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Cyanobacteria are bacteria that perform oxygenic photosynthesis: light-dependent reactions release oxygen from water. Their photosynthetic machinery operates on thylakoid membranes without a chloroplast or a cell nucleus. This is a particularly useful counterexample to equating photosynthesis with being a plant. Chloroplasts descend from an ancestral cyanobacterial partner through endosymbiosis; present-day cyanobacteria are independent descendants, rather than chloroplasts waiting to become plants. See Alberts et al., Molecular Biology of the Cell: chloroplasts and cyanobacteria.

An endosymbiont is the internal partner in an endosymbiosis. Calling an organism an endosymbiont does not by itself classify it as an organelle or imply an irreversible evolutionary transition.

Endosymbiosis is an ecological association in which one organism, the endosymbiont, lives inside another. The definition specifies location, not that both partners benefit, nor that the internal partner has become an organelle. An intracellular association can remain an association between distinct organisms. Endosymbiotic theory addresses a different question: how particular ancestral bacteria became inherited, functionally integrated organelles during evolution.

The striking consequence is that a eukaryotic biological cell can combine histories: its nuclear lineage and its mitochondria need not have the same ancestry. Mitochondria have bacterial ancestry related to Alphaproteobacteria; the plastids of plants and many algae, including chloroplasts, have ancestry within cyanobacteria. These are ancestral lineages, not a claim that a named living bacterial species is the literal ancestor. Present-day bacteria and organelles have both evolved since their shared ancestors. ^[ref]

A eukaryote is an organism belonging to the lineage characterized by a membrane-bounded cell nucleus and extensive cellular compartmentalization. A nuclear envelope surrounds the nuclear genome; nuclear chromosomes are typically linear. Ribosomes perform biological translation outside the cell nucleus. See OpenStax Microbiology, 3.4: nuclear organization and protein synthesis. Specialized biological cells can lose their cell nucleus, as mature mammalian red blood cells do, while remaining parts of eukaryotic organisms; see OpenStax Biology 2e, 40.2: mature red blood cells.

Yeasts, plants and animals are all eukaryotes. Typical cells in these groups have mitochondria, but chloroplasts belong to photosynthetic plant and algae lineages, not to every eukaryote. A cell wall occurs in typical plant and fungus cells but is absent from animal cells. These are comparisons of representative cells, not a checklist every specialized cell must satisfy. See OpenStax Biology 2e, 4.3: nucleus, organelles and representative cells.

The interesting feature is controlled separation: cell membranes and organelle membranes let different cellular processes occupy distinct compartments while membrane transport connects them. The evolution of eukaryotes also involved partnership: mitochondria descend from a bacterial endosymbiosis. Modern phylogenetics supports an archaeal ancestry for the nuclear lineage, alongside this bacterial contribution; see two-domain system. Thus the history of a whole eukaryote cannot be read as the history of just one of its genes.

A mitochondrion is an organelle whose inner membrane houses machinery for much of aerobic cellular respiration and ATP production in typical eukaryotic cells. Mitochondria descend from a bacterial endosymbiosis and retain a genome and ribosomes, although many required proteins are encoded by nuclear genes. This combination connects compartmentalized function to evolution. See OpenStax Biology 2e, 23.1: mitochondrial ancestry.

The two-domain system recognizes bacteria and archaea as the two primary lineages, placing the nuclear ancestry of eukaryotes within archaea. In this model, archaea as a complete clade includes that eukaryotic lineage; restricting the name to prokaryotic members describes a different grouping. Williams and colleagues' study, published online in 2019 and in a 2020 journal issue, found support for this model and a close relationship to Asgard archaea. See Williams et al., 2020: Phylogenomics provides robust support for a two-domains tree of life.

This updates the interpretation of the 1977 and 1990 classifications rather than undoing their discovery of deep differences between bacteria and archaea. Deep phylogenetic trees depend on the sampled genes, organisms and inference model; the precise closest archaeal relatives and early sequence of events require further evidence. Bacterial ancestry of mitochondria through endosymbiosis is a separate part of eukaryotic history.