The results of two recent unrelated studies support the idea that dolphins may share certain cognitive abilities with humans and
great apes; the studies indicate dolphins as capable of recognizing themselves in mirrors—an ability that is often considered a sign of self-awareness—and to grasp spontaneously the mood or intention of humans. A. dolphins as capable of recognizing themselves in mirrors—an ability that is often considered a sign of self-awareness—and to grasp spontaneously
B. dolphins' ability to recognize themselves in mirrors—an ability that is often considered as a sign of self-awareness—and of spontaneously grasping
C. dolphins to be capable of recognizing themselves in mirrors—an ability that is often considered a sign of self-awareness—and to grasp spontaneously
D. that dolphins have the ability of recognizing themselves in mirrors—an ability that is often considered as a sign of self-awareness—and spontaneously grasping
E. that dolphins are capable of recognizing themselves in mirrors—an ability that is often considered a sign of self-awareness—and of spontaneously grasping
In this clause there is a verbal ellipsis after the hyphenated comment because it is not necessary to repeat <em>are capable.</em> However it is still required to keep parallelism and that's why a gerund is used after the preposition <em>of</em> when mentioning the second ability (recognizing - grasping).
Options A, B and C lack parallel structures. Option D is not possible because <em>have the ability </em>should be foll owed by a verb in the infinitive form, e.g "... the ability to recognize..."