Many questions about human genetic history can be addressed by examining the patterns of shared genetic variation between sets of populations. A useful methodological framework for this purpose is F-statistics that measure shared genetic drift between sets of two, three, and four populations and can be used to test simple and complex hypotheses about admixture between populations. This article provides context from phylogenetic and population genetic theory. I review how F-statistics can be interpreted as branch lengths or paths and derive new interpretations, using coalescent theory. I further show that the admixture tests can be interpreted as testing general properties of phylogenies, allowing extension of some ideas applications to arbitrary phylogenetic trees. The new results are used to investigate the behavior of the statistics under different models of population structure and show how population substructure complicates inference. The results lead to simplified estimators in many cases, and I recommend to replace F3 with the average number of pairwise differences for estimating population divergence.
FOR humans, whole-genome genotype data are now available for individuals from hundreds of populations (Lazaridis et al. 2014; Yunusbayev et al. 2015), opening up the possibility to ask more detailed and complex questions about our history (Pickrell and Reich 2014; Schraiber and Akey 2015) and stimulating the development of new tools for the analysis of the joint history of these populations (Reich et al. 2009; Patterson et al. 2012; Pickrell and Pritchard 2012; Lipson et al. 2013; Ralph and Coop 2013; Hellenthal et al. A simple and intuitive approach that has quickly gained in popularity are the F-statistics, introduced by Reich et al. (2009) and summarized in Patterson et al. (2012). In that framework, inference is based on "shared genetic drift" between sets of populations, under the premise that shared drift implies a shared evolutionary history. Tools based on this framework have quickly become widely used in the study of human genetic history, both for ancient and for modern DNA (Green et al. 2010; Reich et al. 2012; Lazaridis et al. 2014; Allentoft et al. 2015; Haak et al. 2015).
Some care is required with terminology, as the F-statistics sensu Reich et al. (2009) are distinct, but closely related to Wright's fixation indexes (Wright 1931; Reich et al. 2009), which are also often referred to as F-statistics. Furthermore, it is necessary to distinguish between statistics (quantities calculated from data) and the underlying parameters (which are part of the model) (Weir and Cockerham 1984).
In this article, I mostly discuss model parameters, and I therefore refer to them as drift indexes. The term F-statistics is used when referring to the general framework introduced by Reich et al. (2009), and Wright's statistics are referred to as FST or f.
Treeness test: Are populations related in a tree-like fashion (Reich et al. 2009)?
Admixture test: Is a particular population descended from multiple ancestral populations (Reich et al. 2009)?
Admixture proportions: What are the contributions from different populations to a focal population (Green et al. 2010; Haak et al. 2015)?
Number of founders: How many founder populations are there for a certain region (Reich et al. 2012; Lazaridis et al. 2014)?
Complex demography: How can mixtures and splits of population explain demography (Patterson et al. 2012; Lipson et al. 2013)?
Closest relative: What is the closest relative to a contemporary or ancient population (Raghavan et al. 2014)?
The demographic models under which these questions are addressed, and that motivated the drift indexes, are called population phylogenies and admixture graphs. The population phylogeny (or population tree) is a model where populations are related in a tree-like fashion (Figure 1A), and it frequently serves as the null model for admixture tests. The branch lengths in the population phylogeny correspond to how much genetic drift occurred, so that a branch that is subtended by two different populations can be interpreted as the "shared" genetic drift between these populations. The alternative model is an admixture graph (Figure 1B), which extends the population phylogeny by allowing edges that represent population mergers or a significant exchange of migrants.
(blue). (B) An admixture graph extends a population phylogeny by allowing gene flow (red, solid line) and admixture events (red, dotted line).
F2(P1, P2) corresponds to the path on the phylogeny from P1 to P2.
F3 (PX; P1, P2) represents the length of the external branch from PX to the (unique) internal vertex connecting all three populations. Thus, the first parameter of F3 has a unique role, whereas the other two can be switched arbitrarily.
(P1, P2; P3, P4) represents the internal branch from the internal vertex connecting P1 and P2 to the vertex connecting P3 and P4 (Figure 1A, blue).
to emphasize the interpretation as a test statistic. For details, see the F4 subsection in Methods and Results.
In an admixture graph, there is no longer a single branch length corresponding to each F-statistic, and interpretations are more complex. However, F-statistics can still be thought of as the proportion of genetic drift shared between populations (Reich et al. 2009). The basic idea exploited in addressing all six questions outlined above is that under a tree model, branch lengths, and thus the drift indexes, must satisfy some constraints (Buneman 1971; Semple and Steel 2003; Reich et al. 2009). The two most relevant constraints are that (i) in a tree, all branches have positive lengths (tested using the F3-admixture test) and (ii) in a tree with four leaves, there is at most one internal branch (tested using the F4-admixture test).
The goal of this article is to give a broad overview on the theory, ideas, and applications of F-statistics. Our starting point is a brief review on how genetic drift is quantified in general and how it is measured using F2. I then propose an alternative definition of F2 that allows us to simplify applications and study them under a wide range of population structure models. I then review some basic properties of distance-based phylogenetic trees, show how the admixture tests are interpreted in this context, and evaluate their behavior. Many of the results that are highlighted here are implicit in classical (Wahlund 1928; Wright 1931; Cavalli-Sforza and Edwards 1967; Felsenstein 1973, 1981; Cavalli-Sforza and Piazza 1975; Slatkin 1991; Excoffier et al. 1992) and more recent work (Patterson et al. 2012; Pickrell and Pritchard 2012; Lipson et al. 2013), but often not explicitly stated or given in a different context.
The next sections discuss the F-statistics, introducing different interpretations and giving derivations for some useful expressions. A graphical summary of the three interpretations of the statistics is given in Figure 2, and the main formulas are summarized in Table 1.
]. For the admixture test, the two possible gene trees contribute to the statistic with different sign, highlighting the similarity to the D-statistic (Green et al. 2010) and its expectation of zero in a symmetric model.
Throughout this article, populations are labeled as P1, P2, … , Pi, … . Often, PX will denote an admixed population. The allele frequency pi is defined as the proportion of individuals in Pi that carry a particular allele at a biallelic locus, and throughout this article I assume that all individuals are haploid. However, all results hold if instead of haploid individuals, an arbitrary allele of a diploid individual is used. I focus on genetic drift only and ignore the effects of mutation, selection, and other evolutionary forces.
(1)(Reich et al. 2009). The expectation is with respect to the evolutionary process, but in practice F2 is estimated from hundreds of thousands of loci across the genome (Patterson et al. 2012), which are assumed to be nonindependent replicates of the evolutionary history of the populations.
Why is F2 a useful measure of genetic drift? As it is infeasible to observe changes in allele frequency directly, the effect of drift is assessed indirectly, through its impact on genetic diversity. Most commonly, genetic drift is quantified in terms of (i) the variance in allele frequency, (ii) heterozygosity, (iii) probability of identity by descent, (iv) correlation (or covariance) between individuals, and (v) the probability of coalescence (two lineages having a common ancestor). In the next sections I show how F2 relates to these quantities in the cases of a single population changing through time and a pair of populations that are partially isolated.
to obtain lines three and five. It is worth noting that this result holds for any model of genetic drift where the expected allele frequency is the current allele frequency and increments are independent. For example, this interpretation of F2 holds also if genetic drift is modeled as a Brownian motion (Cavalli-Sforza and Edwards 1967).
(3)This equation is due to Tavaré (1984), who also provided the following intuition: Given nt individuals are sampled at time t, let E denote the event that all individuals carry allele x, conditional on allele x having frequency p0 at time t0. There are two components to this: First, the frequency will change between t0 and t, and then all nt sampled individuals need to carry x.
Measures of genetic drift in a single population. Shown are interpretations of F2 in terms of (A) the increase in allele frequency variance; (B) the decrease in heterozygosity; and (C) f, which can be interpreted as probability of coalescence of two lineages or the probability that they are identical by descent.
(5)Equating (4) and (5) yields Equation 3.
where f is the probability that two lineage sampled at time t coalesce before time t0.
is the probability two individuals are not identical in P0.
(7)which shows that F2 measures the decay of heterozygosity (Figure 3A). A similar argument was used by Lipson et al. (2013) to estimate ancestral heterozygosities and to linearize F2.
is compared with the number of heterozygotes present due to differences in allele frequencies between populations Hexp (Wahlund 1928; Wright 1931).
The preceding arguments show how the usage of F2 for both single and structured populations can be justified by the similar effects of F2 on different measures of genetic drift. However, what is the benefit of using F2 instead of the established inbreeding coefficient f and fixation index FST? Recall that Wright motivated f and FST as correlation coefficients between alleles (Wright 1921, 1931). Correlation coefficients have the advantage that they are easy to interpret, as, e.g., FST = 0 implies panmixia and FST = 1 implies complete divergence between subpopulations. In contrast, F2 depends on allele frequencies and is highest for intermediate-frequency alleles. However, F2 has an interpretation as a covariance, making it simpler and mathematically more convenient to work with. In particular, variances and covariances are frequently partitioned into components due to different effects, using techniques such as analysis of variance and analysis of covariance (e.g., Excoffier et al. 1992).
