Lineages of various kinds are important in systematics and can be included within other lineages. (A) Tokogeny and phylogeny (modified from Hennig, 1966). A cladogenic event (shaded triangle) results in the division of a founder species into two sister species. The phylogenetic relationships of the two species are shown in the simple diagram on the right. The larger diagram shows the complexity of reticulate (tokogenetic) relationships of individuals within these polymorphic sexually reproducing species with dimorphic male (black dots) and female (white dots) individuals. Mature individuals are shown, each of which underwent metamorphosis, and thus progressed through several morphologically different character-bearing stages (semaphorants: bottom right circle), which could also provide characters for reconstructing relationships. Cyclomorphism = seasonal variation of individuals, again potentially providing characters if comparable semaphorant stages are sampled. A maternally transmitted mitochondrial DNA lineage is shown in blue lines superimposed on the arrows showing genealogical relationships. Note that although one species is fixed for this mitochondrial lineage, the other species is polymorphic for it, such that some individuals in that species possess mitochondrial genomes that are more closely related to mtDNA in the other species than to mtDNA of individuals in their own species. The mitochondrial genomes of this lineage may not be identical—they can accumulate mutations over time. Looking backward in time from the present (top of diagram), pairs of mitochondrial genomes coalesce at their most recent common ancestor. An example is shown with the two red-circled individuals, one from each species, whose mitochondrial genomes coalesce in the earlier circled individual prior to species divergence. (B) Gene trees are embedded within the species tree, and are shaped by the species history, but gene trees can differ from the species tree both in branch length and topology. The tree for three species with topology (A(B,C)) is shown four times, with individual neutrally evolving alleles shown as dots within it. One allele from each species is tracked backward in time from the present (bottom), with lines randomly connecting alleles in each generation and coalescing with alleles from other species until the common ancestor is reached at the top of the species tree. Time (t) in coalescent units (time in generations divided by effective population size) is shown for the two speciation events. Top left: purple lines track an allele coalescent history that closely tracks the species tree, having the same topology (A,(B,C)) and similar divergence times. Top right: red lines track a coalescent history that produces a gene tree topology again identical to that of the species tree, but in which alleles from species B and C coalesce much deeper in the gene tree (compare position of blue arrow in the two trees), which would suggest a much older divergence of species B and C. Bottom left: green lines connect alleles that coalesce to produce a gene tree with topology ((A,B)C), which is incongruent with the species tree; the red arrow shows the coalescence of the species B allele with the species A allele rather than with the species C allele, as in the “purple” gene tree). Bottom right: blue lines connect alleles that coalesce to produce a gene tree with topology (B(A,C)), which again is incongruent with the species tree; the green arrow points to the coalescence of the C allele with the A allele rather than with the B allele. All of the gene trees except the purple tree show deep coalescence of alleles, which in the green and blue trees creates incongruence with the species tree topology through the phenomenon of incomplete lineage sorting (ILS). Tree A has the probability 1–etABC, whereas each of the other trees has the probability 1/3etABC. The probability of inferring the correct species tree from trees from individual genetic loci is dependent on t, and thus on effective population size (small populations harbor fewer alleles and afford less opportunity for deep coalescence and ILS) and time (large tABC allows genetic drift to remove variation from the population, minimizing the chance of deep coalescence and ILS). The dependence of gene tree topologies and branch lengths on species history and demography is what allows species histories to be inferred from a sample of gene trees under the multispecies coalescent (MSC). (C) A simple three species phylogeny (left-hand tree) is complicated by introgression or horizontal transfer between species C and D (center tree), and the formation of a hybrid species (H) between species C and D (right-hand tree).