This paper describes how in 1896, Edward D. Cope first published his law of phylogenetic increase which states that body size and longevity tend to increase during the evolutionary history of a lineage. It shows how this seems to be true for most animal groups, with only a few notable exceptions. It examines how the advantages of having a larger body size are numerous and attempts to establish whether possessing a large body size confers advantage not just ecologically, in the short-term, but also in a long-term evolutionary sense.
From the Paper:
"It is true, and seems obvious, that large animals make better predators. This is because if an animal is considerably larger than its prey, it can subdue this prey simply due to its size as it is bound to be stronger and more powerful. An example is the African lion, Panthera leo, whose paws have such immense strength that they can knock down an ox with one blow. Being larger also offers benefits to herbivores as safety and protection from predators. If an animal is large, a predator is less likely to attack it. It also means that the animal may be more able to defend itself or escape from these predators. Bigger, especially taller, herbivores also have the advantage of being able to reach food that is higher in trees or bushes, which animals that are not so tall cannot reach."