Reich et al. (2009) and Patterson et al. (2012) proposed to partition "drift" (as previously established, measured by covariance, allele frequency variance, or decrease in heterozygosity) between different populations into contribution on the different branches of a population phylogeny. This model has been studied by Cavalli-Sforza and Edwards (1967) and Felsenstein (1973) in the context of a Brownian motion process. In this model, drift on independent branches is assumed to be independent, meaning that the variances can simply be added. This is what is referred to as the additivity property of F2 (Patterson et al. 2012).
Alternative proofs of this statement and more detailed reasoning behind the additivity assumption can be found in Cavalli-Sforza and Edwards (1967), Felsenstein (1973), Reich et al. (2009), and Patterson et al. (2012).
and interpret the two terms in parentheses as two paths between P1 and P2, and F2 as the overlap of these two paths. In a population phylogeny, there is only one possible path, and the two paths are always the same; therefore F2 is the sum of the length of all the branches connecting the two populations. However, if there is admixture, as in Figure 2B, both paths choose independently which admixture edge they follow. With probability α they will go left, and with probability β = 1 − α they go right. Thus, F2 can be interpreted by enumerating all possible choices for the two paths, resulting in three possible combinations of paths on the trees (Figure S1), and the branches included will differ, depending on which path is chosen, so that the final F2 is made of an average of the path overlap in the topologies, weighted by the probabilities of the topologies.
However, one drawback of this approach is that it scales quadratically with the number of admixture events, making calculations cumbersome when the number of admixture events is large. More importantly, this approach is restricted to panmictic subpopulations and cannot be used when the population model cannot be represented as a weighted average of trees.
For this reason, I propose to redefine F2, using coalescent theory (Wakeley 2009). Instead of allele frequencies on a fixed admixture graph, coalescent theory tracks the ancestors of a sample of individuals, tracing their history back to their most recent common ancestor. The resulting tree is called a gene tree (or coalescent tree). Gene trees vary between loci and will often have a different topology from that of the population phylogeny, but they are nevertheless highly informative about a population's history. Moreover, expected coalescence times and expected branch lengths are easily calculated under a wide array of neutral demographic models.
are the expected coalescence times of two lineages sampled in two different populations and the same population, respectively.
Unsurprisingly, given the close relationship between F2 and FST, an analogous expression exists for F2 (P1, P2): The derivation starts by considering F2 for two samples of size 1. I then express F2 for arbitrary sample sizes in terms of individual-level F2 and obtain a sample-size independent expression by letting the sample size n go to infinity.
be an indicator random variable that individual i has a particular allele. For two individuals, F2 (I1, I2) = 1 implies I1 = I2, whereas F2 (I1, I2) = 0 implies I1 ≠ I2. Thus, F2(I1, I2) is another indicator random variable with the parameter equal to the probability that a mutation happened on the tree branch between I1 and I2.
terms of the form F2 (I1,i, I1,j), one for each possible pair of samples in P1.
(12)where the second sum is over all pairs in P1. This equation is equivalent to equation 22 in Felsenstein (1973).
(13)Thus, I can write F2 between the two populations as the average number of differences between individuals from different populations, minus some terms including differences within each sample.
or θ acts as a constant of proportionality that is the same for all statistics calculated from the same data. Since interest is focused on the relative magnitude of F2 or whether a sum of F2 values is different from zero, this constant has no impact on inference.
(16)Unlike FST, the mutation parameter θ does not cancel. However, for most applications, the absolute magnitude of F2 is of little interest, since only the sign of the statistics is used for most tests. In other applications F-statistics with presumably the same θ (Reich et al. 2009) are compared. In these cases, θ can be regarded as a constant of proportionality and will not change the theoretical properties of the F-statistics. It will, however, influence statistical properties, as a larger θ implies more mutations and hence more data.
The last line is the same as equation 10 in the appendix of Reich et al. (2009).
However, while the estimators are identical, the underlying modeling assumptions are different: The original definition considered only loci that were segregating in an ancestral population; loci not segregating there were discarded. Since ancestral populations are usually unsampled, this is often replaced by ascertainment in an outgroup (Patterson et al. 2012; Lipson et al. 2013). In contrast, Equation 17 assumes that all markers are used, which is the more natural interpretation for sequence data.
An important feature of Equation 16 is that it depends only on the expected coalescence times between pairs of lineages. Thus, the behavior of F2 can be fully characterized by considering a sample of size 4, with two random individuals taken from each population. This is all that is needed to study the joint distribution of T12, T11, and T22 and hence F2. By linearity of expectation, larger samples can be accommodated by summing the expectations over all possible quartets.
]. The superscripts refers to the topologies being for F2, and I discard them in cases where no ambiguity arises.
(A–C) Schematic explanation of how F2 behaves conditioned on a gene tree. (A) Equation with terms corresponding to the branches in the tree below. Blue terms and branches correspond to positive contributions, whereas red branches and terms are subtracted. Labels represent individuals randomly sampled from that population. External branches cancel out, so only the internal branches have nonzero contribution to F2. In the concordant genealogy (B), the contribution is positive (with weight 2), and in the discordant genealogy (C), it is negative (with weight 1). The mutation rate as constant of proportionality is omitted.
In this representation, T12 corresponds to a path from a random individual from P1 to a random individual from P2, and T11 represents the path between the two samples from P1.
the internal branch is always included in T12, but never in T11 or T22. External branches, on the other hand, are included with 50% probability in T12 on any path through the tree. T11 and T22, on the other hand, consist only of external branches, and the lengths of the external branches cancel.
each T contains exactly two external branches, cancelling the external branches from T12.
(18)resulting in the representation given in Figure 2, C and D.
This argument can be transformed from branch lengths to observed mutations by recalling that mutations occur on a branch at a rate proportional to its length. F2 is increased by doubletons that support the assignment of populations (i.e., the two lineages from the same population have the same allele), but reduced by doubletons shared by individuals from different populations. All other mutations have a contribution of zero.
as a measure of dissimilarity between P1 and P2, as a large F2 value implies that populations are highly diverged. Thus, the strategy is to calculate all pairwise F2 indexes between populations, combine them into a dissimilarity matrix, and ask whether that matrix is consistent with a tree.
One way to approach this question is by using phylogenetic theory: Many classical algorithms have been proposed that use a measure of dissimilarity to generate a tree (Fitch et al. 1967; Saitou and Nei 1987; Semple and Steel 2003; Felsenstein 2004) and what properties a general dissimilarity matrix needs to have to be consistent with a tree (Buneman 1971; Cavalli-Sforza and Piazza 1975), in which case the matrix is also called a tree metric (Semple and Steel 2003). Thus, testing for admixture can be thought of as testing treeness.
For a dissimilarity matrix to be consistent with a tree, there are two central properties it needs to satisfy: First, the length of all branches has to be positive. This is strictly not necessary for phylogenetic trees, and some algorithms may return negative branch lengths (e.g. Saitou and Nei 1987); however, since in our case branches have an interpretation of genetic drift, negative genetic drift is biologically nonsensical, and therefore negative branches should be interpreted as a violation of the modeling assumptions and hence of treeness.
(19)that is, if the sums of pairs of distances are compared, two of these sums will be the same, and no smaller than the third one. This theorem, due to Buneman (1971, 1974), is called the four-point condition or sometimes, more modestly, the "fundamental theorem of phylogenetics." A proof can be found in Semple and Steel (2003, Chap. 7).
Why are these properties useful? It turns out that the admixture tests based on F-statistics can be interpreted as tests of these properties: The F3 test can be interpreted as a test for the positivity of a branch and the F4 as a test of the four-point condition. Thus, the working of the two test statistics can be interpreted in terms of fundamental properties of phylogenetic trees, with the immediate consequence that they may be applied as treeness tests for arbitrary dissimilarity matrices.
An early test of treeness, based on a likelihood ratio, was proposed by Cavalli-Sforza and Piazza (1975): They compared the likelihood of the observed F2 matrix to that induced by the best-fitting tree (assuming Brownian motion), rejecting the null hypothesis if the tree likelihood is much lower than that of the empirical matrix. In practice, however, finding the best-fitting tree is a challenging problem, especially for large trees (Felsenstein 2004), and so the likelihood test proved to be difficult to apply. From that perspective, the F3 and F4 tests provide a convenient alternative: Since treeness implies that all subsets of taxa are also trees, the ingenious idea of Reich et al. (2009) was that rejection of treeness for subtrees of sizes 3 (for F3) and 4 (for F4) is sufficient to reject treeness for the entire tree. Furthermore, tests on these subsets also pinpoint the populations involved in the non-tree-like history.
