Phylogeny: a) the relationship of organisms, usually presented as a branching diagram (Fig. 1) of the evolutionary pattern, and usually produced by a reproducible method (e.g., cladistics). Strictly speaking, phylogenies are merely explicit hypotheses about a relationship. Hypotheses can be tested, and may have to be falsified; what you see is the current 'best explanation of the available data', not the final truth! b) a loose term for methods and sciences contributing to the understanding of the relationship and evolution of organisms.

Ancestral & derived: 'Ancestral' means something present in the ancestor(s), and is often used to describe a character state inferred to have evolved into a 'derived' state. In a certain context, 'fore legs' (of reptiles) are ancestral and 'wings' (of birds) derived. Note the use depends on the context. If you only study parakeets, there is no point in considering reptile legs, and the 'ancestral' character may be a feature of the general bird wing. Avoid terms like 'primitive' and 'evolved', with an implicit quality assessment. All organisms survive, and generally function very well in their environments.

Apomorphy & plesiomorphy: A plesiomorphy (plesiomorph character, plesiomorph character state) is an ancestral character state and an apomorphy (apomorph character, apomorph character state) is a derived character state. 'Wings' are an apomorphy of birds corresponding to the plesiomorph 'fore legs' of reptiles. Note the words are context specific: wings and fore legs are both apomorph 'articulated fore limbs' in the context of the phylogeny of all vertebrates (vs. plesiomorph non-articulated fins, etc.), but penguins have apomorphic 'flipper wings' relative to the plesiomorph general bird wings. Synapomorphy is a derived feature, common to all members of a clade (uniquely derived organisms) - feathered wings are a synapomorphy of birds. Autapomorphy is a derived feature found in just one member of a clade. The differences between 'apomorphy', 'synapomorphy' and 'autapomorphy' are subtle, and the terms are often used interchangeably.

Autapomorphy: See apomorphy.

Character, character states: A character is a set of homologous features - for example articulated appendages - sharing a common origin, which can be described as separate entities, character states. Character states are mutually exclusive, and every organism in the analysis can have a state assigned, and every state evolved only once. Note that character states do not necessarily describe everything conceivable, only what is relevant to your analysis! If you look at a 'bird', a 'horse' and a 'dog', the character 'articulated fore limb' may have the character states 'wing', 'hoof' and 'foot' - we totally ignore bat wings, hands, etc. They are not relevant to understand our study material, but it is essential that each state evolved only once among the organisms - they must be homologous. If we include bats in the analysis, we need to qualify the state 'wings'.

Clade: Group of organisms sharing common ancestor. The group contains that ancestor and all descendants of that ancestor. In figure 1, (A,B) is a clade, so is (C,D) and (A,B,C,D). (B,C) is not a clade; their last common ancestor had descendants, that are not in (B,C). Clades are monophyletic.

Cladistics: A particular branch of phylogenetic analysis, describing evolutionary patterns from parsimonious analysis of observed characters.

Cladogram: See tree.

Classification: Organizing organisms in a system. Formally classification, taxonomy, and phylogeny are separate issues, but many researchers do all at the same time. Note that few classifications and even less taxonomy are based on phylogeny, and no classification or taxonomy can - unless based on a phylogenetic analysis - be used for phylogenetic interpretations (interpretations of evolutionary patterns).

Derived: See ancestral.

Evolved: See ancestral.

Homology: Characters (character states) are considered homologous if they perform the same function and have the same construction, and are believed to have evolved from the same evolutionary event. Characters (character states) are considered homoplastic if they appear similar or perform similar functions, and are believed to have evolved from different evolutionary events. 'Wings' of birds are homologous - they differ, but are believed to have arisen from one event. In a larger scale 'wings', 'hooves' and 'feet' are homologous - they are different manifestations of 'articulated fore limbs', and share a common evolutionary history (vs. the absence of articulated fore limbs). But note that bird wings and bat wings are homoplastic! They perform similar functions, but evolved at separate events. Note that it is often the scope/level of resolution that determines homology.

Homoplasy: See homology.

Ingroup & outgroup: The group you are interested in analysing, for example (A,B,C,D) in figure 1 is called the 'ingroup'. In the analysis you also include an 'outgroup' (G in figure 1), that you know is more distantly related, and can be used to polarize characters.

Monophyletic: A group of organisms is monophyletic if all members have a common ancestor, the most recent common ancestor is member of the group, and all descendants of the most recent common ancestor are members of the group. In figure 1 (A,B) is monophyletic, so is (A,B,C,D), but (B,C,D) is not. (B,C,D) is paraphyletic - all members have a common ancestor, the most recent common ancestor is member of the group, but not all descendants of that ancestor are members of the group. (B,G) is polyphyletic - their most recent common ancestor is not member of the group.

Numerical taxonomy: Se phenetics.

Outgroup: See ingroup.

Paraphyletic: See monophyletic.

Parsimony (parsimonious): 'Requiring a minimal number of assumptions of events'. Explained like that, it sounds like ideal science! In phylogeny figure 1 will be considered the most parsimonious cladogram/hypothesis/interpretation if that is the arrangement of A, B, C, and D requiring the least number of evolutionary events in the characters. A and B have more in common with each other, than either has with C or D. Furthermore, for the analysis leading to figure 1 to be parsimonious, the characters should be treated as equally important. This may sound trivial, but it is not! There are other - perfectly valid - methods to develop phylogenies. Some (particularly used on DNA data) emulate the evolutionary process emulating, others employ a priori weighting of characters (some characters are treated as more important than others).

Phenetics: Originally (1960s) developed as a tool for taxonomy. Classification of organisms exclusively on 'numerical difference' (hence also known as numerical taxonomy), a calculated difference of measured or counted characters. Initially strictly non-evolutionary to avoid biases in classification, subsequently many workers softened their view to phenetic analyses reflect evolutionary history and phenetic patterns may thus depict it. Almost vanished from evolutionary biology, but techniques still used (and very valuable!) in morphometry.

Plesiomorphy: See apomorphy.

Polarity: Polarity describes the relative occurrence of character states, which are ancestral and which are derived. If a character has more than two states, polarity describes the sequence of their origin, and which evolved to which. In some cases you may define a polarity and let that be part of your analysis or you may infer it from the tree (cladogram) after the analysis. If you include an outgroup in the analysis, you define that as coinciding with the 'root' of the tree (cladogram) and thus use it to establish the polarity of characters.

Polyphyletic: See monophyletic.

Primitive: See ancestral.

Synapomorphy: See apomorphy.

Taxonomy: Strictly speaking, naming of organisms, distinct from phylogeny (establishing evolutionary pattern) and classification (organizing). Most systematists will do several or all of these in the same work, and some even claim they are three terms for the same task.

Tree: Branching diagram showing the inferred evolutionary pattern of organisms. Formally speaking, 'cladograms' and 'trees' differ by cladograms only having organisms at the tips of the branches, but trees have organisms at the nodes. Figure 1 is a cladogram as drawn, but a tree if you imagine or infer actual organisms at the branching points. Trees have a time perspective, cladograms merely depict the branching order. Biologists mostly use cladograms, palaeontologists often use trees.