text:
Identity-by-Descent Estimation and Mapping of Qualitative Traits in Large, Complex Pedigrees
- Mark Abney 1
- 1Address for correspondence: Department of Human Genetics, University of Chicago, 920 E. 58th St., Chicago, IL 60637. E-mail: abney{at}genetics.uchicago.edu
Computing identity-by-descent sharing between individuals connected through a large, complex pedigree is a computationally demanding task that often cannot be done using exact methods. What I present here is a rapid computational method for estimating, in large complex pedigrees, the probability that pairs of alleles are IBD given the single-point genotype data at that marker for all individuals. The method can be used on pedigrees of essentially arbitrary size and complexity without the need to divide the individuals into separate subpedigrees. I apply the method to do qualitative trait linkage mapping using the nonparametric sharing statistic Spairs. The validity of the method is demonstrated via simulation studies on a 13-generation 3028-person pedigree with 700 genotyped individuals. An analysis of an asthma data set of individuals in this pedigree finds four loci with P-values <10−3 that were not detected in prior analyses. The mapping method is fast and can complete analyses of ∼150 affected individuals within this pedigree for thousands of markers in a matter of hours.
COMPUTATION of identical-by-descent (IBD) allele sharing between related individuals is a necessary ingredient in many methods for linkage mapping of complex traits. Typically, IBD allele sharing is used either directly to assess whether affected individuals are sharing more at a locus than expected under the null hypothesis or as a component in the covariance matrix in a variance component model. A number of algorithms for computing IBD exactly exist (e.g., Elston and Stewart 1971; Lander and Green 1987; Kruglyak et al. 1996; Fishelson and Geiger 2002); however, these methods become computationally infeasible when pedigrees are very large and complex. Under such circumstances approximate methods become necessary, whether Markov chain Monte Carlo (Thompson et al. 1993; Sobel and Lange 1996; Heath 1997) or regression based (Fulker et al. 1995; Almasy and Blangero 1998). Even these methods, however, have difficulty when the pedigree is very deep with many generations of individuals with no data.
In humans, very deep, and possibly complex, pedigrees often arise in conjunction with genetic studies of isolated populations. Isolated populations are commonly thought to have characteristics that may prove advantageous for mapping (Wright et al. 1999; Peltonen et al. 2000; Escamilla 2001; Shifman and Darvasi 2001; Service et al. 2006), yet may require specialized statistical methods to both properly leverage these advantages and provide a valid test for the presence of a trait-influencing gene (Bourgain and Genin 2005). Large pedigrees also arise in other animal systems where breeding is carefully controlled. For example, there is interest in methods that are applicable to complex pedigrees for both livestock (Thallman et al. 2001) and dogs (Sutter and Ostrander 2004).
What I present here is a rapid computational method for estimating, in large complex pedigrees, the probability that pairs of alleles are IBD given the single-point genotype data at that marker for all individuals. Because the method is very fast, it can easily be used on genomewide data with many thousands of markers on hundreds of related individuals. It can be used directly to do linkage mapping with affected individuals using the Spairs statistic or to compute approximate multipoint probabilities both for alleles being IBD, using regression-based approaches (e.g., Almasy and Blangero 1998), and for alleles being homozygous by descent (HBD) using a hidden Markov model (HMM) (Abney et al. 2002). Here, I describe this computational method and its application to qualitative trait linkage analysis. Although computing Spairs is straightforward, in principle, a number of challenges must be overcome in creating a practical and valid mapping method for very large, and possibly complex, pedigrees. In particular, it is common in studies involving large pedigrees to have one, or a few, pedigrees, making the asymptotic distribution of the test statistic, which is appropriate when there are many independent pedigrees, not necessarily applicable. Also, the allele-frequency distribution may have a major influence on the test statistic when inheritance information is obscured by missing data. Unfortunately, the relevant allele-frequency distribution is that in the founders of the pedigree, which in large pedigrees may be many generations earlier than the sampled individuals. As a result, estimation of the founder allele-frequency distribution from the sampled data can result in a large bias of the conditional expected sharing statistic. The difficulties posed by not knowing the true allele-frequency distribution can be largely overcome through the use of simulations, but the capacity to do many simulations requires a computationally efficient method, particularly when a large number of markers are involved. Below, I describe the theoretical basis of the IBD estimation method, the approximations used, and how it differs from earlier methods that take a similar approach (Wang et al. 1995; Davis et al. 1996). I then show its application to single-point linkage mapping using Spairs and how the difficulties mentioned above are solved. The appendix describes how to use the IBD estimation method to obtain multipoint estimates of HBD by modifying the HMM of Abney et al. (2002).
IBD estimation
The objective is to compute the probability of two alleles being IBD given all available genotype data at that locus and the entire, unbroken pedigree. The method is based on the recursive strategy suggested by Wang et al. (1995) and Davis et al. (1996). In both of these studies the probability is computed in a manner analogous to the recurrence relation for kinship coefficients, , where and are the mother and the father of individual , and individual is not a descendant of . The equivalent recurrence equation when there are genotype data at the locus, as given by Wang et al. (1995) and Davis et al. (1996), is valid only when there are no missing genotypes and is(1)where is the probability that the ith allele from was inherited from the jth allele of 's mother, given the observed genotype data; and Ai ≡ Bj means allele Ai is IBD with allele Bj. This equation is applied repeatedly until the founders of the pedigree are reached and boundary conditions are used to obtain the probability. When there are no individuals with missing genotypes the method is both fast and returns exact probabilities.
Unfortunately, as recognized by both Wang et al. (1995) and Davis et al. (1996), Equation 1 is not valid when there are missing genotypes in the data. Although neither study formulated a version of Equation 1 that holds under missing data conditions, they each suggested approaches for this case. The most recent version of SimIBD (Davis et al. 1996) uses a Monte Carlo procedure where, for each realization, a random genotype is assigned to each missing genotype, and the recursive algorithm is applied. The final probability is the average of the probabilities computed at each Monte Carlo realization. In contrast, Wang et al. (1995) suggest two different possibilities. In the first, when the recursive algorithm encounters an individual who has a missing genotype, the relevant inheritance probability [e.g., ] is computed by summing over all possible genotypes for the missing data weighted by the probability of the genotype given the observed genotypes. To simplify the computation, one can use the probability of the genotype given only the genotypes of close relatives rather than all observed genotypes. The second possibility is to find the genotype configuration for all individuals with missing genotypes that has the highest probability and apply the recursive algorithm to that configuration. Finding the highest-probability genotype configuration, however, can be computationally demanding if there are many missing genotypes.
A common situation when analyzing large pedigrees is to have several generations of the pedigree completely untyped. None of the above strategies are entirely sufficient in such a situation. The problem is that there is little information in the untyped portion of the genealogy from which to infer the genotype probability distribution in those individuals. Simulating over valid genotype configurations can then be time consuming and, possibly, inaccurate. Summing over all possible genotypes, on the other hand, may be computationally impracticable.
The approach I propose relies on classifying individuals into two groups, A and S. An S individual is someone who either is genotyped or has at least one ancestor who is genotyped, while an A individual is someone who is not among the S group. Note that by this definition the S group may contain individuals for whom no data were actually collected. I also define a set of individuals called "quasi-founders," where each quasi-founder is either an S individual with both parents in the A group or an A individual with a spouse in S. A version of recurrence Equation 1, reformulated to hold true even under missing data, is applied to the S individuals until the quasi-founders are reached, at which point boundary conditions are employed to determine the final probability. This allows one to avoid using the recurrence equation over those generations with no genotype data, thereby speeding up the computation significantly. Furthermore, additional computational efficiency is gained by applying approximations designed specifically to work well when the rate of missing genotype data in S is reasonably low (e.g., <20%). Note that this constraint on the rate of missing genotype data in S still allows for potentially many generations of untyped individuals in A.
The algorithm is described in four parts. First, I describe the general form of Equation 1 and how to use this as a recurrence relation by updating the genotype information the probabilities are conditional on. I then show how the conditional probability of two alleles being IBD given some genotype information should be expressed when the allelic type of either of those alleles is unknown. This provides a general expression that can be applied recursively to compute the IBD probability. Applying this expression requires computing transmission probabilities in the presence of missing data. I derive an equation for calculating this probability and describe the approximations made to assure computational efficiency. Finally, the recursive algorithm is completed by specifying the boundary conditions to the recurrence equations.
Recurrence rules:
The following notation is used throughout the remainder of this article. Individuals are indicated with uppercase script characters (e.g., , , , ), while the true genotype of, for instance, individual comprises two random variables (A1, A2), where the alleles A1 and A2 may each take on one of the L possible allelic types at the locus, . Note that the ordering of A1 and A2 is arbitrary. Throughout, I assume that the pattern of missing genotype data is noninformative and that there is no genotyping error. Hence, observed allelic types indicate the true underlying genotype whereas the event that a genotype is missing provides no information, by itself, on the true genotype. Furthermore, the entire analysis is done conditional on the pattern of missing data. I let G represent the genotype information, which, as I show below, will grow during the course of the algorithm. Then, G = gr represents the information at the rth stage, where gr is a vector with two elements for each quasi-founder and for each person in S, where the element = νi if the allelic type of the first allele of individual at the rth stage is known to be νi (i.e., A1 = νi at stage r) or is equal to zero if unknown. The vector g0, then, has elements representing all directly observed genotype data or data that can be inferred without ambiguity. The vector has the same length as gr with entries equal to zero at all locations except for the two elements representing the alleles of . Then, for instance, , where · is the inner product, is a vector with entries for equal to the corresponding entries of gr and all other entries equal to zero.
To extend Equation 1 to the case when some genotypes are missing, first note that it includes conditional probabilities for descent events involving only one allele at a time from (e.g., {}, {}, etc.). In fact, if A1 came from the mother, for instance, then A2 must have come from the father. A version of Equation 1 that includes the descent events for the other allele and is true even with missing data is(2)where G = gr for all terms. This equation is valid as long as and are not the same individual and is not a descendant of . If and are the same individual the equation becomes(3)
Unlike Equation 1, Equations 2 and 3 are not strictly recurrence equations because the IBD probabilities on the right-hand side have additional descent conditions not present in the left-hand side probability. In the case of no missing genotype data, the equations may be applied recursively by noting that terms such as on the right-hand side of Equations 2 and "expanding" these terms using the appropriate recurrence relation. Also, the descent probabilities , etc., are easily tabulated on the basis of the possible genotype configurations of , , and . When there are missing genotypes, it is still possible to employ a recursive method based on Equations 2 and 3 by updating G with the genotype information provided by the descent events (e.g., ). To show this I describe the application of the updating scheme to the first term on the right-hand side of Equation 2, but the arguments apply equally well to all terms on the right-hand side. First, focus on the conditional IBD probability , keeping in mind that Equation 2 holds only when is neither nor a descendant of . If has a known genotype but either or does not, then the additional information from the conditions and must be included in the probability calculation. If, for example, and have known genotypes, does not, and A2 = νl, then , where gr+1 is identical to gr, but with component . The subsequent applications of the recurrence Equation 2 from this term must be done conditional on G = gr+1 rather than G = gr. Note that this implies that the computations must allow for the case of a partially known genotype, as F2 is known but F1 may not be.
In general, then, the IBD probabilities Pr(A1 ≡ B1 | G = gr) and Pr(A1 ≡ A2 | G = gr) are conditional on both the observed genotype data and the additional genotype information that results from the previous application of recurrence Equations 2 and 3. Even with the additional information, however, it is possible for A1 or B1 to be unknown. In this case, the probabilities must be written as a sum over the allelic types for the unknown alleles before the recurrence equations are applied. So, if A1 is unknown and ,(4)Note that in this equation Pr(A1 ≡ B1 | G = gr, A1 = νk) = Pr(A1 ≡ B1 | G = gr+1). Then, to compute the probability Pr(A1 ≡ B1 | G = gr) one applies Equation 2 to the right-hand side of Equation 4, obtaining(5)In general, if both A1 and B1 are unknown, the summation would be over all possible values of both A1 and B1. Doing such a sum would require applying the recursive algorithm to all terms in the sum, which can be computationally expensive even when there are few alleles. When the missing genotype rate is low this will occur infrequently, and instead of summing both A1 and B1 over all alleles, both alleles are left as unknown and Equation 5 reduces to Equation 2. This strategy is, in effect, equivalent to computing the probabilities conditional only on genotype information ancestral to and (and the other alleles of and if known) and, in practice, generally serves as a very good approximation.
Equation 5 provides a general recurrence equation that may be applied recursively to determine the probability that A1 and B1 are IBD, as long as and are not the same individual and is not a descendant of . If and are the same individual, Equation 3 may be generalized similarly. To compute the IBD probability, it is necessary to determine the transmission probabilities in the presence of missing data. The derivation of these probabilities and the approximations made are described in Equations 6–10. Although only the probability is computed here, extending this derivation to the other transmission probabilities is straightforward.
To compute this probability we must consider the case where A1 or A2 may be unknown. If , one must sum over possible values of A2,(6a)(6b)(6c)where Equation 6b is exact instead of approximate if the genotypes of and are known, and where Equation 6c results from approximating . Approximation (6c) allows one to compute the probability without performing a sum over all alleles by assuming that the sum over all allelic types is approximated by the conditional probability with A2 unknown. Note that when A2 is known and equal to, for instance, νj, Equation 6c becomes + 1 and is exact if and are known. Equation 6c says that we may approximate the conditional probability of transmission events , given all the genotype data with the probability given just the genotype data of , and . In fact, as described below, these probabilities will be computed using the genotype data from first-degree relatives. In computing the conditional probability of these transmission events I assume , where and are allowed to equal either the unknown state 0 or one of the known allelic types . This allows us to replace with in Equation 6c.
The probability in Equation 6c may be computed using Bayes' rule,(7)where , the observed genotypes, at the r + 1 step, of and only. Consider the numerator of this equation,(8)The second probability on the right-hand side is(9)Although the probability in Equation 9 is conditional only on the known values of and , I improve the missing data approximations in Equations 6b and 6c by instead computing this probability conditional on the observed genotypes of all first-degree relatives of .
