  We consider branching processes describing structured, interacting
populations in continuous time. Dynamics of each individuals characteristics
and branching properties can be influenced by the entire population. We propose
a Girsanov-type result based on a spinal construction, and establish a
many-to-one formula. By combining this result with the spinal decomposition, we
derive a generalized continuous-time version of the Kesten-Stigum theorem that
incorporates interactions. Additionally, we propose an alternative approach of
the spine construction for exact simulations of stochastic size-dependent
populations.
