Understanding the cognitive capacities of animals is important, because (a) several animal models of human neurodegenerative disease are considered poor representatives of the human equivalent and (b) cognitive capacities may provide insight into alternative animal models. We used a three-stage process of cognitive and neuroanatomical comparison (using sheep as an example) to assess the appropriateness of a species to model human brain function. First, a cognitive task was defined via a reinforcement-learning algorithm where values/constants in the algorithm were taken as indirect measures of neurophysiological attributes. Second, cognitive data (values/constants) were generated for the example species (sheep) and compared to other species. Third, cognitive data were compared with neuroanatomical metrics for each species (endocranial volume, gyrification index, encephalisation quotient, and number of cortical neurons). Four breeds of sheep (n = 15/sheep) were tested using the two-choice discrimination-reversal task. The 'reversal index' was used as a measure of constants within the learning algorithm. Reversal index data ranked sheep as third in a table of species that included primates, dogs, and pigs. Across all species, number of cortical neurons correlated strongest against the reversal index (r2 = 0.66, p = 0.0075) followed by encephalization quotient (r2 = 0.42, p = 0.03), endocranial volume (r2 = 0.30, p = 0.08), and gyrification index (r2 = 0.16, p = 0.23). Sheep have a high predicted level of cognitive capacity and are thus a valid alternative model for neurodegenerative research. Using learning algorithms within cognitive tasks increases the resolution of methods of comparative cognition and can help to identify the most relevant species to model human brain function and dysfunction.