All but the very briefest sentences contain noun phrases and academic writing is dense with these structures. So it is important to understand their structure when examining various types of sentences.
A noun phrase may consist of a single noun. In the sentence "Koalas can sleep up to 20 hours per day.", "Koalas" is the subject of the sentence; it is the head in a one-word noun phrase. Very often the head is accompanied by a determiner See the glossary definition such as an article, a personal pronoun, a number, etc.
Head nouns can be premodified with adjectives, participial See the glossary definition modifiers and other nouns. They can also be postmodified with prepositional phrases See the glossary definition , relative clauses See the glossary definition , ed-clauses See the glossary definition and to-clauses See the glossary definition .
Heads are obligatory elements, without which we wouldn't have a noun phrase. Determiners are almost always obligatory. Premodifiers and postmodifiers are mainly optional (but see the comments below). Complex noun phrases are common in academic writing so consult the noun premodification and postmodification pages.Indicates an obligatory element. Indicates an optional element.
Sometimes a sentence is not complete when a postmodifier is removed from a head. This is the case with the above example "the spread of disease". Without the prepositional postmodifier "of disease", "the spread" doesn't make sense (although it could in certain contexts). Similarly, the last example "one way that plants defend themselves" is incomplete without the relative clause "that plants defend themselves".
You can see further examples of noun phrase modification on the premodification with adjectives page, the premodification with nouns page, the complex noun premodification page, and the noun postmodification page.