In the previous section, I showed how F2 can be interpreted as a branch length, as an overlap of paths, or in terms of gene trees (Figure 2). Furthermore, I gave expressions in terms of coalescence times, allele frequency variances, and internal branch lengths of gene trees. In this section, I give analogous results for F3.
(20b)If F2 in Equation 20b is generalized to an arbitrary tree metric, Equation 20b is known as the Gromov product in phylogenetics (Semple and Steel 2003). The Gromov product is a commonly used operation in classical phylogenetic algorithms to calculate the length of the portion of a branch shared between P1 and P2 (Fitch et al. 1967; Felsenstein 1973; Saitou and Nei 1987), consistent with the notion that F3 is the length of an external branch in a population phylogeny.
In an admixture graph, there is no longer a single external branch; instead all possible trees have to be considered, and F3 is the (weighted) average of paths through the admixture graph (Figure 2F).
(20d)which was also noted by Pickrell and Pritchard (2012).
They did this by calculating F3 (PO; PU, Pi), where PO is an outgroup population that was assumed widely diverged from PU and all populations in the panel. This measures the shared drift (or shared branch) of PU with the populations from the panel, and high F3 values imply close relatedness.
has a higher correlation with divergence time (R2 = 0.90) than F3 (R2 = 0.73). Hence, the number of pairwise differences may be a better metric for population divergence than F3.
(white) for a panel of populations with linearly increasing divergence time. Both statistics are scaled to have the same range, with the first divergence between the most closely related populations set to zero. F3 is inverted, so that it increases with distance. (B) Simulated (boxplots) and predicted (blue) F3 statistics under a simple admixture model. (C) Comparison of F4 ratio (yellow triangles, Equation 29) and ratio of differences (black circles, Equation 31).
However, F3 is motivated and primarily used as an admixture test (Reich et al. 2009). In this context, the null hypothesis is that F3 is nonnegative; i.e., the null hypothesis is that the data are generated from a phylogenetic tree that has positive edge lengths. If this is not the case, the null hypothesis is rejected in favor of the more complex admixture graph. From Figure 2F it may be seen that drift on the path on the internal branches (red) contributes negatively to F3. If these branches are long enough compared to the branch after the admixture event (blue), then F3 will be negative. For the simplest scenario where PX is admixed between P1 and P2, Reich et al. (2009) provided a condition when this is the case (equation 20 in supplement 2 of Reich et al. 2009). However, since this condition involves F-statistics with internal, unobserved populations, it cannot be used in practical applications. A more useful condition is obtained using Equation 20c.
Thus, the power of F3 to detect admixture is large (1) if the admixture proportion α is close to 50%; (2) if the ratio between the times of the original split and the time of secondary contact is large; and (3) if the probability of coalescence before the admixture event in PX is small, i.e., the size of PX is large.
only two individuals from PX are needed and one each from P1 and P2 to study the joint distribution of all terms in (20c). The minimal case therefore contains again just four samples (Figure S2).
F3 can be interpreted as a test whether mutations that agree with the population tree are more than twice as common as mutations that disagree with it.
I performed a small simulation study to test the accuracy of Equation 22. Parameters were chosen such that F3 has a negative expectation for α > 0.05, and I find that the predicted F3 fitted very well with the simulations (Figure 5B).
measures the overlap between the paths from P1 to P3 and from P2 to P4, which is the internal branch in Figure 1A, and will be positive.
will be zero. Figure 2, I–L, corresponds to the internal branch and Figure 2, M–P, to the "zero" branch.
(26)for any permutations of the samples. This implies that two of the sums need to be the same and larger than the third one. The claim is that if the four-point condition holds, at least one of the F4 values will be zero, and the others will have the same absolute value.
is still zero, and the other two F4 values have the same magnitude.
Evaluating F4 in terms of gene trees and their internal branches, there are three different gene tree topologies that have to be considered, whose interpretation depends on whether the branch length or test-statistic interpretation is considered.
(27)This equation is slightly different from those for F2 and F3, where the coefficient for the discordant genealogy was half that for the concordant genealogy. Note, however, that F4 includes only one of the two discordant genealogies. Under a tree, both discordant genealogies are equally likely (Durand et al. 2011), and thus the expectation of F4 will be the same.
and D are different test statistics for the same null hypothesis.
Two major applications of F4 use its interpretation as a branch length. First, the rank of a matrix of all F4 statistics is used to obtain a lower bound on the number of admixture events required to explain data (Reich et al. 2012). The principal idea of this approach is that the number of internal branches in a genealogy is bounded to be at most n − 3 in an unrooted tree. Since each F4 is a sum of the length of tree branches, all F4 indexes should be sums of n − 3 branches or n − 3 independent components. This implies that the rank of the matrix (see, e.g., section 4 in McCullagh 2009) is at most n − 3, if the data are consistent with a tree. However, admixture events may increase the rank of the matrix, as they add additional internal branches (Reich et al. 2012). Therefore, if the rank of the matrix is r, the number of admixture events is at least r − n + 3.
may reveal the number of branches of that form.
Applications of F4. (A) Visualization of rank test to estimate the number of admixture events. F4 (S1, R1, S2, R2) measures a branch absent from the phylogeny and should be zero for all populations from S1 and S2. (B) Model underlying admixture ratio estimate (Green et al. 2010). PX splits, and the mean coalescence time of PX with PI gives the admixture proportion. (C) If the model is violated, α measures where on the internal branch in the underlying genealogy PX (on average) merges.
(29)Here, PX is the population whose admixture proportion is estimated; P1 and P2 are the potential contributors, where I assume that they contribute with proportions α and 1 − α, respectively; and PO, PI are reference populations with no direct contribution to PX (see Figure 6B). PI has to be more closely related to one of P1 or P2 than the other, and PO is an outgroup.
The canonical way (Patterson et al. 2012) to interpret this ratio is as follows: The denominator is the branch length from the common ancestor population from PI and P1 to the common ancestor of PI with P2 (Figure 6C, yellow line). The numerator has a similar interpretation as an internal branch (Figure 6C, red dotted line). In an admixture scenario (Figure 6B), this is not unique and is replaced by a linear combination of lineages merging at the common ancestor of PI and P1 (with probability α) and lineages merging at the common ancestor of PI with P2 (with probability 1 − α).
Thus, a more general interpretation is that α measures how much closer the common ancestor of PX and PI is to the common ancestor of PI and P1 and the common ancestor of PI and P2, indicated by the red dotted line in Figure 6C. This quantity is defined also when the assumptions underlying the admixture test are violated and, if the assumptions are not carefully checked, might lead to misinterpretations of the data. In particular, α is well defined in cases where no admixture occurred or in cases where either one of P1 and P2 did not experience any admixture.
(31)is another estimator for α that can be used even if no outgroup is available. I compare Equations 29 and 31 for varying admixture proportions in Figure 5C, using the mean absolute error in the admixture proportion. Both estimators perform very well, but (31) performs slightly better in cases where the admixture proportion is low. However, in most cases this minor improvement possibly does not negate the drawback that Equation 31 is applicable only when populations are sampled at the same time.
An area of recent development is how these estimates can be extended to more populations. A simple approach is to assume a fixed series of admixture events, in which case admixture proportions for each event can be extracted from a series of F4 ratios (Lazaridis et al. 2014, SI 13). A more sophisticated approach estimates mixture weights using the rank of the F4 matrix, as discussed in the Rank test section (Haak et al. 2015, SI 10). Then, it is possible to estimate mixture proportions, using a model similar to that introduced in the program structure (Pritchard et al. 2000), by obtaining a low-rank approximation for the F4 matrix.
Here, I use Equation 16 together with Equations 20b and 24b to derive expectations for F3 and F4 under some simple models.
This results in the equation in Figure 7. The derivation of coalescence times for the hierarchical island models is marginally more complicated, but similar. It is given in Slatkin and Voelm (1991).
(33)Here, cx is the probability that the two lineages from PX coalesce before the admixture event.
(34)which is more likely if α is large, the admixture is recent, and the overall coalescent is far in the past.
(35)Once lineages are in the same deme, the system terminates as the time to coalescence time is independent of the deme in isotropic migration models (Strobeck 1987) and cancels from the F-statistics.
Therefore, the vector v of the expected time until two lineages are in the same deme is found using standard Markov chain theory by solving v = (I − T)−1)1, where T is the transition matrix involving only the transitive states in the Markov chain (all but the first state), and 1 is a vector of 1's.
Finding the expected coalescence time involves solving a system of five equations. The terms involved in calculating the F-statistics (Table 1) are the entries in v corresponding to these states.
(36)For F4, I assume that demes 1 and 2 are in P1, demes 3 and 4 are in PX, and demes 5 and 6 correspond to P2 and P3, respectively.
A hierarchical stepping-stone model, where demes are combined into populations, is the only case I studied (besides the admixture graph) where F3 can be negative. This effect indicates that admixture and population structure models may be the two sides of the same coin: Admixture is a (temporary) reduction in gene flow between individuals from the same population. Finally, for a simple serial founder model without migration, I find that F3 measures the time between subsequent founder events.
