scholarly journals A Linear-Time Algorithm for the Isometric Reconciliation of Unrooted Trees

Algorithms ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 225
Author(s):  
Broňa Brejová ◽  
Rastislav Královič

In the reconciliation problem, we are given two phylogenetic trees. A species tree represents the evolutionary history of a group of species, and a gene tree represents the history of a family of related genes within these species. A reconciliation maps nodes of the gene tree to the corresponding points of the species tree, and thus helps to interpret the gene family history. In this paper, we study the case when both trees are unrooted and their edge lengths are known exactly. The goal is to root them and to find a reconciliation that agrees with the edge lengths. We show a linear-time algorithm for finding the set of all possible root locations, which is a significant improvement compared to the previous O(N3logN) algorithm.

PLoS Genetics ◽  
2021 ◽  
Vol 17 (2) ◽  
pp. e1009095
Author(s):  
Thomas C. Nelson ◽  
Angela M. Stathos ◽  
Daniel D. Vanderpool ◽  
Findley R. Finseth ◽  
Yao-wu Yuan ◽  
...  

Inferences about past processes of adaptation and speciation require a gene-scale and genome-wide understanding of the evolutionary history of diverging taxa. In this study, we use genome-wide capture of nuclear gene sequences, plus skimming of organellar sequences, to investigate the phylogenomics of monkeyflowers in Mimulus section Erythranthe (27 accessions from seven species). Taxa within Erythranthe, particularly the parapatric and putatively sister species M. lewisii (bee-pollinated) and M. cardinalis (hummingbird-pollinated), have been a model system for investigating the ecological genetics of speciation and adaptation for over five decades. Across >8000 nuclear loci, multiple methods resolve a predominant species tree in which M. cardinalis groups with other hummingbird-pollinated taxa (37% of gene trees), rather than being sister to M. lewisii (32% of gene trees). We independently corroborate a single evolution of hummingbird pollination syndrome in Erythranthe by demonstrating functional redundancy in genetic complementation tests of floral traits in hybrids; together, these analyses overturn a textbook case of pollination-syndrome convergence. Strong asymmetries in allele-sharing (Patterson’s D-statistic and related tests) indicate that gene-tree discordance reflects ancient and recent introgression rather than incomplete lineage sorting. Consistent with abundant introgression blurring the history of divergence, low-recombination and adaptation-associated regions support the new species tree, while high-recombination regions generate phylogenetic evidence for sister status for M. lewisii and M. cardinalis. Population-level sampling of core taxa also revealed two instances of chloroplast capture, with Sierran M. lewisii and Southern Californian M. parishii each carrying organelle genomes nested within respective sympatric M. cardinalis clades. A recent organellar transfer from M. cardinalis, an outcrosser where selfish cytonuclear dynamics are more likely, may account for the unexpected cytoplasmic male sterility effects of selfer M. parishii organelles in hybrids with M. lewisii. Overall, our phylogenomic results reveal extensive reticulation throughout the evolutionary history of a classic monkeyflower radiation, suggesting that natural selection (re-)assembles and maintains species-diagnostic traits and barriers in the face of gene flow. Our findings further underline the challenges, even in reproductively isolated species, in distinguishing re-use of adaptive alleles from true convergence and emphasize the value of a phylogenomic framework for reconstructing the evolutionary genetics of adaptation and speciation.


2021 ◽  
Vol 16 (1) ◽  
Author(s):  
David Schaller ◽  
Marc Hellmuth ◽  
Peter F. Stadler

Abstract Background The supertree problem, i.e., the task of finding a common refinement of a set of rooted trees is an important topic in mathematical phylogenetics. The special case of a common leaf set L is known to be solvable in linear time. Existing approaches refine one input tree using information of the others and then test whether the results are isomorphic. Results An O(k|L|) algorithm, , for constructing the common refinement T of k input trees with a common leaf set L is proposed that explicitly computes the parent function of T in a bottom-up approach. Conclusion is simpler to implement than other asymptotically optimal algorithms for the problem and outperforms the alternatives in empirical comparisons. Availability An implementation of in Python is freely available at https://github.com/david-schaller/tralda.


2017 ◽  
Author(s):  
Niema Moshiri

AbstractThe ability to sample models of tree evolution is essential in the analysis and interpretation of phylogenetic trees. The dual-birth model is an extension of the traditional birth-only model and allows for sampling trees of varying degrees of balance. However, for a tree with n leaves, the tree sampling algorithm proposed in the original paper is 𝒪(n log n). I propose an algorithm to sample trees under the dual-birth model in 𝒪(n), and I provide a fast C++ implementation of the proposed algorithm.


2020 ◽  
Author(s):  
Manuel Lafond ◽  
Marc Hellmuth

Abstract Background: The history of gene families -- which are equivalent to event-labeled gene trees -- can to some extent be reconstructed from empirically estimated evolutionary event-relations containing pairs of orthologous, paralogous or xenologous genes. The question then arises as whether inferred event-labeled gene trees are "biologically feasible" which is the case if one can find a species tree with which the gene tree can be reconciled in a time-consistent way.Results: In this contribution, we consider event-labeled gene trees that contain speciations, duplications as well as horizontal gene transfer (HGT) and we assume that the species tree is unknown. Although many problems become NP-hard as soon as HGT and time-consistency are involved, we show, in contrast, that the problem of finding a time-consistent species tree for a given event-labeled gene can be solved in polynomial-time. We provide a cubic-time algorithm to decide whether a "time-consistent" species for a given event-labeled gene tree exists and, in the affirmative case, to construct the species tree within the same time-complexity.


2006 ◽  
Vol 17 (3) ◽  
Author(s):  
Andreas Düring ◽  
Martina Brückner ◽  
Dietrich Mossakowski

Phylogenetic analyses of Chrysocarabus taxa using different markers result in different phylogenetic trees. In particular, the mitochondrial gene tree contradicts the results of morphological and inbreeding studies. Two very different haplotypes of Carabus splendens Olivier, 1790 do not form a clade within this phylogenetic tree. We have earlier proposed that contradictory results are due to introgression. To verify our hypothesis, we analysed the internal transcribed spacer 2. No substitutions were observed in these nuclear sequences between the individuals of Carabus splendens, which contain the different mitochondrial haplotypes in question. The differences in the gene trees based on mitochondrial and nuclear sequences can be explained with at least two introgression events.


Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 293
Author(s):  
Xinyue Liu ◽  
Huiqin Jiang ◽  
Pu Wu ◽  
Zehui Shao

For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v)≠0 has a neighbor u with f(u)≠0 for every vertex v∈V(G). The weight of a TR3DF f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a total Roman {3}-dominating function on G is called the total Roman {3}-domination number denoted by γt{R3}(G). In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of γt{R3} for trees.


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