For instance, when the gestures of the trainer suggest a jump followed by a salute, the dolphin understands that it has to jump, and then, to greet the public.
However, even if dolphins seem to understand easily gestures, they do not seem to have abilities to associate an action to a symbolic message.
The dolphin builds easily normal long-range models, not only story-type models as some other animals.
At the same time, they could reach even level 2 of conciousness, if it could be proven that they build their own correlation models with the group to which they belong (as it seems to be the case for captive dolphins).
Note: many species of animals hunt in packs. Usually, the model of correlation is situated in PSM. The superiority of an animal is given by the capacity to build its own correlation model with the pack or with other beings, human or animals, (level 2 of consciousness). It is not easy to see this essential difference, as the apparent behaviour can be the same.
The theory does not exclude the possibility of level 2 consciousness, on image models (of course) for the dolphins.
This would mean e.g. that a dolphin anticipates the action of another and will act in advance, based on prediction, in the frame of a normal model, imposed by the trainer (not a model of the PSM, as the ones associated to instincts). There could be some difficulties to understand what happens, due to the reason shown in the note above.
Some other things result from the theory. Thus, the basic characteristic of the environment where the dolphin lives, is the lack of landmarks. Whatever the capacity of interaction with external reality is, the dolphin in the ocean cannot build models of the environment in which it lives, due to the lack of landmarks. It can't mark the territory to use marks in building models of the territory. Even if it might make maps of the magnetic field of the Earth, these maps are not precise enough to have good landmarks. Even if it had precise landmarks (near the coastline), they could be used only for local navigation.
Using the terminology of my theory, one could say that the dolphin has schizophrenia induced by the environment.
Captivity should increase the level of intelligence of the dolphins, due to an environment with landmarks. These can stimulate it to use its brain to a higher capacity closer to its theoretical possibilities. However, experiments up to date do not show abilities to build symbolic models, as in the case of some monkeys, even if on image models, dolphin brain seems to be very advanced for an animal.