One who eats a Ke'zayit (approx. 30 grams) of fruits from the special species of the Land of Israel grapes, olives, figs, dates, pomegranates must recite after eating the Beracha of "Al Ha'etz Ve'al Peri Ha'etz." Chacham Ovadia Yosef rules (Chazon Ovadia Laws of Berachot, p. 261) that one recites this Beracha even if he did not partake of a Ke'zayit of any single fruit. So long as one partook of a Ke'zayit from these fruits, he must recite the Beracha of "Al Ha'etz." Thus, for example, if a person ate a half-Ke'zayit of grapes and a half-Ke'zayit of dates, he recites "Al Ha'etz" even though he did not eat a Ke'zayit of either fruit, since he consumed a total of a Ke'zayit.
If one ate a Ke'zayit of other fruits, such as apples, oranges, pears, bananas or strawberries, then he recites afterwards the Beracha of "Borei Nefashot." Here, too, the Beracha is recited even if one did not partake of a Ke'zayit of any single fruit. Even if, for example, one ate a half-Ke'zayit of apples and a half-Ke'zayit of stawberries, he recites "Borei Nefashot."
The more complex case is where a person partook of fruits from the special species as well as other fruits. If all the fruit consumed amounts to a Ke'zayit, but the fruit of each group did not amount to a Ke'zayit, which Beracha does one recite? For example, if a person ate a half-Ke'zayit of apples and a half-Ke'zayit of dates, does he recite "Borei Nefashot," as if he ate a full Ke'zayit of apples, or does he recite "Al Ha'etz," as if he ate a full Ke'zayit of dates?
Chacham Ovadia Yosef in Hazon Obadya, Berachot, page 262, rules that in such a case one does not recite any Beracha after eating at all. Since he did not eat an amount of either kind of fruit that requires a Beracha, no Beracha is warranted. Chacham Ovadia notes that the Beracha of "Borei Nefashot" is not an all-encompassing Beracha which can apply to fruits of the special species. Therefore, it cannot cover the half-Ke'zayit of dates, just as "Al Ha'etz" cannot be recited to cover the half-Ke'zayit of apples. Although Chacham Bentzion Abba Shaul (Jerusalem, 1924-1998) disagrees in Or L'sion Helek 1, siman 19, Chacham Ovadia applies here the rule of "Safek Berachot Le'hakel" meaning, we do not recite a Beracha when its obligation is in doubt, and thus in this situation one does not recite a Beracha Acharona at all.
Summary: If one ate a Ke'zayit of fruit from the special species (grapes, olives, dates, pomegranates and figs), he recites afterwards the Beracha of "Al Ha'etz," and if one ate a Ke'zayit of other fruit, he recites "Borei Nefashot." If one ate a half-Ke'zayit of a fruit from the special species and a half-Ke'zayit of other fruits, he does not recite a Beracha Acharona.