The master equation of an ecosystem in evolution on a static fitness landscape can be written as a sum over all possible phylogenetic generations of individuals. Such a time trajectory represents alternating phases of selection (the fitness landscape) and mutation (during reproduction). This approach permits to restrict the sum to the most probable paths. For medium and small time scales, a smooth landscape and long-range mutations it is shown that the equilibrium distribution is of Boltzmann type, with the fitness as an energy and mutations as temperature.
Path integral formulation of evolving ecosystems / Franco Bagnoli; Michele Bezzi. - STAMPA. - (1999), pp. 493-496. (Intervento presentato al convegno Path Integrals from Pev to Tev: 50 Years After Feynmann's Paper tenutosi a Firenze, italy nel 25-29 August 1998).
Path integral formulation of evolving ecosystems
BAGNOLI, FRANCO;
1999
Abstract
The master equation of an ecosystem in evolution on a static fitness landscape can be written as a sum over all possible phylogenetic generations of individuals. Such a time trajectory represents alternating phases of selection (the fitness landscape) and mutation (during reproduction). This approach permits to restrict the sum to the most probable paths. For medium and small time scales, a smooth landscape and long-range mutations it is shown that the equilibrium distribution is of Boltzmann type, with the fitness as an energy and mutations as temperature.
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