for the outgroup F3 statistic (Figure 5A). Sample sizes and population sizes were picked randomly, but kept the same over all 100 replicates. Additionally, I randomly assigned each population an error rate uniformly between 0 and 0.05. Errors were introduced by adding additional singletons and flipping alleles at that rate.
with the admixture proportion $ALPHA set to increments of 0.025 from 0 to 0.5, with 200 data sets generated per $ALPHA.
Here, the admixture proportion $ALPHA was varied in increments of 0.1 from 0 to 1, again with 200 data sets generated per $ALPHA.
F3 and F4 statistics were calculated using the implementation from Pickrell and Pritchard (2012).
In this article, I focused almost exclusively on the theoretical properties of the F-statistics, glancing over the statistical problems of how they are estimated. Many procedures are implemented in the software package ADMIXTOOLS and described in Patterson et al. (2012). Alternatively, the software package treemix (Pickrell and Pritchard 2012) contains lightwight alternatives for calculating F3 and F4 statistics. Both use a block-jackknife approach to estimate standard errors, taking linkage between markers into account.
There are three main ways to interpret F-statistics: In the simplest case, they represent branches in a population phylogeny. In the case of an admixture graph, the idea of shared drift in terms of paths is most convenient. Finally, the expressions in terms of coalescence times and the lengths of the internal branches of gene genealogies are useful for more complex scenarios. This last interpretation makes the connection to the ABBA-BABA statistic explicit and allows the investigation of the behavior of the F-statistics under arbitrary demographic models.
If drift indexes exist for two, three, and four populations, should there be corresponding quantities for five or more populations (e.g., Pease and Hahn 2015)? Two of the interpretations speak against this possibility: First, a population phylogeny can be fully characterized by internal and external branches, and it is not clear how a five-population statistic could be written as a meaningful branch length. Second, all F-statistics can be written in terms of four-individual trees, but this is not possible for five samples. This seems to suggest that there may not exist a five-population statistic as general as the three F-statistics I discussed here, but they will still be useful for questions pertaining to a specific demographic model.
A well-known drawback of F3 is that it may have a positive expectation under some admixture scenarios (Patterson et al. 2012). Here, I showed that F3 is positive if and only if the branch supporting the population tree is longer than the two branches discordant with the population tree. Note that this is (possibly) distinct from the probabilities of tree topologies, although the average branch length of the internal branch in a topology and the probability of that topology are frequently strongly correlated. Thus, negative F3 values indicate that individuals from the admixed population are likely to coalesce with individuals from the two other populations, before they coalesce with other individuals from their own population!
For practical purposes, it is useful to know how the admixture tests perform under demographic models different from population phylogenies and admixture graphs and in which cases the assumptions made for the tests are problematic. In other words, under which demographic models is population structure distinguishable from a tree? Equation 16 enables the derivation of expectations for F3 and F4 under a wide variety of models of population structure (Figure 7). The simplest case is that of a single panmictic population. In that case, all F-statistics have an expectation of zero, consistent with the assumption that no structure and therefore no population phylogeny exists. Under island models, F4 is also zero, and F3 is inversely proportional to the migration rate. Results are similar under a hierarchical island model, except that the number of demes has a small effect. This corresponds to a population phylogeny that is star-like and has no internal branches, which is explained by the strong symmetry of the island model. Thus, looking at different F3 and F4 statistics may be a simple heuristic to see whether data are broadly consistent with an island model; if F3 values vary a lot between populations, or if F4 is substantially different from zero, an island model might be a poor choice. When looking at a finite stepping-stone model, F3 and F4 are both nonzero, highlighting that F4 (and the ABBA-BABA D-statistic) is susceptible to migration between any pair of populations. Thus, for applications, F4 should be used as an admixture test only if there is good evidence that gene flow between some pairs of the populations was severely restricted.
Overall, when F3 is applicable, it is remarkably robust to population structure, requiring rather strong substructure to yield false positives. Thus, it is a very striking finding that in many applications to humans, negative F3 values are commonly found (Patterson et al. 2012), indicating that for most human populations, the majority of markers support a discordant gene tree, which suggests that population structure and admixture are widespread and that population phylogenies are poorly suited to describe human evolution.
Ancient population structure was proposed as possible confounder for the D-statistic and F4 statistic (Green et al. 2010). Here, I show that nonsymmetric population structure such as in stepping-stone models can lead to nonzero F4 values, showing that both ancestral and persisting population structure may result in false positives when assumptions are violated.
Furthermore, I showed that F2 can be seen as a special case of a tree metric and that using F-statistics is equivalent to using phylogenetic theory to test hypotheses about simple phylogenetic networks (Huson et al. 2010). From this perspective, it is worth raising again the issue pointed out by Felsenstein (1973) of how and when allele-frequency data should be transformed for within-species phylogenetic inference. While F2 has become a de facto standard, different transformations of allele frequencies might be useful in some cases, as both F3 and F4 can be interpreted as tests for treeness for arbitrary tree metrics.
This relationship provides ample opportunities for interaction between these currently diverged fields: Theory (Huson and Bryant 2006; Huson et al. 2010) and algorithms for finding phylogenetic networks such as Neighbor-Net (Bryant and Moulton 2004) may provide a useful alternative to tools specifically developed for allele frequencies and F-statistics (Patterson et al. 2012; Pickrell and Pritchard 2012; Lipson et al. 2013), particularly in complex cases. On the other hand, the tests and different interpretations described here may be useful to test for treeness in other phylogenetic applications, and the complex history of humans may provide motivation to further develop the theory of phylogenetic networks and stress its usefulness for within-species demographic analyses.
I thank Heejung Shim, Rasmus Nielsen, John Novembre, and all members of the Novembre laboratory for helpful comments and discussions. I am further grateful for comments from Nick Patterson and an anonymous reviewer. B.M.P. is supported by a Swiss National Science Foundation early postdoctoral mobility fellowship. Additional funding for this work was provided by National Institutes of Health grant R01 HG007089 to John Novembre.
Supplemental material is available online at www.genetics.org/lookup/suppl/doi:10.1534/genetics.115.183913/-/DC1.
, 2004 Neighbor-Net: an agglomerative method for the construction of phylogenetic networks. Mol. Biol. Evol. 21: 255–265.
Buneman, P., 1971 The recovery of trees from measures of dissimilarity, Mathematics in the Archaeological and Historical Sciences.
, 1974 A note on the metric properties of trees. J. Comb. Theory Ser. B 17: 48–50.
Cavalli-Sforza, L. L. and A. W. F. Edwards, 1967 Phylogenetic analysis: models and estimation procedures. Evolution 21: 550–570.
, 1975 Analysis of evolution: evolutionary rates, independence and treeness. Theor. Popul. Biol. 8: 127–165.
, 1973 Maximum-likelihood estimation of evolutionary trees from continuous characters. Am. J. Hum. Genet. 25: 471–492.
, 1981 Evolutionary trees from gene frequencies and quantitative characters: finding maximum likelihood estimates. Evolution 35: 1229–1242.
, 2004 Inferring Phylogenies. Sinauer Associates, Sunderland, MA.
, 1967 Construction of phylogenetic trees. Science 155: 279–284.
Green, R., J. Krause, A. Briggs, T. Maricic, U. Stenzel et al., 2010 A draft sequence of the Neandertal genome. Science 328: 710–722.
, 2014 A genetic atlas of human admixture history. Science 343: 747–751.
Huson, D. H., R. Rupp, and C. Scornavacca, 2010 Phylogenetic Networks: Concepts, Algorithms and Applications. Cambridge University Press, Cambridge/London/New York.
, 2013 Efficient moment-based inference of admixture parameters and sources of gene flow. Mol. Biol. Evol. 30: 1788–1802.
, 2009 Marginal likelihood for distance matrices. Stat. Sin. 19: 631.
Patterson, N. J., P. Moorjani, Y. Luo, S. Mallick, N. Rohland et al., 2012 Ancient admixture in human history. Genetics 192: 1065–1093.
, 2015 Detection and polarization of introgression in a five-taxon phylogeny. Syst. Biol. 64: 651–662.
, 2015 The effective founder effect in a spatially expanding population. Evolution 69: 721–734.
Petkova, D., J. Novembre, and M. Stephens, 2014 Visualizing spatial population structure with estimated effective migration surfaces. Nat. Genet. 48: 94–100.
, 2014 Toward a new history and geography of human genes informed by ancient DNA. Trends Genet. 30: 377–389.
, 2013 The geography of recent genetic ancestry across Europe. PLoS Biol. 11: e1001555.
, 2012 Reconstructing Native American population history. Nature 488: 370–374.
, 2015 Methods and models for unravelling human evolutionary history. Nat. Rev. Genet. 16: 727–740.
Semple, C., and M. A. Steel, 2003 Phylogenetics. Oxford University Press, London/New York/Oxford.
, 1991 FST in a hierarchical island model. Genetics 127: 627–629.
, 1987 Average number of nucleotide differences in a sample from a single subpopulation: a test for population subdivision. Genetics 117: 149–153.
, 1984 Line-of-descent and genealogical processes, and their applications in population genetics models. Theor. Popul. Biol. 26: 119–164.
, 1928 Zusammensetzung von populationen und korrelationserscheinungen vom standpunkt der vererbungslehre aus betrachtet. Hereditas 11: 65–106.
, 2009 Coalescent Theory: An Introduction. Roberts & Co. Greenwood Village, CO.
Weir, B. S., and C. C. Cockerham, 1984 Estimating F-statistics for the analysis of population structure. Evolution 38: 1358–1370.
, 1921 Systems of mating. Genetics 6: 111–178.
, 2015 The genetic legacy of the expansion of Turkic-speaking nomads across Eurasia. PLoS Genet. 11: e1005068.


