# Fitness response relation of a multitype age-structured population dynamics.

@article{Sughiyama2019FitnessRR, title={Fitness response relation of a multitype age-structured population dynamics.}, author={Yuki Sughiyama and So Nakashima and Tetsuya J. Kobayashi}, journal={Physical review. E}, year={2019}, volume={99 1-1}, pages={ 012413 } }

We construct a pathwise formulation for a multitype age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational representation of the stationary population growth rate; the representation comprises a tradeoff relation between growth effects and a single-cell intrinsic dynamics described by a semi-Markov process. This variational representation leads to a response relation of the…

## 4 Citations

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## References

SHOWING 1-10 OF 43 REFERENCES

Pathwise thermodynamic structure in population dynamics.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

The thermodynamic structure in population dynamics with phenotype switching is revealed and the strength of the selection is discussed by using the difference between time-forward and time-backward (retrospective) processes.

OPTIMAL LINEAGE PRINCIPLE FOR AGE‐STRUCTURED POPULATIONS

- Biology, MedicineEvolution; international journal of organic evolution
- 2012

It is shown 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.

Mutation, selection, and ancestry in branching models: a variational approach

- Biology, MedicineJournal of mathematical biology
- 2007

The quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites is used, and the fitness of letter compositions is worked out explicitly.

Kinetic theory of age-structured stochastic birth-death processes.

- Mathematics, MedicinePhysical review. E
- 2016

It is shown that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy.

Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models

- Biology, MedicinePloS one
- 2016

This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity, and proposes a few equations on adaptive life strategies in r/K selection where density effects are absent or present.

Making sense of snapshot data: ergodic principle for clonal cell populations

- Biology, MedicineJournal of The Royal Society Interface
- 2017

The correspondence between cells of known age in a population with their histories represents an ergodic principle that provides a new interpretation of population snapshot data and is illustrated using analytical solutions of stochastic gene expression models in cell populations with arbitrary generation time distributions.

Noise-driven growth rate gain in clonal cellular populations

- Biology, MedicineProceedings of the National Academy of Sciences
- 2016

A striking finding is presented showing that a bacterial population grows faster on average than its constituent cells, and an empirical growth law is identified that constrains the maximal growth rate of Escherichia coli.

Steady-state thermodynamics for population growth in fluctuating environments.

- Mathematics, MedicinePhysical review. E
- 2017

It is reported that population dynamics in fluctuating environments is characterized by a mathematically equivalent structure to steady-state thermodynamics, and a Clausius inequality is obtained, which gives the upper bound of the excess growth.

Tunability and Noise Dependence in Differentiation Dynamics

- MedicineScience
- 2007

This work analyzed the probabilistic and transient differentiation of Bacillus subtilis cells into the state of competence to reveal a noise-dependent circuit that is remarkably resilient and tunable in terms of its dynamic behavior.

Individual histories and selection in heterogeneous populations

- Biology, MedicineProceedings of the National Academy of Sciences
- 2010

It is shown that reproduction events alone, recorded in the population’s tree of cell divisions, may be sufficient to accurately measure selection and is applicable in a wide range of biological systems, from microorganisms to cellular populations, such as tumors and stem cells, where detailed temporal data are becoming available.