An alternative construction of internodons: the emergence of a multi-level tree of life.

Internodons are a formalization of Hennig's concept of species. We present an alternative construction of internodons imposing a tree structure on the genealogical network. We prove that the segments (trivial unary trees) from this tree structure are precisely the internodons. We obtain the following spin-offs. First, the generated tree turns out to be an organismal tree of life. Second, this organismal tree is homeomorphic to the phylogenetic Hennigian species tree of life, implying the discovery of a multi-level tree of life: this phylogenetic tree can be obtained by zooming out from the organismal tree, or conversely, the organismal tree of life can be generated by expanding the phylogenetic nodes into unary trees. Finally, the definition of the organismal tree allows an efficient algorithmic transformation of a given genealogical network into its corresponding phylogenetic species tree of life. The latter will be presented in a separate paper.

A Posteriori and a Priori Methodologies for Testing Hypotheses of Causal Processes in Vicariance Biogeography.

Methods used in vicariance biogeography fall into the categories of a posteriori methods (e.g., Component Compatibility Analysis and Brooks Parsimony Analysis) and a priori methods (e.g., Component Analysis, Reconciled Tree Analysis, and Three Area Statement Analysis). Each category corresponds to a particular methodology that arrives at general area cladograms by testing null hypotheses in a particular way. A posteriori methods assume the process of vicariance only (A0) as a common cause of the distribution of different monophyletic groups of taxa under the null hypothesis. Whenever a parsimony analysis of combined data from these monophyletic groups results in a general area cladogram with homoplasy, the null hypothesis is rejected and extinction and dispersal are invoked a posteriori as ad hoc process explanations. A priori methods assume not only vicariance (A0) but also combinations of vicariance with the processes of extinction (A1) and dispersal (A2) as possible causes of the distribution of the taxa of different monophyletic groups. Each assumed set of processes corresponds to a different null hypothesis. Under the assumption of independence and thus additivity of the processes involved, the sets of area cladograms obtained under A0, A1, and A2 from data of each monophyletic group must be inclusive (requirement I). Whenever no congruent area cladograms are found in the intersection of sets of area cladograms derived under the same assumption for different monophyletic groups (II), the corresponding null hypothesis is rejected.

Measures for Obtaining Inclusive Sets of Area Cladograms under Assumptions Zero, 1, and 2 with Different Methods for Vicariance Biogeography.

We present modifications to computer programs of a posteriori and a priori methods for vicariance biogeography that enable them to obtain inclusive sets of area cladograms under assumptions zero, 1, and 2. With CAFCA (Component Compatibility Analysis) an upper limit for area cladogram selection by the number of steps is not always sufficient for inclusive sets. CAFCA needs additionally a lower limit for the number of components used to derive area cladograms when noninclusion arises because CAFCA selects area cladograms with different resolutions. PAUP (Brooks Parsimony Analysis) derives inclusive sets when it selects area cladograms under assumptions zero, 1, and 2 by using an upper limit for the number of steps and not collapsing unsupported nodes. For the computer programs Component 1.5 (Component Analysis), Component 2.0 (Reconciled Tree Analysis), and TAS (Three Area Statement Analysis) we suggest a two-step procedure for inclusive sets. The first step involves dealing with widespread taxa a priori under assumptions zero, 1, or 2. The second step involves dealing with sympatric taxa "as is" (Component 1.5 and TAS) or by tree reconciliation using an upper limit for the number of losses (Component 2.0).

Methods in Vicariance Biogeography: Assessment of the Implementations of Assumptions 0, 1, and 2.

As we have argued previously, for the valid derivation of general area cladograms in vicariance biogeography, two requirements should be met. First, sets of area cladograms derived under assumptions 0, 1 and 2 should be inclusive (requirement I). Second, general area cladograms should be based on area cladograms, for different monophyletic groups, derived under the same assumption (requirement II). We now assess for their actual implementation of assumptions A0, A1, and A2 and for the extent to which they meet requirements I and II, the following methods (and correlated computer programs): Component Compatibility Analysis (CAFCA), Brooks Parsimony Analysis (PAUP), Component Analysis (Component 1.5), Reconciled Tree Analysis (Component 2.0), and Three Area Statement Analysis (TAS). For this purpose we use empirical (Heterandria, Xiphophorus, Cyttaria, Eriococcus/Madarococcus) and theoretical data sets. All programs appear to violate, to a different degree, requirement I (deriving inclusive sets of area cladograms under assumptions) when dealing with sympatric taxa under A1 or A2. Dealing with sympatric taxa a posteriori only prevents this violation. All programs examined appear to meet requirement II (deriving general area cladograms under a single assumption).

Coding polymorphism for phylogeny reconstruction.

The methodology of coding polymorphic taxa has received limited attention to date. A search of the taxonomic literature revealed seven types of coding methods. Apart from ignoring polymorphic characters (sometimes called the fixed-only method), two main categories can be distinguished: methods that identify the start of a new character state with the origin of an evolutionary novelty, and methods that identify the new state with the fixation of a novelty. The methods of the first category introduce soft reversals, yielding signals that support cladograms incompatible with true phylogenies. We conclude that coding the plesiomorphy is the method to be preferred, unless the ancestral state is unknown, in which case coding as ambiguous is recommended. This holds for coding polymorphism in species as well as in supraspecific taxa. In this light we remark on methods proposed by previous authors.

Two Requirements for Obtaining Valid Common Patterns under Different Assumptions in Vicariance Biogeography.

In vicariance biogeography, widespread or sympatric taxa can be dealt with under assumptions 0, 1, and 2. Data from cladogenetic relationships among taxa of a monophyletic group and their distribution over areas are assumed, in the order 0 → 1 → 2, to represent decreasing information about vicariance events. A less strict assumption carries a larger solution set, i.e., the number of possible area cladograms increases with the decrease in strictness of the assumption applied. We formulate two requirements for obtaining valid general area cladograms from data of several monophyletic groups of taxa. First, the assumptions, and with them the sets of area cladograms derived under these assumptions, should be inclusive. Second, sets of single group area cladograms should be compared for different monophyletic groups under a single assumption. When these two requirements are met, area cladograms become consistent with respect to the processes (vicariance, extinction, and dispersal) that are a priori assumed. The explanatory power increases for any particular monophyletic group of taxa when the set of valid general area cladograms contains a subset of area cladograms derived under a more strict assumption. We discuss examples from literature of how violation of these two requirements affects the results.