Chlamydomonas reproduces both asexually and sexually.
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In the shifting sands of current taxonomy, the taxon Chlorophyta generally applies to green algae in one way or another. It sometimes is called the division to which green algae belong. As you may recall, in an earlier classification system, the plant kingdom was divided into four divisions: Thallophyta, Bryophyta, Pteridophyta, and Spermatophyta. While all algae were originally thallophytes, later classifications granted a special division to each one. Red algae then belonged to the division Rhodophyta, green algae to Chlorophyta, etc.
At any rate, Chlamydomonas reinhardtii is a chlorophyte. Its body has only one cell, somewhat oval in form. It swims about with two whip-like structures called flagella.
The life cycle of the various members of the genus Chlamydomonas is interesting. Usually they reproduce asexually. While doing so, they find that their flagella are a nuisance. So they somehow cause them to withdraw into their respective bodies. They then divide in half at least twice. All this takes place within the cell membrane of the original alga. Eventually, four new individuals, each equipped with two flagella, break through the cell membrane of the parent cell, and a new generation is born.
Sexual reproduction usually occurs in times of crisis. A healthy Chlamydomonas needs nitrogen. They also need water in which to swim. If nitrogen is in short supply or if their environment suddenly becomes to dry, they must become dormant until the situation improves. This they do by sexual reproduction.
Within the parent cell, mitosis occurs many times. The resultant algae are called gametes because they are about to look for a compatible mate and become a zygote as soon as they emerge from the cell membrane of their parent. However, it is impossible to tell the difference between male and female gametes, for they both look alike. To differentiate between the gametes, scientists call one of them a plus and the other a minus. Gametes that look alike are called isogametes.
The zygote needs a place to sleep. So it forms a sort of crust around itself. It looks like a prickly little ball. Of course, you would not be able to see it without a microscope.
Chlamydomonas reinhardtii normally has only one set of 17 chromosomes. It is therefore called haploid. But it doubles its chromosome number when it becomes a zygote and goes to sleep. It then has 34 chromosomes and is called diploid.
The zygote does not have any flagella. You do not need them when you are sleeping.
As soon as conditions improve, the zygote of Chlamydomonas reinhardtii divides into four different individuals by a process called meiosis. As a result of this process, all four individuals are haploid with only 17 chromosomes. As far as future mating is concerned, two of the new individuals are pluses and two are minuses. When they emerge from their enclosing crust, they are equipped with two flagella and are ready to swim.
“Biology” by Campbell, Reece, and Mitchell