Feedback between life and its environment is ubiquitous but the strength of coupling and its global implications remain hotly debated. Abrupt changes in the abundance of life for small changes in forcing provide one indicator of regulation, for example, when vegetation-climate feedback collapses in the formation of a desert. Here we use a two-dimensional "Daisyworld" model with curvature to show that catastrophic collapse of life under gradual forcing provides a testable indicator of environmental feedback. When solar luminosity increases to a critical value, a desert forms across a wide band of the planet. The scale of collapse depends on the strength of feedback. The efficiency of temperature regulation is limited by mutation rate in an analogous manner to the limitation of adaptive fitness in evolutionary theories. The final state of the system emerging from single-site rules can be described by two global quantities: optimization of temperature regulation and maximization of diversity, which are mathematically analogous to energy and entropy in thermodynamics.