The short answer is: there is no equivalent of "to be" in Arabic. In nominal phrases, that is, phrases that doesn't require a verb, you can simply append the adjective to the noun to change its meaning. As in your example, " النمـلة صغـيــرة" which means "the ant is small". English is very different than Arabic, they belong to different language families, so it is not safe to assume that the concepts that apply to one would also apply to the other.
p.s: for the long answer, please refer to Emir's post! :)