Relativity for the Realm of the Living: a geometric framework for eco-evolutionary dynamics

Richard A Fariña

Abstract: Biological systems are here reinterpreted through a geometric lens that extends the insight of general relativity: organisms and their interactions are modelled as deformations of a multidimensional biological hyperspace. In this view, each entity acts as a source that locally bends a relational field defined by molecular, morphofunctional and ecological axes, thereby altering the trajectories of others through both attractive (for example, trophic or mutualistic) and repulsive (for example competitive or avoidance) effects. The framework is explicitly multiscale, intending to accommodate hierarchical organisation from genes to ecosystems, with a data-fixed ecological metric g estimated from observations (e.g. Mahalanobis/Fisher–Rao) and updated through time, and it incorporates evolutionary directionality, with state-dependent geometry that changes through time. A minimal mathematical programme is outlined that links curvature, interaction tensors and geodesic motion, together with falsifiable predictions, including curvature-dependent convergence or divergence of trajectories, finite-speed propagation of ecological influence with a system-dependent upper bound ceco and local reduction to classical models. Field equations are derived from a variational principle in which the geometric–matter coupling is carried by a scalar field ϕ, so that κ=κ(ϕ); this yields covariant conservation of the total ecological–geometric current (Noether/Bianchi). The aim is methodological rather than doctrinal: to provide a coherent language that unifies ecology, evolution and complexity science and to invite collaboration on a dynamic geometry of life. If successful, this approach could inform both the interpretation of large-scale historical events and practical ecosystem management by making explicit constraints, couplings (via κ(ϕ)) and distributed, porous sources.