scholarly journals Models of long term artificial selection in finite population

1986 ◽  
Vol 48 (1) ◽  
pp. 41-50 ◽  
Author(s):  
William G. Hill ◽  
Jonathan Rasbash
Keyword(s):  
Population Size ◽  
Frequency Distribution ◽  
Selection Response ◽  
Initial Distribution ◽  
Gene Frequencies ◽  
Frequency Distributions ◽  
Gene Effect ◽  
Wide Range ◽  
Breeding Programmes ◽  
Two Parameters

SummaryThe effects of population size and selection intensity, which are in the breeder's control, are investigated for ranges of values of quantities outside his control, namely the number, initial distribution of frequencies and effects of genes influencing the trait. Two alleles are assumed to be initially segregating at each locus, with no linkage, dominance or epistasis. The effects are assumed to follow a gamma distribution, using a wide range of its two parameters which specify both mean gene effect or selective value and the shape of the distribution, or the ratio of Wright's effective number to actual number of genes. The initial gene frequencies (q) are assumed to be either 0·5 at all loci, uniformly distributed over the range 0–1, or to have a U-shaped distribution, proportional to [q(1 − q)]−1 such as derives from neutral mutation, with gene effect and frequency distributions independent. The mean and variance of selection response and limits, in the absence of new mutation, are derived.The shape of the distribution of effects is not usually important even up to the selection limit. With appropriate parametrization, the influence of the initial frequency distribution is small over a wide range of parameters. For reasonable choices of parameters, the effects of changing population size from those typically used in animal breeding programmes are likely to be small, but not negligible. For the initial U-shaped frequency distribution, further increases in population size are always expected to give a greater limit, regardless of present value, but not for the other distributions.

scholarly journals The effect of initial reverse selection upon total selection response

1964 ◽  
Vol 5 (1) ◽  
pp. 68-79 ◽  
Author(s):  
J. S. Allan ◽  
Alan Robertson
Keyword(s):  
Population Size ◽  
Gene Frequency ◽  
Initial Period ◽  
Low Frequency ◽  
Selection Response ◽  
Selection Intensity ◽  
Forward Selection ◽  
Frequency Distributions ◽  
Gene Effect ◽  
Recessive Genes

A computer has been used to investigate the effect of an initial period of reverse selection on the subsequent response of a population to renewed forward selection with the same population size and selection intensity. As the computer was used to derive gene frequency distributions, there was no random element in the results obtained. A theoretical solution to the problem was obtained for genes with small effects.The process can be adequately described by the duration of the reverse selection (expressed in terms of the population size N), the product of population size and gene effect, Ns, and the initial gene frequency. If the duration of reverse selection, t, is less than N/2, the loss in selection advance due to the reverse selection is roughly t/N, though slightly greater than this for genes with low frequency. The ‘point of no return’ after which it is impossible, with the same population size and selection intensity, to return even to the starting frequency is 1·4N generations for genes with small effect and this declines as the gene effect increases.Some extension of results to recessive genes is also given.

scholarly journals The effect of finite population size on models of linked overdominant loci

1978 ◽  
Vol 31 (3) ◽  
pp. 239-254 ◽  
Author(s):  
P. J. Avery
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Genetic Drift ◽  
High Probability ◽  
Finite Population ◽  
Equilibrium Points ◽  
Gene Frequencies ◽  
Wide Range ◽  
Stable Equilibria ◽  
Range Of Values

SUMMARYModels of two linked overdominant loci in moderately large, but finite, populations are examined by looking at the variance-covariance matrix of the two gene frequencies and the linkage disequilibrium around stable deterministic equilibrium points. In particular, the effect of genetic drift is examined in cases where, in infinite populations, two stable equilibria with non-zero linkage disequilibrium, D, are maintained. Theoretical formulae are produced and checked by computer simulation. In general, the results show that unless the population size is very large indeed, genetic drift causes the values of D to vary considerably about the equilibrium values and that for many models, where stable equilibria exist at non-zero D values, a wide range of values of D have a high probability. Thus it is very difficult to draw conclusions about the selection regime by measuring Linkage disequilibrium in a finite population.

