Save a newbie from the insects!

Hi Guys,
OK, let's start of by telling you what I (think I) know about gardens: 1. They need water 2. I like 'em colourful... 3. ...but colourful doesn't work for the lawn.
Now that you know to use small words when explaining, I a problem that has stumped me.
I have a coconut palm that has never seemed very happy. For years now, everything around it has grown well, while this five-foot tree seemed to be drying out.
Then, a few days ago, I discovered (ahem, my five-year old discovered) that the mother of all ant colonies where living in the tree, with a zillion or more eggs in the folds left by the old leaves (the ones around the base).
Convinced that this was my problem, I proceeded to remove those leaves as carefully as I could and killed the ants once they were off the tree. Then, following the advice of family who claims to have green fingers, I rinsed the tree with a water/washing powder mix.
There are certainly fewer ants now, but looking at the tree closely two days later, it was clear that it hasn't quite worked. A significant portion of the colony has survived, and they have simply moved their eggs to the leaves that are higher up.
Short of ripping off every last leave and spraying the tree with insecticide (lethal to the tree?), how do I fix this? I'd like to keep the tree alive, but those tiny buggers must go.
Any ideas,
Regards,
Cobus
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I don't know otherwise, but how do you know the ants are harming the tree?
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Cobus Kruger wrote:

The ants are a non issue to the tree and probably more of a benefit than anything else. With the coconut palm the trouble may be more where you are trying to grow it. Not sure of elsewhere in the country but in Florida I don't think I have seen them happily grow much further North than Port Charlotte for example.
Lar
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I think there is actually a town called Florida in South Africa but I don't live anywhere near it :-) I have a couple of other palms in the yard and they all do just fine - the one is probably almost three stories high! Also, there is a healthy-looking fan palm about three metres (yards) closer to the house.
I suspected the dreary look may have been caused by the insects because: 1. They seemed to be the only variable from the successful palms in the yard. 2. They live on plant material (or don't they?) 3. I don't particularly like ants, so they seem to be a good scapegoat :-)
Are there any other good reasons why the tree would suffer? Perhaps it is just in need of some fertilizer?
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Yes -- palms have some pretty specific fertilizer requirements, especially for potassium and minor elements (magnesium, manganese, boron). See http://edis.ifas.ufl.edu/MG043 for overall information. Here in Florida (USA) ants nests in palm trees are a common nuisance and not responsible for tree health problems. "Lethal Yellowing" disease is the usual problem with coconut palms here.
Not all palms do well in the same climate. If your climate is such that it could approach 0 degrees C anytime in the winter, it's probably too cold for a coconut palm, but possibly not for other varieties.
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