The Gaia hypothesis is the work of James Lovelock, and is a scientific outlook that is interested in the planet as a whole, and more specifically as having its geology, oceanography and meteorology understood as intimately shaped by the forces of life, rather than forces of the inanimate. Sheldrake draws on this idea, but his animism is not found in Lovelock's work, and is not a necessary consequence of it.
What is of interest to us is to what extent a scientific understanding of Nature, and in particular a sophisticated one like the Gaia hypothesis, can change the way that a Nature mystic may engage with Nature. We saw that it was not until the late 18th and mid-19th centuries that a Nature Mysticism emerged that relied partly on a close observation of Nature; Traherne in contrast was not so interested in discriminating one part of it from another. What Muir does is effectively an early version of Gaia, in that he sees the rocks, glaciers, and skies as intimately living as he does the flowers and forests. What Lovelock has done is to put Muir's intuitions on a sound scientific footing. The transcendent sense of awe that may touch one in a high mountain can only be deepened by seeing how the rocks themselves have been formed by the lives and deaths of billions of living creatures, and that the clouds and vapours that form the glorious capping to the mountains are an indirect result of the most intimate of physical processes within these organisms: breathing. In short, the analytic processes of science, which chop reality into smaller and smaller pieces, can also help in the vision of Nature as a whole. Indeed, what some of the biologists of Sheldrake's generation are doing is to create a 'holistic' science which looks at organisms as a whole.