other, and impossible for AdaNet to distinguish between a priori. The quality factors may be assessed in different ways. There are a few quantitative measures which have been shown to indicate software quality. However, it is believed that there exists many factors that indicate quality and have not been empirically validated due to their subjective nature. These subjective factors are characterized by the way in which they support the software engineering principles of abstraction, information hiding, modularity, localization, confirmability, uniformity, and completeness

Visualising errors in animal pedigree genotype data

Genetic analysis of a breeding animal population involves determining the inheritance pattern of genotypes for multiple genetic markers across the individuals in the population pedigree structure. However, experimental pedigree genotype data invariably contains errors in both the pedigree structure and in the associated individual genotypes, which introduce inconsistencies into the dataset, rendering them useless for further analysis. The resolution of these errors requires consideration of the genotype inheritance patterns in the context of the pedigree structure. Existing visualisations of pedigree structures are typically more suited to human pedigrees and are less suitable for large complex animal pedigrees which may exhibit cross generational inbreeding. Similarly, current table-based viewers of genotype marker information can highlight where errors become apparent but lack the functionality and interactive visual feedback to enable users to locate the underlying source of errors within the pedigree. In this paper, we detail a design study steered by biologists who work with pedigree data, and describe successive iterations through approaches and prototypes for viewing genotyping errors in the context of a displayed pedigree. We describe how each approach performs with real pedigree genotype data and why eventually we deemed them unsuitable. Finally, a novel prototype visualisation for pedigrees, which we term the ‘sandwich view’, is detailed and we demonstrate how the approach effectively communicates errors in the pedigree context, supporting the biologist in the error identification task

Understanding the construction of marketers’ credibility by NZ senior managers: An interpretive study

Academics report that marketers are losing their influence in the boardroom due in part to serious challenges to marketing’s credibility. Although the credibility of marketing sources has received much attention since the early 1950s, research into how individuals in business organisations construct the credibility of marketers is scarce. This study, using in-depth interviews, describes how seven senior managers from different New Zealand businesses construct the credibility of marketers. For these senior managers, the credibility of marketers is grounded in their performance in delivering commercial outcomes. The findings also suggest that senior managers construct credibility in terms of a work aspect and a social aspect of a marketer’s performance, and that both these aspects have to be present if the marketer is to be considered credible. The work aspect of performance is made up of a marketer’s Pedigree, Projects, and Pervasive Influence. The Pedigree of a marketer includes their qualifications, skills and background. A degree is usually the minimum qualification required, particularly for more senior marketing roles. Skills expected from marketers include leadership, management, sales and intuition. With regard to background, the marketer needs to demonstrate they have achieved commercial outcomes in previous employment to be considered credible. Projects describes how marketers must design and implement cogent marketing plans, work effectively without supervision, achieve commercial outcomes in a clever or creative way, and provide evidence that their projects have contributed to commercial outcomes. Pervasive Influence describes how marketers influence others in the organisation toward customer-centricity. Marketers can lose credibility in the work aspect of their performance when they have no structured purpose to their marketing research, are unable to execute marketing plans or are unable to demonstrate the results of a marketing project. The social aspect of a marketer’s performance is made up of Personal Integrity and Professional Conduct. Personal Integrity describes marketers who are respected, take pride in their work, strive to improve themselves and are not precious. Professional Conduct describes a marketer who relates and collaborates competently and professionally with others, and is a team fit. Marketers lose credibility in the social aspect of their performance when they are precious, flighty, argumentative, and only out for themselves. This paper contributes a framework that describes the construction of a marketer’s credibility from a senior manager’s perspective. It also introduces a new understanding of credibility, grounded in performance terms, which is distinct from past conceptualisations of credibility found in the literature, which is based on expertise and trustworthiness. These findings demonstrate that while a marketer might be considered an expert and trustworthy, if they are not delivering commercial outcomes then they may not be considered credible, from a senior manager’s perspective