Unique Reconstruction of Tree-Like Phylogenetic Networks from Distances Between Leaves

In this paper, a class of rooted acyclic directed graphs (called TOM-networks) is defined that generalizes rooted trees and allows for models including hybridization events. It is argued that the defining properties are biologically plausible. Each TOM-network has a distance defined between each pair of vertices. For a TOM-network N, suppose that the set X consisting of the leaves and the root is known, together with the distances between members of X. It is proved that N is uniquely determined from this information and can be reconstructed in polynomial time. Thus, given exact distance information on the leaves and root, the phylogenetic network can be uniquely recovered, provided that it is a TOM-network. An outgroup can be used instead of a true root.     

An algorithm to equiprobably generate all directed trees withk labeled terminal nodes and unlabeled interior nodes

A computer algorithm is presented which equiprobably generates any member of the set of all directed trees withk labeled terminal nodes and unlabeled interior nodes. The algorithm requires roughlyk ² /2 storage locations. The one-time initialization requiresO(k ² ) time, while generating each tree requiresO(k) time. Contribution No. 477 in Ecology and Evolution, State University of New York at Stony Brook. This research was supported by Grant No. DEB8003508 from the National Science Foundation to Robert R. Sokal.     

Properties of the nearest neighbor interchange metric for trees of small size

The crossover or nearest neighbor interchange metric has been proposed for use in numerical taxonomy to obtain a quantitative measure of distance between classifications that are modeled as unrooted binary trees with labeled leaves. This metric seems difficult to compute and its properties are poorly understood. A variant called the closest partition distance measure has also been proposed, but no efficient algorithm for its computation has yet appeared and its relationship to the nearest neighbor interchange metric is incompletely understood. I investigate four conjectures concerning the nearest neighbor interchange and closest partition distance measures and establish their validity for trees with as many as seven labeled vertices. For trees in this size range the two distance measures are identical. If a certain decomposition property holds for the nearest neighbor interchange metric, then the two distance measures are also identical at small distances for trees of any size.     

A dynamic model of an environmental system withn interacting components andp degrees of freedom

The nonlinear differential equations of growth proposed by Volterra (1931) are used as the basis for a dynamic model of ann-element system withp specified, terminal conditions andp missing initial conditions. The resulting two-point boundary-value problem can be solved, ifp is not large, by the shooting method used previously by Huddleston (1967). A numerical example withn=4 andp=2 is solved on a digital computer, and some results are presented.     

Counting glycans revisited

We present an algorithm for counting glycan topologies of order \(n\) that improves on previously described algorithms by a factor \(n\) in both time and space. More generally, we provide such an algorithm for counting rooted or unrooted \(d\) -ary trees with labels or masses assigned to the vertices, and we give a “recipe” to estimate the asymptotic growth of the resulting sequences. We provide constants for the asymptotic growth of \(d\) -ary trees and labeled quaternary trees (glycan topologies). Finally, we show how a classical result from enumeration theory can be used to count glycan structures where edges are labeled by bond types. Our method also improves time bounds for counting alkanes.     

Ants on swollen-thorn acacias: species coexistence in a simple system

 On the black cotton soils of the Laikipia ecosystem in Kenya, two swollen-thorn acacia species support nine ant species, four of which are apparently obligate plant-ants. Among the ants, there are five species of Crematogaster, two species of Camponotus, and one each of Tetraponera and Lepisota. Acacia drepanolobium is host to four ant species that are both common and mutually exclusive. These four ant species, and an additional non-exclusive ant species, tend to occur on trees of different sizes, implying a succession of ant occupants. Nonetheless, all four exclusive species occur in substantial proportions on trees of intermediate size. There is direct evidence that an early successional ant species (Tetraponera penzigi) is actively evicted by two late successional ant species in the genus Crematogaster. There was also some evidence of height differentiation among ant species resident on A. seyal. Different acacia-ant species had different direct effects on A. drepanolobium. Extrafloral nectaries were eaten and destroyed only on trees inhabited by Tetraponera. Axillary shoots were eaten only on trees inhabited by C. nigriceps (potentially another early successional ant). This was associated with more new terminal shoots and healthier leaves than other trees, but also the virtual elimination of flowering and fruiting. Different resident acacia-ant species also had characteristic relationships with other insects. Among the four mutually exclusive ant species, only Crematogaster sjostedti was associated with two species of Camponotus, at least one of which (C. rufoglaucus) appears to be a foraging non-resident. A. drepanolobium trees occupied by C. sjostedti were also far more heavily infested with leaf galls than were trees occupied by other ant species. A. drepanolobium trees occupied by C. mimosae and C. sjostedti uniquely had tended adult scale insects. This diversity of ant inhabitants, and their strikingly different relationships with their hosts and other insect species, are examples of coexisting diversity on an apparently uniform resource. Received: 13 November 1995 / Accepted: 16 May 1996     

