A reconsideration of inapplicable characters, and an approximation with step-matrix recoding.

Evidence for phylogenetic analysis comes in the form of observed similarities, and trees are selected to minimize the number of similarities that cannot be accounted for by homology (homoplasies). Thus, the classical argument for parsimony directly links homoplasy with explanatory power. When characters are hierarchically related, a first character may represent a primary structure such as tail absence/presence and a secondary (subordinate) character may describe tail colour; this makes tail colour inapplicable when tail is absent. It has been proposed that such character hierarchies should be evaluated on the same logical basis as standard characters, maximizing the number of similarities accounted for by secondary homology, i.e. common ancestry. Previous evaluations of the homology of a given ancestral reconstruction contain the unintuitive quantity "subcharacters" (number of regions of applicability). Rather than counting subcharacters, this paper proposes an equivalent but more intuitive formulation, based on counting the number of changes into each separate state. In this formulation, x-transformations, the homoplasy for the reconstruction is simply the number of changes into the state beyond the first, summed over all states. There is thus no direct connection between homoplasy and number of steps, only between homoplasy and extra steps. The link between the two formulations is that, for any region of applicability of any character, a subcharacter can be interpreted as the change into the state that is plesiomorphic in that region. Although some authors have claimed that the equivalence between maximizing explanatory power and minimizing independent originations of similar features (i.e. the standard justification of parsimony) does not hold for inapplicable characters, evaluating homoplasy with x-transformations clearly connects the two sides of that equation. Furthermore, as the evaluation with x-transformations provides a direct count and a straightforward interpretation of homoplasy, it extends naturally into implied weighting, and sheds light on problems with additive, step-matrix or continuous characters. It also allows deriving transformation costs for recoding hierarchies as step-matrix characters (where recoded states correspond to permissible combinations of states in primary and secondary characters), so that homology of the original observations is properly measured. Those transformation costs set the cost of gaining the primary structure to the maximum difference between "present" states plus cost of loss, and difference between "present" states to the sum of user-defined transformation costs between secondary features. With such recoding, invoking multiple independent derivations of the structure and similar features will cost as many extra "steps" as the instances of similarities (in both original characters) that are not being homologized. The step-matrix recoding also can take into account nested dependences. We present a simple convention for naming characters, which TNT can use to automatically convert the original data into a step-matrix form and set the proper transformation costs. Finally, the basic elements for handling inapplicable characters in the context of maximum-likelihood inference are outlined, and some quantitative comparisons between different approaches to inapplicables are provided.

Analysis of endemism of world arthropod distribution data supports biogeographic regions and many established subdivisions.

We analyzed 769 242 occurrence records for 115 424 species of terrestrial arthropods, from three biodiversity repositories (Global Biodiversity Information Facility (GBIF), Natural History Museum, London, and "Sistema de Informação Distribuído para Coleções Biológicas" (SpeciesLink)), to test the use of global-scale data points for quantitative assessments of areas of endemism. The data include Insecta (105,941 species), Arachnida (7984 species), Myriapoda (1229) and terrestrial crustaceans (270 Branchiopoda). The species were assigned to 14 543 higher taxonomic groups because such groups often characterize larger areas of endemism. Putative areas of endemism were visualized as sets of cells displaying unique groups of species without the assumption of hierarchical relationships. Yet, the use of 10° grid cells recovered many large areas broadly corresponding to biogeographic Regions (Nearctic, Neotropical, Panamanian, Palaearctic, Afrotropical, Australian, Oceanian and Oriental) albeit with the limits poorly defined. An analysis of 5° grids resulted in 306 sets included in the different biogeographic Realms: Afrotropical, Australian, Madagascan, Nearctic, Neotropical, Oceanian, Oriental, Palaearctic, Saharo-Arabian and Sino-Japanese. The Panamanian Realm comprises 89 partly overlapping sets, crossing the Nearctic and Neotropical boundaries. A total of 7338 species of Insecta were endemic to some areas (Sino-Japanese, Afrotropical, Panamanian, Palaearctic, among others), followed by Arachnida (412 spp) and 105 species in other clades ranked as "classes". Six sets were supported only by genera, except for Panamanian sets that were supported by genera and families. Many of the species in the dataset are included in IUCN red lists, but probably most of those have distributions more restricted than global areas of endemism; only 102 appear as endemic to some area (Neartic, Madagascan, Panamanian, Afrotropical, among others). The results show that data from global databases can be used to identify areas of endemism on a worldwide basis but-owing to their incompleteness-only at a relatively coarse level. At the level of resolution currently allowed by such databases, such global studies are only complementary to studies where areas are determined subjectively by systematists (instead of actual point records), or studies using point records in datasets for specific taxonomic groups curated and compiled by specialists.

