Combining mathematical theory with experiments and/or observational data benefits both: theory can generate hypotheses that are then tested with data, and data can keep theory grounded in reality. Statistics is the tool for combining theory and data. For anything other than testing the simplest of hypotheses, familiar statistical methods are inadequate and even misleading. For example, how would you analyze global patterns of greening (NDVI) from remote-sensing datasets? There are millions of pixels of data yet nearby pixels all show similar trends: the millions of pixels are all correlated, so there aren’t millions of independent data points. Statistically bridging the gap between mathematical theory and data is challenging, but the payoff is new insights into the complex spatio-temporal ecological and evolutionary dynamics shown by real systems.
