  Finite strict gammoids, introduced in the early 1970's, are matroids defined
via finite digraphs equipped with some set of sinks: a set of vertices is
independent if it admits a linkage to these sinks. An independent set is
maximal precisely if it admits a linkage onto the sinks.
  In the infinite setting, this characterization of the maximal independent
sets need not hold. We identify a type of substructure as the unique
obstruction to the characterization. We then show that the sets linkable onto
the sinks form the bases of a (possibly non-finitary) matroid precisely when
the substructure does not occur.
