What does this equation mean?

The same population-level tools — mark-recapture-based abundance and survival estimates, genetic estimates of $N_e$ and diversity, and distribution models tracking range contraction — are the instruments behind the field’s most consequential empirical claims about anthropogenic biodiversity change. Dirzo and colleagues’ 2014 synthesis in Science compiled vertebrate, invertebrate, and plant population trend data across terrestrial ecosystems and documented widespread declines in abundance and range even among species not yet classified as globally threatened with extinction — a phenomenon the authors term “defaunation,” distinct from outright extinction because it captures functional loss (reduced pollination, seed dispersal, predation pressure) that occurs well before a species formally disappears [ 7 ] . Ceballos, Ehrlich, and Dirzo’s 2017 follow-up in the Proceedings of the National Academy of Sciences quantified this at larger scale, analyzing range contraction and population loss across thousands of vertebrate species and concluding that population-level declines are far more widespread than species-level extinctions alone would indicate — describing the pattern as a “biological annihilation” already underway rather than a future risk [ 8 ] .