Why scaling up uncertain predictions to higher levels of organisation will underestimate change

AO_SCPLOWBSTRACTC_SCPLOWUncertainty is an irreducible part of predictive science, causing us to over- or underestimate the magnitude of change that a system of interest will face. In a reductionist approach, we may use predictions at the level of individual system components (e.g. species biomass), and combine them to generate predictions for system-level properties (e.g. ecosystem function). Here we show that this process of scaling up uncertain predictions to higher levels of organization has a surprising consequence: it will systematically underestimate the magnitude of system-level change, an effect whose significance grows with the systems dimensionality. This stems from a geometrical observation: in high dimensions there are more ways to be more different, than ways to be more similar. This general remark applies to any complex system. Here we will focus on ecosystems thus, on ecosystem-level predictions generated from the combination of predictions at the species-level. In this setting, the ecosystems dimensionality is a measure of its diversity. We explain why dimensional effects do not play out when predicting change of a single linear aggregate property (e.g. total biomass), yet are revealed when predicting change of non-linear properties (e.g. absolute biomass change, stability or diversity), and when several properties are considered at once to describe the ecosystem, as in multi-functional ecology. Our findings highlight and describe the counter-intuitive effects of scaling up uncertain predictions, effects that will occur in any field of science where a reductionist approach is used to generate predictions.