The taxonomy of Anacystis, Synechococcus, and related genera
 
The experimental strain Anacystis (Synechococcus) nidulans consists of small, rod-like unicells that may aggregate into irregular clumps.
 
Other species of the genus Anacystis have been included by some authors in the genus Microcystis (as have some species of Polycystis). Some species within the genera Aphanothece and Aphanocapsa and sometimes Gleothece have been placed within Anacystis.
 
According to Whitford and Schumacher (1984), the genus Synechococcus contains cylindrical or ellipsoidal unicells that may form small groups. The pale blue-green or yellowish cells do not have mucous sheaths, but do have granules. The genus Polycystis has irregular or perforate colonies of bright to pale blue-green cells with distinct black or purple pseudovacuoles. Some species of Polycystis may be part of the genera Anacystis, Clathrocystis, or Microcystis.
 
Prescott (1982) describes the genus Anacystis Kützing as free-floating or sedentary colonies of many spherical cells packed tightly in copious mucilage. Each colony may be globose or irregular. Each pale or bright blue-green colored cell has its own distinct individual mucilage envelope within the larger gelatinous matrix. The cells have black or purple pseudovacuoles that may be large, or small and numerous. Aphanocapsa cells are similar in shape to Anacystis, but are spaced widely and regularly within the mucilaginous colony and lack the pseudovacuoles seen in Anacystis or Microcystis.
 
Prescott distinguishes the genus Synechococcus Nägeli by its cylindrical or elliptical, free-floating, pale blue-green to yellow unicells. The cells do not have a mucous sheath but may have visible granules. Groups of 2-4 cells may remain connected following cell division.
 
Colonies of Aphanothece Nägeli are made of oval-shaped or oblong cells clustered densely and evenly within firm and abundant mucilage, although the mucous sheaths of individual cells are indistinct. The colonies are often macroscopic, well-defined or irregular in shape, and may be free-floating or sedentary. The cells are gray, olive, or bright blue-green in color, and have granules but lack vacuoles. In contrast, Gleothece has distinct individual mucilage sheaths. Gleothece and Aphanothece are both included within "Anacystis" Meneghini according to Prescott.

Prescott describes Microcystis Kützing as similar to Aphanocapsa, but with pseudovacuoles. It is a free-floating or sedentary colony of spherical cells closely and irregularly arranged in copious mucilage. It may be ovate, globose, or perforate. The cells are pale to bright blue-green and have black or purple pseudovacuoles that are either large and conspicuous or numerous and small.
 
Drouet and Daily (Daily 1942) use "Polycystis" Kützing for Microcystis species.
 
Smith (1950) describes Anacystis as mucilaginous colonies of cells with distinct individual sheaths. This author thinks only Aphanothece spp. with clear mucilage sheaths should be synonymized with Anacystis - not species of Aphanocapsa.

Smith describes Polycystis as colonies of spherical cells with pseudovacuoles within a watery matrix, and includes Microcystis and Clathrocystis Henfrey within this genus.

In contrast, Smith describes Synechococcus as straight or curved cells with either an absent or inconspicuous gelatinous sheath. Colonies of 2-4 cells may form if cells don't separate after division.
 

References

Daily, W.A. 1942. The Chrooccoccaceae of Ohio, Kentucky, and Indiana. American Midland Naturalist 27: 636-661.
 
Prescott, G.W. 1982. Algae of the Western Great Lakes Area. Otto Koeltz Science Publishers: Koenigstein, W. Germany.
 
Smith, G.M. 1950. The Freshwater Algae in the United States. McGraw-Hill:
New York, NY.
 
Wehr, J.D., and R.G. Sheath. Eds. 2003. Freshwater Algae of North America: Ecology and Classification. Academic Press: San Diego, CA.
 
Whitford, L.A., and G.J. Schumacher. 1984. A Manual of Freshwater Algae. Sparks Press: Raleigh, NC.