Abstract
Holobionts, consisting of a host and diverse microbial symbionts, function as distinct biological entities anatomically, metabolically, immunologically, and developmentally. Symbionts can be transmitted from parent to offspring by a variety of vertical and horizontal methods. Holobionts can be considered levels of selection in evolution because they are well-defined interactors, replicators/reproducers, and manifestors of adaptation. An initial mathematical model is presented to help understand how holobionts evolve. The model offered combines the processes of horizontal symbiont transfer, within-host symbiont proliferation, vertical symbiont transmission, and holobiont selection. The model offers equations for the population dynamics and evolution of holobionts whose hologenomes differ in gene copy number, not in allelic or loci identity. The model may readily be extended to include variation among holobionts in the gene identities of both symbionts and host.

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Acknowledgements
We thank Snait Gissis, Ehud Lamm, and Ayelet Shavit for organizing a workshop that brought the authors of this manuscript together and for their encouragement and helpful comments on the manuscript. We also thank Michael Wade, John Dupre, James Griesemer, Oren Kolodny, Marcus Feldman, Tadashi Fukami, and three anonymous reviewers for helpful suggestions. SG is funded by NSF Grant IOS 145177. JR was funded by The John Templeton Foundation Grant 51473.
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Roughgarden, J., Gilbert, S.F., Rosenberg, E. et al. Holobionts as Units of Selection and a Model of Their Population Dynamics and Evolution. Biol Theory 13, 44–65 (2018). https://doi.org/10.1007/s13752-017-0287-1
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DOI: https://doi.org/10.1007/s13752-017-0287-1