Combinatorial and Computational Investigations of Neighbor-Joining Bias.

The Neighbor-Joining algorithm is a popular distance-based phylogenetic method that computes a tree metric from a dissimilarity map arising from biological data. Realizing dissimilarity maps as points in Euclidean space, the algorithm partitions the input space into polyhedral regions indexed by the combinatorial type of the trees returned. A full combinatorial description of these regions has not been found yet; different sequences of Neighbor-Joining agglomeration events can produce the same combinatorial tree, therefore associating multiple geometric regions to the same algorithmic output. We resolve this confusion by defining agglomeration orders on trees, leading to a bijection between distinct regions of the output space and weighted Motzkin paths. As a result, we give a formula for the number of polyhedral regions depending only on the number of taxa. We conclude with a computational comparison between these polyhedral regions, to unveil biases introduced in any implementation of the algorithm.

Dimensions of Group-Based Phylogenetic Mixtures.

Mixtures of group-based Markov models of evolution correspond to joins of toric varieties. In this paper, we establish a large number of cases for which these phylogenetic join varieties realize their expected dimension, meaning that they are nondefective. Nondefectiveness is not only interesting from a geometric point-of-view, but has been used to establish combinatorial identifiability for several classes of phylogenetic mixture models. Our focus is on group-based models where the equivalence classes of identified parameters are orbits of a subgroup of the automorphism group of the abelian group defining the model. In particular, we show that for these group-based models, the variety corresponding to the mixture of r trees with n leaves is nondefective when [Formula: see text]. We also give improved bounds for claw trees and give computational evidence that 2-tree and 3-tree mixtures are nondefective for small n.

Family Politics: Campaigning for Child Benefits in the 1980s.

Child benefit was seen by some to encourage the sort of welfare dependency that the moralistic individualism of Thatcherism opposed. Yet, surprisingly, the benefit survived the Thatcher years. Its survival reveals the conundrum the Conservative party have had regarding benefits for the family and family policy more broadly. Neo-liberals were supportive of the family as a vehicle for reinforcing Conservative values. Yet, the late 1970s and 1980s were periods of social change where the traditional family of the Conservative imagination was breaking down and consequently 'family policy' became a key political theme. By emphasizing the utility of child benefit as being fair to families, rather than its role in poverty alleviation, the Child Poverty Action Group (CPAG) was able to draw on this increased concern. As a result, their campaigns to save child benefit profited from increased support from across Conservatism. In tracing the development of CPAG's campaign, this article will demonstrate the cautiousness of Conservatives, even in the neo-liberal era, to changing some aspects of social policy. It will also highlight the challenge changing family patterns posed to the male breadwinner model that had long been embedded within the welfare policy prescriptions of both main parties.

Efficient Quartet Representations of Trees and Applications to Supertree and Summary Methods.

Quartet trees displayed by larger phylogenetic trees have long been used as inputs for species tree and supertree reconstruction. Computational constraints prevent the use of all displayed quartets in many practical problems with large numbers of taxa. We introduce the notion of an Efficient Quartet System (EQS) to represent a phylogenetic tree with a subset of the quartets displayed by the tree. We show mathematically that the set of quartets obtained from a tree via an EQS contains all of the combinatorial information of the tree itself. Using performance tests on simulated datasets, we also demonstrate that using an EQS to reduce the number of quartets in both summary method pipelines for species tree inference as well as methods for supertree inference results in only small reductions in accuracy.

A comparative study of SVDquartets and other coalescent-based species tree estimation methods.

BACKGROUND: Species tree estimation is challenging in the presence of incomplete lineage sorting (ILS), which can make gene trees different from the species tree. Because ILS is expected to occur and the standard concatenation approach can return incorrect trees with high support in the presence of ILS, "coalescent-based" summary methods (which first estimate gene trees and then combine gene trees into a species tree) have been developed that have theoretical guarantees of robustness to arbitrarily high amounts of ILS. Some studies have suggested that summary methods should only be used on "c-genes" (i.e., recombination-free loci) that can be extremely short (sometimes fewer than 100 sites). However, gene trees estimated on short alignments can have high estimation error, and summary methods tend to have high error on short c-genes. To address this problem, Chifman and Kubatko introduced SVDquartets, a new coalescent-based method. SVDquartets takes multi-locus unlinked single-site data, infers the quartet trees for all subsets of four species, and then combines the set of quartet trees into a species tree using a quartet amalgamation heuristic. Yet, the relative accuracy of SVDquartets to leading coalescent-based methods has not been assessed. RESULTS: We compared SVDquartets to two leading coalescent-based methods (ASTRAL-2 and NJst), and to concatenation using maximum likelihood. We used a collection of simulated datasets, varying ILS levels, numbers of taxa, and number of sites per locus. Although SVDquartets was sometimes more accurate than ASTRAL-2 and NJst, most often the best results were obtained using ASTRAL-2, even on the shortest gene sequence alignments we explored (with only 10 sites per locus). Finally, concatenation was the most accurate of all methods under low ILS conditions. CONCLUSIONS: ASTRAL-2 generally had the best accuracy under higher ILS conditions, and concatenation had the best accuracy under the lowest ILS conditions. However, SVDquartets was competitive with the best methods under conditions with low ILS and small numbers of sites per locus. The good performance under many conditions of ASTRAL-2 in comparison to SVDquartets is surprising given the known vulnerability of ASTRAL-2 and similar methods to short gene sequences.

