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In cladistics, a synapomorphy or synapomorphic character state is a trait that is shared ("symmorphy") by two or more taxa and inferred to have been present in their most recent common ancestor, whose own ancestor in turn is inferred to not possess the trait. A synapomorphy is thus an apomorphy visible in multiple taxa, where the trait in question is assumed to have originated in their last common ancestor. The word "synapomorphy," coined by German entomologist Willi Hennig, is derived from the Greek words σύν, syn = with, in company with, together with; ἀπό, apo = away from; and μορφή, morphe = shape.
"True" synapomorphies uniquely characterise a given set of terminal groups, but it is not strictly necessary that all members of a clade possess the same trait (they may exhibit instead a further-modified version of the trait).
For the sake of precision, the term "derived" is preferred to "advanced," a term which may inaccurately imply superiority. Simplicity is often secondarily derived. For example, the absence of mitochondria in the anaerobic protist Entamoeba histolytica is a result of their secondary loss, and when considered in the context of eukaryotes as a whole, is a derived trait. Likewise, the primitive character state for birds (i.e. the state possessed by their last common ancestor) is flight, which was secondarily lost by penguins and dodos.
Whether or not a trait is considered derived depends on the group in question. For example, among the (crown group) tetrapods, having five fingers is the primitive trait - as their last common ancestor bore a five-digit hand. However, amongst the vertebrates, five fingers is a derived trait, as the last common ancestor to the vertebrates did not even bear fingers.
A synapomorphy should not be confused with other types of shared traits:
Synapomorphies are used to establish phylogenetic hypotheses in cladistic analysis. As such they are empirical data which can support a certain hypothesis that terminal groups form a clade (monophyletic group) together to the exclusion of certain other groups – whereas character-states that are shared, but also shared by other terminal groups descending from an earlier common ancestor, cannot be used to exclude these other groups. The latter character-states can consist of symplesiomorphies ("primitive" character-states inferred to have originated in an earlier common ancestor) or homoplasies (features that are superficially similar but, based on the weight of evidence are inferred to have been independently evolved derived character-states).
The key problem is to identify the polarity of the transformation series to which several character-states belong, i.e. to tell which character-state is apomorphic and which is plesiomorphic. Various criteria were used to polarize transformation series in earlier cladistics; however in recent decades pattern criteria based on outgroup comparison have dominated the field. An outgroup is a taxon assumed to be outside of the group of interest in the study. Under the outgroup criterion, character states shared between the outgroup and some members of the ingroup are inferred to be plesiomorphic, while alternative states of the same feature that are shared by a subset of the ingroup are considered to be apomorphic.
The concepts of apomorphy and plesiomorphy are relative to a certain level of generality in the hierarchy of life. What counts as an apomorphy at one level of generality may well be a plesiomorphy at a less inclusive level. For example, the presence of mammary glands is a synapomorphy for mammals in relation to tetrapods more broadly, but is a symplesiomorphy for mammals in relation to one another, e. g., rats and apes.
It is not essential that all members of a clade possess exhibit a synapomorphy; even if some members of the clade have secondarily lost the trait it could still be a synapomorphy of the clade as a whole. A good example of this is the "absence" of legs in snakes, which are nevertheless members of Tetrapoda. Among paleontologists, a character state that is a synapomorphy for a clade, but for lineages in this clade is a plesiomorphy that is altered in some lineages, is called an underlying synapomorphy. If no crown group taxa are known, it is sometimes difficult to decide which character state is the underlying synapomorphy and which the autapomorphy that overlies it.
Clades are not defined by synapomorphies as such, though it is possible to define them by apomorphies in general.
Relative apparent synapomorphy analysis is a method that some use to determine whether a given character is shared between taxa due to shared ancestry or due to convergence.
Schuh, R. T. and A. V. Z. Brower. 2009. Biological Systematics: Principles and Applications (2nd edn.). Cornell University Press, Ithaca, NY.