Structure of populations under mixed random and sib mating

Summary The present investigation relates to various properties of population bred by mixture of breeding systems namely mixed random and sib mating. Expressions have been derived which give the genotypic frequencies in any given generation in terms of the initial values. Under the mating system considered the population will eventually become stable having a certain amount of heterozygosis depending upon the amounts of random and sib mating. The loss of heterozygosity in successive generations has been examined for varying amounts of sib mating in the population.The formulae have been derived giving the mean and genotypic variance in any given generation of continued mixed mating. The effect of the mating system considered on mean and genotypic variance in successive generations has been discussed in detail in case of (i) absence of dominance and (ii) complete dominance.

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Zusammenfassung Die vorliegende Untersuchung bezieht sich auf verschiedene Eigenheiten des Populationsverhaltens unter Einfluß einer Mischung von Paarungssystemen, nämlich der Panmixie und der Geschwisterpaarung. Es wurden Formeln abgeleitet, die die genotypischen Frequenzen in jeder beliebigen Generation in Beziehung zu den Ausgangswerten angeben. Unter dem betrachteten Paarungssystem kann die Population gegebenenfalls stabil werden mit einem bestimmten Heterozygotieanteil, der vom Ausmaß der Panmixie und der Geschwisterpaarung abhängt. Für verschiedene Anteile der Geschwisterpaarung wurde der Verlust der Heterozygotie in aufeinanderfolgenden Generationen untersucht.Die abgeleiteten Formeln liefern das Mittel und die genotypische Varianz in jeder beliebigen Generation fortgesetzter gemischter Paarung. Die Wirkung des betrachteten Paarungssystems auf Mittel und genotypische Varianz in aufeinanderfolgenden Generationen wurde (1) für den Fall der Abwesenheit der Dominanz und (2) den der vollständigen Dominanz ausführlich diskutiert.

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Journal paper No. J-6127, of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 1669. This work was supported by the National Institutes of Health, Grant No. GM-13827.     

Selection under random mutations in stochastic eigen model

The concept of natural selection is examined, which is one of basic principles for the Darwinian interpretation of evolution. In this model selection is defined as a solution of the deterministic Eigen equation. Next, the random effect is introduced through the mutation term. However, the probability of finding the solution expressing the selection is shown to be smallest. The validity of the model and its applicability to polynucleotide replication are discussed.     

The covariance of relatives derived from a random mating population.

Attention is drawn to errors common in the derivation of forms for the genotypic covariance of noninbred relatives from a Hardy-Weinberg population of diploids. A synthesis of Fisher's least-squares method of partitioning the genotypic variance and Malécot's probability method of expressing kinship, yields a general form. For one locus, the form is $\text{(P}{}_{\mathrm{ss}}\text{+ P}{}_{\mathrm{sd}}\text{+ P}{}_{\mathrm{ds}}\text{+ P}{}_{\mathrm{dd}}\text{)}\text{1}\text{2}\text{σ}{}_{\mathrm{a}}{}^2\text{+ (P}{}_{\mathrm{ss}}\text{P}{}_{\mathrm{dd}}\text{+ P}{}_{\mathrm{sd}}\text{P}{}_{\mathrm{ds}}\text{) σa}{}_{\mathrm{d}}{}^2$, where σ_a² is the additive genetic variance, α_d² is the variance of dominance deviations, p_ij is the probability that parental gamete i is identical by descent to parental gamete j, i = s, d indexes the parents of one relative, and j = s, d indexes those of the other. The form provides a framework for obtaining the covariance of relatives from an equilibrium population with linkage.     

Characteristics of the het mutations in the Escherichia coli chromosome causing an increase in Tn1 transposition frequency

Four mutations were studied which lead to increasing the frequency of transposon Tn1 translocation into different replicons. These mutations (het1, het2, het3 and het4) increase the frequency of Tn1 translocation 10-20-fold. The het1 mutation is recessive and has been localized in the 90-94.5 min region of the bacterial chromosome. The mutation effects Tn1 transposition in the presence of F plasmid only. As we have demonstrated recently, F-plasmid inhibits Tn1 transposition in Escherichia coli cells. The het1 mutation eliminates this inhibition. Unlike het2, het3 and het4 mutations, het1 is responsible for resistance to male phages f1, f2, MS2 and inhibition of conjugative transfer in F+ bacteria.     