text:
César Pedro Fernández  (Capital Federal, Provincia de Buenos Aires, Argentina, 13 de enero de 1988) es un ex futbolista argentino. Se desempeñó como mediocampista ofensivo.

Trayectoria

Nació el 13 de enero de 1988 en la ciudad de Buenos Aires. Comenzó su carrera en Deportivo Armenio hasta el año 2008 , en 2009 llegó al Club Atlético Independiente hasta mediados del año 2010 y luego pasó por el Club Atlético Excursionistas hasta fines del 2011.

Clubes

Futbolistas de la Ciudad de Buenos Aires
Futbolistas del Club Atlético Independiente
Futbolistas del Club Atlético Excursionistas

redpajama_set_name: RedPajamaWikipedia


"Baby Easter Nails" will begin after the advertisement.
There's nothing like the sweet rush of the holidays! You get a nice care, put on your favorite accessories, and wear your best dress! Here's Pam who can't wait to try her new nail accessories and clothes! Help her choose some stickers in happy colors and then dress her up!


The Penguin Markets is one of the largest markets in Tasmania offering around 200 stalls in the one location, making the Penguin Market unique among all other markets in Tasmania. Regulars and visitors alike flock to the Penguin Market that features quality products including fresh local fruit and vegetables and produce, artisan made Tasmanian arts, crafts and jewellery, gift and home wares. Cooked food is also a feature – you will find a food area selling pizzas and pastas, souvlaki, seafood, fresh juice, Asian food and health food along with an espresso and ice-cream bar.


In the context of Brexit, things would be so much tidier if it wasn't for Northern Ireland. The province not only obstinately voted Remain, but also inconveniently promises to bring with it a new, uniquely porous, EU land border. If somehow one could leave Northern Ireland as a member of the EU and have the frontier redrawn in the Irish Sea, life would immediately become a great deal more straightforward. Since political tidiness is popular with both nationalists and technocrats, it is not surprising that in the last month an Ulster combination of remainers and united Irelanders should have tried to throw yet another quasi-legal spanner in the Brexit works. If what appears below seems a little technical, please forgive this: but technicalities matter here.
It all started in April this year with what looked like a stunningly boring question: http://www.europarl.europa.eu/doceo/document/E-8-2018-002232_EN.html?redirect in the European Parliament by Sinn Féin MEP Martina Anderson, vocal nationalist, socialist and, incidentally, unrepentant convicted IRA terrorist bomber. What EU rights, she asked, would the people of Northern Ireland be entitled to after Brexit? Would they include, for instance, such things as the right to vote in EU elections? Two months later, a 12-line response: http://www.europarl.europa.eu/doceo/document/E-8-2018-002232-ASW_EN.html came from the Commission. Irish citizens in Northern Ireland would remain EU citizens after Brexit, with all the rights that entailed for those living outside the EU; but this would not include the right to the Irish EU franchise, since as a matter of Irish law that was limited to those actually resident in the Republic.
Cue, a couple of weeks later, an angry letter: https://s3-eu-west-1.amazonaws.com/caj.org.uk/2018/10/09135254/caj-letter-to-EC-president.pdf to Jean-Claude Juncker saying this would not do, and that the EU27 had to put matters right in any negotiations with the UK. This was followed by a formal complaint: https://www.rte.ie/news/2018/1009/1001863-ni_brexit_rights/ in September to the (as it happens Southern Irish) EU Ombudsman on much the same lines. Both these documents came from a Northern Ireland body known as the Committee on the Administration of Justice, in practice a congeries of nationalist-leaning and achingly progressive human rights activists (mainly law professors) from Queens Belfast and the University of Ulster.
Essentially their demands came to this. First, because of a phrase in Para 52 of the December 2017 Joint Report: https://ec.europa.eu/commission/sites/beta-political/files/joint_report.pdf that Irish citizens would "continue to enjoy rights as EU citizens, including where they reside in Northern Ireland", Irish nationals resident in Northern Ireland had (it was said) to be assured that they would be given the right to vote in EU elections, if not in the UK then in the Republic. Secondly, another provision of the Report (Para 53) dealing with discrimination law, that "no diminution of rights" would result from Brexit, meant that not only equal treatment but every single provision of the Good Friday Agreement had to be permanently enshrined in any agreement with the EU27. In so far as the Northern Irish protocol to the provisional UK-EU agreement: https://ec.europa.eu/commission/sites/beta-political/files/draft_agreement_coloured.pdf did not do this, it had – despite having been already agreed in principle between the parties – to be rewritten. And lastly, as if this was not enough, they insisted that because of the UK's promise not to discriminate between Northern Ireland residents who did and did not elect for Irish citizenship, anything done for the Irish had to be done for those who wished nothing to do with the Republic and opted for purely British status.
Three comments are in order. First, as regards EU rights, the demands, in so far as one can understand them at all, are grotesque. In all but name, what is being suggested seems to be that Northern Ireland, albeit entirely outside the EU and not even a dependent territory of an EU state, should be either a Euro-constituency in its own right, or part of the Irish Midlands-North-West constituency. In addition, the Euro-franchise for Northern Ireland would have to include those who did not live in the EU and had deliberately chosen not to be EU citizens. In either case the result would be, to put it mildly, a democratic abortion.
Secondly, the 2017 agreement merely requires the Good Friday Agreement to be "protected"; meaning that its effect not be diminished by Brexit. On any ordinary reading, Para 53 of that agreement, concerned with discrimination and requiring "no diminution of rights", is concerned with rights to equality. It could easily have been drafted so as to require the entire gamut of rights under the Good Friday Agreement to be incorporated, but was not. The attempt to argue that it has that effect does not give the impression of a good faith or constructive attempt to solve the problems of the Irish border difficulty. Rather, it looks suspiciously like a combination of Remainer and nationalist mischief-making, aimed at wrecking Brexit or, if that cannot be done, recruiting Brussels indirectly as a guarantor of the nationalist cause (or even both).
More generally, all this is clearly an attempt to bounce the EU into insisting, and the war-weary UK government into agreeing, that Northern Ireland should in all but name become separated from the United Kingdom and de facto tied to an EU Ireland. If anything came of these proposals, Ulster would end up in a kind of limbo; of but not in the EU, in but not of the United Kingdom. And, one suspects, deliberately so. A few years down the line, no doubt, the idea is that a final push could deliver a united Ireland: not for nothing is Martina Anderson, the MEP who started all this, on record as having decorously told the EU Parliament that as regards an Irish border of any kind, the UK would have to "stick it where the sun doesn't shine". We can only hope that the EU continues to have the good sense to avoid being used as a pawn in this particular nasty little game.


