Dasycladalean algae, a long-ranging clade of unicellular-, uninucleate-grade shallow marine chlorophytes, have a tightly constrained and readily quantifiable relationship between form and fecundity, and a body plan that is highly amenable to mathematical modeling. Because of this combination of features, it is possible to construct an "R landscape" for dasycladaleans, that is, a theoretical morphospace wherein each morphotype is characterized by R, the number of offspring per unit time. The resulting dasycladalean R landscape possesses a varied and rugged topology, with steep-sided peaks, ridges, and plateaus (regions of high R values) separated by deep chasms (regions of low R values). If extra-clade selection pressure is uniform between dasycladalean morphotypes, then R describes relative fitness, and the R landscape approximates the dasycladalean fitness landscape. Optimal and non-optimal adaptive walks, the latter either maintaining or increasing fitness at each step, provide means to explore this landscape and develop a range of evolutionary insights. We will present examples of both optimal and non-optimal walks generated in the R landscape, and discuss the use of such walks as tools to (1) illuminate the topology of biophysically available "evolutionary pathways" through the dasycladalean theoretical morphospace, (2) examine the sensitivity of the R landscape to differential selection pressure, (3) test the R landscape as being consistent with a fitness landscape for a given interval of dasycladalean evolutionary history, (4) evaluate dasycladalean phylogenetic hypotheses derived by other means (e.g., cladistic analysis), and (5) explore possible causes of particular dasycladalean extinction events.