  In this work we model the dynamics of a population that evolves as a
continuous time branching process with a trait structure and ecological
interactions in form of mutations and competition between individuals. We
generalize existing microscopic models by allowing individuals to have multiple
offspring at a reproduction event. Furthermore, we allow the reproduction law
to be influenced both by the trait type of the parent as well as by the mutant
trait type.
  We look for tractable large population approximations. More precisely, under
some natural assumption on the branching and mutation mechanisms, we establish
a superprocess limit as solution of a well-posed martingale problem. Standard
approaches do not apply in our case due to the lack of the branching property,
which is a consequence of the dependency created by the competition between
individuals. For showing uniqueness we therefore had to develop a
generalization of Dawson's Girsanov Theorem that may be of independent
interest.