To complete the computation of Equation 8 one needs to determine the probability . This probability is D(A1, M1), but in the case where is known and is unknown, the two conditions and result in the conditional probability on the right-hand side of Equation 9 becoming , when and . Hence, , and combining this with Equations 9, 8, and 7, Equation 6c becomes(10)Equation 10 provides a rapid means of computing the necessary descent probabilities, even in the presence of missing data, and may be applied to the recurrence relation of Equation 5 to find the probability of any two alleles being IBD. This is effective because the approximations in Equation 10 were chosen to minimize computation while maintaining accuracy under the assumption that the fraction of individuals in S with missing genotypes is not large. This strategy works well in practice because markers are usually included in a genetic analysis only if the rate of missing genotype data is low.
Computing Equation 9 may require knowing the conditional genotype distribution of if is unknown. Although this distribution is computed conditional on the genotypes of first-degree relatives, it also depends on the relatedness of and (which is zero in outbred individuals). The current implementation of the algorithm to compute this probability ignores the relatedness of and because, when there are a fair amount of genotype data among the first-degree relatives, this has a relatively small effect, unless and are very closely related. The algorithm for obtaining the conditional genotype distribution for an individual is to descend through the pedigree, one generation at a time, beginning with the quasi-founders, and for each person encountered who has missing genotype data, compute the genotype-frequency distribution given the genotypes of the parents, the spouse, and the offspring. If the person is a quasi-founder, the computation is done conditional only on the offspring and population allele frequencies. If the person is not a quasi-founder, but one or both of the parents are untyped, the computation is done conditional on the genotype-frequency distribution already computed for that parent. If an offspring is untyped, that offspring is ignored in the computation. To propagate information from more distant relatives when close relatives are untyped, additional iterations could be done, as needed. Experience suggests, however, that when the rate of missing genotypes is fairly low (< ∼20% in the set S), a single pass through the pedigree is sufficient to obtain reasonably accurate estimates of the conditional genotype distributions in individuals with missing genotype data.
The general form of Equation 10 is particularly useful in that it naturally provides a framework to include effects such as mutation and genotyping error. In particular, while normally D(A1, M1) is the zero or one indicator function when and are known, this may be generalized to a nontrivial function of the observed genotypes. Selecting a particular model for mutation or genotyping error where the observed genotypes depend on the true underlying genotypes would allow one to devise a more general form for D(A1, M1) than what is given in Equation 9.
Boundary conditions:
The recursive algorithm is completed by specifying boundary conditions that are applied to Equations 2 and 3 when and are quasi-founders. I assume below that the boundary conditions are applied at step t of the recurrence. The first rule is a general condition that applies to all sample individuals.
Boundary condition 1:
For any allele Ai of individual , Pr(Ai ≡ Ai | G = gt) = 1.
For the next two boundary conditions pi is the frequency of allele i in the founding population. To properly account for missing allele information I encode a missing allele as 0 and use the convention p0 = 1. I also define the following two functions,andFor notational convenience, label the alleles of 's genotype and the alleles of 's genotype , where any of i, j, k, l may be unknown (i.e., there may be partial or no genotype information on one or both individuals). The conditional probabilities given the genotypes of and in boundary conditions 2 and 3 are exact, even in the presence of missing data, but approximate the conditional probability given all the genotype data.
Boundary condition 2:
Let be the inbreeding coefficient of individual . When is a quasi-founder,When the alleles are from two separate quasi-founders and , one needs the condensed identity coefficients (Jacquard 1974) for the pair. Without loss of generality, I consider only the probability that A1 and B1 are IBD.
Boundary condition 3:
When and are quasi-founders,
where Sr is condensed identity state r and Δr is its unconditional probability.
Furthermore, the probabilities in the sum are
Frequency estimation:
When and are not just quasi-founders but actual founders, the boundary conditions reduce to those given in Wang et al. (1995) and Davis et al. (1996). Both boundary conditions 2 and 3 depend on the allele frequencies in the founding population, unless all the founders are genotyped. These frequencies may be estimated either from the founding population itself, if available, or through the genotypes of those individuals in the pedigree. With deep pedigrees, where the founders lived many generations ago, it may be impossible to obtain accurate estimates of the allele frequencies in the founding population. Unless this population is large enough that genetic drift will have had a negligible effect, sampling from the present-day population from which the pedigree originated might not provide accurate estimates of the founder-allele frequencies. Instead, allele frequencies are often estimated from the genotyped study sample.
The current method uses the best linear unbiased estimator of allele frequencies of McPeek et al. (2004) to obtain estimates from the genotyped study sample. The estimator of the frequency pν for allele ν is given bywhere 1 is a vector with each element equal to one, K is a matrix with elements Kij = 2ϕij with ϕij being the kinship coefficient between individuals i and j, and yν is the vector whose ith element equals one-half the number of alleles of type ν in individual i.
The danger of using the same population both for estimating frequencies and for computing sharing is that the sharing estimate will now be negatively biased. This is a general phenomenon when estimating IBD sharing among individuals and can be understood as follows. When related individuals share an allele identical by state there is some probability that this allele is also shared IBD. The rarer this allele is in the founding population, the higher the probability is that these two copies were inherited from a common ancestral allele and are IBD. Conversely, an allele shared between individuals that was fairly common in the founders is relatively unlikely to be IBD. Because of genetic drift, the frequency of an allele in the typed individuals will vary from its frequency in the founding population, and, when IBD is estimated for individuals sharing this allele, the estimate will be either too high or too low depending on whether the allele frequency has drifted down or up, respectively. Underestimating the probability will, on average, happen more often because common alleles, where underestimation most often takes place, are necessarily more frequent than rare alleles. Without some adjustment for this effect, Pr(A1 ≡ B1 | G) will tend to be below its expected value. The approach taken here is to use simulations to estimate the amount of bias when the allele frequencies are estimated. This is discussed in more detail below.
Linkage mapping
I implement a nonparametric, affecteds-only mapping method by using the sharing statistic Spairs. For affected pair k (composed of individuals and ),where 1E is 1 if E is true and 0 when E is false and is the kinship coefficient between and . Here, the summation for Spairs is done over all possible pairs, including when and represent the same individual, in which case and , where is the inbreeding coefficient of . Under the null hypothesis of no linkage, we haveand
The definition of Spairs,k relies on knowing the true, unobserved IBD state of the alleles. Instead, we use its expectation given the available genotype data at that locus G,Linkage mapping may be undertaken by ascertaining a sample of affected individuals and computing for every possible pair of individuals at a locus. Under the null hypothesis of no linkage will form a distribution with a mean of zero, whereas under the alternative of linkage there should be excess sharing and will generally be positive. Hence, to test for linkage one would do a one-sided test of and reject the null hypothesis if for some value of t.
A major challenge of the method is determining the proper statistical significance of the estimated sharing at a marker. Three problems, in particular, must be overcome: (1) Computation of an exact likelihood-ratio statistic, as done in Kong and Cox (1997), is computationally prohibitive; (2) with only a single large pedigree, asymptotic theory for the distribution of might not hold and, hence, using a normal distribution approximation, as in Kruglyak et al. (1996), might not be valid; and (3) obtaining an empirical distribution for for each marker, conditional on that marker's allele frequency, could entail analysis of 102–105 simulated data sets per locus, depending on the degree of evidence for linkage at the locus. (The varying number of simulations per locus results from a time-saving strategy of using a limited number of simulations to screen out potentially interesting markers for which more accurate empirical distributions are then found.) This may be computationally impractical for data sets with many markers.
A potential solution is to develop a more computationally efficient variation on approach (3), in which the screening step is based on an appropriate transformation of the empirical distribution from a single completely informative marker. Because a completely informative marker allows immediate identification of which alleles are IBD, it is possible to rapidly compute the distribution of Spairs. A first-pass P-value could then be estimated at each locus by comparing at the marker against this distribution. For markers showing strong evidence of linkage, the more accurate and time-consuming approach (3) could be used. The difficulty with this approach is twofold. First, the variance of Spairs is much larger than the variance of . The less informative the marker, the greater the difference in the variances. For essentially any marker the P-value obtained by comparing to the distribution of Spairs is far too conservative to be useful. Second, when allele frequencies are estimated from the sample is negatively biased. Without some form of correction the P-value becomes even more conservative.
With a fast enough method, simulations can be used to estimate the bias and variance at a marker and correct the estimate of . Note that the number of simulations needed to correct the bias and variance at a marker would typically be much less than the number needed to assess the empirical P-value at the marker by method (3). To do this, for each simulation the founders are given marker alleles according to the allele-frequency distribution estimated in the real data set. The allele frequencies for each simulated data set are computed from the same individuals who are typed in the real data set, and these frequencies are used to compute for that simulation. The mean value over the simulated is used as an estimator for the bias, , where Nsim is the number of simulations. The statistic for that marker is adjusted by this bias. Although this procedure can dramatically reduce the bias, it cannot completely eliminate it, even as Nsim becomes very large, because estimates of the bias are themselves biased. This comes about because the estimated frequencies are, in general, larger than the true frequencies (e.g., rare alleles are often lost) and simulating founder genotypes using these estimated frequencies results in the simulated estimates of being slightly more biased than the actual data. The final result is a slight overcorrection. The ideal solution would be to use allele frequencies determined not from the study sample itself but from the population from which the founders originated.
The distribution problem is solved by assuming that the distributions of Spairs and have the same shape, but different variance. Normalizing both Spairs and to have a variance of one would allow one to compare to the distribution of Spairs. I estimate the variance of from the values of obtained from the bias estimation procedure. A new statistic is defined as . The statistic can now be compared directly against the empirical distribution obtained for to obtain an approximate P-value. The amount of computation per marker now includes a single analysis of the real data and analysis of Nsim simulated data sets with allele frequencies and marker informativeness based on the real marker data. Note that in the case where the founder-allele frequencies are known, adjusting for the bias is unnecessary, but simulations are still needed to estimate . The procedure of adjusting the bias and normalizing the variance has the benefit that now (and, hence, the approximate P-value) is directly comparable across all markers, regardless of markers' allele-frequency distributions. This is unlike , where the distribution depends significantly on the informativeness and allele frequencies of the marker.
In practice, the assumption that the shapes of the distribution for Spairs and are identical does not always hold for very large values of the statistics, where P-values are very small. In this case, the approximate P-value obtained using the above method tends to be highly conservative. Estimates for very small P-values can be obtained empirically by doing many simulations under the null hypothesis, using either the given or the estimated allele frequencies. Although many simulations are needed, the method is fast enough to be able to determine the empirical distribution of a marker under the null hypothesis for a small number of markers.
Simulations were done to test the accuracy and validity of the proposed methods. Genotype data for a designated set of individuals were obtained by assigning the founders of a pedigree a genotype at a single locus on the basis of given allele frequencies and allowing these alleles to "drop" through the pedigree according to Mendelian inheritance. Only a single locus (i.e., not multiple linked markers) was simulated. Three different types of markers were used in the simulations. The first was a single-nucleotide polymorphism (SNP) having two alleles of equal frequency. The second marker represented a microsatellite and had five equifrequent alleles. The third marker was meant to be representative of a "super marker," where each allele is actually a haplotype of tightly linked SNPs. The strategy of using haplotypes as alleles of a marker provides a straightforward means of using multipoint data to increase information about the inheritance process. Hence, the marker has 21 alleles with allele frequencies given by 2 × 0.2, 0.12, 0.07, 0.06, 0.05, 15 × 0.02. This allele-frequency distribution was chosen as being approximately representative of haplotype distributions for 90-kb segments on the basis of HAPMAP data for Caucasians.
Using both the method proposed here and an exact computation as done by MERLIN (Abecasis et al. 2002), I checked the accuracy of the proposed method by estimating the number of alleles shared IBD for the two individuals in the pedigree shown by solid symbols in Figure 1. For each of the three types of markers, 1000 simulations were done with the genotypes from the top two generations removed and 10% of the remaining genotypes randomly set to be missing. For the purposes of the proposed method, then, all individuals in the third generation from the top were considered quasi-founders. Both exact and approximate estimates of the number of alleles shared IBD were computed for each simulation with the results shown in Figure 2. The plots show good agreement between the approximate and the exact computations with the square root of the mean squared error being 0.024, 0.049, and 0.044 for the SNP, microsatellite, and haplotype markers, respectively.
The above methods were applied to simulated data sets in a large, complex pedigree taken from the Hutterite population. The Hutterites are an isolated religious sect that originated in the Tyrolean Alps during the 1500s and now largely reside in the northern United States and western Canada (Mange 1964; Hostetler 1974). The pedigree used here is an extension of the pedigree described in Abney et al. (2000), comprising 3028 individuals in 13 generations. To assess the efficacy of the bias-correcting and scaling procedures, simulations were done with 700 individuals' assigned genotypes. These 700 are the same sample that is currently being genotyped using the Affymetrix 500k SNP array. From this group of 700, 148 have been diagnosed with bronchial hyperresponsiveness and were labeled as "affected." Figures 3 and 4 show the histograms of Spairs and from 10,000 simulations with the haplotype marker before and after the bias-correction and scaling procedure was applied. The distributions in Figure 4 are fairly well matched over much of the range of statistic values, indicating that the scaled distribution of Spairs can be used as a reference distribution from which approximate P-values can be obtained. It is also evident that Spairs has a heavier tail at very large values, resulting in generally conservative estimates for very small approximate P-values.