All galls are divided into three or more parts: recursive enumeration of labeled histories for galled trees

Objective

In mathematical phylogenetics, a labeled rooted binary tree topology can possess any of a number of labeled histories, each of which represents a possible temporal ordering of its coalescences. Labeled histories appear frequently in calculations that describe the combinatorics of phylogenetic trees. Here, we generalize the concept of labeled histories from rooted phylogenetic trees to rooted phylogenetic networks, specifically for the class of rooted phylogenetic networks known as rooted galled trees.

Results

Extending a recursive algorithm for enumerating the labeled histories of a labeled tree topology, we present a method to enumerate the labeled histories associated with a labeled rooted galled tree. The method relies on a recursive decomposition by which each gall in a galled tree possesses three or more descendant subtrees. We exhaustively provide the numbers of labeled histories for all small galled trees, finding that each gall reduces the number of labeled histories relative to a specified galled tree that does not contain it.

Conclusion

The results expand the set of structures for which labeled histories can be enumerated, extending a well-known calculation for phylogenetic trees to a class of phylogenetic networks.

     

Reconstruction of certain phylogenetic networks from the genomes at their leaves

A network N is a rooted acyclic digraph. A base-set X for N is a subset of vertices including the root (or outgroup), all leaves, and all vertices of outdegree 1. A simple model of evolution is considered in which all characters are binary and in which back-mutations occur only at hybrid vertices. It is assumed that the genome is known for each member of the base-set X. If the network is known and is assumed to be “normal,” then it is proved that the genome of every vertex is uniquely determined and can be explicitly reconstructed. Under additional hypotheses involving time-consistency and separation of the hybrid vertices, the network itself can also be reconstructed from the genomes of all members of X. An explicit polynomial-time procedure is described for performing the reconstruction.     

A Phylogeny for the African Treefrog Family Hyperoliidae Based on Mitochondrial rDNA

Mitochondrial 12S rRNA sequences were used to construct a phylogeny for the African treefrog family, Hyperoliidae. The sequences were aligned using the well-established mt 12S rRNA secondary structure as a map to designate stem and loop positions. Conservation of secondary structure permits a more accurate basis for assessing homologies than does primary sequence alone. The molecular trees showed many similarities to the morphological trees constructed previously. Species within a genus always grouped together. The generaHyperolius, Heterixalus, Afrixalus,andKassinawere resolved, but not with statistical significance.Leptopeliswas the basal group. The analysis shows clearly thatPhlyctimantisgroups withKassinaas it did in Drewes' morphological tree and thatTachycnemisgroups closely withHeterixalus,a relationship not suggested by the morphological data. Character weighting (including compensatory base changes), mitochondrial trees vs gene trees, and the biogeography of the group are discussed.     

DNA hybridization,cladistics, and the phylogeny of phalangerid marsupials

Summary Single-copy DNA/DNA hybridization experiments and numerical cladistic analyses of anatomical characters were used to investigate relationships among nine phalangerid (Marsupialia) species from four different genera. Both rate-dependent and rate-independent analyses of molecular data indicate that species ofTrichosurus form one clade and thatStrigocuscus, Phalanger, andSpilocuscus form a second. Within the latter group,Spilocuscus is excluded from aStrigocuscus-Phalanger calde, which, in turn, is not fully resolved on a jackknife strict consensus tree. Minimum-length Dollo, Wagner, and Camin-Sokal parsimony trees based on 35 anatomical characters, in contrast, suggest placement ofStrigocuscus withTrichosurus rather than withSpilocuscus andPhalanger. However, there are two derived characters that support the alternative arrange ofStrigocuscus withSpilocuscus andPhalanger and one character that further unitesStrigocuscus andPhalanger. Thus, DNA hybridization results are not inconsistent with the distribution of derived character states among anatomical characters, only with minimum-length trees based on character data.     

