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OPTIMAL LINEAGE PRINCIPLE FOR AGE-STRUCTURED POPULATIONS

Authors

  • Yuichi Wakamoto,

    1. Research Center for Complex Systems Biology, University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8902, Japan
    2. PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan
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  • Alexander Y. Grosberg,

    1. Department of Physics and Center for Soft Matter Research, New York University, 4 Washington Place New York, NY 10003
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  • Edo Kussell

    1. Department of Physics and Center for Soft Matter Research, New York University, 4 Washington Place New York, NY 10003
    2. Center for Genomics and Systems Biology, Department of Biology, New York University, 100 Washington Square East, 1009 Silver Center, New York, NY 10003
    3. E-mail: elk2@nyu.edu
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Abstract

We present a formulation of branching and aging processes that allows age distributions along lineages to be studied within populations, and provides a new interpretation of classical results in the theory of aging. We establish a variational principle for the stable age distribution along lineages. Using this optimal lineage principle, we show that the response of a population’s growth rate to age-specific changes in mortality and fecundity—a key quantity that was first calculated by Hamilton—is given directly by the age distribution along lineages. We apply our method also to the Bellman–Harris process, in which both mother and progeny are rejuvenated at each reproduction event, and show that this process can be mapped to the classic aging process such that age statistics in the population and along lineages are identical. Our approach provides both a theoretical framework for understanding the statistics of aging in a population, and a new method of analytical calculations for populations with age structure. We discuss generalizations for populations with multiple phenotypes, and more complex aging processes. We also provide a first experimental test of our theory applied to bacterial populations growing in a microfluidics device.

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