The main utility of the bias-correction and scaling procedure is to put all markers in the study, regardless of informativeness, on a common scale over which they may be compared. This allows one to select the best markers to follow up with an empirical analysis by choosing those with the largest (or, equivalently, those with the smallest approximate P-value). Figure 5 compares the distributions of for the microsatellite and SNP markers over 10,000 simulations. The two distributions show good agreement, suggesting is a reliable measure for selecting the markers that have the largest amount of IBD sharing. In Figure 6 the distribution of for the haplotype marker is compared against the distributions of the microsatellite and SNP markers. In this case, where the allele-frequency distributions of the markers are radically different, the distributions do not compare as well, although the microsatellite marker distribution is notably closer to the haplotype marker distribution than is the SNP marker distribution. Most genetic mapping studies, however, tend to have markers with allele-frequency distributions that are relatively similar (e.g., all SNPs, all microsatellites, or possibly a mixture of the two), suggesting that will generally be an effective measure of sharing across markers. It is worth noting that the haplotype marker allele-frequency distribution, with many alleles with small frequencies, presents the most challenging scenario when trying to estimate the bias and scale of the distributions. Inevitably, genetic drift within the sampled population results in a number of lost alleles and frequencies within the current population that may not be very representative of the frequencies in the founding population. This results in inefficiency in the bootstrapping method used and a less accurate estimate of the bias of .
To check the type-I error rate of the empirical P-value estimates, 5000 replicates were generated for each marker type in the Hutterite pedigree. In each replicate 910 individuals in the bottom three to four generations of the pedigree were assigned genotypes and analyses were done with 71 individuals assigned as affected, the same individuals as were previously diagnosed with asthma in this population (Ober et al. 2000). In each replicate the empirical P-value of the marker was estimated on the basis of 5000 simulations. Two analyses were done within each replicate, one where 10% of the genotype data was removed at random to emulate missing data and another with no missing genotypes in the sample individuals. Results are in Table 1 and, when there are no missing data, show good agreement with the nominal type I error. With 10% of data missing, the empirical P-values are slightly conservative. This results from the empirical distribution being computed under simulations with no missing data. Although this results in slightly conservative P-values, the computation time can be significantly reduced when doing 10,000–100,000 simulations. Optionally, with data sets that can be analyzed quickly, one can condition on a particular set of individuals having missing data to obtain more accurate empirical P-values.
Asthma data set:
A genome screen for asthma using 563 markers, including both microsatellites and SNPs, that was previously published (Ober et al. 2000) was reanalyzed using the method described here. In the previous analysis, the pedigree was divided into 20 subpedigrees with all inbreeding loops trimmed. A single-point, semiparametric method was used where a likelihood was maximized over parameters representing the penetrances, disease-susceptibility allele frequency, and recombination frequency. A likelihood-ratio χ2 was obtained by comparing to a maximized likelihood where the recombination frequency was set to 0.5. Because of the size of the subpedigrees, each marker was analyzed separately. This analysis resulted in five markers with P-values <0.001 with the smallest P-value being 0.0002.
The genome screen data were analyzed using the methods described here and approximate P-values were obtained for each marker. Four markers had approximate P-values <0.01 and these were selected for follow-up with empirical P-value estimates. Empirical P-values were estimated on the basis of 100,000 simulations for each marker. Results for these four markers are shown in Table 2. Three of the four markers had smaller P-values than the smallest P-value of the previous analysis with two being much more significant. There was no overlap between these markers and the five markers reported previously. Approximate P-values for the five markers identified earlier ranged from 0.13 to 0.65. Of the four markers identified with the new method all had P-values >0.05 in the old analysis except for D5S1505, which had a P-value of 0.0441. That the markers found to have significant linkage in the two studies are different is not surprising, considering the very different methods used. The previous analysis finds markers that show some evidence for linkage under some genetic model in at least some of the subpedigrees. Although this may, it does not necessarily indicate higher than expected levels of IBD sharing among affecteds when looking at the pedigree as a whole, which is what the current method detects.
I also assessed the computation time required to do the analyses. These were accomplished on an AMD Opteron 252 at 2.6 GHz, running Linux 2.6. The exact computation of the number of alleles shared IBD, as done by MERLIN, for 1000 simulations, took 9.4 × 104, 3930, and 2880 sec for the SNP, microsatellite, and haplotype markers, respectively. In contrast, the approximate computations took 0.4, 0.2, and 1.5 sec for the same data sets. The empirical P-value estimates, using the asthma sample, took 41, 9.5, and 7 hr to estimate P-values for 1000 markers, for the SNP, microsatellite, and haplotype markers, respectively, where the estimates were based on 5000 replicates for each marker. That is, 5 × 106 estimates of IBD sharing were computed over all 2556 pairs, averaging 0.03, 0.0068, and 0.0052 sec per estimate. When analyzing the real genotype data for the asthma sample, where markers consisted of both microsatellites and SNPs of varying informativeness, each estimate of took ∼0.074 sec. This corresponds to obtaining approximate P-values in a genome screen of 1000 markers, with bias estimated using 50 simulations for each marker, in ∼1 hr. In contrast, obtaining empirical P-values based on 100,000 replicates took ∼2 hr per marker.
Linkage mapping in very large and complex pedigrees has been a computationally daunting task. The methods proposed here are a significant step forward in making the estimation of IBD sharing feasible in pedigrees of even extremely large size and complexity. This is possible, in part, by focusing on computing pairwise IBD probabilities, rather than computing the entire distribution of IBD sharing among all individuals, and by implementing a single-point method. Also, a great deal of computational effort is saved by doing computations only on the set of quasi-founders and their descendants and using precomputed values of the identity coefficients to determine the sharing probabilities among the quasi-founders. This allows for efficient computation even when there are many generations of untyped individuals at the top of the pedigree. Although determining the identity coefficients in the quasi-founders can also be computationally challenging if the pedigree is very large, recently developed methods can accomplish this very efficiently (e.g., identity coefficients for all pairs in the genotyped sample from the pedigree described above can be done in <1 day) (M. Abney, unpublished data). The most significant weakness of this approach is the single-point nature of the method. However, being able to do a single-point computation is often an integral part of a more general multipoint method. Indeed, as described in the appendix, I have used the method described here to extend the multipoint HBD method (Abney et al. 2002) to use the genotype data from all individuals in the pedigree. Nevertheless, even a single-point method of estimating IBD can prove useful. In particular, as markers become more informative the amount of information gained from a multipoint method decreases. Tightly linked SNPs, for instance, can be combined into haplotypes that can be treated as alleles of a highly informative super marker. Such a super marker would require inferring haplotypes from SNPs that have not recombined in the pedigree. This can be a challenging task in and of itself, but a number of methods have been proposed recently to address this problem (O'Connell 2000; Windig and Meuwissen 2004; Zhang et al. 2005; Baruch et al. 2006; Albers et al. 2007).
A direct application of the method is linkage mapping for qualitative traits. In this case, one computes the statistic for affected individuals and determines significance from a simulated distribution. There are a number of challenges inherent in accomplishing this, using pedigrees such as the one described here. A major difficulty is determining the distribution of the statistic . Because studies involving large pedigrees often are restricted to a single, or a few, pedigrees rather than many independent ones, the usual central limit theorem argument may not lead to an accurate approximation of the null distribution. Without a theoretical basis for the nature of the distribution, we must simulate to determine its characteristics under the null. Because an empirical distribution for a marker depends on the characteristics of that particular marker (e.g., founder allele frequencies, rates of missing data, etc.), one would, in principle, need to determine the null distribution for each marker in the study. This approach is problematic not only when there are many markers, but also for any single marker if the founder allele frequencies are not known. Here, I propose an alternative approach that may be used even when the number of markers is large. The distribution for a marker with perfect information is determined through simulation and scaled to have a mean of zero and a variance of one. The score at a marker is then shifted—to remove bias—and scaled to also have a variance of one, on the basis of a limited number of simulations. If the shape of the perfect marker distribution matches that of the real marker, then this provides a computationally efficient means of obtaining a reference distribution for and an approximate P-value. Although the approximate P-values obtained in this manner are fairly accurate over much of the 0–1 interval, the P-values tend to become increasingly conservative as they approach zero. Nevertheless, being able to obtain rapid estimates of the P-value allows one to select those "best" markers for which to obtain a more accurate, empirical P-value from a large number of simulations. Note that when allele frequencies are estimated from the data, additional error beyond the Monte Carlo uncertainty of simulations is introduced due to the bootstrap nature of simulating data conditional on the estimated allele frequencies. If at all possible, then, it is best to obtain population allele frequencies that are independent of the data. A further complication of the need to do simulations to obtain a P-value is the difficulty of including genotyping error. Although it is straightforward to include genotyping error in the computation for IBD, when estimating significance, genotyping error would also have to be included in the simulations. An accurate P-value, then, necessitates simulating from a genotyping error model that is representative of the actual errors in the data. Because determination of this model may be difficult, at present the best strategy is to take any necessary precautions to ensure that errors in the genotype data are minimized.
Although the current method obtains P-values that are smaller than those done in an earlier analysis with different methods, these results do not directly address the question of the relative power of the two approaches. The merits of the proposed method, however, can be evaluated in light of the findings of the Genetic Analysis Workshop 12, where the asthma data set described here was analyzed by a number of different research groups. As summarized by Chapman and Wijsman (2001, pp. S222–S223), none of the groups were able to perform linkage analysis on the entire, intact pedigree, including those who used Markov chain Monte Carlo or regression-based approaches that are normally capable of handling large genealogies. They also suggest that two lessons could be learned from the results as a whole: "First, the results were sensitive to the method used to simplify the pedigree." They conclude that "minimal simplification of the pedigree is desirable. In general, stronger linkage signals came from data sets that used larger sub-pedigrees." Second, they conclude that "the method used to simplify the pedigree may be more important than the exact method of analysis used." The method described here is unique and advantageous in that it is capable of performing linkage mapping without any pedigree simplification. This should not only maximize the power but also avoid the difficulties of both creating appropriate subpedigrees and interpreting the results when multiple pedigree splittings have been analyzed. A power comparison with other methods involving possible pedigree simplification strategies (Falchi et al. 2004; Brocklebank et al. 2007; Liu et al. 2008) and genetic models would, nevertheless, be informative and will be pursued in future work.
In addition to linkage mapping for a qualitative trait, the proposed IBD estimation method is directly applicable to quantitative trait linkage mapping based on variance components (Amos 1994; Almasy and Blangero 1998). There, the covariance due to a quantitative trait locus (QTL) is modeled by the IBD sharing between all pairs of individuals in the pedigree. The method described here would allow rapid determination of the QTL covariance matrix for pedigrees that have been too large to consider as a whole. The variance component mapping strategy is, in many ways, considerably more straightforward than the Spairs linkage mapping approach. Because the hypothesis test is not based explicitly on the degree of sharing estimated, the problems associated with determining the proper distribution of the statistic (e.g., bias) are avoided. Although bias will still exist in the IBD estimates, if allele frequencies are estimated, the amount of bias for any particular pair will generally be small. In contrast, the bias when computing can be large because it is the sum over very many pairs, each of which has a small amount of bias. Furthermore, an empirical distribution for the sharing statistic need not be constructed to determine statistical significance. The consequence is that it is not necessary to do the simulations at each marker to determine the bias and variance of the statistic.
The utility of a method that addresses a computationally difficult problem depends critically on the time it takes to solve the problem, particularly when many analyses and simulations are necessary. The above methods have been implemented in freely available software coded in C (available at http://www.genes.uchicago.edu/abney.html) that can analyze the data presented here with, as yet, unprecedented speed. The analyses accomplished here, using both simulated and real data, show that it is possible to analyze large data sets (∼700 genotyped individuals, ∼150 affecteds) in a large pedigree (∼3000 individuals) on a timescale of hours for thousands of markers. As far as I am aware, there are no other available methods that can perform linkage mapping with this quantity of data on such a large, unbroken pedigree in any reasonable length of time. With the methods and software tools introduced here researchers with large, complex pedigrees will be able to leverage their genetic data to a degree that was not possible before.
When the above algorithm is applied to the two alleles in a single individual, it provides an estimate of the probability of that individual being HBD conditional on the entire pedigree and all ancestral genotype data at that locus. A previous method (Abney et al. 2002) computed this probability given the pedigree and the multipoint genotype data of that individual, while the ancestral genotype data were ignored. Here I describe how to extend the HMM in Abney et al. (2002) to include ancestral genotype data.
An HMM is normally defined in the following way (Baum 1972; Rabiner 1989). Letwhere Ok are the observed genotypes at marker k, Qk is the true HBD state (i.e., HBD or not HBD) at marker k, and M is the number of genotyped markers. These variables follow the recurrence formulaswhere Tij is the transition probabilities between states i and j. The probability of HBD at marker t is(A1)Note that the quantity Pr(Ok+1 | Qk+1 = i) in the recurrence equations is the probability of all the genotype data at the marker given the HBD state of a single individual. To use the single-point algorithm that now includes ancestral genotype data, the HMM is modified so that the probabilities found in the recurrence formulas are rewritten using Bayes' rule,The probability Pr(Qk = I | Ok) is computed as described in the methods section, and Pr(Qk) is the inbreeding coefficient. We do not need to compute the unconditional probability of the observed genotype data at the marker Pr(Ok) because it cancels out in Equation A1. The result is a method for computing multipoint HBD given all of an individual's ancestral genotype data and the entire pedigree. These probabilities can then be used in the homozygosity mapping method discussed in Abney et al. (2002).
I thank Carole Ober for allowing me to use the Hutterite pedigree and asthma data and Don Conrad for his assistance in evaluating haplotype frequencies in the HAPMAP data. This work was supported by National Institutes of Health grant HG002899.
Communicating editor: R. W. Doerge
- Received April 4, 2008.
- Accepted May 2, 2008.
- Copyright © 2008 by the Genetics Society of America