Simultaneous Measurement of Nicotinic Acid and Its Major Metabolite,Nicotinuric Acid in Blood and Urine by a Reversed-phase High-performance Liquid Chromatography

The linear chromosome of Streptomyces griseus IFO13350 contains not only atypical telomere sequences but also probable pseudogenes for two typical telomeric proteins. Two identical operons (SGR98t-SGR97t near one telomere and SGR7041t-SGR7042t near the other telomere) in the terminal inverted repeat sequence were predicted to encode a novel pair of telomeric proteins. SGR97t, a 185-amino-acid protein showing only 18% amino acid sequence identity to typical terminal proteins of Streptomyces, was found to be attached to the chromosomal ends, as determined by immunological analysis. On the other hand, electrophoretic mobility shift assays showed that SGR98t, an 837-amino-acid protein having a DnaB-like helicase C-terminal domain, was capable of binding specifically to the single-stranded terminal DNA corresponding to the 3′ overhang of the replication intermediate. These results indicate that SGR97t (and SGR7042t) and SGR98t (and SGR7041t) were the functional telomeric proteins in the replication of the linear chromosome of S. griseus IFO13350.     

Tree-average distances on certain phylogenetic networks have their weights uniquely determined

ABSTRACT: A phylogenetic network N has vertices corresponding to species and arcs corresponding to direct genetic inheritance from the species at the tail to the species at the head. Measurements of DNA are often made on species in the leaf set, and one seeks to infer properties of the network, possibly including the graph itself. In the case of phylogenetic trees, distances between extant species are frequently used to infer the phylogenetic trees by methods such as neighbor-joining. This paper proposes a "tree-average" distance for networks more general than trees. The notion requires a "weight" on each arc measuring the genetic change along the arc. For each displayed tree the distance between two leaves is the sum of the weights along the path joining them. At a hybrid vertex, each character is inherited from one of its parents. We will assume that for each hybrid there is a probability that the inheritance of a character is from a specified parent. Assume that the inheritance events at different hybrids are independent. Then for each displayed tree there will be a probability that the inheritance of a given character follows the tree; this probability may be interpreted as the probability of the tree. The "tree-average" distance between the leaves is defined to be the expected value of their distance in the displayed trees. For a class of rooted networks that includes rooted trees, it is shown that the weights and the probabilities at each hybrid vertex can be calculated given the network and the tree-average distances between the leaves. Hence these weights and probabilities are uniquely determined. The hypotheses on the networks include that hybrid vertices have indegree exactly 2 and that vertices that are not leaves have a tree-child.     

Bounds on the total particle number for species governed by reaction-diffusion equations in the infinite spatial domain

Differential inequality methods are developed for establishing upper and lower bounds on the total particle numberN(t)=∫θ(x,t) d³ x associated with solutions to nonlinear reaction-diffusion equations of the form ∂θ/∂t=D∇²θ+fθ-gθ ⁿ⁺¹ , whereD(>0),n(>0),f andg are constant parameters. If finite in a neighborhood oft=0,N(t) is bounded below for allt≥0 by a certain derived function oft for equations withg≥0. An upper bound onN(t) is obtained for equations withn=1,f<0 andg<0. These results provide general preservation and extinction criteria for the total particle number.     