Problems with supertrees based on the subtree prune-and-regraft distance, with comments on majority rule supertrees.

This paper examines a recent proposal to calculate supertrees by minimizing the sum of subtree prune-and-regraft distances to the input trees. The supertrees thus calculated may display groups present in a minority of the input trees but contradicted by the majority, or groups that are not supported by any input tree or combination of input trees. The proponents of the method themselves stated that these are serious problems of "matrix representation with parsimony", but they can in fact occur in their own method. The majority rule supertrees, being explicitly clade-based, cannot have these problems, and seem much more suited to retrieving common clades from a set of trees with different taxon sets. However, it is dubious that so-called majority rule supertrees can always be interpreted as displaying those clades present (or compatible with) with a majority of the trees. The majority rule consensus is always a median tree, in terms of the Robinson-Foulds distances (i.e. it minimizes the sum of Robinson-Foulds distances to the input trees). In contrast, majority rule supertrees may not be median-different, contradictory trees may minimize Robinson-Foulds distances, while their strict consensus does not. If being "majority" results from being median in Robinson-Foulds distances, this means that in the supertree setting a "majority" is ambiguously defined, sometimes achievable only by mutually contradictory trees.

Identifying unstable taxa: Efficient implementation of triplet-based measures of stability, and comparison with Phyutility and RogueNaRok.

This paper describes an efficient implementation of triplet-based measures of stability, in the program TNT. The only available implementations of such measures are much slower than the present one, either because of an inefficient implementation (Phyutility, Thor) or because the stability is evaluated with quartets (RogueNaRok, requiring O(t(4)), instead of the O(t(3)) possible for triplets). The method to quickly calculate triplets is applied to solving IterPCR (Pol and Escapa, 2009). It is shown that, in some cases, IterPCR or other algorithms in the program TNT (e.g. commands prunnelsen, prunmajor, or chkmoves) produce more informative results than analysis with RogueNaRok.

Higher taxa and the identification of areas of endemism.

Quantitative analyses of areas of endemism have rarely considered higher taxa. This paper discusses aspects related to the use of higher taxa in the analysis of areas of endemism, and computer implementations. An example of the application of the method is provided, with a data set for Nearctic mammals, showing that some of the areas recognized by species-level taxa also adjust well to the distribution of other taxa of higher level (genera, monophyletic groups).

Endemicity analysis, parsimony and biotic elements: a formal comparison using hypothetical distributions.

There is as yet no general agreement regarding the most appropriate solution to the problem of identifying areas of endemism, not even in particular cases. In this study, we compared Endemicity Analysis (EA), Parsimony Analysis of Endemicity (PAE), and Biotic Elements Analysis (BE) based on their ability to identify hypothetical predefined patterns that represent nested, overlapping, and disjoint areas of endemism supported by species with different degrees of sympatry. We found that PAE performs poorly when applied to patterns that either overlap with each other or are supported by species with imperfect sympatry. BE exhibits a counterintuitive sensitivity to the degree of congruence among the distributions of endemic species, being unable to recognize areas of endemism supported by perfectly sympatric species. In contrast, in all cases examined we found that EA results in a high proportion of correctly identified distributional patterns. In addition to highlighting the strengths and limitations of these approaches, our results show how different methods can lead to seemingly conflicting conclusions and caution about the possibility of identifying distributional patterns that are merely methodological artefacts. © The Willi Hennig Society 2012.

Spatial analysis of vicariance: a method for using direct geographical information in historical biogeography.