text:
现在位置: 首页 > reviewingwriting > 文章
2019年04月16日 ⁄ reviewingwriting ⁄ 共 5662字 ⁄ 暂无评论
In the event you still are employed on the proper time of the interview, embrace how a lot you would favor this opportunity because it delivers a problem and pleasure. The supplier is designed with a energetic reply where precisely shoppers can discover tailor made printed paperwork at reasonable prices. Along with just offering up this type of system, anybody can within the process have speedy...阅读全文
2019年04月15日 ⁄ reviewingwriting ⁄ 共 5538字 ⁄ 暂无评论
At our business, you can purchase a customized made college assignment ready notably and mainly for do your homework you by our personal expert freelance writers. All learners have the ability to faculty solely to be astonished each time a coach informs them there are particular codecs for composing a key phrase newspaper. If they've offered their accreditations, these are normally normally mot...阅读全文
2019年04月15日 ⁄ reviewingwriting ⁄ 共 4044字 ⁄ 暂无评论
Very unusual is the teenager who is devoid of character yet college or university essays typically seem like they have been compiled by somebody putting on an obnoxiously over-starched tuxedo whereas dealing with a firing squad. I used the superb CMA evaluate supplies from Gleim to prepare for my CMA examinations and acquired the ICMA Gold Medal for achieving the very best scores on the earth i...阅读全文
2019年04月15日 ⁄ reviewingwriting ⁄ 共 6320字 ⁄ 暂无评论
Our main writing service provides customized written papers in eighty+ disciplines. LP: And your interviewer can take notes and can do their best, however at the end of the day, maybe you've interviewed 5 other folks and actually loads of instances issues all sound the same, everybody says they're arduous-working, everyone says that they are passionate, it's like, we get that. You want a distin...阅读全文
2019年04月15日 ⁄ reviewingwriting ⁄ 共 4690字 ⁄ 暂无评论
Are you out of the university and instantly obtained important to make an essay? Related Post: advice If a bot had a plot, then perhaps readers can be motivated to complete it, similar to the text-based mostly iOS adventure sport Lifeline Ultimately, the problem with literary bots is likely to be the identical that plagued the nice cul-de-sac of hypertext literature : the initiatives are extr...阅读全文
2019年04月14日 ⁄ reviewingwriting ⁄ 共 4915字 ⁄ 暂无评论
Papercheck provides enhancing and proofreading companies. Funds made with credit cards, bank wires or private checks are exempt from these policies. To file this report, JM Bullion must fill out IRS Kind 8300 , through which we're required to provide each your data as well as the details papercheck of the transaction. Please rest assured that we solely doc the cost portion of the transaction, n...阅读全文
2019年04月14日 ⁄ reviewingwriting ⁄ 共 4109字 ⁄ 暂无评论
Get your genuine research paper written from scratch by the professional writer. Get 10% Off for All Orders with this Coupon Code. Technically, writing an annotated bibliography still means making an inventory of sources. On-line writing services seem unreliable to many students - simply assume how terrible it might be to get a chunk of copied writing as a substitute of an authentic paper based...阅读全文
2019年04月14日 ⁄ reviewingwriting ⁄ 共 7273字 ⁄ 暂无评论
It isn't a simple job for a pupil to prepare a evaluation paper of the easiest high quality, it takes numerous efforts, vitality and dedication. In case you're having a look at this net page, you're absolutely conscious that a dissertation is the epitome of excellence in academia. Related Submit: learn here In case you are looking out for best customized dissertation source on the World Large I...阅读全文
2019年04月12日 ⁄ reviewingwriting ⁄ 共 4977字 ⁄ 暂无评论
What is 123helpme? There are no customer expertise representatives there. The whole website is administrating by means of one small contact window and electronic 123 help me mail notifications. There are a few managers that work at some explicit time. Get ready to attend a few days to get a easy answer. 124. Essay Have () Active, unchanged. Not parked by GoDaddy", by February 20, 2016. Tackle a...阅读全文
2019年04月11日 ⁄ reviewingwriting ⁄ 共 4425字 ⁄ 暂无评论
Is a comprehensive on-line instructional useful resource. Studypool has helped 1, students. An individual that helps you along with your homework - aktywni z psami. Is to assist on-line programs offering tutoring help for science skilled pc science tutors prepared to use our computer science homework assist and studying ability enotes reviewingwriting. Don't just ask for homework assist, tweet ...阅读全文