The nature of inbreeding in a seed orchard of Douglas fir as shown by an efficient multilocus model

Summary The amounts of self-fertilization versus consanguineous matings (as measured by effective selfing) was estimated in a seed orchard of Douglas-fir, using progeny array data at six allozyme loci. The orchard is family structured, consisting several grafts (clones) and/or open-pollinated (o-p) progeny from each of several plus-trees. Population-wide selfing rates were found to be 7% for the o-p trees and 2% for the cloned trees. Estimates of mating system parameters for individual trees showed this difference for average outcrossing rate t (1) still largely remained when outcrossingpollen gene frequency p was not allowed to vary among trees and (2) disappeared when p was allowed to vary among trees. Under this joint t and p estimation, o-p trees showed both significant variation of t (based upon a one-way ANOVA grouped by common plus-tree) and significant regressions of p on ovule genotype (indicative of consanguineous matings); cloned trees showed neither. This higher rate of consanguineous mating for o-p trees might be explained by the larger and more variable size of o-p families in the orchard. Estimates of outcrossing rate t and outcrossingpollen gene frequency p were based upon a multilocus model which makes full use of the information in the data. The increased information it gives over observed outcross models is equivalent to adding 30–50% more loci, and it gives enough degrees of freedom to jointly estimate t and p for individual trees (individual progeny arrays) under certain conditions. In addition, inclusion of megagametophyte data nearly doubles the information about the mating system of individual trees.     

Nouvelle expérimentation à grande échelle de la lutte biologique contre la Mouche de l'olive (Dacus oleae Gmel.) au moyan D'Opius concolor siculus Mon. en Sicile en 1967

Summary In 1967 the artificial biological control against the olive fly was undertaken in Palermo (Sicily) on about 300,000 olive trees, grown in an area of about 2,800 hectares, partly on dry soil and partly on irrigated soil. From June 26th until October 31th 32,000,000Opius concolor Szepl.siculus Mon. were released, which had been produced in special insectaries onCeratitis larvae. In 1967 theDacus oleae infestation was tardy on the whole; nevertheless, in some biotopes of the area covered by olive trees where the biological control was carried out, olives infested withDacus could observed since June 20th with eggs and larvae in the first stage. In September and October the olive fly was present in all olive groves of the coastal and hill areas and immediately multiplied and spread to such a point that between September 15th and October 15th most of the olives had fallen to the ground and almost 100% of those that had remained on the trees were infested withDacus. The results of the biological control have been, on the contrary, most satisfactory and the olives in the entire area not only were almost completely healthy for the most part, but nearly all of them had remained on the trees until the crop was gathered. In 1967 the cost of the biological control amounted to Lit. 81 per tree and Lit. 0.60 perOpius produced, with a considerable saving as compared to1966. It is remarkable that about 100Opius were released per tree in 1967, whereas in 1966 about 28 had been released per tree. The good results of the biological control much depend on the mass releases made at the beginning of July in order to check the firstDacus generation; mass releases should be made also when apparently there are noDacus in the olive grove and the olives are for the most part intact. The biological control undertaken in Sicily against theDacus in 1967 is the first large-scale application of this control method in Europe and the results obtained clearly prove the certainty that by this method olives can be protected against theDacus and men defended against the residual toxic products, at less cost than that required for a chemical control.      

Nitrogen source effects on rhizosphere pH and nutrient accumulation by Pacific Northwest conifers

Growth responses ofCasuarina cunninghamiana to inoculation withFrankia are described in unsterilized field soils at three sites. At Mt Crawford, South Australia, seedlings of three provenances ofC. cunninghamiana were inoculated with a singleFrankia source just prior to planting out. Forty-four months after planting, inoculation had more than doubled wood production by twoC. cunninghamiana provenances, whilst a third provenance grew poorly and did not respond to inoculation. In Zimbabwe, seedlings of one provenance ofC. cunninghamiana were inoculated in the nursery with one of four differentFrankia strains. In an N deficient soil at Kadoma, three of theseFrankia increased tree height 14 months after planting by between 50% and 70% in comparison to the uninoculated seedlings. The fourthFrankia strain resulted in increased tree height to three times that of the uninoculated controls and up to double that of the other threeFrankia strains. At Gympie, Queensland, Australia, seedlings ofC. cunninghamiana raised open-rooted in a nursery bed were inoculated withFrankia seventeen weeks before planting out. During the 22 months following planting in the field, tree growth was limited by soil P status and there was no response in tree height or stem diameter to inoculation withFrankia or to N fertilizer unless P was applied. In the presence of added P there was a significant response both toFrankia inoculation and to N fertilizer. This positive interaction between P application and N treatment was reflected in wood volumes-inoculated trees and those trees supplied N fertilizer produced 34% and 95% more wood volume than did the uninoculated trees. These results demonstrate the potential to increase the productivity of Casuarina plantings by inoculation withFrankia and by alleviation of P deficiency.     

