Two trees will form a non-edge if and only if they are trees that have three cherries, and differ by the pair of leaf exchanges shown in the figure

There are two ways to perform each leaf-exchange, so each binary tree with three cherries is not adjacent to 4 trees.<p><b>Copyright information:</b></p><p>Taken from "On the optimality of the neighbor-joining algorithm"</p><p>http://www.almob.org/content/3/1/5</p><p>Algorithms for Molecular Biology : AMB 2008;3():5-5.</p><p>Published online 30 Apr 2008</p><p>PMCID:PMC2430562.</p><p></p

Structures of the indole-diterpene biosynthesis loci (<i>IDT/LTM</i>) in sequenced genomes.

<p><i>IDT/LTM</i> genes are indicated by single letters, whereby <i>Q = idtQ</i> or <i>ltmQ</i> (in <i>E. festucae</i>), and so forth. Tracks from top to bottom of each map represent the following: genes, repeats, MITEs, and graphs of AT (red) and GC (blue) contents. Each gene is represented by a filled arrow indicating its direction of transcription. Closed circles indicate telomeres, and distances from the telomere on the <i>E. festucae</i> map are indicated in kilobasepairs (kb). Cyan bars representing repeat sequences are labeled with names or numbers to indicate relationships between repeats in the different species. Vertical bars beneath the repeat maps indicate MITEs. Genes for the first fully cyclized intermediate, paspaline, are indicated in blue, those for subsequent chemical decorations are shown in red, and <i>idt/ltmS</i>, with undetermined function, is in purple. Identifiable genes flanking the clusters are indicated in gray, and unfilled arrows indicate pseudogenes. The major pathway end-product for each strain is listed at the right of its map, abbreviated as indicated in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1003323#pgen-1003323-g003" target="_blank">Figure 3</a>, and in bold for those confirmed in this study.</p

Phylogenies of <i>rpbA</i> from sequenced isolates and other Clavicipitaceae.

<p>The phylogenetic tree is based on nucleotide alignment for a portion of the RNA polymerase II largest subunit gene, <i>rpbA</i>. This tree is rooted with <i>Fusarium graminearum</i> as the outgroup. Epichloae are indicated in green, <i>Claviceps</i> species are indicated in blue, <i>Periglandula</i> species are indicated in red, and <i>Aciculosporium take</i> is in black. Species for which genomes were sequenced in this study are shown in bold type, and asterisks indicate plant-associated fungi. Alkaloids listed are the major pathway end-products predicted from the genome sequences, abbreviated as shown in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1003323#pgen-1003323-g002" target="_blank">Figure 2</a>, <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1003323#pgen-1003323-g003" target="_blank">Figure 3</a>, <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1003323#pgen-1003323-g004" target="_blank">Figure 4</a>. Other abbreviations: (−) = some genes or remnants present, but not predicted to make alkaloids of this class, – = no genes present for this alkaloid class, EA = ergot alkaloids may be produced; IDT = indole-diterpenes may be produced, (ΔR*) = deletion of terminal reductase domain of <i>perA</i>.</p

Alkaloid profiles of sequenced isolates.^a

a<p>Strains are abbreviated as follow: <i>Cpu</i> = <i>Claviceps purpurea</i> 20.1, <i>Cfu</i> = <i>C. fusiformis</i> PRL 1980, Cpa = <i>C. paspali</i> RRC-1481, <i>Eam</i> = <i>Epichloë amarillans</i> E57, <i>Ebe</i> = <i>E. brachyelytri</i> E4804, <i>Eel</i> = <i>E. elymi</i> E56, <i>Ef</i>1 = <i>E. festucae</i> Fl1, <i>Ef</i>2 = <i>E. festucae</i> E2368, <i>Egl</i> = <i>E. glyceriae</i> E2772, <i>Et</i>8 = <i>E. typhina</i> E8, <i>Et</i>5 = <i>E. typhina</i> E5819, <i>Nga</i> = <i>N. gansuense</i> E7080, <i>Ngi</i> = <i>N. gansuense</i> var. <i>inebrians</i> E818, <i>Nun</i> = <i>N. uncinatum</i> E167, <i>Pip</i> = <i>P. ipomoeae</i> IasaF13. Symbols: + = present, (+) = intermediate inferred to be synthesized because downstream product is present, − = not predicted and not detected, (−) = predicted but not detected, nt = predicted but not tested, ERA = ergotamine, ERB = ergobalansine, ERC = ergocryptine, ERV = ergovaline. Blank cells indicate compounds not predicted from genotype, and not tested.</p>b<p>Identification of IDT-436 and terpendoles E, I, J, K, M, M, and A are tentative because authentic standards are unavailable.</p

Summary of loline alkaloid-biosynthesis pathway.

