The tips of a phylogenetic tree can be living taxa or fossils, and represent the "end" or the present time in an evolutionary lineage. A phylogenetic diagram can be rooted or unrooted. A rooted tree diagram indicates the hypothetical common ancestor of the tree. An unrooted tree diagram (a network) makes no assumption about the ancestral line, and does not show the origin or "root" of the taxa in question or the direction of inferred evolutionary transformations.
In addition to their use for inferring phylogenetic patterns among taxa, phylogenetic analyses are often employed to represent relationships among genes or individual organisms. Such uses have become central to understanding biodiversity, evolution, ecology, and genomes.
Taxonomy is the identification, naming and
classification of organisms. Classifications are now usually based on phylogenetic data, and many systematists contend that only
monophyletic taxa should be recognized as named groups. The degree to which classification depends on inferred evolutionary history differs depending on the school of taxonomy:
phenetics ignores phylogenetic speculation altogether, trying to represent the similarity between organisms instead;
cladistics (phylogenetic systematics) tries to reflect phylogeny in its classifications by only recognizing groups based on shared, derived characters (
evolutionary taxonomy tries to take into account both the branching pattern and "degree of difference" to find a compromise between them.
Even in the field of cancer, phylogenetics makes it possible to study the clonal evolution of tumors and molecular chronology, showing how cell populations vary throughout the progression of the disease, even during treatment, using whole genome sequencing techniques. 
Prior to 1950, phylogenetic inferences were generally presented as
narrative scenarios. Such methods are often ambiguous and lack explicit criteria for evaluating alternative hypotheses.
The term "phylogeny" derives from the German Phylogenie, introduced by Haeckel in 1866, and the
Darwinian approach to classification became known as the "phyletic" approach.
Ernst Haeckel's recapitulation theory
During the late 19th century,
recapitulation theory, or "biogenetic fundamental law", was widely accepted. It was often expressed as "
ontogeny recapitulates phylogeny", i.e. the development of a single organism during its lifetime, from germ to adult, successively mirrors the adult stages of successive ancestors of the species to which it belongs. But this theory has long been rejected. Instead,
ontogeny evolves – the phylogenetic history of a species cannot be read directly from its ontogeny, as Haeckel thought would be possible, but characters from ontogeny can be (and have been) used as data for phylogenetic analyses; the more closely related two species are, the more
apomorphies their embryos share.
Timeline of key points
Branching tree diagram from Heinrich Georg Bronn's work (1858)
Phylogenetic tree suggested by Haeckel (1866)
14th century, lex parsimoniae (parsimony principle),
William of Ockam, English philosopher, theologian, and Franciscan friar, but the idea actually goes back to
Aristotle, precursor concept
1763, Bayesian probability, Rev. Thomas Bayes, precursor concept
18th century, Pierre Simon (Marquis de Laplace), perhaps first to use ML (maximum likelihood), precursor concept
1809, evolutionary theory, Philosophie Zoologique,Jean-Baptiste de Lamarck, precursor concept, foreshadowed in the 17th century and 18th century by Voltaire, Descartes, and Leibniz, with Leibniz even proposing evolutionary changes to account for observed gaps suggesting that many species had become extinct, others transformed, and different species that share common traits may have at one time been a single race, also foreshadowed by some early Greek philosophers such as
Anaximander in the 6th century BC and the atomists of the 5th century BC, who proposed rudimentary theories of evolution
1837, Darwin's notebooks show an evolutionary tree
1843, distinction between
analogy (the latter now referred to as
homoplasy), Richard Owen, precursor concept
1858, Paleontologist Heinrich Georg Bronn (1800–1862) published a hypothetical tree to illustrating the paleontological "arrival" of new, similar species following the extinction of an older species. Bronn did not propose a mechanism responsible for such phenomena, precursor concept.
1858, elaboration of evolutionary theory, Darwin and Wallace, also in Origin of Species by Darwin the following year, precursor concept
Ernst Haeckel, first publishes his phylogeny-based evolutionary tree, precursor concept
1893, Dollo's Law of Character State Irreversibility, precursor concept
1912, ML recommended, analyzed, and popularized by Ronald Fisher, precursor concept
1921, Tillyard uses term "phylogenetic" and distinguishes between archaic and specialized characters in his classification system
^Richard C. Brusca & Gary J. Brusca (2003). Invertebrates (2nd ed.). Sunderland, Massachusetts: Sinauer Associates.
^Bock, W. J. (2004). Explanations in systematics. Pp. 49–56. In Williams, D. M. and Forey, P. L. (eds) Milestones in Systematics. London: Systematics Association Special Volume Series 67. CRC Press, Boca Raton, Florida.
^Auyang, Sunny Y. (1998). Narratives and Theories in Natural History. In: Foundations of complex-system theories: in economics, evolutionary biology, and statistical physics. Cambridge, U.K.; New York: Cambridge University Press.[page needed]
^Blechschmidt, Erich (1977) The Beginnings of Human Life. Springer-Verlag Inc., p. 32: "The so-called basic law of biogenetics is wrong. No buts or ifs can mitigate this fact. It is not even a tiny bit correct or correct in a different form, making it valid in a certain percentage. It is totally wrong."
^Ehrlich, Paul; Richard Holm; Dennis Parnell (1963) The Process of Evolution. New York: McGraw–Hill, p. 66: "Its shortcomings have been almost universally pointed out by modern authors, but the idea still has a prominent place in biological mythology. The resemblance of early vertebrate embryos is readily explained without resort to mysterious forces compelling each individual to reclimb its phylogenetic tree."
^Hennig, Willi (1950). Grundzüge einer Theorie der Phylogenetischen Systematik [Basic features of a theory of phylogenetic systematics] (in German). Berlin: Deutscher Zentralverlag.
^Wagner, Warren Herbert (1952). "The fern genus Diellia: structure, affinities, and taxonomy". University of California Publications in Botany. 26 (1–6): 1–212.
^Nelson, G (1979). "Cladistic Analysis and Synthesis: Principles and Definitions, with a Historical Note on Adanson's Familles Des Plantes (1763-1764)". Systematic Biology. 28: 1–21.
^Archie, James W (1989). "Homoplasy Excess Ratios: New Indices for Measuring Levels of Homoplasy in Phylogenetic Systematics and a Critique of the Consistency Index". Systematic Zoology. 38 (3): 253–269.
^Wilkinson, M (1994). "Common Cladistic Information and its Consensus Representation: Reduced Adams and Reduced Cladistic Consensus Trees and Profiles". Systematic Biology. 43 (3): 343–368.