STOCHASTIC ECO-EVOLUTIONARY DYNAMICS OF MULTIVARIATE TRAITS: A Framework for Modeling Population Processes Illustrated by the Study of Drifting G-Matrices
I derive a novel stochastic equation for the evolution of the additive genetic variance-covariance matrix G in response to mutation, selection, drift, and fluctuating population size. Common wisdom holds that the effect of drift on G is simply to reduce each of its entries by a common proportional amount while preserving its orientation. In contrast, I find that drift causes significant and directional shifts in the orientation of G by driving genetic correlations to their extremes. Biologically, this is a consequence of linkage build-up introduced by drift. I compare these theoretical results to empirical observations based on experiments conducted by Phillips et al., (2001). Additionally, to derive the model of G-matrix evolution, I developed a novel synthetic framework for modelling ecological and evolutionary dynamics of populations carrying multivariate traits. This framework is optimized for deriving new models across a wide range of topics in population biology. Foundations of the framework are formalized by the theory of measure-valued processes, but application of the framework only requires multivariate calculus, and heuristics are presented in the main text for making additional calculations involving stochastic processes. Collectively, this work establishes a powerful framework enabling efficient formal analysis of integrated population processes across evolution and ecology, and its potential for making new discoveries is illustrated by novel findings on fundamental aspects of G-matrix evolution.
@article{Week2026,title={STOCHASTIC ECO-EVOLUTIONARY DYNAMICS OF MULTIVARIATE TRAITS: A Framework for Modeling Population Processes Illustrated by the Study of Drifting G-Matrices},volume={625},issn={0022-5193},url={http://dx.doi.org/10.1016/j.jtbi.2026.112428},doi={10.1016/j.jtbi.2026.112428},journal={Journal of Theoretical Biology},publisher={Elsevier BV},author={Week, Bob},year={2026},month=may,pages={112428},}
2025
Applying evolutionary theory to understand host–microbiome evolution: New Tricks for Old Dogs
Bob Week, Shelbi L. Russel , Hinrich Schulenburg , and 2 more authors
@article{Week2024b,title={Applying evolutionary theory to understand host–microbiome evolution: New Tricks for Old Dogs},author={Week, Bob and Russel, Shelbi L. and Schulenburg, Hinrich and Bohannan, Brendan J. M. and Bruijning, Marjolein},year={2025},doi={10.1038/s41559-025-02846-w},dimensions={true},journal={Nature EcoEvo},}
Quantitative Genetics of Microbiome Mediated Traits
Bob Week, Peter L. Ralph , Hannah F. Tavalire , and 2 more authors
@article{Week2024c,title={Quantitative Genetics of Microbiome Mediated Traits},publisher={Oxford University Publishing},author={Week, Bob and Ralph, Peter L. and Tavalire, Hannah F. and Cresko, William A. and Bohannan, Brendan J. M.},year={2025},doi={10.1093/evolut/qpaf171},dimensions={true},journal={Evolution},google_scholar_id={UebtZRa9Y70C},}
2024
The Evolution of Microbiome-Mediated Traits
Bob Week, Andrew H. Morris , and Brendan J. M. Bohannan
@article{Week2024,title={The Evolution of Microbiome-Mediated Traits},publisher={Cold Spring Harbor Laboratory},author={Week, Bob and Morris, Andrew H. and Bohannan, Brendan J. M.},year={2024},doi={10.1101/2024.03.29.587374},journal={bioRxiv},}
2023
Host-Parasite Coevolution in Continuous Space Leads to Variation in Local Adaptation Across Spatial Scales
@article{week2023host,title={Host-Parasite Coevolution in Continuous Space Leads to Variation in Local Adaptation Across Spatial Scales},author={Week, Bob and Bradburd, Gideon},journal={The American Naturalist},year={2023},doi={10.1086/727470},dimensions={true},google_scholar_id={_FxGoFyzp5QC},}
@article{nuismer2022uncovering,title={Uncovering cryptic coevolution},author={Nuismer, Scott L and Week, Bob and Harmon, Luke J},journal={The American Naturalist},volume={199},number={6},pages={869--880},year={2022},publisher={The University of Chicago Press Chicago, IL},doi={10.1086/717436},dimensions={true},google_scholar_id={W7OEmFMy1HYC},}
2021
A white noise approach to evolutionary ecology
Bob Week, Scott L Nuismer , Luke J Harmon , and 1 more author
Although the evolutionary response to random genetic drift is classically modelled as a sampling process for populations with fixed abundance, the abundances of populations in the wild fluctuate over time. Furthermore, since wild populations exhibit demographic stochasticity and since random genetic drift is in part due to demographic stochasticity, theoretical approaches are needed to understand the role of demographic stochasticity in eco-evolutionary dynamics. Here we close this gap for quantitative characters evolving in continuously reproducing populations by providing a framework to track the stochastic dynamics of abundance density across phenotypic space using stochastic partial differential equations. In the process we develop a set of heuristics to operationalize the powerful, but abstract theory of white noise and diffusion-limits of individual-based models. Applying these heuristics, we obtain stochastic ordinary differential equations that generalize classical expressions of ecological quantitative genetics. In particular, by supplying growth rate and reproductive variance as functions of abundance densities and trait values, these equations track population size, mean trait and additive genetic variance responding to mutation, demographic stochasticity, random genetic drift, deterministic selection and noise-induced selection. We demonstrate the utility of our approach by formulating a model of diffuse coevolution mediated by exploitative competition for a continuum of resources. In addition to trait and abundance distributions, this model predicts interaction networks defined by niche-overlap, competition coefficients, or selection gradients. Using a high-richness approximation, we find linear selection gradients and competition coefficients are uncorrelated, but magnitudes of linear selection gradients and quadratic selection gradients are both positively correlated with competition coefficients. Hence, competing species that strongly affect each other’s abundance tend to also impose selection on one another, but the directionality is not predicted. This approach contributes to the development of a synthetic theory of evolutionary ecology by formalizing first principle derivations of stochastic models tracking feedbacks of biological processes and the patterns of diversity they produce.