<p>Arrows indicate one or more steps catalyzed by products of the genes indicated. Arrows and genes in blue indicate steps in synthesis of the first fully cyclized intermediate (NANL). Arrows and genes in red indicate steps in modification of NANL to give the variety of lolines found in the epichloae. Asterisks indicate <i>LOL</i> genes that were newly discovered in the genome sequence of <i>E. festucae</i> E2368.</p

GC proportions in genic and repeat DNA of sequenced genomes.^a

a<p>Abbreviations: CDS = coding sequence, GC = proportion of sequence that is G or C, non-Rpt-IG = nonrepetitive intergenic DNA, Rpt = repetitive DNA.</p>b<p>Statistics for <i>P. ipomoeae</i> are tentative because the assembly was filtered by selecting only contigs containing tBLASTx matches to genome sequences from the other Clavicipitaceae.</p

Structures of the ergot alkaloid biosynthesis loci (<i>EAS</i>) in sequenced genomes.

<p>Tracks from top to bottom of each map represent the following: genes, repeats, MITEs, and graphs of AT (red) and GC (blue) contents. Each gene is represented by one or more boxes representing the coding sequences in exons, and an arrow indicating the direction of transcription. Double-slash marks (//) indicate sequence gaps within scaffolds of the assembled <i>E. festucae</i> genome sequences. Closed circles indicate telomeres, and distances from the telomere on the <i>E. festucae</i> map are indicated in kilobasepairs (kb). Cyan bars beneath each map represent repeat sequences, and are labeled with names or numbers to indicate relationships between repeats in the different species. Vertical bars beneath the repeat maps indicate MITEs. Gene names are abbreviated <i>A</i> through <i>P</i> for <i>easA</i> through <i>easP</i>, <i>W</i> for <i>dmaW</i>, and <i>clo</i> for <i>cloA</i>. Genes for synthesis of the ergoline ring system (skeleton) are shown in dark blue for the steps to chanoclavine-I (<i>W</i>, <i>F</i>, <i>E</i>, and <i>C</i>), and in light blue (<i>D</i>, <i>A</i>, and <i>G</i>) for steps to agroclavine. Genes for subsequent chemical decorations are shown in red (<i>clo</i>, <i>H</i>, <i>O</i>, <i>P</i>, <i>lpsA</i>, <i>lpsB</i>, and <i>lpsC</i>). Identifiable genes flanking the clusters are indicated in gray, and unfilled arrows indicate pseudogenes. The major pathway end-products for each strain are listed below each species name, abbreviated as indicated in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1003323#pgen-1003323-g002" target="_blank">Figure 2</a>, and in bold for those confirmed in this study. Note that LAH is a reported product of <i>C. paspali</i>, but the sequenced strain is predicted not to synthesize it due to a defective <i>easE</i> gene.</p

Symbiosis of meadow fescue with <i>Epichloë festucae</i>, a heritable symbiont.

<p>Single optical slice confocal micrographs of <i>E. festucae</i> expressing enhanced cyan-fluorescent protein were overlain with DIC bright field images of (A) ovules (bar = 100 µm), (B) embryos (bar = 200 µm), and (C) shoot apical meristem and surrounding new leaves (bar = 200 µm). (D) Asymptomatic (left) and “choked” (right) inflorescences simultaneously produced on a single grass plant infected with a single <i>E. festucae</i> genotype. Vertical (seed) transmission of the symbiont occurs via the asymptomatic inflorescence, whereas the choked inflorescence bears the <i>E. festucae</i> fruiting structure (stroma), which produces sexually derived spores (ascospores) that mediate horizontal transmission.</p

Genic and repeat DNA contents of sequenced genomes.^a

a<p>Abbreviations: CDS = coding sequence, MT = mating type, non-Rpt-IG = nonrepetitive intergenic DNA, Rpt = repetitive DNA.</p>b<p>Based on total of contigs ≥500 bp. These sizes differ slightly from total scaffold lengths given in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1003323#pgen-1003323-t001" target="_blank">Table 1</a> for <i>C. purpurea</i> 20.1, <i>E. festucae</i> E2368, and <i>E. festucae</i> Fl1.</p>c<p><i>C. fusiformis</i> PRL 1980 mating type genes include <i>mtBA</i> and <i>mtAC</i>. <i>P. ipomoeae</i> IasaF13 mating type genes <i>mtAA</i> and <i>mtAC</i> appear to have premature stop codons.</p>d<p>Statistics for <i>P. ipomoeae</i> are tentative because the assembly was filtered by selecting only contigs containing tBLASTx matches to genome sequences from the other Clavicipitaceae.</p

Relationships of <i>ltmE</i> and <i>ltmJ</i> with other <i>LTM</i> genes.

<p>Filled boxes indicate coding sequences of exons. Gray polygons indicate closest BLASTp matches to inferred polypeptide sequences for each exon, and are labeled with percent amino-acid identities.</p