Data from: Ecological specialization in fossil mammals explains Cope's rule

Cope’s rule is the trend toward increasing body size in a lineage over
geological time. The rule has been explained either as passive diffusion
away from a small initial body size or as an active trend upheld by the
ecological and evolutionary advantages that large body size confers. An
explicit and phylogenetically informed analysis of body size evolution in
Cenozoic mammals shows that body size increases significantly in most
inclusive clades. This increase occurs through temporal substitution of
incumbent species by larger-sized close relatives within the clades. These
late-appearing species have smaller spatial and temporal ranges and are
rarer than the incumbents they replace, traits that are typical of
ecological specialists. Cope’s rule, accordingly, appears to derive mainly
from increasing ecological specialization and clade-level niche expansion
rather than from active selection for larger size. However, overlain on a
net trend toward average size increase, significant pulses in origination
of large-sized species are concentrated in periods of global cooling.
These pulses plausibly record direct selection for larger body size
according to Bergmann’s rule, which thus appears to be independent of but
concomitant with Cope’s.