David Quammen (author of one of my all-time favorite nonfiction books, The Song of the Dodo: Island Biogeography in an Age of Extinction) has a long article in National Geographic about Yellowstone National Park which touches on some of the same things.

The Greater Yellowstone Ecosystem is bigger than any other park complex in the lower 48 states. And size matters. A resonant study published in the journal Nature back in 1987, by a young ecologist named William Newmark, revealed that among 12 national parks and park complexes in the western United States, all except two had lost mammal species in the years since they had been established, but that Greater Yellowstone, as the largest, had lost fewer species than almost all others. Most of those local extinctions had resulted not from direct human persecution—as the wolves of Yellowstone had been persecuted to oblivion—but from the natural processes of extinction characteristic of islands: When habitat is constrained within a limited area, animal populations remain small, and small populations tend to wink out, over time, because of accidental factors such as disease, fire, hard weather, and bad luck. Greater Yellowstone had lost less of its mammal diversity by natural attrition than had small parks such as Zion, Bryce Canyon, and Mount Rainier. Its size, evidently, had served it well.

Newmark’s original work has been challenged in some particulars during the decades since, but its basic conclusion remains sound: Size matters. The size of the Yellowstone complex helped preserve big, fearsome, wide-ranging, combative animals such as the grizzly, each one of which demands a large territory. No other park in the lower 48, apart from Glacier National Park along Montana’s Canadian border, now supports robust populations of the three greatest living North American carnivores—the grizzly, the wolf, the mountain lion—as well as such other predaceous animals as the wolverine, the coyote, the bobcat, and the red fox. Yellowstone is our wildest park south of the border complex that includes Glacier, in part because it’s our biggest.

The other good thing about geographical bigness is that, besides giving space to large predators with broad territorial needs, it usually encompasses habitat diversity as well as sheer space, thereby sheltering a greater variety of creatures at all levels of size, living all modes of life.

Because I am interested in island biogeography and I like the idea of having seminal papers at my fingertips, I looked up the Newmark article mentioned above.

A land-bridge island perspective on mammalian extinctions in western North American parks
WILLIAM D. NEWMARK
Nature 325, 430 – 432 (29 January 1987); doi:10.1038/325430a0

In recent years, a number of authors have suggested several geometric principles for the design of nature reserves based upon the hypothesis that nature reserves are analogous to land-bridge islands. Land-bridge islands are islands that were formerly connected to the mainland and were created by a rise in the level of the ocean. Land-bridge islands are considered supersaturated with species in that the ratio of island to mainland species numbers is higher than expected from the area of the island. As a result, the rate of extinction should exceed the rate of colonization on a land-bridge island, resulting in a loss of species that is suggested to be related to the size and degree of isolation of the island. If nature reserves are considered to be similar to land-bridge islands, because most are slowly becoming isolated from their surroundings by habitat disturbance outside the reserves, several predictions follow. First, the total number of extinctions should exceed the total number of colonizations within a reserve; second, the number of extinctions should be inversely related to reserve size; and third, the number of extinctions should be directly related to reserve age. I report here that the natural post-establishment loss of mammalian species in 14 western North American national parks is consistent with these predictions of the land-bridge island hypothesis and that all but the largest western North American national parks are too small to retain an intact mammalian fauna.

It’s easy to get depressed. Even if we preserved a lot of big open spaces, left them completely alone, and there were no such thing as pollution or climate change, a smaller nature would still be a less healthy nature. The only silver lining is that if we had a really thorough knowledge of how the shapes of preserved lands and the connections between determine their ecosystem health, we could theoretically come up with land use policies and practices to produce the best possible ecosystem health in the remaining space available.

There is research going on in this area:

A simplified econet model for mapping and evaluating structural connectivity with particular attention of ecotones, small habitats, and barriers
Wei Houa, Marco Neubertb, Ulrich Walzc
Landscape and Urban Planning
Volume 160, April 2017, Pages 28–37

Small habitats and ecotones are recognized as key structures in preserving biodiversity and maintaining landscape connectivity. However, most analyses of landscape pattern have not fully accounted for these elements. This leads to an underestimation of the landscape heterogeneity, especially at the local scale. This research aims to evaluate the structural connectivity for a source habitat (i.e., forest) with particular consideration of the roles of ecotones, small habitats, and barriers. A multi-buffer mapping procedure based on vector data is applied on two comparative test sites for mapping ecological networks (econets) which are composed of forest patches, ecotones, corridors, small habitats, and barriers. On this basis, several indices are proposed for quantitative evaluation of structural connectivity of econets. The application of the indices show that our approach can be useful for analyzing econet connectivity and identifying the roles of critical landscape elements, for example the barriers’ effect on overall forest connectivity. Within an econet, ecotones function as extension of forest edges which can increase the intrapatch connectivity; small habitats play the role of stepping stones which can enhance interpatch connections among forest habitats. The proposed econet model provides a generalized illustration of landscape connectivity and can be used to compare and monitor forest pattern.