  We introduce and study an interacting particle system evolving on the
$d$-dimensional torus $(\mathbb Z/N\mathbb Z)^d$. Each vertex of the torus can
be either empty or occupied by an individual of type $\lambda \in (0,\infty)$.
An individual of type $\lambda$ dies with rate one and gives birth at each
neighboring empty position with rate $\lambda$; moreover, when the birth takes
place, the newborn individual is likely to have the same type as the parent,
but has a small probability of being a mutant. A mutant child of an individual
of type $\lambda$ has type chosen according to a probability kernel. We
consider the asymptotic behavior of this process when $N\to \infty$ and the
parameter $\delta_N$ tends to zero fast enough that mutations are sufficiently
separated in time, so that the amount of time spent on configurations with more
than one type becomes negligible. We show that, after a suitable time scaling
and deletion of the periods of time spent on configurations with more than one
type, the process converges to a Markov jump process on $(0,\infty)$, whose
rates we characterize.