Heritability of the Effect of Corticosteroids on Intraocular Pressure

1970 ◽  
Vol 19 (1-2) ◽  
pp. 264-267 ◽  
Author(s):  
F.H. Reuling ◽  
J.T. Schwartz
Keyword(s):  
Intraocular Pressure ◽  
Clinical Signs ◽  
Topical Steroids ◽  
Frequency Distributions ◽  
Steroid Response ◽  
Large Numbers ◽  
Wide Range ◽  
Allele Pair ◽  
High Level ◽  
Genetically Determined

In the late 1950's and early 1960's, it became evident that some glaucoma patients developed elevations of intraocular pressure, which were difficult to control, following prolonged use of systemic or ocular medications containing corticosteroids (Chandler, 1955, Alfano, 1963; Armaly, 1963). In addition, some patients without glaucoma, when treated with steroids for long periods of time, developed clinical signs of chronic simple glaucoma (McLean, 1950; François, 1954; Covell, 1958; Linner, 1959; Goldman, 1962). Fortunately, the elevation of intraocular pressure was reversible if the drug was discontinued.Over the past decade, extensive investigation of the “steroid response” has been undertaken. For this presentation, the steroid response may be considered as a gradual elevation of intraocular pressure, occurring over several weeks, in an eye being medicated with corticosteroid drops several times a day. The elevation in pressure is usually accompanied by a reduction in the facility of aqueous outflow. When relatively large numbers of subjects were tested with topical steroids, so that a wide range of responsiveness could be observed, a variation in individual sensitivity was demonstrated. Frequency distributions of intraocular pressure or change in pressure following steroids showed a skew toward the high side. On the basis of trimodal characteristics which they observed in such frequency distributions, Becker and Hahn (1964), Becker (1965) and Armaly (1965, 1966) considered the possible existence of several genetically determined subpopulations. These investigators distinguished three subpopulations on the basis of low, intermediate, and high levels of pressure response. It was hypothesized that these levels of response characterized three phenotypes, corresponding to the three possible genotypes of an allele pair, wherein one member of the pair determined a low level of response, and the other member determined a high level of response (Armaly, 1967).

scholarly journals EFFECTS OF POPULATION SIZE AND SELECTION INTENSITY ON SHORT-TERM RESPONSE TO SELECTION FOR POSTWEANING GAIN IN MICE

Genetics ◽  
1973 ◽  
Vol 73 (3) ◽  
pp. 513-530
Author(s):  
J P Hanrahan ◽  
E J Eisen ◽  
J E Legates
Keyword(s):  
Population Size ◽  
Selection Response ◽  
Selection Intensity ◽  
Realized Heritability ◽  
Family Selection ◽  
Effective Population ◽  
Population Sizes ◽  
Selection For ◽  
Selection Intensities ◽  
Term Response

ABSTRACT The effects of population size and selection intensity on the mean response was examined after 14 generations of within full-sib family selection for postweaning gain in mice. Population sizes of 1, 2, 4, 8 and 16 pair matings were each evaluated at selection intensities of 100% (control), 50% and 25% in a replicated experiment. Selection response per generation increased as selection intensity increased. Selection response and realized heritability tended to increase with increasing population size. Replicate variability in realized heritability was large at population sizes of 1, 2 and 4 pairs. Genetic drift was implicated as the primary factor causing the reduced response and lowered repeatability at the smaller population sizes. Lines with intended effective population sizes of 62 yielded larger selection responses per unit selection differential than lines with effective population sizes of 30 or less.

scholarly journals A Comparison of Some Methods of Deriving the Instantaneous Unit Hydrograph

1985 ◽  
Vol 16 (1) ◽  
pp. 1-10 ◽  
Author(s):  
V. P. Singh ◽  
C. Corradini ◽  
F. Melone
Keyword(s):  
Peak Flow ◽  
Central Italy ◽  
Effective Rainfall ◽  
Unit Hydrograph ◽  
Time To Peak ◽  
Wide Range ◽  
Instantaneous Unit Hydrograph ◽  
Similar Accuracy ◽  
Two Parameters ◽  
Range Of Values

