Equation 50 · The Valley of Stability Is a Fitness Landscape
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Symbol N
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Symbol Z
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Stated most narrowly, the part of evolutionary theory’s formal apparatus that maps onto the chart of nuclides without qualification is this: a scalar objective function defined over a discrete state space, together with a rule for what counts as a local move, together with the observation that a system occupying a given state will, given the opportunity, take a move that increases the objective. Binding energy per nucleon is the objective; the (N,Z) lattice is the state space; single beta decay, or the small number of other elementary transitions available at a given point, is the local move. An adaptive walk under strong selection and weak mutation — a population that reliably takes the…
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Stated most narrowly, the part of evolutionary theory’s formal apparatus that maps onto the chart of nuclides without qualification is this: a scalar objective function defined over a discrete state space, together with a rule for what counts as a local move, together with the observation that a system occupying a given state will, given the opportunity, take a move that increases the objective. Binding energy per nucleon is the objective; the (N,Z) lattice is the state space; single beta decay, or the small number of other elementary transitions available at a given point, is the local move. An adaptive walk under strong selection and weak mutation — a population that reliably takes the fitness-increasing step available to it and rarely does anything else — is mathematically the same object as a beta-decay chain descending an isobaric parabola. Basins of attraction exist in both pictures: a beta-stable nuclide is a local optimum that no single beta step can improve on, exactly as a local fitness peak is a state no single mutational step can improve on, and both pictures admit barriers between adjacent basins that a purely local, gradient-following process cannot cross.
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