Comma after introductory material in a sentence or clause

In English, the normal word order in sentences and clauses that make a statement is Subject-Verb-Object. This means that the default first element in such sentences and clauses is the subject, in the sense of the word or phrase that identifies the entity that does something or causes something to happen. 

SubjectVerbObject
The guestsatedinner.
The dogburiedthe bone.
Genesregulateprotein synthesis.

In authentic sentences and clauses, whether in academic writing or other contexts, the subject is often preceded by introductory material that may vary considerably in form, ranging from single words and short phrases to complete clauses.

The introductory material typically functions as an adverbial. In other words, it may indicate when, where, why, or under what circumstances something happens, or the order in which events occur. 

Introductory material can also consist of other types of subordinate clauses as well as of transitional or linking words and phrases that connect sentences and signal relationships between them, such as addition, contrast, cause and effect, or sequence.
 

A common feature of such material is that it is separated from the sentence or clause subject by a comma. 

Introductory materialSubjectVerbObject
Yesterday,the guestsatedinner.
After the conference,the guestsatedinner
When the keynote speech ended,the guestsatedinner.
Typically, the digburiedthe bone.
In the backyard,the dogburiedthe bone.
When no one was watching,the dogburiedthe bone.
Fundamentally,genesregulateprotein synthesis.
In living cells,genesregulateprotein synthesis.
When environmental conditions change,plants facenew challenges.
Because environmental conditions have changed,many speciesfaceextinction.

In some contexts, a comma also helps clarify the intended meaning of a sentence or clause by preventing ambiguity.
 

Potentially ambiguousCorrected
When the cat ate the mouse wanted to eat too.When the cat ate, the mouse wanted to eat too.
After the enemy attacked the country was in ruins.After the enemy attacked, the country was in ruins.
Seriously good historians evaluate their sources critically.Seriously, good historians evaluate their sources critically.

Tricky cases

Introductory material that is followed by a comma should not be confused with the sentence subject. 

As we saw above, a comma can be used to mark the boundary between introductory material and the sentence subject. However, it should not be used to separate the sentence subject from the finite verb. 

This also applies to cases when the sentence subject takes the form of a long phrase or clause. 

FaultyCorrected
The keynote speaker at the conference who spoke after you, happens to be my supervisor.The keynote speaker at the conference who spoke after you happens to be my supervisor. (compare: She happens to be my supervisor.)
Playing the piano at least for an hour every day, has become my favourite way to relax.Playing the piano at least for an hour every day has become my favourite way to relax. (compare: It has become my favourite way to relax.) 
To study geography, is to explore the world.To study geography is to explore the world. 
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