The geomorphological instantaneous unit hydrograph (IUH) proposed by Gupta et al. (1980) was compared with the IUH derived by commonly used time-area and Nash methods. This comparison was performed by analyzing the effective rainfall-direct runoff relationship for four large basins in Central Italy ranging in area from 934 to 4,147 km2. The Nash method was found to be the most accurate of the three methods. The geomorphological method, with only one parameter estimated in advance from the observed data, was found to be little less accurate than the Nash method which has two parameters determined from observations. Furthermore, if the geomorphological and Nash methods employed the same information represented by basin lag, then they produced similar accuracy provided the other Nash parameter, expressed by the product of peak flow and time to peak, was empirically assessed within a wide range of values. It was concluded that it was more appropriate to use the geomorphological method for ungaged basins and the Nash method for gaged basins.

Using Tolerance-Maps to Generate Frequency Distributions of Clearance and Allocate Tolerances for Pin-Hole Assemblies

2007 ◽  
Vol 7 (4) ◽  
pp. 347-359 ◽  
Author(s):  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Mathematical Model ◽  
Statistical Method ◽  
Frequency Distribution ◽  
Probabilistic Representation ◽  
Worst Case ◽  
Frequency Distributions ◽  
One Dimensional ◽  
Material Condition ◽  
Geometric Tolerances ◽  
Case Basis

A new mathematical model for representing the geometric variations of lines is extended to include probabilistic representations of one-dimensional (1D) clearance, which arise from positional variations of the axis of a hole, the size of the hole, and a pin-hole assembly. The model is compatible with the ASME/ ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map (T-Map) (Patent No. 69638242), a hypothetical volume of points that models the 3D variations in location and orientation for a segment of a line (the axis), which can arise from tolerances on size, position, orientation, and form. Here, it is extended to model the increases in yield that occur when maximum material condition (MMC) is specified and when tolerances are assigned statistically rather than on a worst-case basis; the statistical method includes the specification of both size and position tolerances on a feature. The frequency distribution of 1D clearance is decomposed into manufacturing bias, i.e., toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is built from geometric bias, and it is presumed that manufacturing bias is uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled pin and hole. A comparison is made between the effects of choosing the optional material condition MMC and not choosing it with the tolerances that determine the allowable variations in position.

Bias in Using an Age–Length Key to Estimate Age-Frequency Distributions

1978 ◽  
Vol 35 (2) ◽  
pp. 184-189 ◽  
Author(s):  
S. J. Westrheim ◽  
W. E. Ricker
Keyword(s):  
Frequency Distribution ◽  
Age Distribution ◽  
Length Distribution ◽  
Fish Population ◽  
Systematic Bias ◽  
Parental Age ◽  
Frequency Distributions ◽  
Class Strength ◽  
Key Words Age ◽  
Age Frequency Distribution

Consider two representative samples of fish taken in different years from the same fish population, this being a population in which year-class strength varies. For the "parental" sample the length and age of the fish are determined and are used to construct an "age–length key," the fractions of the fish in each (short) length interval that are of each age. For the "filial" sample only the length is measured, and the parental age–length key is used to compute the corresponding age distribution. Trials show that the age–length key will reproduce the age-frequency distribution of the filial sample without systematic bias only if there is no overlap in length between successive ages. Where there is much overlap, the age–length key will compute from the filial length-frequency distribution approximately the parental age distribution. Additional bias arises if the rate of growth if a year-class is affected by its abundance, or if the survival rate in the population changes. The length of the fish present in any given part of a population's range can vary with environmental factors such as depth of the water; nevertheless, a sample taken in any part of that range can be used to compute age from the length distribution of a sample taken at the same time in any other part of the range, without systematic bias. But this of course is not likely to be true of samples taken from different populations of the species. Key words: age–length key, bias, Pacific ocean perch, Sebastes alutus

Frequency distribution of Wuchereria bancrofti microfilariae in human populations and its relationships with age and sex

Parasitology ◽  
1990 ◽  
Vol 101 (3) ◽  
pp. 429-434 ◽  
Author(s):  
P. K. Das ◽  
A. Manoharan ◽  
A. Srividya ◽  
B. T. Grenfell ◽  
D. A. P. Bundy ◽  
...  
Keyword(s):  
Frequency Distribution ◽  
Negative Binomial ◽  
Age Distribution ◽  
Indirect Evidence ◽  
Wuchereria Bancrofti ◽  
Parameter Estimates ◽  
Human Populations ◽  
Sampling Errors ◽  
Frequency Distributions ◽  
Age And Sex