I had the pleasure of being a guest on a video podcast filming today. It was my first guest podcast, let alone a video podcast. So, I was rather excited to be part of it.
It was great and we chatted about various things from my background from competitive sport to yoga, the benefits of yoga and w also touched on the 40+ female market.
It's that thing isn't it, where you're thinking of buying a Mercedes and you suddenly see Mercedes cars everywhere. Well, since I've been experiencing hormonal changes over the past 18 months, or so, I've become more aware of women in their forties and fifties, who are also experiencing changes. From conversations with them, and having attended a workshop and worked with a nutritionist, this change is just part of being a woman and yet, we tend to not think about it till it hits.
Yet, why is it we tend to feel alone when we realise that it's happening?
For me, it a big part was the realisation that I had made choices about delaying having children because I loved what I did and was busy working. I was now faced with the fact that the window of being a mother was closing rather rapidly. I also realised that the image the fitness industry carries of fit, healthy females was one that was much younger and I am now entering what seems like the next phase of my life. I am also now more aware of my mortality.
I honestly don't feel any different with regards to what I do, and want to do with my life; the legacy that I want to leave behind.
Yet, I am faced with this fact.
That time is moving on.
What I am practicing patiently is self-acceptance.
Acceptance that I will only have fur babies.
Acceptance that my body, my skin will change.
Acceptance that time and life moves on.
Acceptance that nothing defines me.
Acceptance that I am who I am and I have my own unique journey.
Acceptance that I am enough.
How do you practice acceptance?


text:
Libya rates as most-worsened country in world for past decade: FSI
By Sami Zaptia.
(Photo: FSI).
London, 10 September 2020:
A report by Patricia Taft in the 2020 Fragile States Index (FSI) rates Libya as ''the most-worsened country in the world for the past decade''. It also holds the record for the greatest year-on-year worsening, when it worsened by 25.8 points in the 2012 FSI'', the report says. The report says Libya has again ''featured among the most-worsened countries, tying with Mozambique for the second most worsened country for the year''.
The report says that despite a surge of hope in January 2019, when a meeting in Berlin brought the main warring factions together with international stakeholders in an ultimately unsuccessful attempt to secure a ceasefire, chaos continued to reign for most of the year. With an estimated 300,000 Libyans displaced since the ouster of Qaddafi in 2011, and thousands killed and injured by indiscriminate attacks on civilian population centres, Libya remained one of the world's most dangerous conflicts in 2019.
The war in Libya, it adds, is one of overlapping conflicts fuelled by multiple, often competing, internal and external interests. While securing a ceasefire remains key to bringing an end to Libya's near constant cycle of conflict escalation and resultant misery, without a concurrent focus on addressing the deep structural weaknesses of the Libyan state, it is unlikely true peace will ever take hold. And with so many competing external and internal interests, which seem to be compounding and growing daily, it appears that chaos will continue to reign in Libya for the foreseeable future, the report concludes.

redpajama_set_name: RedPajamaCommonCrawl


text:
Is Ten Percent Really Enough?
My friend Lina, who lives in Chicago, thinks that 10% is enough, but to be honest, I've thought about it long and hard and I'm still not sure that it is.
Metro Industrial Areas Foundation (Metro IAF), a coalition made up predominately of religious organisations, community groups and some trade unions and covering cities from Chicago to Boston, New York and Charlotte in North Carolina, has launched a campaign, "10 Percent is Enough", calling for the reinstatement of anti-usury laws and a cap on interest rates at 10%.
Metro IAF argues that the abolition of anti-usury legislation in the early 1980s, the starting point for sweeping deregulation under President Reagan, "helped shift the investment of American capital and talent away from manufacturing and material innovation and into an unproductive financial sector based on trading paper rather than producing long-term wealth." This has encouraged a growth in predatory lending to the poorest in society that has seen a spiralling of personal debt with interest rates at extortionate levels. For the campaign's organisers, the issue is therefore a moral as well as a practical one. "Moral and civic prohibitions against usury", they argue, "stretch back deep into our religious and national history. Our prophets and founding fathers made the clear case long before us that usury is patently wrong, against God, and against our national interest."
Hoping to be "most exciting social movement to come out of the financial crisis", the campaign has been taken up in Britain by London Citizens, a coalition that the charity I work for helped to found. In July it held a march to the headquarters of the now publicly-owned Royal Bank of Scotland, to present the chairman of RBS, Sir Philip Hampton, with copies of the Bible, Torah and Qur'an. Two weeks later, it returned for a meeting with RBS executives to press the bank to launch a new low-interest credit card.
Perhaps surprisingly, my reservations about the campaign are not primarily about its overtly religious character, although I can imagine there will be atheists who will uncomfortable with the language and emphasis on religious morality.
In part, this hasn't been helped by the way the story has been covered by the press, by the unseemly row over the suspension of the rabbi from Bevis Marks Synagogue for participating in the campaign, or the religious connotations associated with the word 'usury' (many of them deeply anti-Semitic). Neither has it been helped by the increasingly ludicrous Dr Muhammad Abdul Bari of the Muslim Council of Britain focusing on the rather narrow benefits of "interfaith action", a subject that the irreligious and, I would imagine, the secular and trade union members of London Citizens care rather less about than the central message about fighting poverty.
But fellow atheists shouldn't sneer: the motivation behind the campaign comes from genuine concern by compassionate people for the suffering of hundreds of thousands of others. "Our people are hurting", say Metro IAF, and they should be applauded for demanding action now, rather than waiting and praying for comfort in the 'next life'.
My problem is that the solution offered by Metro IAF is rather like that most famous graduate of its community organiser training, Barack Obama. It sounds radical but is actually rather conservative.
You see, the global financial crisis wasn't caused primarily by bankers imposing high rates of interest on credit to borrowers, but rather on their desire to maximise profits by making credit more easily available, even to those who had little prospect of repaying it. In the aftermath of the dot.com bubble and the 11 September 2001 attacks, US interest rates were slashed to 1% to prevent deflation and with the inflow of capital from the booming economies in Asia and the oil producing countries, the banks had money to loan. Credit became easier to obtain but to generate new profits, the US financial sector had to find new borrowers, especially as the traditional mortgage market was exhausted by about 2003. This is why they embarked on increasingly risking lending in the 'sub-prime' housing market and in apparently endless personal credit. It was the scale of debt, as much as its cost, which brought about the global financial crisis.
The way to encourage people to spend more is to boost their aspirations to consume more. The desire for a better home, the idea of property as an 'investment' (as symbolised by the many appalling 'Location, Location' style television programmes), the desperate wish for the right brand or the essential new gadget: never mind whether these were really necessary, or about the impact of our over-consumption on the planet, corporations encouraged us to believe that we needed to consume in order to be happy. Essentially, modern corporate capitalism has as much interest in selling the idea of our personal deficiencies as it does in selling us things we can own. And in the process, we have become more and more disconnected from each other.
This is why it is so disingenuous for those, especially on the US Right, to blame consumer's greed, or specifically minorities, for the credit crunch to justify the transfer of private-sector losses to taxpayers, as though corporate capitalists had nothing to do with the housing bubble or the explosion in credit and were merely the innocent intermediaries.
This is by far the bigger immorality. And yet this is not one that Metro IAF and its British counterpart seems to have considered. "What we need now," according to Metro IAF, "more than thousands of pages of new regulations, or the sour faces of executives forced to reduce their eight-figure salaries to a mere seven, is a 10% cap on interest rates," because "ten percent puts proportion and equity into the relationship between the lender and the borrower. Ten percent restores our capacity to form right relationships."
This rather like the approach of governments: seeing the financial crisis as just a 'banking crisis', saving the banks who got us into this mess in the first place and essentially hoping to return to the way things were, with more stability but otherwise with a system largely unchanged. In the case of most governments, it's back to a period before the housing bubble. For Metro IAF, it's back to a period before anti-usury laws were abolished. In neither case does it involve an understanding that there really can be no 'proportion and equity' in relationships between lenders and borrowers in a system designed in favour of corporations maximising profit and consumption.
The idea of encouraging the Royal Bank of Scotland – of all the banks – to introduce a new credit card doesn't challenge the status quo in any way, but that doesn't mean that other radical solutions can't be found, ones that the compassionate people involved in Metro IAF and London Citizens can get behind. The financial crisis offers a unique opportunity not to save the banks, but to change them forever. This can mean radically de-merging the banking sector, wholesale nationalisation, the development of grassroots trading alternatives, local banking based on cooperative principles, or even practical ideas for new forms of local money, as Douglas Rushkoff advocates (see his fascinating video below).
My own view is that these ideas may just be stop-gaps and that neo-libealism needs a far more wide-ranging overhaul, one where the sour-faced executives find their eight-figure salaries reduced to zero. But these ideas are still more ambitious than the objective sought by the '10% is Enough' campaign.
I have no doubt whatsoever that the campaign has the very best of intentions, but considering the predicament that millions of people all over the world have been placed in by the global financial sector, ten percent is simply nowhere near enough.
Life Inc. The Movie from Douglas Rushkoff on Vimeo.
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Labels: Campaigns, Politics, United States
About Random Blowe
Random Blowe is the personal and political blog of Kevin Blowe, a community centre worker, campaigner and proud 'stopper' based in Newham in east London - more
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Take the Late Train: Funny and wise, intelligent and disturbing – a memorable journey into the heart of life, love and memory.
Stephen Ketley's life goes off the rails on the night of his tenth wedding anniversary. Suddenly, his marriage to Sarah is not quite as secure as it seems. Meanwhile, his stepdaughter Emma relies on him to mediate between her warring parents, his sister refuses to speak to him, and Audrey his mother drinks too much and shouts too loud. As his certainties fragment, Stephen recalls an idyllic summer in Florence with his first love, Giuliana. Forced to choose between career and love, authenticity and conformity, how can he make a decision when nothing is certain, least of all himself?
Is the past – in the shape of Giuliana and the love they shared – really over or is it waiting for him at the end of the line?
Take the Late Train shows how it's better to arrive late than not to arrive at all. The choices we make are not always irreversible, even if they seem so.


