There are 2 main theories for the comparison of animal intelligence:
A phylogenetic based approach: since the time of aritotle people have tried to organise the animal kingdom into a sequence of intelligence or “scala naturae” great chain of being. What has now become known as the phylogenetic scale of intelligence is based upon Darwins theory of evolution as laid out in his on the origin of the species 1859. As intelligence serves an adaptive purpose it is a reasonable assumption that the more evolved an animal is the more intelligent it will be. For instance we evolved from homo-sapiens around 100,000 years ago and we are much more intelligent than them. However this had been proven not to be the case. In fact evolution encourages tree like not linear organisation of organisms and their characteristics. As gould said 1996 our species is a “tiny twig on the floridly aborescent bush of life” Evolution provides an example of the diversity of a species, it does not provide any grounds for ranking animals according to their intelligence.
An alternative approach to comparing animal intelligence is the niche specific theory of intelligence. This theory argues that animals have different environmental pressures and that is reflected in their intellectual ability for example a bird has excellent navigation skills and a dog has an excellent sense of smell. However there are also common evolutionary pressures which all species share such as food illness learning. The underlying mechanisms for learning which foods to avoid is the same in all animals so this theory is also a shite way to explain the distribution of intelligence.
The main problem when comparing species intellects is how to define a test which is a fair test. All animals differ in their intellectual abilities and are better at some things than others so how can we define a test which tests