Grammatically, both the to-infinitive and the participle(present or past) of a verb can function as a complement for another verb. But these three forms impart different senses as a complement. - to-infinitive => suggest a potential, or general tendency or future action. (I will tell him to leave). - present participle => the action is happening at the same moment. (I saw him playing) - past participle => indicates a resulting state caused by the action. (I discovered him intoxicated) For example, - He was expected to carry out the task. (The expectation is that he can/will carry it out - ability and future action). - He was seen entering the building. (He was seen as he was entering the building - simultaneous occurrence) - He was considered incapacitated. (It was judged that he was in an incapacitated state - an already present state). In your example, if you say "they have been shown distinguishing ...", it would sound like the tests showed the bats were actually distinguishing shapes during the tests. If you use "to distinguish", it is more about the ability and tendency, that they can and will generally do that. So when it comes to inherent ability or tendency or future action as in your example, the to-infinitive is the right choice (excluding the special "to be (adjective/participle)" form, which indicates a state and/or quality). Other examples. - he was made to resign => He had to resign afterwards, not at the same time. - He is known to react sensitively to criticisms. => He generally does so - it's not talking about an actual instance.

Hello, you are correct, it is 'to distinguish'. The reason is because you are saying that bats can tell the difference between different shapes and colours. An example could be - a friend of mine thinks it is possible to distinguish the difference between Coca Cola and Pepsi, but they taste the same to me. Distinguished - means that something or someone has done something to / is doing something to stand out, or has made a name for itself / themselves. Distinguishing - means that someone has something about their character or appearance that stands out and possibly unique to them. I hope this helps, best wishes, Annie