Quarnet Inference Rules for Level-1 Networks

An important problem in phylogenetics is the construction of phylogenetic trees. One way to approach this problem, known as the supertree method, involves inferring a phylogenetic tree with leaves consisting of a set X of species from a collection of trees, each having leaf-set some subset of X. In the 1980s, Colonius and Schulze gave certain inference rules for deciding when a collection of 4-leaved trees, one for each 4-element subset of X, can be simultaneously displayed by a single supertree with leaf-set X. Recently, it has become of interest to extend this and related results to phylogenetic networks. These are a generalization of phylogenetic trees which can be used to represent reticulate evolution (where species can come together to form a new species). It has recently been shown that a certain type of phylogenetic network, called a (unrooted) level-1 network, can essentially be constructed from 4-leaved trees. However, the problem of providing appropriate inference rules for such networks remains unresolved. Here, we show that by considering 4-leaved networks, called quarnets, as opposed to 4-leaved trees, it is possible to provide such rules. In particular, we show that these rules can be used to characterize when a collection of quarnets, one for each 4-element subset of X, can all be simultaneously displayed by a level-1 network with leaf-set X. The rules are an intriguing mixture of tree inference rules, and an inference rule for building up a cyclic ordering of X from orderings on subsets of X of size 4. This opens up several new directions of research for inferring phylogenetic networks from smaller ones, which could yield new algorithms for solving the supernetwork problem in phylogenetics.     

Patterns of success in game bird introductions in the United States

Better predictions of the success of species’ introductions require careful evaluation of the relative importance of at least three kinds of factors: species characteristics, characteristics of the site of introduction, and event-level factors such as the numbers of individuals released. (Henceforth, we call this propagule pressure.) The 1644 introductions of 17 Phasianid species released in various US states during the Foreign Game Investigation Program provides a particularly rich source of data to test these ideas. An examination of these records indicates that 13 of these 17 species always failed, despite generally numerous individual releases and large numbers of individuals in each release. Moreover, ten of these species have been successfully introduced elsewhere. Only four of the 17 species were successful in at least one state. Some 20 sets of releases of three of these four species always failed in some states, again given generally numerous individual releases of large numbers of individuals in each release. Simply, the combination of site and species factors explain the lack of successes. This leaves a combination of 18 states where one or more of the four species succeeded. For these, there are significant differences in the numbers of birds introduced from state to state. But only for two species Alectoris chukar and; Tetraogallus himalayensis are there significant differences that show a greater chance of success when more individuals are introduced. These results support the conclusion that the number of individuals released, meaning propagule pressure, is not as important as characteristics of the species and the location to where its introduction occurred.     

Null matrices and the analysis of species co-occurrences

Patterns in species occurrences on islands have been analyzed by several authors. At issue is the number of non-occurring pairs of species (also known as checkerboards). Previous authors have suggested that if the number of checkerboards differs from what is expected by chance, then island communities might have been structured by competition. Investigators have pursued this problem by first generating random (or null) matrices and then testing a metric derived from the collection of null matrices against the metric calculated from the actual species co-occurrence matrix. The random matrices were constrained by requiring the number of species on each island, and the number of islands on which each species occurred to be equal to their observed values. We show that results from previous studies are generally flawed. We present a fast, efficient algorithm to generate null matrices for any set of fixed row and column sums, and propose a modification of a previously proposed metric as a test statistic. We evaluated the efficacy of our construction method for null creation and our metric using incidence matrices from the avifauna of Vanuatu (formerly New Hebrides). Received: 31 March 1997 / Accepted: 8 April 1998