SUMMARYThis paper examines the effects of host age and sex on the frequency distribution of Wuchereria bancrofti infections in the human host. Microfilarial counts from a large data base on the epidemiology of bancroftian filariasis in Pondicherry, South India are analysed. Frequency distributions of microfilarial counts divided by age are successfully described by zero-truncated negative binomial distributions, fitted by maximum likelihood. Parameter estimates from the fits indicate a significant trend of decreasing overdispersion with age in the distributions above age 10; this pattern provides indirect evidence for the operation of density-dependent constraints on microfilarial intensity. The analysis also provides estimates of the proportion of mf-positive individuals who are identified as negative due to sampling errors (around 5% of the total negatives). This allows the construction of corrected mf age–prevalence curves, which indicate that the observed prevalence may underestimate the true figures by between 25% and 100%. The age distribution of mf-negative individuals in the population is discussed in terms of current hypotheses about the interaction between disease and infection.

Frequency distribution of space groups in soluble and membrane proteins and their complexes

2021 ◽  
Vol 77 (6) ◽  
pp. 187-191
Author(s):  
Rajneesh K. Gaur
Keyword(s):  
Membrane Proteins ◽  
Frequency Distribution ◽  
Data Bank ◽  
Frequency Distributions ◽  
Space Group ◽  
Space Groups ◽  
Group Frequency ◽  
Different Types ◽  
Analytical Assessment ◽  
Three Space

The space-group frequency distributions for two types of proteins and their complexes are explored. Based on the incremental availability of data in the Protein Data Bank, an analytical assessment shows a preferential distribution of three space groups, i.e. P212121 > P1211 > C121, in soluble and membrane proteins as well as in their complexes. In membrane proteins, the order of the three space groups is P212121 > C121 > P1211. The distribution of these space groups also shows the same pattern whether a protein crystallizes with a monomer or an oligomer in the asymmetric unit. The results also indicate that the sizes of the two entities in the structures of soluble proteins crystallized as complexes do not influence the frequency distribution of space groups. In general, it can be concluded that the space-group frequency distribution is homogenous across different types of proteins and their complexes.

scholarly journals Regional parent flood frequency distributions in Europe – Part 1: Is the GEV model suitable as a pan-European parent?

2014 ◽  
Vol 18 (11) ◽  
pp. 4381-4389 ◽  
Author(s):  
J. L. Salinas ◽  
A. Castellarin ◽  
A. Viglione ◽  
S. Kohnová ◽  
T. R. Kjeldsen
Keyword(s):  
Statistical Model ◽  
Frequency Distribution ◽  
Climatic Factors ◽  
Extreme Value ◽  
Flood Frequency ◽  
Generalized Extreme Value Distribution ◽  
Statistical Hypothesis ◽  
Generalized Extreme Value ◽  
Frequency Distributions ◽  
Hypothetical Scenario

Abstract. This study addresses the question of the existence of a parent flood frequency distribution on a European scale. A new database of L-moment ratios of flood annual maximum series (AMS) from 4105 catchments was compiled by joining 13 national data sets. Simple exploration of the database presents the generalized extreme value (GEV) distribution as a potential pan-European flood frequency distribution, being the three-parameter statistical model that with the closest resemblance to the estimated average of the sample L-moment ratios. Additional Monte Carlo simulations show that the variability in terms of sample skewness and kurtosis present in the data is larger than in a hypothetical scenario where all the samples were drawn from a GEV model. Overall, the generalized extreme value distribution fails to represent the kurtosis dispersion, especially for the longer sample lengths and medium to high skewness values, and therefore may be rejected in a statistical hypothesis testing framework as a single pan-European parent distribution for annual flood maxima. The results presented in this paper suggest that one single statistical model may not be able to fit the entire variety of flood processes present at a European scale, and presents an opportunity to further investigate the catchment and climatic factors controlling European flood regimes and their effects on the underlying flood frequency distributions.

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