Analogies between the virial theorem and the Price equation
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1.
California Institute of Technology
- 2. Flintridge Preparatory School, La Cañada, California
Abstract
We observe that the time-averaged continuous Price equation is identical to the positive momentum virial theorem, and we discuss the applications and implications of this connection. We also introduce ecological models using a maternal effect, which can describe arbitrary population size cycles and trait evolution across spatially separated populations. The virial theorem sheds light on the time-averaged behavior of these models.
Copyright and License
©2025 American Physical Society.
Acknowledgement
S.L. thanks Manoj Kaplinghat and Gopolang Mohlabeng for their introduction to the virial theorem. L.P. thanks Junhyong Kim for discussions on the connection of this work to ecological orbits. C.F. was partially supported by funding from Caltech's CI2 grant program.
Funding
C.F. was partially supported by funding from Caltech's CI2 grant program.
Contributions
S.L. and L.P. developed the connections between the virial theorem and the Price equation. C.F. identified and developed the connection to ecological orbits and simple harmonic motion via the maternal effect. S.L. and L.P. drafted the initial manuscript; C.F., S.L., and L.P. edited the final version and code.
Data Availability
The data and scripts for generating figures are available at [63].
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Additional details
Additional titles
- Alternative title
- The virial theorem and the Price equation
Related works
- Is new version of
- Discussion Paper: arXiv:2312.06114 (arXiv)
- Is supplemented by
- Dataset: https://github.com/pachterlab/FLP_2024 (URL)
Funding
- California Institute of Technology
- Caltech CI2 Grant Program
Dates
- Submitted
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2025-01-03
- Accepted
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2025-10-16