Can genomic analysis actually estimate past population size?

Genomic data can be used to reconstruct population size over thousands of generations, using a new class of algorithms (SMC methods). These analyses often show a recent decline in $N_e$ (effective size), which at face value implies a conservation or demographic crisis: a population crash and loss of genetic diversity. This interpretation is frequently mistaken. Here we outline how SMC methods work, why they generate this misleading signal, and suggest simple approaches for exploiting the rich information produced by these algorithms. In most species, genomic patterns reflect major changes in the species' range and subdivision over tens or hundreds of thousands of years. Consequently, collaboration between geneticists, palaeoecologists, palaeoclimatologists, and geologists is crucial for evaluating the outputs of SMC algorithms.