subset: commoncrawl


text:
Weight - 11st 3 1/2lbs- A loss of 1/2lb since last week making 19lbs loss total.
Body fat - 35% - No change since last week/5% total loss
No change on chest/hips
1/4in lost from my waist making 4 1/4in total loss.
I wasn't expecting to lose anything (weight or inches) this week so to see losses on weight and waist was great. I am so close to weighing less than my husband. Crazy goal but for such a long time now (about 12 years) I have weighed more than him. Anything up to 4 1/2 stone more. He is 6 inches taller than me so it shows. So no matter how crazy that is my next goal. To weigh less than my husband. His weight varies depending on how much triathlon training he is doing. At the moment he is in a not training much state which means he is at the upper end of his normal weight. In another 4lbs I will be less than him (unless he starts full on training again before then in which case I am frying all his food and making him eat cake after every meal!). The lower end for him is about 10st 7lbs. Once I have got to less than his current weight I will be aiming for that as my goal before moving on to the next one.
I ran last night. I was going to swim but while Bookworm had her lesson I took Hyperboy swimming. I really didn't want to have to get back in my wet costume after getting dressed to hand children over to my husband to take home so decided to head straight home then run. I covered just over 4km in 26m 15s. I felt so good about that. It was 2 minutes faster than the same distance last week. The last part of my run is a long incline and my legs just won't do that at the end yet. I covered the whole 5.12k route from home to home in just over 33m with only 4 minutes of walking. Go me.
I have 1 1/2 weeks to go until the 5k I have entered.When I entered it I had an aim in my head of completing it. Once I realised I was definitely going to be able to do that I decided that I would be happy with being able to finish it in 45 minutes. As I realised that was going to be easily do-able I decided that I am aiming for running the whole thing. While I haven't quite covered that distance yet I really feel that I can and if I can do it in under 35 minutes I will be over the moon. I find it much easier to keep on running when I have someone to follow. Last night if you were running round my local park with your other half you may well have had a heavy breathing, red-faced woman following you for about 1k. I'm not a scary stalker person, I was just using you ahead of me as my focus so I could keep going.
Food is still a bit up and down at the moment. I start each day with the intention to eat right but I am finding it hard to keep away from chocolate and cakes. The only reason I am still losing is because of the exercise. I know that I will get back to the state of having the eating going right but for now I have set my weight loss goal on myfitnesspal at maintaining. I may not be able to stick at the losing goals right now but there is no way I am reversing back up the road away from what I have achieved so far. The place I have reached for now is too damn nice to throw it all away.


text:
In the week leading up to the midterm elections, Washington, D.C., journalists and pundits were focused on one politician: President Trump. Trump is not up for re-election until 2020, but the media continues to view the president as a key player in this year's election.
The Fourth Branch's mentions of the president rose to nearly 1,400 tweets this week, compared to only 529 tweets that discussed voting or the election. It appears the media sees the midterms as a referendum on the president.
Tomorrow, we will see what the country decides.


text:
In an exciting and ironic turn of events, tonight on 24:
Dennis Hopper as Serbian ultra-baddie Victor Drazen SHOT THE HOSTAGE!
Yep! He totally foiled Kiefer (who was not on tonights episode nearly enough).
Oh, and Kim was kidnapped, again.
Next week, BadMuthaKiefer gets down with his bad self. Hoo-HAH!
God, I love this show.off topic | from inside the mind of krix at May 07, 2002 10:31 PM .
I kept thinking, "at least take that damn sack off his head so we can see him!" Jack was SO not gonna cut that girl's throat, and Drazen shot her anyway. Now that Jack's free I can't wait til next Tuesday.
Hey, BTW, what's up with stuff you posted yesterday? It takes forever to load for me when I try to open it, and yesterday the whole site took forever to come up.Posted by: Lori on May 8, 2002 09:42 AM
I'm not sure what's going on, maybe the server was just slow yesterday.


