Hi Oscar. Thank you for your opinion regarding Terminalia catappa.
From the sea shore which kind of non-human disperse it over 30 miles interior and over hundreds of feet above the sea level? FRUIT bats is the answer. Long time ago while attending a Tropical Naturalist club annual meeting, there was a discussion on this particular subject attended by some Internationally known Doctorates in Science. It is mainly the Fruit Bats that carry the Terminalia catappa fruit far away and after consuming it drops it's hard shelled seed. Whoever thinks otherwise should answer 1.How it is dispersed 30 + miles interior and about 100 feet or so above the sea level from the shore line, and 2. What and who planted or helped germinate these seeds there?
Since 80 plus years I am also familiar with bats carrying and dropping the Kidney shaped Cashew fruits (nut covered by shell) far away places after consuming the pear shaped juicy false fruit. In those days there was no known commercial farming of cashew. Most of the produce of Cashew nuts in India were harvested from the Forest and Wooded areas. Mostly Bats were responsible for India's Cashew crop then. So also in Brazil, Tropical Americas, Tropical Africa and Tropical Asia. We know that the Portuguese introduced this from Brazil through their African Colonies into India.Similarly bats suck the outer juicy part of the Arecanut fruit and drops the hard nut, usually far away from the source.
Regarding the Jamaican cherry as an invasive plant. Nowadays with Internet sales, Nursery trade, Seed trade by mail, Ebay, and of course mainly through the dispersal by bats and birds it will spread faster. High percentage of seeds coming out of the bat's gut germinate and at a faster rate! It was introduced in Hawaii by the then Government in 1922 and you don't have to worry because of the absence of fruit bats in Hawaii!
My views of what I saw and experienced all these years in a small scale in the practical fields of 'Flora and Fauna. Will be away in zones 11 to 13b for the next 4 months. Season's Greetings.