"Not to want someone doing something." What shade of meaning is attached to using the gerund rather than infinitive?

On page 137 of First Certificate Trainer by Peter May (Cambridge Books for Cambridge Exams), the last paragraph in Test 4, Use of English Part 2 (a cloze test on a short text entitled Safe camping), reads:

After meals, pick up any bits of food that might be left on the ground, as these can attract insects – or larger creatures. It also makes sense, for the same reason to keep unused food in closed containers well away from the camp. You don't want a hungry bear or other animal suddenly appearing in your tent!

Why not the structure "(not) to want someone to do something"? Why not "You don't want a hungry bear or other animal to suddenly appear in your tent"? (Or "suddenly to appear in your tent", or "to appear in your tent suddenly"… it is not the place of the adverb I am interested in here.)

The structure "(not) to want someone doing something" is found in the Cambridge Dictionary online, with the example sentence "I don't want a load of traffic going past my house all night, waking me up." But no explanation is given as to when one structure should be used, and when the other.

Solution 1:

I commented that I don't think OP's turning up was a gerund, but I'm somewhat backtracking on that point now. Whatever - even if it's not formally a gerund, it looks quite like one. And there's been a general tendency over the past century or so for gerunds to replace infinitive forms.

The main factor controlling the gerund/infinitive choice seems to be the specific verb involved. Thus, looking at a simpler construction...

He enjoys swimming (not He enjoys to swim)
He wants to swim (not He wants swimming)
He likes swimming/to swim (both are okay)

There's also this from englishpage.com, pointing out that infinitives sound more abstract...

Gerunds sound more natural and would be more common in everyday English.
Infinitives emphasize the possibility or potential for something and sound more philosophical.

Learning is important (normal subject)
To learn is important (abstract subject - less common)
The most important thing is learning (normal complement)
The most important thing is to learn (abstract complement - less common)

To which I would add my own example...

I like you to kiss me (sounds dated, formal, starchy to me, and all 6 results are from long ago)
I like you kissing me (sounds perfectly natural, but all 58 results are from the past couple of decades)

Putting all that together, what it means is native speakers today like using gerunds wherever possible, whereas a century ago they liked to use infinitives. Actually, I just used those two forms to illustrate my point. Strictly speaking if we go back far enough, native speakers had no choice (because using gerunds like that simply wasn't grammatically possible).

As to whether there's any semantic difference, I think the answer is No, not usually. But when I consider the following pair...

I hate to eat alone
I hate eating alone

...I can easily convince myself it's more likely the first speaker doesn't actually eat alone very often. There's more "immediacy" in the gerund/continuous verb form used by the second speaker, which suggests to me he's currently eating alone (or at least, frequently does so).

Here's another related context where the infinitive/gerund choice definitely makes a difference. I know it's only because of the "when", but still...

Sports teacher: "Okay, you kids get changed and go outside while I finish my paperwork - I want you running/to run round the track when I come out".

EDIT: By way of explaining @user58319's assertion that the infinitive "implies some kind of control or influence". This just arises because in some contexts the implied subject is in fact the speaker...

"I don't like to smoke in bed" (so I don't)
"I don't like smoking in bed" (so please can you not do it)

Solution 2:

I agree; the use of the present participle here does seem rather illogical. However much we would like to think that English constructions are well-behaved, we'll quite often be disappointed. It might be instructive to examine the behaviour of other verbs in similar complex catenations here, after an example of a simple catenation:

He remembered paying.

is obviously (and famously – but I would use '-ing form' rather than 'gerund' here; see FF's comment) different in meaning from the catenation with the to-infinitive:

He remembered to pay.

So we see the participle 'paying' used in a punctive (completed short action) role.

With

I don't want him turning up.

I don't want him to turn up.

either is acceptable, and there is little change in meaning. This pair come close to OP's examples, but even the inclusion of the adverb 'suddenly' alters 'how it sounds'. 'I don't want him suddenly to turn up' sounds very formal, even starchy; 'I don't want him to suddenly turn up' sounds better but still not as idiomatic as 'I don't want him suddenly turning up'.

With

I didn't allow him to come.

the to-infinitive is mandatory.

With

I can't see/imagine him coming / turning up [...: he never goes to parties.]

the -ing form is mandatory, even though 'turn up' is punctive.

So, -ing form catenations are not restricted to continuous processes. Even where there otherwise seems a fairly straight choice, with the -ing form perhaps not as appropriate, it may be perversely preferred with some verbs. Choice is probably influenced by the over-formal sound of the to-infinitive alternative.