When a single gene controls the expression of more than one character, it is said to be pleiotropic. Pleiotropy occurs when a single gene has multiple effects on an organism`s phenotype. This means that a change in this gene can result in various observable characteristics or traits in the organism.

Option 1, heterotrophic, refers to an organism that obtains its energy from organic compounds. This is unrelated to the concept of a single gene controlling multiple traits.

Option 2, autotrophic, refers to an organism that can produce its own food through photosynthesis or chemosynthesis. Again, this is not related to pleiotropy.

Option 3, allotropic, refers to different physical or chemical forms or states of an element. This is not relevant to the genetic concept of a single gene controlling multiple characters.

Therefore, the correct answer is option 4, pleiotropic.