Predicting the Genomic Resolution of Bulk Segregant Analysis

Bulk segregant analysis (BSA) is a technique for identifying the genetic loci that underlie phenotypic trait differences. The basic approach of this method is to compare two pools of individuals from the opposing tails of the phenotypic distribution, sampled from an interbred population. Each pool is sequenced and scanned for alleles that show divergent frequencies between the pools, indicating potential association with the observed trait differences. BSA has already been successfully applied to the mapping of various quantitative trait loci in organisms ranging from yeast to maize. However, these studies have typically suffered from rather low mapping resolution, and we still lack a detailed understanding of how this resolution is affected by experimental parameters. Here, we use coalescence theory to calculate the expected genomic resolution of BSA. We first show that in an idealized interbreeding population of infinite size, the expected length of the mapped region is inversely proportional to the recombination rate, the number of generations of interbreeding, and the number of genomes sampled, as intuitively expected. In a finite population, coalescence events in the genealogy of the sample reduce the number of potentially informative recombination events during interbreeding, thereby increasing the length of the mapped region. This is incorporated into our theory by an effective population size parameter that specifies the pairwise coalescence rate of the interbreeding population. The mapping resolution predicted by our theory closely matches numerical simulations. Furthermore, we show that the approach can easily be extended to modifications of the crossing scheme. Our framework enables researchers to predict the expected power of their mapping experiments, and to evaluate how their experimental design could be tuned to optimize mapping resolution.

Urban Expansion in Ethiopia from 1987 to 2017: Characteristics, Spatial Patterns, and Driving Forces

Rapid urban growth in major cities of a country poses challenges for sustainable development. Particularly in Africa, the process of rapid urbanization is little understood and research is mostly limited to single cities. Thus, this study provides a comprehensive comparative analysis of the growth and spatial patterns of urban development in the three major cities of Ethiopia (Addis Ababa, Adama, and Hawassa) from 1987 to 2017. Also, the applicability of diffusion and coalescence theory on the evolution of these cities has been tested. Remote sensing and GIS technologies were combined with spatial metrics and morphological analysis was employed to undertake this study. The result revealed that all the studied cities experienced accelerated growth in the urbanized areas, but the cities with a larger initial urbanized size were associated with lower expansion rates. Differences in extent and direction of expansion in each city were mostly related to physical features, urban master plans, and policies, with an increase in the irregularity and dispersion of urban growth, representing strong evidence of urban sprawl. The spatiotemporal analysis confirmed that the urbanization processes of Addis Ababa and Adama were consistent and Hawassa city diverged from expectations based on diffusion and coalescence theory. In general, large cities with strong economic growth in a country fail to effectively control the scattered nature of urban growth, thus requiring aggressive policy intervention. The approach used in this study permits a deeper exploration of urban development patterns and the identification of priority areas for effective urban planning and management.

An Application of the Coalescence Theory to Branching Random Walks

In a discrete-time single-type Galton--Watson branching random walk {Zn, ζn}n≤ 0, where Zn is the population of the nth generation and ζn is a collection of the positions on ℝ of the Zn individuals in the nth generation, let Yn be the position of a randomly chosen individual from the nth generation and Zn(x) be the number of points in ζn that are less than or equal to x for x∈ℝ. In this paper we show in the explosive case (i.e. m=E(Z1∣ Z0=1)=∞) when the offspring distribution is in the domain of attraction of a stable law of order α,0 <α<1, that the sequence of random functions {Zn(x)/Zn:−∞<x<∞} converges in the finite-dimensional sense to {δx:−∞<x<∞}, where δx≡ 1{N≤ x} and N is an N(0,1) random variable.

An Application of the Coalescence Theory to Branching Random Walks

In a discrete-time single-type Galton--Watson branching random walk {Z n , ζ n } n≤ 0, where Z n is the population of the nth generation and ζ n is a collection of the positions on ℝ of the Z n individuals in the nth generation, let Y n be the position of a randomly chosen individual from the nth generation and Z n (x) be the number of points in ζ n that are less than or equal to x for x∈ℝ. In this paper we show in the explosive case (i.e. m=E(Z 1∣ Z 0=1)=∞) when the offspring distribution is in the domain of attraction of a stable law of order α,0 &lt;α&lt;1, that the sequence of random functions {Z n (x)/Z n :−∞&lt;x&lt;∞} converges in the finite-dimensional sense to {δ x :−∞&lt;x&lt;∞}, where δ x ≡ 1 {N≤ x} and N is an N(0,1) random variable.

Study on Adhesion-Resistant Materials for Improving the Restoration of Exercise-Induced Muscle Tendon Fracture

The muscle tendon is connective tissue, the fracture can occur when its stress is not reasonable. With the establishment of tendon external and endogenous coalescence theory, the suppression of external coalescence and promotion of endogenous coalescence became the crucial problem of resolve adhesion of tendon. The application of adhesion prevention materials in the part of tendon surrounding was the hotspot of recent research. At present, the research about adhesion prevention materials has made remarkable achievements. However, the materials studied in exercise-induced tendon rupture were cut both ways, therefore, as a material for adhesion prevention and functional reconstruction to treatment of tendon rupture. There are still many unsolved problems in the application of adhesion prevention materials.

Alu Evolution in Human Populations: Using the Coalescent to Estimate Effective Population Size

There are estimated to be ~1000 members of the Ya5 Alu subfamily of retroposons in humans. This Subfamily has a distribution restricted to humans, with a few copies in gorillas and chimpanzees. Fifty-seven Ya5 elements were previously cloned from a HeLaderived randomly sheared total genomic library, sequenced, and screened for polymorphism in a panel of 120 unrelated humans. Forty-four of the 57 cloned Alu repeats were monomorphic in the sample and 13 Alu repeats were dimorphic for insertion presence/absence. The observed distribution of sample frequencies of the 13 dimorphic elements is consistent with the theoretical expectation for elements ascertained in a single diploid cell line. Coalescence theory is used to compute expected total pedigree branch lengths for monomorphic and dimorphic elements, leading to an estimate of human effective population size of ~18,000 during the last one to two million years.