  We study the impact of many-body effects on the fundamental precision limits
in quantum metrology. On the one hand such effects may lead to non-linear
Hamiltonians, studied in the field of non-linear quantum metrology, while on
the other hand they may result in decoherence processes that cannot be
described using single-body noise models. We provide a general reasoning that
allows to predict the fundamental scaling of precision in such models as a
function of the number of atoms present in the system. Moreover, we describe a
computationally efficient approach that allows for a simple derivation of
quantitative bounds. We illustrate these general considerations by a detailed
analysis of fundamental precision bounds in a paradigmatic atomic
interferometry experiment with standard linear Hamiltonian but with both single
and two-body losses taken into account---a model which is motivated by the most
recent Bose-Einstein Condensate (BEC) magnetometry experiments. Using this
example we also highlight the impact of the atom number super-selection rule on
the possibility of protecting interferometric protocols against decoherence.
