OPTIMAL LINEAGE PRINCIPLE FOR AGE-STRUCTURED POPULATIONS
Article first published online: 13 SEP 2011
© 2011 The Author(s). Evolution © 2011 The Society for the Study of Evolution.
Volume 66, Issue 1, pages 115–134, January 2012
How to Cite
Wakamoto, Y., Grosberg, A. Y. and Kussell, E. (2012), OPTIMAL LINEAGE PRINCIPLE FOR AGE-STRUCTURED POPULATIONS. Evolution, 66: 115–134. doi: 10.1111/j.1558-5646.2011.01418.x
- Issue published online: 3 JAN 2012
- Article first published online: 13 SEP 2011
- Accepted manuscript online: 29 JUL 2011 02:10PM EST
- Received Jan 14, 2011, Accepted July 8, 2011, Data Archived: Dryad doi:10.5061/dryad.6mj22
- Age structure;
- population structure;
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.