We show that “Malthusian flocks” – i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being “born” and “dying” during their motion – belong to a new universality class in spatial dimensions
d
>
2
. We calculate the universal exponents and scaling laws of this new universality class to
O
(
ϵ
)
in an
ϵ
=
4
−
d
expansion, and find these are different from the “canonical” exponents previously conjectured to hold for “immortal” flocks (i.e., those without birth and death) and shown to hold for incompressible flocks in
d
>
2
. Our expansion should be quite accurate in
d
=
3
, allowing precise quantitative comparisons between our theory, simulations, and experiments.