Using Fishery Models to Examine Self- and Co-Regulation Processes Across Multiple Timescales

Abstract

Differential equation models have intuitively meaningful parameters that can be mapped to developmental theories emphasizing nonlinear multiple timescale processes. Following this tradition, we map theoretical propositions of infant-parent self-/co-regulation to intrinsic and extrinsic dynamics captured by fishery models wherein fish’s reproduction and farmers’ harvesting contribute to population size. Integrated and estimated within a multilevel growth modeling framework, the model captures distinct components of self-/co-regulation and changes with age. We use simulations to examine viability of the model’s application to real-world data and illustrate the model’s utility using exemplar data drawn from a multiple timescale study of infant distress and mother soothing behaviors (N = 144 dyads) as the infant received routine immunizations at ages 2 and 6 months. Results highlight the benefits of articulating theoretical propositions within a differential equations framework, and using multiple timescale study designs with natural or experimentally induced perturbations in the study of self-/co-regulation and its development.

Keywords:

• differential equation model
• growth modeling
• simulation
• human development
• intraindividual variability

Acknowledgments

Thanks very much to the study participants and members of the Emotional Beginnings Project.

Additional information

Funding

This work was supported by a Pennsylvania State University Graduate Fellowship, the National Institutes of Health (R01 HD076994, R01 MH50843, P2C HD041025, UL1 TR002014) and the Penn State Social Science Research Institute.