Phylogenomic species tree estimation in the presence of incomplete lineage sorting and horizontal gene transfer.

BACKGROUND: Species tree estimation is challenged by gene tree heterogeneity resulting from biological processes such as duplication and loss, hybridization, incomplete lineage sorting (ILS), and horizontal gene transfer (HGT). Mathematical theory about reconstructing species trees in the presence of HGT alone or ILS alone suggests that quartet-based species tree methods (known to be statistically consistent under ILS, or under bounded amounts of HGT) might be effective techniques for estimating species trees when both HGT and ILS are present. RESULTS: We evaluated several publicly available coalescent-based methods and concatenation under maximum likelihood on simulated datasets with moderate ILS and varying levels of HGT. Our study shows that two quartet-based species tree estimation methods (ASTRAL-2 and weighted Quartets MaxCut) are both highly accurate, even on datasets with high rates of HGT. In contrast, although NJst and concatenation using maximum likelihood are highly accurate under low HGT, they are less robust to high HGT rates. CONCLUSION: Our study shows that quartet-based species-tree estimation methods can be highly accurate under the presence of both HGT and ILS. The study suggests the possibility that some quartet-based methods might be statistically consistent under phylogenomic models of gene tree heterogeneity with both HGT and ILS.

Distance-Based Phylogenetic Methods Around a Polytomy.

Distance-based phylogenetic algorithms attempt to solve the NP-hard least-squares phylogeny problem by mapping an arbitrary dissimilarity map representing biological data to a tree metric. The set of all dissimilarity maps is a Euclidean space properly containing the space of all tree metrics as a polyhedral fan. Outputs of distance-based tree reconstruction algorithms such as UPGMA and neighbor-joining are points in the maximal cones in the fan. Tree metrics with polytomies lie at the intersections of maximal cones. A phylogenetic algorithm divides the space of all dissimilarity maps into regions based upon which combinatorial tree is reconstructed by the algorithm. Comparison of phylogenetic methods can be done by comparing the geometry of these regions. We use polyhedral geometry to compare the local nature of the subdivisions induced by least-squares phylogeny, UPGMA, and neighbor-joining when the true tree has a single polytomy with exactly four neighbors. Our results suggest that in some circumstances, UPGMA and neighbor-joining poorly match least-squares phylogeny.

A service-based evaluation of a therapist-supported online cognitive behavioral therapy program for depression.

BACKGROUND: Evidence suggests that Internet-delivered cognitive behavioral therapy (CBT) may be as effective as face-to-face delivery for depression, but attrition and engagement rates remain a challenge. OBJECTIVE: This service-based study aimed to evaluate an online, therapist-supported, CBT-based program for depression. The program was specifically designed to address engagement issues, most notably by integrating online therapist support and communication within the platform. METHODS: Participants were 80 adults who were registered university students. Participants used the modular online program over 8 weeks, supported by a therapist. Engagement information was gathered automatically by the online system, and analyzed for all participants. Severity of participants' self-reported symptoms of depression were assessed preintervention and postintervention using the Beck Depression Inventory-II (BDI-II). Postintervention measures were completed by 53 participants. RESULTS: A high level of engagement was observed compared to a previous study within the same service, along with extensive use of a range of program features. A statistically significant (P<.001) decrease in self-reported depressive symptomatology from preintervention (mean BDI-II 25.47) to postintervention (mean BDI-II 15.53) with a large effect size (d=1.17) was also observed. CONCLUSIONS: The results indicate the potential of unintrusive and easily provided online support to enhance engagement with online interventions. The system described in the paper also illustrates how such online support can be tightly integrated with interactive online programs by using a range of design strategies intended to improve the user experience.

Metal ion selectivity and substrate inhibition in the metal ion chelation catalyzed by human ferrochelatase.

Protoporphyrin IX ferrochelatase (EC 4.99.1.1) catalyzes the terminal step in the heme biosynthetic pathway, the insertion of ferrous iron into protoporphyrin IX. Ferrochelatase shows specificity, in vitro, for multiple metal ion substrates and exhibits substrate inhibition in the case of zinc, copper, cobalt, and nickel. Zinc is the most biologically significant of these; when iron is depleted, zinc porphyrins are formed physiologically. Examining the k(cat)/K(m)(app) ratios for zinc and iron reveals that, in vitro, zinc is the preferred substrate at all concentrations of porphyrin. This is not the observed biological specificity, where zinc porphyrins are abnormal; these data argue for the existence of a specific iron delivery mechanism in vivo. We demonstrate that zinc acts as an uncompetitive substrate inhibitor, suggesting that ferrochelatase acts via an ordered pathway. Steady-state characterization demonstrates that the apparent k(cat) depends on zinc and shows substrate inhibition. Although porphyrin substrate is not inhibitory, zinc inhibition is enhanced by increasing porphyrin concentration. This indicates that zinc inhibits by binding to an enzyme-product complex (EZnD(IX)) and is likely to be the second substrate in an ordered mechanism. Our analysis shows that substrate inhibition by zinc is not a mechanism that can promote specificity for iron over zinc, but is instead one that will reduce the production of all metalloporphyrins in the presence of high concentrations of zinc.