text:
Title XIV ROADS AND WATERWAYS
Chapter 238 Transportation Districts and Transportation Corporations, Special Projects
238.200  Citation of law. (5/30/1990)
238.202  Definitions. (8/28/2011)
238.205  Purpose of district — district to be political subdivision. (5/30/1990)
238.207  Creation of district, procedures — district to be contiguous, size ... (8/28/2009)
238.208  Annexation of property adjacent to a transportation district, procedure — ... (8/28/2007)
238.210  Hearing, how conducted — opposition to district, how filed — appeals, how. (8/28/2008)
238.212  Notice to public, how. (8/28/2009)
238.215  Election, when — ballot, form of — results. (8/28/2003)
238.216  Election procedure, duties of court — application for ballot, contents — ... (8/28/2006)
238.217  Costs of petition process, how paid. (5/30/1990)
238.220  Directors, election of, how, qualifications — advisors, appointed when, duties. (8/28/2007)
238.222  Powers of board, generally — officers, meetings, expenses — quorum — ... (8/28/2016)
238.225  Projects, submission of plans to commission, approval — submission to local ... (8/28/2011)
238.227  Funding mechanisms authorized — deposits with commission or authority, purpose. (8/28/1997)
238.230  Special assessments, vote required — election, ballot form — petition form ... (8/28/2007)
238.232  Property tax, vote required — election, ballot form — collection of tax. (8/28/1997)
238.233  Collection of revenues. (8/28/1997)
238.235  Sales tax, certain districts, exemptions from tax — election, ballot form — ... (8/28/2011)
238.236  Sales tax for transportation development district on all retail sales ... (8/28/2003)
238.237  Toll roads, allowed when — election, ballot form. (8/28/1997)
238.240  Indebtedness, authorized — bonds, authority to issue — limitations. (8/28/1998)
238.242  Revenue bonds, authorized — procedures, requirements — refunding bonds — ... (5/30/1990)
238.245  Property, district may purchase and control access. (5/30/1990)
238.247  Condemnation, subject to commission or authority approval, ordinance of ... (8/28/2006)
238.250  Contractual powers. (5/30/1990)
238.252  Powers — generally. (6/26/2001)
238.255  Insurance, district may obtain — purposes — self-insurance not allowed, ... (5/30/1990)
238.257  Projects, number of, changes — procedures, election required, ballot form. (5/30/1990)
238.260  Commission and authority may provide assistance, how. (5/30/1990)
238.262  Rules, commission may adopt. (5/30/1990)
238.265  Conveyance of property to district, how. (5/30/1990)
238.267  Projects, regulation of — treatment as part of state or local system, when. (5/30/1990)
238.270  Local transportation authority not to control project improvements, exception. (5/30/1990)
238.272  Audit authorized, when — costs, payment of. (8/28/2016)
238.275  Projects, transfer to commission or authority, when — abolishment of ... (8/28/2007)
Official Website for the Revised Statutes of Missouri
@05:45:32.2 304 :)


text:
Golden Cross Resources Dividends
Study the historical dividends for Golden Cross Resources. Dividends are payments made by a corporation to its shareholder members. It is the portion of corporate profits paid out to stockholders. If Golden Cross Resources Ltd has declared a dividend, you may be eligible to receive GCR dividends if the trader the company's stock on the ex-dividend date. Investors must have purchase the shares before the ex dividend date to be entitled to the dividend declared by the company.
Norfolk Group Dividends
Research the list of historical dividends for Norfolk Group. Dividends are payments made by a corporation to its shareholder members. It is the portion of corporate profits paid out to stockholders. If Norfolk Group Limited has declared a dividend, you may be eligible to receive NFK dividends if the investor the company's shares on the ex-dividend date. To be entitled to the dividend, investors must purchase the stock before the ex dividend date. If you buy the stocks on or after the ex dividend date, the previous owner of the shares will receive the dividend.
Reward Minerals Dividends
Research the list of dividend records for Reward Minerals. Dividends are a portion of company profits paid out to shareholders. If Reward Minerals Ltd has announced a dividend, you may be eligible to receive RWD dividends if the stock trader the company's shares on the ex-dividend date. In order to receive the dividend payout, investors must purchase the shares before the ex dividend date. The previous owner of the shares will receive the dividend if you buy the stocks on or after the ex dividend date.
Imperial Corporation Dividends
Read about the list of historical dividends for Imperial Corporation. Dividends are a portion of company profits paid out to shareholders. If Imperial Corporation Limited has announced a dividend, you may be eligible to receive IMP dividends if the stock trader the company's shares on the ex-dividend date. In order to receive the dividend payout, investors must purchase the shares before the ex dividend date. The previous owner of the shares will receive the dividend if you buy the stocks on or after the ex dividend date.
Medigard Dividends
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Empire Resources Dividends
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Shaw River Resources Dividends
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Caltex Australia Dividends
26 August, 2010 - 23:45
Study the historical dividends for CALTEX AUSTRALIA LIMITED. Dividends are a portion of company profits paid out to shareholders. You are eligible to receive CTX dividends if you own the company's stock on the ex-dividend date. Investor's must have purchased the stock before the ex dividend date to be entitled to the dividend. The previous owner of the shares will receive the CTX dividend if you buy the stocks on or after the ex dividend date. The Pay Date or the Date Payable is the day when the dividend is paid to shareholders.
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"O Tempo É Meu Amigo" é um CD single de inéditos da banda portuguesa de rock UHF. Editado em 23 de março de 2009 pela AM.RA Discos, com distribuição da Sony Music.

Trata-se do single extra incorporado no pacote da primeira edição do álbum de vídeo Absolutamente Ao Vivo (2009), não estando disponível para venda individual. Esse álbum recuperou o concerto no Coliseu dos Recreios, em Lisboa, em setembro de 2006 e, como o título confere, é a reprodução fiel de tudo o que aconteceu no palco. A canção foi selecionada para integrar a banda sonora da telenovela Deixa Que Te Leve, exibida nesse ano de 2009.

Lista de faixas
O single disco compacto é composto por uma faixa em versão padrão e outra em edição rádio, da autoria de António Manuel Ribeiro.

