From Individual Trajectories to Population Densities: Weak-Form Inference of Heterogeneous Growth Laws
Abstract
Single-cell time-lapse microscopy now provides high-resolution size trajectories for thousands of individual cells, yet principled methods for simultaneously learning the functional form of growth laws and the distribution of cell-to-cell physiological variability remain limited. We present a data-driven framework based on the recent Weak-form Estimation of Nonlinear Dynamics (WENDy) algorithm to (i) select the best supported growth law from a set of candidate laws, and (ii) recover individual-level growth parameters via empirical Bayes shrinkage within a random-effects model. We demonstrate the approach on both synthetic individual size data incorporating commonly found growth laws and recorded real size trajectories, showing that the method accurately recovers both growth-law structure and parameter heterogeneity at reasonable noise levels. We finally end with a discussion on how the results obtained by the method here can be upscaled to the population level.
Related
- Characterizing Individual and Population-Level Heterogeneity in Infant BMI Trajectories Using Flexible and Functional Modeling Approaches
- Individual-Specific Gaussian Graphical Models for Heterogeneous Populations with Application to Epigenetic Gene Regulation in Lung Adenocarcinoma
- Digital twins forecast individual immune trajectories
- Single-Case Design for Network-based BCI Rehabilitation: Individual Learning Trajectories and Effects of Motor Imagery Timing in Stroke Patients
- Individual variation in glucocorticoid plasticity to temperature is not associated with reproductive success in a wild songbird population
BibTeX
@misc{lyons2026from,
title = {{From Individual Trajectories to Population Densities: Weak-Form Inference of Heterogeneous Growth Laws}},
author = {Rainey Lyons and Vanja Dukic and David M Bortz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31955},
eprint = {2609.31955},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31955},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Individual Trajectories to Population Densities: Weak-Form Inference of Heterogeneous Growth Laws
AU - Rainey Lyons
AU - Vanja Dukic
AU - David M Bortz
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31955
UR - https://arxiv.org/abs/2609.31955
AB - Single-cell time-lapse microscopy now provides high-resolution size trajectories for thousands of individual cells, yet principled methods for simultaneously learning the functional form of growth laws and the distribution of cell-to-cell physiological variability remain limited. We present a data-driven framework based on the recent Weak-form Estimation of Nonlinear Dynamics (WENDy) algorithm to (i) select the best supported growth law from a set of candidate laws, and (ii) recover individual-level growth parameters via empirical Bayes shrinkage within a random-effects model. We demonstrate the approach on both synthetic individual size data incorporating commonly found growth laws and recorded real size trajectories, showing that the method accurately recovers both growth-law structure and parameter heterogeneity at reasonable noise levels. We finally end with a discussion on how the results obtained by the method here can be upscaled to the population level.
ER -