Biologists in the last 50 years have increasingly emphasized the role of historical contingency in explaining the distribution and dynamics of biological systems. However, recent work in philosophy of biology has shown that historical contingency carries various interpretations and that we are still lacking a general understanding of historicity, i.e., a framework from which to interpret why and to what extent history matters in biological processes. Building from examples and analyses of the long-term experimental evolution (LTEE) project, this paper argues (...) that historicity possess three essential conditions: (1) multiple possible pasts, (2) multiple possible outcomes at a given instant, and (3) a relationship of causal dependence between these two sets. These criteria can be further specified in two general forms of historicity: dependence on initial conditions and path dependence. More attention is devoted to developing a rigorous account of the latter, which captures the type of historicity displayed by stochastic processes. This paper also highlights that it is often more productive to adopt an instant-relative approach and think in terms of degree of historicity instead of trying to maintain a rigid and absolute dichotomy between historical and ahistorical (completely convergent) processes. (shrink)