text:
Choose your room
Located in Cusco (Cusco Historic Center), Hostal Valicha Wasi is minutes from Centro de Textiles and Qorikancha. This hotel is within close proximity of Temple of the Sun and Cusco Craft Center. Make use of convenient amenities, which include complimentary wireless Internet access and tour/ticket assistance. Guests can catch a ride to nearby destinations on the area shuttle (surcharge). Featured amenities include a business center, a 24-hour front desk, and multilingual staff. A roundtrip airport shuttle is provided for a surcharge (available on request). Stay in one of 26 guestrooms featuring plasma televisions. Complimentary wireless Internet access keeps you connected, and cable programming is available for your entertainment. Bathrooms have showers and hair dryers. Conveniences include phones, housekeeping is provided daily, and you can request cribs/infant beds (complimentary).


text:
Good day,
There are various products that Afrihost offer that will give you a wifi connection:-
- Fibre (https://www.afrihost.com/fibre/uncapped)
- Fixed wireless (https://www.afrihost.com/landing/rain_fixed_wireless/)
- Mobile devices and data (https://www.afrihost.com/site/product/mobile_data) (https://www.afrihost.com/site/hardware/mobile_hardware/#/)
As you have put this under the ADSL category, here is what you need for an ADSL connection:
You must have a post - paid / excon (no contract) Telkom voice line installed before you can use Afrihost's services. Please be sure you do not sign up for a contract with Telkom or any other service provider.
You could either choose to get the ADSL and voice line installed directly through Telkom or get the ADSL line installed by Afrihost (this takes 14-30 working day waiting period).
You then need to decide if you wish to leave the line with Telkom and only get data through Afrihost, or you can move the line to Afrihost, for Afrihost to manage both your line and data.
Bundled means your Telkom DSL Line is included in the sign up
- To sign up for a bundled ADSL line
You will then need to choose an ADSL package. You can choose between Capped or Uncapped DSL either Home, Premium or Business packages.
Please follow this link for uncapped bundled packaged (https://www.afrihost.com/site/product/dsl_uncapped_bundles)
Please follow this link for capped bundled packages (https://www.afrihost.com/site/product/capped_dsl_bundles)
Please note that you will be charged a pro-rata billing when your line has been transferred to us, this process usually takes 10-14 days and your line does not go off in the process.
When signing up with Afrihost please specify that it is a new convert or migrate in from another ISP and we will ensure it is activated on your side so you are able to use data.
Once you have decided then you can easily sign up online:
1. Select from the capped or uncapped options above
2. Select the line speed and data package you want. Using the
3. Select your package and click on the "Sign up Now!" button
4. This will take you to Client Zone. Confirm the Connectivity type, DSL line and Connectivity package are all correct and proceed to next step.
5. Complete the sign up steps that follow and check out.
If you require further assistance please
send a message to our whatsapp help line: https://whatsapp.afrihost.com
or visit our Help Centre: https://www.afrihost.com/site/help_centre
or see our FAQ page: http://faq.afrihost.com
Thank you
Recommend the latest Huawei E5885Ls-93a mobile WiFi hotspot.


text:
Gold mine stamp mill in Bodie, CA Gold collaboration seal stamp illustration Gold Wanted rubber stamp Gold Wanted rubber stamp Gold Wanted rubber stamp Gold WantedGet Price
Stamp Mill Distributors In South Africa gold stamp mill manufacturers in South Africa,used Gold Rush Mining Equipment and Gold Stamp Mill for Sale in SouthGet Price
We have passed the sign for Reed Gold Mine a dozen times but never visited. CharlotteFive Podcast; Stamp mill. This 121 year oldGet Price
for steel stamp mills: good metal manufacturers, possible production of stamps For this reason, the use of the stamp mill in metal mining, except for gold ores,Get Price
Mining mills for sale,Mining equipment for sale,Mining machine for SBM Company has been making and export crusher and grinding mill for more than 20 years, mainGet Price
Stamp MillRitchieWiki . Several stamps were often lined up in stamp mills where gold bearing ore, gathered from hard rock gold mining, ↑ Stamp Mill.Get Price
Ward, Colorado, history and culture of an old gold mining town in the Front Range of the Duncan Family at the Dew Drop Mine. Inside a stamp mill. Ward, ColoradoGet Price
· gold stamp mill suppliers gauteng Crusher News. gold stamp mill suppliers gauteng. The Zenith Mining Machine is custom designed to reduce your operatingGet Price
gold ore mobile crushers made in south africa . Latest Events. service tax category of stone crusher; contoh jurnal mengenai proses grinding; industrial belt feedGet Price
HISTORIC GOLD MINE FOR SALE!!! GOVERNOR MINE NEARBY GOLD MINE OPERATIONS $100,000 in gold. A five stamp mill was then in operation.Get Price
portable gold mills south africa. portable gold ore grinder Gold Stamp mill Ciros Gold Ore Crusher, Mining Process, Gold Hammer mills are actually crushers, notGet Price
To get more information about gold stamp mill for sale, Please stamp mill sale, drum crusher gold mining, plaster crusher South Africa,ball mills forGet Price
Industry News. grinding mill suppliers in zimbabwe Solution for ore mining . grinding mills in zimbabwe – Grinding Mill China. Cost of gold stamp mills in zimbabweGet Price
gold ore stamp mill design mining stamp mill design. small scall mining stamp mill design south africa 60mm grind balls gold ore,Ball mill for GOLDGet Price
Bodie's source of gold came from hard rock mining – mining that requires breaking apart ore to extract gold that's intermingled with the rock. The Stamp Mill.Get Price
Gold Mountain Mine & Mill Desert. photo tour of stamp mill ruins at lucky baldwin mine Big Bear California. Chat Online; Mining Claims and Mill Sites BureauGet Price
Quincy Mine Stamp Mill Henan Mining Prompt : Caesar is a famous mining equipment manufacturer well known both at home and abroad, major in producing stoneGet Price
Geology Gold Mines Desert Mining History Stamp Mill A stamp mill was a mechanical crusher, noisy, heavy and somewhat awkward to operate. The stamps were heavy metal .Get Price
Stamp Mill South Africa,Mining Gold Stamp Mill for sale in Zimbabwe. A stamp mill was a mechanical crusher, noisy, heavy and somewhat awkward to operate.Get Price
Job Interview Online Practice Tests. Get Prepared For Any Interview in only 30 minutes! Because you may not have a lot of time to prepare, we've designed a focusedGet Price
gold rush mining stamp mill gold rush era stamp mills india Crusher&mill gold rush era stamp mills; Early Gold Mining Methods,Get Price
E Clampus Vitus ecv Major William Downie Chapter 1849 Downie Chapter Del Norte and Scotia Mine Company Stamp Mill to supply equipment to Gold RushGet Price
How Gold Mining in North Georgia Was Affected by the Civil War By Anne Dismukes Amerson When gold was first discovered in north Georgia in An abandoned stamp mill.Get Price
Stock Footage of Gold Mining Stamp Mill in OperationGet Price


text:
Irishwoman claims second London attacker was also in Ireland
Convert 'Sister Aaliya' says at least 150 radicalised Muslims living in Ireland
A second of the three men who killed eight people in the terror attack in London last weekend spent some time in Ireland, according to an Irish-born woman who was radicalised and who claims to have met him here.
The 26-year-old woman, originally from the Limerick area and a convert to Islam, said she met British citizen Khuram Shazad Butt and other extremists about 20 times in Ireland and the UK about 2½ years ago. Several of these meetings included Butt. This included a meeting at a house in the Santry area of Dublin, about 2½ years ago, she claimed.
She spoke at a press conference held by the Irish Muslim Peace and Integration Council in the Al-Mustafa Islamic Centre in Blanchardstown in west Dublin on Friday.
Chairman of the council and head imam at the centre, Shaykh Dr Umar Al-Qadri, said Sister Aaliya, a convert to Islam at age 18, had been successfully de-radicalised by a Muslim scholar at at mosque in London.
The three people named as responsible for the London attack on June 3rd were Khuram Shazad Butt, Rachid Redouane and Youssef Zaghba. It has already been confirmed that Redouane, a 30-year-old Moroccan-Libyan pastry chef, had until recently been living in Dublin.
The 27-year-old British citizen Butt, who was born in Pakistan, was known to the police and MI5 and was the subject of an investigation in 2015.
The woman, who identified herself only as Sister Aaliya and who wore sunglasses and black niqab covering the lower part of her face during the press conference, said she did not know Redouane.
She said she feared for her safety and had been threatened several times by the extremists. She had been in a relationship with a man who associated with extremists for about 10 months. She said the man was "very controlling" and she had fled London late last year . "I've been threatened on numerous occasions . . . I came back to Ireland to get away from all that."
Asked what the extremists she met in Dublin had discussed, the woman said she had been excluded from meetings they had and that they discussed things in their own language, but that their dream was "to have an army for jihad".
She also claimed there were at least 150 radicalised Muslims living in Ireland. She alleged some extremists were coming in to Ireland on buses and via Belfast to avoid immigration.
Dr Al-Qadri told several hundred men and boys attending Friday prayers at the mosque that those extremists who said they were engaged in jihad were perverting Islam. He told them not to be afraid to challenge those individuals in their communities.
"Because if we don't challenge these individuals what will happen is they will slowly spread their cancerous ideology to others and one way to tackle this, to refute this radicalisation is education," he said.
Asked about the claims made at the press conference, An Garda Síochána said the force continued to liaise closely with security and law enforcement agencies in the UK and internationally "to share and assess any relevant intelligence and provide assistance where appropriate".