Flexible mating system in a logged population of <Emphasis Type="Italic">Swietenia macrophylla</Emphasis> King (Meliaceae): implications for the management of a threatened neotropical tree species

Microsatellites were used to evaluate the mating system of the remaining trees in a logged population of Swietenia macrophylla, a highly valuable and threatened hardwood species, in the Brazilian Amazon. A total of 25 open pollinated progeny arrays of 16 individuals, with their mother trees, were genotyped using eight highly polymorphic microsatellite loci. Genotypic data analysis from the progeny arrays showed that 373 out of the 400 seedlings (93.25%) were unambiguously the result of outcrossed matings and that the remaining 6.75% had genotypes consistent with self-fertilisation. Apomixis could be ruled out, since none of the 400 seedlings analysed had a multi-locus genotype identical to its mother tree. The high estimate of the multi-locus outcrossing rate (t _m = 0.938 ± 0.009) using the mixed mating model also indicated that the population in this remnant stand of S. macrophylla was predominantly allogamous. The relatively large difference between the multi-locus and single-locus outcrossing estimates (t _m −t _s = 0.117 ± 0.011) provides evidence that, in spite of the high outcrossing rate, a considerable degree of biparental inbreeding has contributed to the genetic structure of this population. Levels of outcrossing were not evenly distributed among maternal trees (t _m ranging from 0.39 to 1.00), suggesting the occurrence of a variable degree of self-incompatibility and/or dichogamy among individual trees of this monoecious species. Due to its generalist pollination system and some level of tolerance for selfing, S. macrophylla seems to be resilient to environmental disturbances such as those caused by logging, since it sets fruits with predominantly outcrossed seeds even at low stand densities. Therefore, the remaining individuals in logged areas or in relict fragments may be very important for long-term population recovery and genetic conservation programmes.     

Zum zeitlichen Verlauf von Substratkonzentrationsprofilen in einer Enzymträgerkugel

In this paper the time evolution of substrate concentration profiles in spherical particles with homogeneous enzyme distribution is investigated. It turns out that the concentration S ? S(x, t) is monotone increasing in the time variable t against the uniquely defined steady state ? ? ?(x). Explizit formulas are derived for the estimation of the difference between the steady state ? and the presteady state S, that hold for all t ≧ 0, i.c., it is not only determined the order of magnitude of the convergence for sufficiently large t.     

Transfer of copper from metallothionein to nonmetallothionein proteins in cultured cells

Copper uptake and distribution with time among cytoplasmic proteins were followed in cultured cells under several conditions: (1) CHO cells, which cannot synthesize metallothioneins, were labeled with⁶⁷Cu in the presence of 100 μM ZnCl₂; (2) Cd^r30F9 cells, which contain some constitutive metallothionein (MT), were labeled in the absence of additional ZnCl₂ and; (3) Cd^r30F9 cells were labeled in the presence of ZnCl₂, under which conditions they synthesized additional metallothioneins. The exogenous⁶⁷Cu and ZnCl₂, where present, were then removed, and the distributions of⁶⁷Cu among size fractions of the cellular proteins were observed at intervals for 16 h. In addition, a culture identical to condition (3) above was also treated with 100 μM ZnCl₂ during the redistribution period. The⁶⁷Cu was initially resolved into three peaks by Sephadex G-75 chromatography: high molecular weight, intermediate molecular weight, and MT. The⁶⁷Cu in the MT fraction decreased with at _1/2 of 10–12 h. In contrast to this, generally, in cells with a higher initial⁶⁷Cu bound to metallothionein, there was a progressive increase in the amount of⁶⁷Cu eluting with the high- and intermediate-molecular-weight fractions. Since no other source of⁶⁷Cu was available, these experiments suggest that copper stored in MT can be transferred to other proteins in these cells.