@article{week2021white,title={A white noise approach to evolutionary ecology},author={Week, Bob and Nuismer, Scott L and Harmon, Luke J and Krone, Stephen M},journal={Journal of Theoretical Biology},volume={521},pages={110660},year={2021},publisher={Academic Press},doi={10.1016/j.jtbi.2021.110660},dimensions={true},google_scholar_id={IjCSPb-OGe4C},}
Coevolutionary Arms Races and the Conditions for the Maintenance of Mutualism
@article{week2021coevolutionary,title={Coevolutionary Arms Races and the Conditions for the Maintenance of Mutualism},author={Week, Bob and Nuismer, Scott L},journal={The American Naturalist},year={2021},doi={10.1086/714274},dimensions={true},google_scholar_id={Y0pCki6q_DkC},}
A unified model of species abundance, genetic diversity, and functional diversity reveals the mechanisms structuring ecological communities
Isaac Overcast , Megan Ruffley , James Rosindell , and 8 more authors
@article{overcast2021unified,title={A unified model of species abundance, genetic diversity, and functional diversity reveals the mechanisms structuring ecological communities},author={Overcast, Isaac and Ruffley, Megan and Rosindell, James and Harmon, Luke and Borges, Paulo AV and Emerson, Brent C and Etienne, Rampal S and Gillespie, Rosemary and Krehenwinkel, Henrik and Mahler, D Luke and others},journal={Molecular Ecology Resources},volume={21},number={8},pages={2782--2800},year={2021},publisher={Wiley Online Library},doi={10.1111/1755-0998.13514},dimensions={true},google_scholar_id={WF5omc3nYNoC},}
@article{week2019measurement,title={The measurement of coevolution in the wild},author={Week, Bob and Nuismer, Scott L},journal={Ecology letters},volume={22},number={4},pages={717--725},year={2019},doi={10.1111/ele.13231},dimensions={true},google_scholar_id={d1gkVwhDpl0C},}
Approximate Bayesian estimation of coevolutionary arms races
@article{nuismer2019approximate,title={Approximate Bayesian estimation of coevolutionary arms races},author={Nuismer, Scott L and Week, Bob},journal={PLoS Computational Biology},volume={15},number={4},pages={e1006988},year={2019},publisher={Public Library of Science San Francisco, CA USA},doi={10.1371/journal.pcbi.1006988},dimensions={true},google_scholar_id={9yKSN-GCB0IC},}
Identifying models of trait-mediated community assembly using random forests and approximate Bayesian computation
Megan Ruffley , Katie Peterson , Bob Week, and 2 more authors
@article{ruffley2019identifying,title={Identifying models of trait-mediated community assembly using random forests and approximate Bayesian computation},author={Ruffley, Megan and Peterson, Katie and Week, Bob and Tank, David C and Harmon, Luke J},journal={Ecology and Evolution},volume={9},number={23},pages={13218--13230},year={2019},publisher={Wiley Online Library},doi={10.1002/ece3.5773},dimensions={true},google_scholar_id={ufrVoPGSRksC},}
2018
Coevolution slows the disassembly of mutualistic networks
@article{nuismer2018coevolution,title={Coevolution slows the disassembly of mutualistic networks},author={Nuismer, Scott L and Week, Bob and Aizen, Marcelo A},journal={The American Naturalist},volume={192},number={4},pages={490--502},year={2018},publisher={University of Chicago Press Chicago, IL},doi={10.1086/699218},dimensions={true},google_scholar_id={u-x6o8ySG0sC},}
