"Our collective actions are negatively affecting body sizes of many living species," said Roy.
It is well known that humans tend to hunt or fish larger animals, creating a selective pressure that favors the smaller ones that can reproduce while they are still small.
Several species of cod are smaller as a result of pressures of the fishing industry.
The degradation of natural environments around the world is having the same effect by limiting the amount of food available to animals, according to Roy, meaning smaller animals that need less food have a head start.
But, another factor threatens the world's most impressive animals.
"Global warming may reinforce this trend towards smaller sizes through the temperature-size rule," said Roy.
The temperature-size rule, also known as Bergmann's rule, says that species size increases with latitude: they tend to be smaller in the tropics, and larger closer to the poles.
Bergmann's rule is debated, but one explanation for it is that larger animals have a lower surface-area-to-volume ratio, allowing them to retain more heat and fare better in cooler climes.
Conversely, smaller species radiate their heat more easily and so are better adapted to living in warm temperatures. There is also some experimental evidence that rearing animals in higher temperatures generally results in smaller individuals.
Roy has shown that the average body size of tiny ocean shrimps, known as ostracodes, gradually became bigger several million years ago. As the world cooled by 12 degree Celsius during the Cenozoic era, fossil ostracodes got about 30 microns bigger for every degree of cooling.
Although he does not yet have the data, Roy has said that we should expect the opposite consequence from human-induced global warming.
"In effect, our actions have set up a grand selection experiment where bigger is no longer better," said Roy, who has also shown that species evolve faster in cooler temperatures.
"It makes sense to be bigger when it's colder," said Wendy Foden, a biologist at the World Conservation Union who is studying the effects of climate change on species.
"As the world gets warmer, the converse will happen, species will shrink," she added.