Based on Hovenkamp's ideas on historical biogeography, we present a method for analysis of taxon history, spatial analysis of vicariance, which uses observed distributions as data, thus requiring neither predefined areas nor assumptions of hierarchical relations between areas. The method is based on identifying sister nodes with disjunct (allopatric/vicariant) distributions. To do this across the tree, internal nodes are assigned distributions (as the sum of the distributions of the descendant nodes). When distributions are less than ideal, ignoring the distribution of the problematic node(s) when assigning a distribution to their ancestors may allow us to consider additional sister nodes (i.e. those resulting from splits basal to the problematic node) as having disjunct distributions. The optimality criterion seeks to find the best (possibly weighted) compromise between the maximum possible number of disjunct sister nodes and the minimum number of eliminated distributions. The method can also take overlap into account. The methodology presented is implemented in VIP, a computer program available at http://www.zmuc.dk/public/phylogeny/vip. © The Willi Hennig Society 2011.

Bats and marsupials as indicators of endemism in the Yungas forest of Argentina.

Several studies have characterized the Yungas as a separate biogeographic unit, mainly based in floristic components. However, these characterizations were mainly qualitative and did not include faunal groups. The Yungas have been assumed as a region with rich floral and faunal diversity, but without testing how well they are described by animal distributions. Our study consists of a formal analysis of endemism based on distribution of small mammals in the southernmost portion of the Yungas. This area is biogeographically very interesting because the Yungas are comprised of discontinuous fragments of forests that extend into temperate arid and semiarid habitats. As a first approximation, we contrasted a group of volant species (bats) versus a group of non-volant species (marsupials). Our results show that small mammals are efficient indicators of endemism in Yungas. Eighty percent of the species of small marsupials included in the analysis supported the identified areas as being zones of endemism. Regarding bats, almost 55 percent of the species supported a designation of endemism. The results also show that the areas we considered are congruent with the botanical definition of the Yungas of northwestern Argentina and their subdivisions, an assumption that had not been previously tested with a formal quantitative method. We also found that non-volant species are better indicators of endemism than volant ones at regional scales, but volant species are better indicators than was previously thought.

Quantitative biogeography in the South America highlands-recognizing the Altoandina, Puna and Prepuna through the study of Poaceae.

The distribution data of 340 grass species sampled in a region of 53.219 km2 in the northwestern corner of Argentina (between ∼21°S and ∼24°S) were analyzed to search for concordance in species distributions by using the program NDM/VNDM. Here, the traditional biogeographic hypothesis proposed for the region is evaluated for the first time by using a quantitative method and an optimal criterion specifically developed within the context of areas of endemism. Three different grid sizes (0.5° × 0.5°, 0.35° × 0.35 ° and 0.2° × 0.2°) were used to analyze three nested data sets: species found in the Andes of Argentina, Bolivia and/or Chile; Andean distributed species; and all grass species found in the study region. The main areas supported by the analyses correspond generally to the traditional biogeographic hypothesis proposed for the region. Local distribution patterns defined by species restricted to the study region were best supported under the small grid sizes, while the bigger grid sizes recovered areas defined by species with a broader distribution. The local distribution patterns emerged in all the analyses even when widespread species were added to the data set. © The Willi Hennig Society 2009.

Phylogenetic analysis of 73 060 taxa corroborates major eukaryotic groups.

Obtaining a well supported schema of phylogenetic relationships among the major groups of living organisms requires considering as much taxonomic diversity as possible, but the computational cost of calculating large phylogenies has so far been a major obstacle. We show here that the parsimony algorithms implemented in TNT can successfully process the largest phylogenetic data set ever analysed, consisting of molecular sequences and morphology for 73 060 eukaryotic taxa. The trees resulting from molecules alone display a high degree of congruence with the major taxonomic groups, with a small proportion of misplaced species; the combined data set retrieves these groups with even higher congruence. This shows that tree-calculation algorithms effectively retrieve phylogenetic history for very large data sets, and at the same time provides strong corroboration for the major eukaryotic lineages long recognized by taxonomists.

An optimality criterion to determine areas of endemism.

A formal method was developed to determine areas of endemism. The study region is divided into cells, and the number of species that can be considered as endemic is counted for a given set of cells (= area). Thus, the areas with the maximum number of species considered endemic are preferred. This is the first method for the identification of areas of endemism that implements an optimality criterion directly based on considering the aspects of species distribution that are relevant to endemism. The method is implemented in two computer programs, NDM and VNDM, available from the authors.