Biodiversity is sustained by and is essential to the services that ecosystems provide. Different species would use these services in different ways, or adaptive strategies, which are sustained in time by continuous innovations. Using this framework, we postulate a model for a biological species (Homo sapiens) in a finite world where innovations, aimed at increasing the flux of ecosystem services (a measure of habitat quality), increase with population size, and have positive effects on the generation of new innovations (positive feedback) as well as costs in terms of negatively affecting the provision of ecosystem services. We applied this model to human populations, where technological innovations are driven by cumulative cultural evolution. Our model shows that depending on the net impact of a technology on the provision of ecosystem services (θ), and the strength of technological feedback (ξ), different regimes can result. Among them, the human population can fill the entire planet while maximizing their well-being, but not exhaust ecosystem services. However, this outcome requires positive or green technologies that increase the provision of ecosystem services with few negative externalities or environmental costs, and that have a strong positive feedback in generating new technologies of the same kind. If the feedback is small, then the technological stock can collapse together with the human population. Scenarios where technological innovations generate net negative impacts may be associated with a limited technological stock as well as a limited human population at equilibrium and the potential for collapse. The only way to fill the planet with humans under this scenario of negative technologies is by reducing the technological stock to a minimum. Otherwise, the only feasible equilibrium is associated with population collapse. Our model points out that technological innovations per se may not help humans to grow and dominate the planet. Instead, different possibilities unfold for our future depending on their impact on the environment and on further innovation.This article is part of the themed issue 'Process and pattern in innovations from cells to societies'.