text:
New product
The water stream down to the class cup with few river stone surrounded and then travels downward into the base. Water Glass fountain brings the calming feeling and the soft sound of cascading water to your desk.
Product (Item) Number: EWF1106097
In stock
Warning: Last items in stock!
Availability date:
Equipment Include:


text:
Welcome parents of Height's Students!!! This blog is a venture that we as a staff have been thinking and praying about for a while and are extremely excited to begin. You got a little taster of the blog during Beach Camp 2014, but this time we are back for good and will be posting weekly! You may have some questions as to "what is a blog?", "what is the purpose of this blog?", or "why should I read this?" Those are great questions that I am going to answer to the best of my ability in order to cast the vision of what we envisage this space looking like. Here we go!
What is a blog?
A blog is a website in which individuals regularly record opinions, offers tips, and provide resources on whatever their platform is.
What is the purpose of this blog?
This blog is birthed out of an increased desire to better support the parents of our students. As our ministry grows, our burdening to build relationships with and walk along side you as parents has grown exponentially. We believe wholeheartedly in the Biblical view of parents as the primary discipler in a child's life. Just as a Momma bird feeds her baby birds and teaches them everything they need to know to thrive, you get the beautiful opportunity to feed and teach your children everything they need to know to thrive in life. This includes teaching, modeling, and investing in their relationship with Jesus. This passage of Scripture paints the picture of the call God has placed upon parents much better than I can—
"Hear, O Israel: The Lord our God, the Lord is one. You shall love the Lord your God with all your heart and with all your soul and with all your might. And these words that I command you today shall be on your heart. You shall teach them diligently to your children, and shall talk of them when you sit in your house, and when you walk by the way, and when you lie down, and when you rise. You shall bind them as a sign on your hand, and they shall be as frontlets between your eyes. You shall write them on the doorposts of your house and on your gates." Deuteronomy 6:4-9
You may have read this passage before and feel confident in your ability to disciple your children. Or you may have read this passage before and still have absolutely no idea how to invest in your child's relationship with Jesus. Or you may have never read this passage before and feel really inadequate to live up to this command. Or you may fall into a completely different category. The good news is, whatever category you fall into, you aren't alone. You aren't parenting and discipling your children out of your own ability, strength and understanding. It is all because God's love for you that you are entrusted with the gift of your children. He always equips His people with what they need for the call that He's placed on their life. We, as your church family, want to help you see the tools and resources that He's made available to you as you lovingly point your kids to Jesus in all things. This blog is an avenue for us to do just that!
Why should you read this blog?
- To be equipped with resources to assist you as you disciple your children
- To stay up to date on upcoming events and happening for Height's Students
- To see pictures and read recaps from Height's Students trips or events
- To know what Truths your children are currently being taught
- To be entertained (some of us are pretty funny!)
There we have it, folks—the overall vision for this space! We hope you will find this a helpful tool in the coming days. If you want to follow along, you can sign up to receive email updates every time the blog is updated by simply clicking "follow" at the top of the page. You can comment or email any feedback and/or requests for topics that you would like to see discussed in this space. We love you and are grateful for you, parents. Excited to see what God does through this space!!


text:
What is an MTO account for Michigan and do I need one for each company?
Avalara has sent me a letter asking me to create MTO online filing accounts for Michigan. I have multiple companies, do I need an account for each one?
Avalara Avatax
You need one MTO account for each company that we file for if they are on separate returns with separate FEIN numbers. If you have one parent company and all the others are child companies of the parent filed on the same form you would only need one MTO account.


text:
Folks tend the belief of Sigmund Freud, a natural leather chair, as well as a lengthy therapy of psychoanalysis when they had to begin with, invoke up pictures of therapy. Contemporary therapy, pros point out, does not automatically resemble its own very early origins.
"The area of psychiatric therapy has developed a great deal over a final couple of years," Vilhauer claims. "It is no more what our experts would certainly name a one-size-fits-all style."
Some kinds of therapy exist, pros state, and also, they come under a variety of "universities" of the notion, each along with their ideas and also approaches. Equally, there are actually "various kinds of medicine, or even training class of drugs, for numerous types of anxiety," Vilhauer mentions, "there are a bunch of various forms of psychiatric therapies that folks will make use of to alleviate trouble."
What are Therapy Types
Still, there are two main profound designs of psychiatric therapy: cognitive/behavioral as well as psychodynamic. Psychodynamic therapy concentrates on a person's cold method through possessing that individual to speak openly concerning his/her emotions or even ideas, as well as it targets to look into previous moments that could produce an understanding of current complications. Subtypes of compelling therapy consist of psychoanalysis-- a long-lasting therapy that clients can easily take part in several opportunities a full week-- to temporary psychodynamic therapy, which possesses a 20-session method.
Cognitive/behavioral therapy, on the contrary, is based upon comprehending one's believed procedure or even actions in the here and now as well as determining exactly how inefficient designs in these regions might add to a bigger lifestyle issue. Through obtaining recognition of these believed designs, people may collaborate with counselors to alter all of them. Cognitive/behavioral therapy is a lot more organized than psychodynamic therapy as well as often tend to become briefer in duration, relying on the individual's requirements.
If you decrease the material as well as irrational abnormalities of the mistaken notion designs, and also show individuals to believe regarding the activities of their lifestyle in an even more sensible method, bad emotions such as clinical depression and also anxiousness are going to lessen. Transforming one's habits as well as conforming favorable problem management systems can easily lead and also minimize troublesome routines to an enhancement in total wellness. So, choose the right ACT therapist for you.


text:
15 galleries
Loading ()...
103 images
17 imagesThis series was shot in Westfield, MA. In high school we heard stories of an empty neighborhood- that was watched over by a single crazy man. In high school I found out this was true. As an adult I wandered back there and photographed it.
100 imagesI grew up a mile from the Massachusetts State Police Training Barracks. As a child I would see the officers in training running by our bus stop. I learned to ride my bike in the parking lot of this building. Years later I discovered it was abandoned. It was not an easy place to get into, but was incredibly special to capture.
63 imagesThis shoot was a 50% permission/50% break in. Truthfully not sure what this building previous was utilized for- but its massive open rooms and preserved details kept us engaged for hours.
12 images"The Belchertown State School for the Feeble-Minded was established in 1922 in Belchertown, Massachusetts. It became known for inhumane conditions and poor treatment of its patients, and became the target of a series of lawsuits prior to its eventual closing in 1992. The building complex was listed on the National Register of Historic Places in 1994." - Wikipedia This school was the first Urbex site I discovered, and have returned to several times since. Turning a corner in this place reveals history- the good, the bad, and the ugly.
25 imagesGames and Lanes was a bowling alley, indoor soccer, and arcade all in one. As a child I went here for birthday parties, or friday nights. Years ago it shut down and it has slowly been losing the battle to nature.
50 imagesCamp Windigo is one of those places where the rumors and folklore permeate the internet more than actual history. Some tales exist of ghosts, murders, and famous residents. I am not sure of anything of this- and my research didn't turn anything up- however it was an incredible place to visit, and the air was thick.
22 imagesAnother one of my early Urbex locations. I discovered this during a drive through the Berkshires. The smoke stack always begged attention as it peered over the tree line from the Mass Turnpike. A small detour, and sketchy bridges brings you to this building which is not 100% abandoned. These are the shots I got prior to being chased off the grounds.
13 imagesThis is an exploration of Holyoke, MA. Its not abandoned- its just a mess.
6 imagesAgawam Sportsman's Club was a small venue that had been empty for as long as I can remember. Many times I drove by- one time I got out with my camera.
21 imagesDropped in on this place with only our iPhones. Located on Cape Cod this massive property holds dozens of buildings including bowling alleys, radar sites, missile silos and an entire community which was once thriving. Now its desolate with lots of dead birds.
6 images"The 69th Street Transfer Bridge, part of the West Side Line of the New York Central Railroad, was a dock for car floats which allowed the transfer of railroad cars from the rail line to car floats which crossed the Hudson River to the Weehawken Yards in New Jersey. Its innovative linkspan design kept the boxcars from falling into the river while being loaded.[1] After it fell into disuse, it was in danger of being torn down and removed, but around the year 2000, during renovations of Riverside Park, following the example of Gantry Plaza State Park, it became a prominent feature of the park. It was listed on the National Register of Historic Places in 2003." - Wikipedia
8 imagesA few years back I was lucky enough to get to run around this incredible park. All shots here are from my iPhone, as this was not planned.
9 images
14 images


