  A matroid of rank $r$ on $n$ elements is a positroid if it has a
representation by an $r$ by $n$ matrix over $\mathbb{R}$, each $r$ by $r$
submatrix of which has nonnegative determinant. Earlier characterizations of
connected positroids and results about direct sums of positroids involve
connected flats and non-crossing partitions. We prove another characterization
of positroids of a similar flavor and give some applications of the
characterization. We show that if $M$ and $N$ are positroids and $E(M)\cap
E(N)$ is an independent set and a set of clones in both $M$ and $N$, then the
free amalgam of $M$ and $N$ is a positroid, and we prove a second result of
that type. Also, we identify several multi-parameter infinite families of
excluded minors for the class of positroids.