Quantification of random genomic mutations

Cancer cells contain numerous clonal mutations. It has been theorized that malignant cells sustain an elevated mutation rate and, as a consequence, harbor yet larger numbers of random point mutations. Testing this hypothesis has been precluded by lack of an assay to measure random mutations-that is, mutations that occur in only one or a few cells of a population. We have established a method that has permitted us to detect and identify rare random mutations in human cells, at a frequency of 1 per 10(8) base pairs. The assay is based on gene capture, by hybridization with a uracil-containing probe, followed by magnetic separation. Mutations that render the mutational target sequence non-cleavable by a restriction enzyme are quantified by dilution to single molecules and real-time quantitative PCR amplification. The assay can be extended to quantify mutation in any DNA-based organism, at different sites in the genome, in introns and exons, in unselected and selected genes, and in proliferating and quiescent cells.     

Generalized linear models with random effects; salamander mating revisited.

In recent years much effort has been devoted to extending regression methodology to non-Gaussian data, where responses are not independent. These methods for dependent responses are suitable for data from longitudinal studies or nested designs. However, use of these methods for crossed designs seems to have serious limitations due to the intensive computations involved because of the intractable nature of the joint distribution. In this paper, we cast the problem in a Bayesian framework and use a Monte Carlo method, the Gibbs sampler, to avoid current computational limitations. The flexibility of this approach is illustrated by analyzing the interesting salamander mating data reported by McCullagh and Nelder (1989, Generalized Linear Models, 2nd edition, London: Chapman and Hall).     

Quantification of random mutations in the mitochondrial genome

Mitochondrial DNA (mtDNA) mutations contribute to the pathology of a number of age-related disorders, including Parkinson disease [A. Bender et al., Nat. Genet. 38 (2006) 515,Y. Kraytsberg et al., Nat. Genet. 38 (2006) 518], muscle-wasting [J. Wanagat, Z. Cao, P. Pathare, J.M. Aiken, FASEB J. 15 (2001) 322], and the metastatic potential of cancers [K. Ishikawa et al., Science 320 (2008) 661]. The impact of mitochondrial DNA mutations on a wide variety of human diseases has made it increasingly important to understand the mechanisms that drive mitochondrial mutagenesis. In order to provide new insight into the etiology and natural history of mtDNA mutations, we have developed an assay that can detect mitochondrial mutations in a variety of tissues and experimental settings [M. Vermulst et al., Nat. Genet. 40 (2008) 4, M. Vermulst et al., Nat. Genet. 39 (2007) 540]. This methodology, termed the Random Mutation Capture assay, relies on single-molecule amplification to detect rare mutations among millions of wild-type bases [J.H. Bielas, L.A. Loeb, Nat. Methods 2 (2005) 285], and can be used to analyze mitochondrial mutagenesis to a single base pair level in mammals.     

Comparison of lifetime performance in mice under crisscross,repeat hybrid male cross and random mating systems

Summary Mating systems that capitalize on heterosis in dairy cattle are the criss-cross (CC), the repeat hybrid male cross (RHMC) and random mating within a synthetic population (SYN). When performance is determined solely by direct additive genetic and dominance genetic effects, expected performance under CC (averaged over four generations after F₁ generation), relative to that under RHMC (or SYN) is (59 G1+69 G2 +82 H)/64(G1+G2+H), where Gi is direct additive genetic effect of breed i and H is direct heterosis. Five CC, five RHMC and one SYN population of mice were prepared to test 533, 534 and 410 females, respectively for performance during lifetime (155 days after mating). Each female was pair-mated at day 42 with a male from the SYN population and the number of lactations during the lifetime (NL), total number (TN) and weight (TW in g) of young born alive during lifetime, total number (AN) and weight (AW in g) of young raised to weaning (18 days), and actual length of reproductive life (RL in days) were recorded. Observed performance averaged over four generations was, under CC, RHMC and SYN, 4.74, 4.62 and 4.56 for NL, 49.9, 48.2 and 48.8 for TN, 86.0, 83.6 and 85.1 g for TW, 47.5, 45.5 and 46.3 for AN, 512.1, 517.9 and 521.1 g for AW, and 120.0, 117.6 and 116.7 for RL, respectively. Heterosis due to the female (H) was 10, 30, 33, 34, 43 and 9% for NL, TN, TW, AN, AW and RL, respectively. Direct additive genetic values were estimated for each pair of lines involved with CC or RHMC. These values were used in the formula to calculate expected performance in each mating system. The ratio of CC to RHMC for the expected and observed performance was 1.01 and 1.01 for NL, 1.04 and 1.04 for TN, 1.04 and 1.03 for TW, 1.04 and 1.04 for AN, 1.05 and 0.99 for AW, and 1.01 and 1.02 for RL, respectively. The ratio of CC to SYN for the observed performance was 1.04 for NL, 1.02 for TN, 1.01 for TW, 1.03 for AN, 0.98 for AW, and 1.03 for RL. As expected, the observed mean performance under CC was slightly larger than that under RHMC or SYN.Animal Research Centre Contribution No. 1262