  We consider Markov jump processes describing structured populations with
interactions via density dependance. We propose a Markov construction with a
distinguished individual which allows to describe the random tree and random
sample at a given time via a change of probability. This spine construction
involves the extension of type space of individuals to include the state of the
population. The jump rates outside the spine are also modified. We apply this
approach to some issues concerning evolution of populations and competition.
For single type populations, we derive the diagram phase of a growth
fragmentation model with competition and the growth of the size of birth and
death processes with multiple births. We also describe the ancestral lineages
of a uniform sample in multitype populations.