Membros da banda
 António Manuel Ribeiro (vocal)
 António Côrte-Real (guitarra elétrica e acústica)
 Luís 'Cebola' Simões (baixo e vocal de apoio)
 Fernando Rodrigues (piano, sintetizador e pandeireta
 Ivan Cristiano (bateria e vocal de apoio)

Ligações externas

Ver também

Canções gravadas por UHF
Singles de 2009
Álbuns de músicos de Portugal


SCENTCOLUX SAS (Parfums M.Micallef), capital of 700 000 €, registered at RCS Grasse N°437 653 884 0043, the Head Office is situated: 133 chemin de St. Marc, Grasse, France.
The V.A.T. N° is FR25437653884.
Publishing Director is: Lesley Nejman.
CNIL: n° 1795809v0, date: 22/09/2014.


They say that beauty is in the eye of the beholder, well this beauty certainly knows how to look fantastic that's for sure.
This is the latest release of our Equihunter Encore 39 – 3.9t horsebox.
This one sports a safe and robust Stallion layout with a full length partition in two parts. Plus the partition is also fully sliding, operated by one hand and moves from one side to the other with ease.
The uprated chassis delivers over 1,200 kgs of payload on this build.
Built on a long wheelbase Peugeot Boxer, this project offers practical transport for your horses and looks fantastic as well. What more could a horse owner wish for…?
See the full gallery below for more high quality images.
Viewings can be arranged in Surrey, the vehicle is based near the M3 / M25 area.
An early viewing is recommended as this will sell quickly…. Contact Chris on 07904 818389 to arrange a viewing.
Contact details below, or click here for our full contacts page and map….
Some original information on the build….
Our 3.5 tonne vehicle has some impressive features Stalled for two, the Arena can carry a payload of over 1100 kilograms but can be driven by anyone holding a car license.
The Chassis The Arena is based on a 3.5 tonne chassis from a Vauxhall Movano, a Renault Master or a Peugeot Boxer.
Fully re-covered seats in easy clean beige vinyl with our logo on the headrest.
The Horse Area Stalled for 2 with rear facing travel for a stress free journey, the robust central partition is an all steel construction. There's an optional integral horse area camera available with a remote 7 inch wireless screen in the cab for the driver and passengers to review when driving.
A combined ramp & access door is split horizontally, this allows for easier loading and unloading in cramped venue conditions, this shorter fully assisted ramp easily lowers into position with the top door swinging up out of the way providing an element of cover from rain or sun. Both sections are powered by powerful gas rams that allow for a seamless and easy operation.
Day Living The rear section of the vehicle is set aside for day living which makes for a more comfortable day out. A bulkhead separates this section from the horse area but there is access to each of the horse stalls via two doors with protected windows, one to each stall.
There is also a large lockable access door to the rear of the vehicle. As an optional extras we can fit a wardrobe with a hanging rail for your riding gear, also a padded seating plus a concealed flushing toilet.
Also available as an optional extra is a gas hob and sink with an electrically pumped water supply. Two saddle racks and bridle hooks are positioned in the living area for greater security.
The wide rear access door is fitted with flush bonded opening window with heavily tinted privacy glass providing discrete changing facilities at your venue and event.
There is also ample storage area in the Luton cab, this is accessed via a full width hatch from the horse area, it can hold an impressive amount of equipment for days out and away.


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2009 Midlands Regional Championship - Second Section - retrospective
Everyone had a great time of it in the Second Section - from listeners, judges, players and MDs. None enjoyed it as much as the winners though we are sure...
Who's a lucky girl? Shirland get ready to celebrate
From the first band on stage in the Civic Hall on Sunday morning, it was clear that the Second Section bands at Bedworth were having a great time with Dan Price's New World Sketches.
With the composer on hand throughout, it made for an enjoyable experience as eleven bands all succeeded in expressing their enthusiasm for the music in a manner that was both refreshing and often great fun.
Something out of it
As Colin Hardy commented afterwards, there wasn't one band that didn't manage to get something out of the music and their performance.
If there was a point to be proved, it was the simple truth that the right choice of test piece for the right section will motivate, enthuse and challenge the players simultaneously; and in every Second Section Regional contest so far this year, Dan Price's piece has done just that.
The fact that it was refreshing to listen to was in part due to the fact that in the First Section contest the previous day few, if any bands securely negotiated the very basics of note production, let alone the technical challenges that Graham Cole's Pentacle presented. Here though, it was a different story as the players expressed themselves with belief rather than abject fear.
In the final analysis there were six bands that separated the field into two halves for us, all of whom produced worthy, often pleasingly musical performances although it was both musicality and straightforward consistency that saw Shirland win through to take the title in some style.
Shirland's was a remarkably assured, mature and confident performance for a band that as always, had a healthy mix of young players and older heads around the stands. After the disappointment of dropping down to the Second Section last year, there could be no better way of bouncing back than this and having taken over the baton from Marie Smith, Andrew Dennis will no doubt have been a proud man on Sunday afternoon.
It was a performance marked out by strong basics of note production, tuning and stylistic awareness as the band slipped with ease from Gershwin to Copland in the outer movements whilst capturing the central movement with a suitably relaxed manner.
The band sound was strong, if anything perhaps a little overly so on occasions, but the stars were the young members of the team, ranging from easily the youngest percussion section of the day to an all girl horn section that were the coolest (and prettiest!) under pressure of any in the Second Section field.
If the band can recreate this kind of form in Harrogate, it will be a fine representative for the Midlands later in the year.
Much speculation centred on Stephen Curtis and Wellington Telford as they took to the stage as National Third Section Champions with an early number three draw.
With David Maplestone bolstering the ranks on soprano and fresh from his victory with Phoenix West Midlands the previous day, it was a carefully thought through, finely shaped performance that for our money ran Shirland closer than might have been implied by the adjudicators.
There were some terrific solo contributions from the band's principal cornet and Eb bass in the slow movement although it was a final hoe-down that just lost its focus and concentration to some degree that was to be the final divider between first and second places. Harrogate will feel like home territory for the band when they join Shirland at the finals.
Moving down through the top six places, consistency gradually started to tail away as the performances fell into place and it was Oddfellows Brass, our pre-contest prediction for fourth place, that just missed out on a trip to the north as they took to the stage as the last band of the eleven contenders.
For us there was a fair margin between second and third places on the day, as Oddfellows commenced with a tempo that was almost as bright as Rob Boulter's characteristically bobby-dazzling shirt.
It was certainly spirited stuff although ultimately it was the occasional passage of blurred detail and some loss of precision in the Coplandesque Rodeo that became the deciding factor.
Nervy start
Tintwistle did well from a slightly nervy start and the dreaded number one draw to hold its own for fourth place. We had the band a couple of places lower but this was one of a few performances on the day that whilst broadly technically sound, did not quite get to grips with the stylistic contrasts in Dan Price's highly colourful score.
Having dropped down from the First Section last year however, it was a performance that should give the band the encouragement that it can more than hold its own at Second Section level.
Early markers
In fifth spot, Graham Jacklin and Leicestershire Co-op were one of the early markers for us from the number two draw, producing a bold, confident sound and good individual contributions from euphonium, trombone and a very young front row cornet section.
The Deep South did seem to move along at a particularly slow pace that inhibited the flow of the music though and there were balance problems here and there that would have pushed the band down the rankings with Colin Hardy and Chris Wormald.
Unluckiest
Matlock were one of the unluckiest bands on the day for us, with Roger Jepson and his team capturing the style of the music very well, albeit without achieving quite the same level of accuracy in ensemble that would have ranked them with Shirland and Wellington Telford.
We had them third and having been promoted as Third Section champions in 2008, this is a band more than capable of making its mark at this level of contesting.
Started well
Bilton Silver (Rugby) started well, with SideWalk as confident as any on the day, but concentration gradually faded away with The Deep South not quite capturing the atmosphere as well as some and Rodeo falling victim to increasingly loose ensemble. In the end it became a case of so near and yet so far. Seventh place was about right for us.
In eighth and ninth positions respectively, Arrow Valley and West Mercia Constabulary both succeeded in getting into the spirit of the music without being able to match the technical standards of the bands higher up the table.
Tuning issues
Issues of tuning figured in both performances as did nerves, whilst Stourport on Seven and Long Eaton Silver, two bands that are capable of solid performances on their day, both found the going that little bit too tough on this occasion.
A lively, entertaining contest then that was clearly enjoyed by those in the audience as much as the players themselves.
We have no doubt that the two bands heading to Harrogate will represent the Midlands well, whilst credit should also go to Dan Price for a test piece eminently suitable for Second Section contesting. Let's hope we hear more from him soon.
Christopher Thomas


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