text:
'Full Moon Fever': Tom Petty's Shining Debut Solo Album
Following their seventh studio set, 1987's platinum-certified Let Me Up (I've Had Enough), Tom Petty briefly took a break from working with his long-term backing group, The Heartbreakers, and joined The Traveling Wilburys. Nothing less than a solid-gold rock'n'roll supergroup, this remarkable, though short-lived, outfit also included Bob Dylan, George Harrison, Roy Orbison and ELO frontman Jeff Lynne, and their debut LP, The Traveling Wilburys Vol.1, peaked at No.3 on the US Billboard 200, where it sold over three million copies. Petty, however, had already announced that his next album would be a solo record, even before he embarked on the sessions for The Traveling Wilburys Vol.1. This controversial decision reputedly provoked mixed emotions among The Heartbreakers, yet all of the band, barring drummer Stan Lynch, eventually contributed to their leader's solo debut, Full Moon Fever, which was released on 24 April 1989.
Listen to Full Moon Fever on Apple Music and Spotify.
Though relaxed and low-key, the Full Moon Fever sessions were also a hotbed of creativity. Primarily tracked in lead guitarist Mike Campbell's garage studio, the songs were mostly laid down by a core group of Petty, Campbell, drummer Phil Jones and producer Jeff Lynne (who played bass and subtle textural keyboards), though the remaining Heartbreakers and two of Petty's fellow Wilburys also pitched in. Roy Orbison made a brief cameo on quirky rocker 'Zombie Zoo', while George Harrison played guitar and added decisive vocal harmonies to the LP's first 45, 'I Won't Back Down'.
Though defiant in tone, 'I Won't Back Down' was also eminently catchy. Its success on the Billboard Hot 100 (where it peaked at No.12) set Full Moon Fever on the road to multi-platinum success. Driven by Mike Campbell's memorable, zig-zagging riffs, the Del Shannon-referencing road song 'Runnin' Down A Dream' quickly followed it into the US Top 30, while the yearning, nostalgic 'Free Fallin'' later peaked at an impressive No.7.
Long-term staples of all self-respecting classic rock radio stations, this evergreen trio of 45s have since dominated reappraisals of their parent album, yet in reality Full Moon Fever was refreshingly filler-free. Indeed, Petty and co were right on the money throughout. Whether they were treading well-worn ground on tough, Heartbreakers-esque rockers ('Depending On You') or veering off on sublime stylistic departures such as the glorious, lullaby-style love song 'Alright For Now', nothing could detour them from the path of greatness.
On the back of its three hits and a string of positive reviews, Full Moon Fever outstripped the success of The Travelling Wilburys Vol.1, peaking at No.3 on the Billboard 200 and going quintuple platinum in North America. Despite stiff competition from 1994's Rick Rubin-produced Wildflowers, it arguably remains the high-water mark of Tom Petty's solo career, though its mainstream pop sensibility remained intact on 1991's robust, Jeff Lynne-produced Heartbreakers reunion, Into The Great Wide Open.
Full Moon Fever can be bought here.
Listen to the best of Tom Petty on Apple Music and Spotify.


text:
NuoDB on Amazon Kubernetes (EKS)
To gain measurable value from your Digital Transformation initiatives, you need to move beyond lightweight workloads and transition your critical applications to the cloud and industry leading container orchestration platform, Kubernetes. NuoDB and AWS Cloud offer a full-stack, cloud-native solution that makes it easier to modernize your existing SQL applications and/or build new ones instead of re-writing your applications for NoSQL, adding caching layers, or force-fitting "oldSQL" architecture into your cloud and container environments.
Try it now
NuoDB Insights
Enable NuoDB Insights to access a dashboard of database and systems metrics to help you optimize your database environment.


text:
It all started off for Brandon in 2015 when he attended the Romsey Mill studio at the Meadows Community Centre. He initially wanted to become and MC but after a few months realised he wasn't particularly gifted in this area and was much was more interested in the tech side of music! He attended Romsey Mill's studio every Thursday; watching KD for the whole hour and hoping to learn something more about music production. Finally, he picked up the courage to ask KD to teach him how to produce beats and since this time has not looked back quickly realising that making music was something that really made him feel alive. Brandon was a quick learner and, after picking up production, mixing and mastering skills, started to move into the field of DJ'ing. Subsequently, Brandon played the opening set for Rapademic 2016 and this was the spingboard for him taking DJ'ing seriously.
In autumn 2016 Brandon started DJ'ing at an under 18's event in Newmarket which, as well as raising his profile, introduced him to successful and well renowned DJ's including DJ Sebadee. The result of this introduction has been an invitation for Brandon to join Sebadee on his upcoming European tour and particularly to open up an event in Bulgaria!
Brandon is committed to pursuing a career as a full-time DJ and is certainly on the right track. As he says himself; "knowing that I have achieved so much through DJ'ing throughout the past year has made me realise just how much potential I have. I have made a lot of friends and contacts all around the UK which can help me a lot to move forward in this career as I leave school this summer."


text:
Between Past Failure and Future Promise: Racial Discrimination and the Education System
The focus of this article is to examine the theme of racial discrimination within the context of education policymaking. It will draw on an ongoing conceptual debate that analyses contemporary education and social policy evidence within an integrationist/multicultural framework, but also analyse the "extreme" concepts of assimilation and anti-racist education policy. The method draws on policy evidence and documentary analysis of the evolution of integration and multiculturalism concepts within education policymaking.
The primary and secondary data sources are education and social policy documents from 1965 up to the present day, from an English and Welsh context. The concepts, as shown in the table below on the education policy in England and Wales, 1950-2007, give readers an idea of where the theme of anti-discrimination sits, or does not sit, in the education policymaking discourse. This article concludes with recommendations on how future promise could be achieved in relation to anti-discrimination education policymaking.
Multiculturalism, as a concept, is still relevant in 2007 and is crucial in social debates concerning cultural diversity and citizenship. It is perhaps even more important after the terrorist attacks of 9/11 (2001) and 7/7 (2005) than it was before. The political discourse and rhetoric of integration sit uncomfortably alongside both multicultural realities, e.g. the civil disturbances in Birmingham (October 2005), Paris (November 2005) and Sydney (December 2005), and the social scientific notions of where multiculturalism positions itself domestically and internationally. The period from 9/11 to 7/7 witnessed global Governments moving toward integrationist approaches concerning political and social policy.
Trevor Phillips, the then Chairperson of the Commission for Racial Equality in the United Kingdom, suggested in 2004 that multiculturalism had brought us in a position of racial segregation, where ethnic groups within London and the United Kingdom live in separate entities with no interaction with each other. "In recent years", he said, "we've focused far too much on the 'multi' and not enough on the common culture." What Phillips called for was a social and cultural debate on the plural realities of British culture, calling for an examination of multiculturalism, racial segregation and what is actually applicable in contemporary society.
Education policy documents provide evidence in how politicians and civil servants, in an English and Welsh context, have handled large influxes of immigrants into the United Kingdom in the recent past. Some of the terminology is significant. In the Education of Immigrants, an education circular published in 1965 and 1971, minority communities are asked to participate and be responsible -- but responsible to whom? Racial stereotypes are reinforced, with West Indian and Pakistani families being singled out for criticism for not being responsible enough. The policy documents do not focus on schools, teachers and the education system itself, and highlight the assimilation and integrationist social discourse of the day. However, despite education policies that helped integration, and local authorities and educationalists who acknowledged the complexity of the issues, the integrationist approach (integration with cultural diversity, as Roy Jenkins described in 1967) predominated until the mid-1970s.
It is worth focusing on the Rampton and Swann reports on education because of what was not achieved, rather than what was. Swann called for greater cultural diversity within the education curriculum -- the focus was not on minority communities but on what was actually being taught in the classroom. The fact that the interim and final reports took eight years to complete suggests "past failure", but again good practice and new initiatives were highlighted by both committees that suggest past successes. Barry Tronya reflects on the period from the publication of Swann in 1985 and the creation of the National Curriculum in England and Wales in 1988. A conservative government was never going to implement Swann's more radical "multicultural and anti-racial" recommendations -- this underlines that political parties have the right to implement or reject report recommendations. Educationalists in 2008 will reflect upon the twentieth "anniversary" of the creation of the National Curriculum in England and Wales. Citizenship has been a major curriculum development, although it is not compulsory in England and Wales at Key Stages 1-2 (children aged 5 to 11). This curriculum covers elements of multiculturalism, human rights, anti-racism and even anti-discrimination. But how do individual governments incorporate these ideas and respond educationally to the changing global world? The governmental discourse has slipped back towards an integrationist social framework in England and Wales with the extreme danger of a return to assimilation education and social policies.
With the expansion of the European Community and large numbers of immigrants from Poland and Bulgaria entering the United Kingdom, there are wider social issues that need to be addressed. These "social issues", in an environment of risk and terror, do not just come from Muslim communities; we need greater insight and coherence into the wider multicultural picture, which have consequences for teachers, schools and the wider education community.
The educational thrust of this article highlights the importance of the concept of multiculturalism and encourages continued debates into its usage and applicability to the education systems of today. Have we reached a stage that goes back and beyond the Phillips debate, where we need to move on from multiculturalism and redefine the debate? If we are to move forward towards more anti-racial, more anti-discriminatory and away from integrationist and assimilation education policies, I would recommend the following:
- Politicians and civil servants at the national, central, federal and local levels need to get into schools to see what is going on and report back to their Government about good practices within culturally diverse environments. Administration and bureaucracy can prevent anti-racial policies, but as Michael Barber has recently written in Instruction to Deliver, administrative hurdles need to be reduced to allow political policies to be created, developed and delivered.
- International comparisons are important and best practices need to be examined and reported upon in global communities, such as the United Nations and the Organization for Economic Cooperation and Development, as well as in publications like the UN Chronicle. It is interesting that a policy document commented on by my students at Roehampton University is the Salamanca Agreement, which promotes special needs within an inclusive education framework. How many politicians, civil servants and education researchers are walking or being invited into schools to see how these proposals are being implemented or not?
- I feel it is crucial that policymakers and policy implementers actually see what is going on. It is all very well being conceptual, but what is practically going on in schools and how relevant, for example, is school curriculum today? The education basics -- literacy and numeracy -- are crucial, but we need to ask more of the education curriculum. In England and Wales, the creation and development of citizenship as a compulsory subject for 11- to 16-year-olds is an important development, but is it enough?
We are at a stage whereby in 2007 "future promise" resides, in England and Wales, in a core subject of education that needs to sit alongside English, math and science, with the focus on, among other things, multicultural, anti-racist and anti-discrimination themes, which use domestic, international and global case studies.


text:
Unless you have enabled auto-renew, your proxies will expire at the end of your subscription period.
If in case your card is being charged even after canceling your subscription, please submit a request at email@example.com so we could look into the issue.
- For payments made via Fastspring: Kindly write to our billing team for cancelling the auto subscription.
- For payments made via Paypal/ Paymentwall: The subscription needs to be cancelled by you from your Paypal/ Paymentwall account.
- For Credit Renewals: In case you use credits from your Limeproxies account for renewing your products, and you wish to cancel the renewal for a particular product, then please change the Auto Subscription option to disable on your Limeproxies Panel.