Coalescent histories for lodgepole species trees

Coalescent histories are combinatorial structures that describe for a given gene tree and species tree the possible lists of branches of the species tree on which the gene tree coalescences take place. Properties of the number of coalescent histories for gene trees and species trees affect a variety of probabilistic calculations in mathematical phylogenetics. Exact and asymptotic evaluations of the number of coalescent histories, however, are known only in a limited number of cases. Here we introduce a particular family of species trees, the \emph{lodgepole} species trees $(\lambda_n)_{n\geq 0}$, in which tree $\lambda_n$ has $m=2n+1$ taxa. We determine the number of coalescent histories for the lodgepole species trees, in the case that the gene tree matches the species tree, showing that this number grows with $m!!$ in the number of taxa $m$. This computation demonstrates the existence of tree families in which the growth in the number of coalescent histories is faster than exponential. Further, it provides a substantial improvement on the lower bound for the ratio of the largest number of matching coalescent histories to the smallest number of matching coalescent histories for trees with $m$ taxa, increasing a previous bound of $(\sqrt{\pi} / 32)[(5m-12)/(4m-6)] m \sqrt{m}$ to $[ \sqrt{m-1}/(4 \sqrt{e}) ]^{m}$. We discuss the implications of our enumerative results for phylogenetic computations

Axiomatic opportunities and obstacles for inferring a species tree from gene trees

The reconstruction of a central tendency `species tree' from a large number of conflicting gene trees is a central problem in systematic biology. Moreover, it becomes particularly problematic when taxon coverage is patchy, so that not all taxa are present in every gene tree. Here, we list four apparently desirable properties that a method for estimating a species tree from gene trees could have (the strongest property states that building a species tree from input gene trees and then pruning leaves gives a tree that is the same as, or more resolved than, the tree obtained by first removing the taxa from the input trees and then building the species tree). We show that while it is technically possible to simultaneously satisfy these properties when taxon coverage is complete, they cannot all be satisfied in the more general supertree setting. In part two, we discuss a concordance-based consensus method based on Baum's `plurality clusters', and an extension to concordance supertrees.Comment: 19 pages, 2 figure

A polynomial time algorithm for calculating the probability of a ranked gene tree given a species tree

In this paper, we provide a polynomial time algorithm to calculate the probability of a {\it ranked} gene tree topology for a given species tree, where a ranked tree topology is a tree topology with the internal vertices being ordered. The probability of a gene tree topology can thus be calculated in polynomial time if the number of orderings of the internal vertices is a polynomial number. However, the complexity of calculating the probability of a gene tree topology with an exponential number of rankings for a given species tree remains unknown

Tree species effect on natural control of H. albipunctella de Joannis in a millet agroforestry system in Senegal

Association of several tree species in and around a plot can have a positive impact on ecosystem services. Thus, traditional agroforestry systems, characterized by a high plant diversity, constitute an ideal model of study to test if the natural tree vegetation provides both shelter and food resources for insects that could potentially improve biocontrol services. The main objective of this study was to test if tree species presence and diversity could enhance the natural regulation of the millet head miner Heliocheilus albipunctella (MHM) in agroforestry systems of the Senegalese Peanut Basin. To address our objective, we realized an inventory of tree species in a total of 30 millet fields surveyed in Bambey area, during 2013 and 2014 (Fig.1). These data were used to calculate indices related to the abundance and diversity of tree species. The natural regulation was estimated using the biocontrol service index (BSI) for each millet field. In addition, data on MHM egg and larval predation and parasitism rates were also collected to estimate biocontrol services. Statistical analysis of the effect of tree presence and diversity on natural regulation variables were tested using a linear regression. Surprisingly, we found that BSI decreased with tree diversity and that it increased with the presence of the tree species Faidherbia albida. Morever, the presence of Anogeissus leiocarpus enhanced MHM egg parasitism and the presence of Azadirachta indica favored MHM egg predation