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OPTIMAL LINEAGE PRINCIPLE FOR AGE‐STRUCTURED POPULATIONS
Author(s) -
Wakamoto Yuichi,
Grosberg Alexander Y.,
Kussell Edo
Publication year - 2012
Publication title -
evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.84
H-Index - 199
eISSN - 1558-5646
pISSN - 0014-3820
DOI - 10.1111/j.1558-5646.2011.01418.x
Subject(s) - biology , fecundity , lineage (genetic) , population , evolutionary biology , branching process , interpretation (philosophy) , statistical physics , statistics , demography , genetics , mathematics , computer science , gene , programming language , physics , sociology
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.