  Two families of denotational models have emerged from the semantic analysis
of linear logic: dynamic models, typically presented as game semantics, and
static models, typically based on a category of relations. In this paper we
introduce a formal bridge between a dynamic model and a static model: the model
of thin concurrent games and strategies, based on event structures, and the
model of generalized species of structures, based on distributors. A special
focus of this paper is the two-dimensional nature of the dynamic-static
relationship, which we formalize with double categories and bicategories.
  In the first part of the paper, we construct a symmetric monoidal oplax
functor from linear concurrent strategies to distributors. We highlight two
fundamental differences between the two models: the composition mechanism, and
the representation of resource symmetries. In the second part of the paper, we
adapt established methods from game semantics (visible strategies, payoff
structure) to enforce a tighter connection between the two models. We obtain a
cartesian closed pseudofunctor, which we exploit to shed new light on recent
results in the theory of the lambda-calculus.
