Researchers suggest so based on studies of early fossil rabbit and horse types. From ScienceDaily:
More than 50 million years ago, when the Earth experienced a series of extreme global warming events, early mammals responded by shrinking in size. While this mammalian dwarfism has previously been linked to the largest of these events, new research has found that this evolutionary process can happen in smaller, so-called hyperthermals, indicating an important pattern that could help shape an understanding of underlying effects of current human-caused climate change.
Researchers propose that the body change could have been an evolutionary response to create a more efficient way to reduce body heat. A smaller body size would allow the animals to cool down faster. Nutrient availability and quality in plants may have also played a role. Previous research shows that both the PETM and the ETM2 hyperthermals coincided with increased levels of carbon dioxide in the atmosphere and that could have limited nutrient quality in plants, which may have contributed to the smaller mammal body size. Hydrological records during the PETM also suggest less precipitation and drought which could have led to drier soils and even fire which may have affected vegetation growth and eventually possibly offspring size. After both hyperthermal events, body sizes on all mammals rebounded. Paper. (public access) – Abigail R. D’Ambrosia, William C. Clyde, Henry C. Fricke, Philip D. Gingerich, Hemmo A. Abels. Repetitive mammalian dwarfing during ancient greenhouse warming events. Science Advances, 2017; 3 (3): e1601430 DOI: 10.1126/sciadv.1601430More.
It’s logical from a physics perspective, of course (increasing surface to volume area). And size variations can be due to a variety of other factors. Islands, for example, can produce great changes in size, probably due to specialized food sources and predation. These change may be more flexible than we think. It will be interesting to find out if some of them are enabled by that vast library of “junk” in the genome.
From USA Today:
Three different species shrank noticeably about 54 million years ago when the planet suddenly heated up. One of them — an early, compact horse — got 14 percent smaller, going from about 17 pounds (7.7 kilograms) to 14.6 pounds (6.6 kilograms), according to an analysis of fossil teeth in Wednesday’s journal Science Advances.
In hotter climates, mammals and other warm-blooded animals need to shed heat so they shrink. Smaller animals have more skin — or fur — per pound than bigger animals so more heat can escape, making them better adapted for warmer climate. Larger animals do better in the cold because they have less skin per pound and keep their heat.
See also: Researchers: Island rule of size evolution does apply to rodents
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By contrast, Ice Age mammals could get pretty big