Dear colleague, check for one-step meiosis in several algae and lower plants. See also J Evol Biol. 2004 Sep;17(5):1098-105.

Dear Zhang,

I think, that you mean Schizogony (especially merogony !!!), as asexual reproduction by multiple fission with producing merozoits. If appear in some development stage of unicellular organism, so it has parasitic or semiparasitic stage, like some Dinoflagellates, look

Gerhard Drebes (1978) Dissodinium pseudolunula (Dinophyta), a parasite on copepod eggs, British Phycological Journal, 13:4, 319-327, DOI: 10.1080/00071617800650381

 Some of other protists, like Foraminifera, have practically the same reproduction, but it is gametogony.

 As well you can check some fungi -like protists.

Perfect book on nuclear transformations in protists was written by Professor Igor Raikov from St. Petersburg. I attache his perfect book for you, sorry it is in Russian, but well illustrated. I knew him personally from about 35 years ago (died long time ago).

 Andrey

Dear Zhang,

so, if we have open discussion, I'll put question and my reply in this form, as possibly smbd will correct me, as I'm not cytologist, just explaining some questions for my students during lectures.

Dear Prof.

In Karl G. Grell’s book Protozoology, multiple fission is “usually preceded by nuclear multiplication with the mother cell, which then cleaves rapidly to form a corresponding number of daughter cells (simultaneous multiple fission).”

However, “in some Protozoa, multiple fission resembles total cleavage of animal eggs. The mother cell is divided into smaller and smaller daughter cells without cell growth between the fissions. Each fission is accompanied by nuclear division (successive multiple fission)”.

The following figure is my comprehension; and I don’t know whether my comprehension is correct.

 Does that the simultaneous multiple fission refers to “Schizogony”? Does the stage marked by black triangle named syncytium?

I’m waiting for your reply.

The SYNCYTIUM (from al-Greek. σύν "together" κύτος "complex cell") is a type of tissue in animals, plants and fungi with incomplete differentiation of cells, in which separate portions of cytoplasm with nuclei are interconnected by cytoplasmic bridges.

So, Zhang, you are wright with 1st explanation but till the end it is SCHIZOGONY.

An example of a syncytium is embryonic connective tissue — mesenchyme.

The person in the form of syncytium develop the precursors of germ cells — oogonia in female embryos and male germ cells in sexually Mature men.

 Second process has a lot of forms. On yours figure is shown not usual process in the problem we are discussing. For the free living protists it is used by Volvox, Eudorina, Pandorina etc. (oospora like No 1 yours figure, but it is reductional dividing – meiosis, as Emmanuel told you in her explanation) colonial forms till stage 4.  It can be (in some cases) characteristic for species freshly started like semi parasitic. So, in my opinion it is not

SCHIZOGONY (from Greek. schizo — split, split and... Gonia), multiple asexual reproductions of the protozoa (sporozoa, foraminifera) and some algae. The organism becomes multi-core and splits into many (according to the number of cores) mononuclear cells merozoites.

 So, the second figure process is much rarer. On details should consult cytologists !