Statistically derived species distribution models (SDMs) are increasingly used to predict ecological changes on a warming planet. For Prochlorococcus, the most abundant phytoplankton, an established statistical prediction conflicts with dynamical models as they predict large, opposite, changes in abundance. We probe the SDM at various spatial-temporal scales, showing that light and temperature fail to explain both temporal fluctuations and sharp spatial transitions. Strong correlations between changes in temperature and population emerge only at very large spatial scales, as transects pass through transitions between regions of high and low abundance. Furthermore, a two-state model based on a temperature threshold matches the original SDM in the surface ocean. We conclude that the original SDM has little power to predict changes when Prochlorococcus is already abundant, which resolves the conflict with dynamical models. Our conclusion suggests that SDMs should prove efficacy across multiple spatial-temporal scales before being trusted in a changing ocean.

Given a finite set S in [0, 1] 2 including the origin, an anchored rectangle packing is a set of non-overlapping rectangles in the unit square where each rectangle has a point of S as its left-bottom corner and contains no point of S in its interior. Allen Freedman conjectured in the 1960's one can always find an anchored rectangle packing with total area at least 1/2. We verify the conjecture for point configurations whose relative positions belong to certain classes of permutations.