MS02 - ECOP-05 Part 2 of 4

Celebrating 60 Years of Excellence: Honoring Yang Kuang’s Contributions to Mathematical Biology (Part 2)

Monday, July 14 at 4:00pm

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Note: this minisymposia has multiple sessions. The other sessions are: Part-1 Part-3 and Part-4.

Tin Phan (Los Alamos National Laboratory), Yun Kang (Arizona State University); Tracy Stepien (University of Florida)

Description:

This session is organized to honor Professor Yang Kuang for his pioneering contributions to mathematical biology, his spirit of collaboration, and his dedication to mentoring 28 PhD students, as well as numerous postdoctoral, master's, and undergraduate researchers. Invited speakers will present cutting-edge research inspired by Dr. Kuang’s foundational work, spanning ecological stoichiometry, delay and partial differential equations, and data-driven modeling in biology. Together, we highlight Dr. Kuang’s achievements and the profound influence his work has on guiding the next generation of researchers in mathematical biology.

Jianhong Wu

York University

"Population dynamics involving perceived risk-structured behavioural changes"

Behaviour changes and intervention takes place in response to perceived risks in the vector-host and pathogen-host interactions, leading to rich and complex population dynamics including multi-stability and oscillation birth and death. We will review a few models and analyses involving coupled systems of delay-differential equations and algebraic-integral equations.

Angela Peace

Texas Tech University

"Nutrient-Driven Adaptive Foraging Behaviors"

This study investigates nutrient-driven adaptability of foraging efforts in producer-grazer dynamics of simple food web models. Using dynamical systems theory, we develop and two systems of ordinary differential equations using adaptive dynamics theory; a two-dimensional base model incorporating a fixed energetic cost of feeding and a three-dimensional adaptive model where feeding costs vary over time in response to environmental conditions. By comparing these models, we examine the effects of adaptive foraging strategies on population dynamics. Our adaptive model suggests a potential mechanism for evolutionary rescue, where the population dynamically adjusts to environmental changes—such as fluctuations in food quality—by modifying its feeding strategies. However, when population densities oscillate in predator-prey limit cycles, fast adaptation can lead to very wide amplitude cycles, where populations are endanger of stochastic extinction. Overall, this increases our understanding of the conditions under which nutrient-driven adaptive foraging strategies can yield benefits to grazers.

Rebecca Everett

Haverford College

"Stoichiometric ontogenetic development influences population dynamics: Stage-structured model under nutrient co-limitations"

Ecological processes depend on the flow and balance of essential elements such as carbon (C) and phosphorus (P), and changes in these elements can cause adverse effects to ecosystems. The theory of Ecological Stoichiometry offers a conceptual framework to investigate the impact of elemental imbalances on structured populations while simultaneously considering how ecological structures regulate nutrient cycling and ecosystem processes. While there have been significant advances in the development of stoichiometric food web models, these efforts often consider a homogeneous population and neglect stage-structure. The development of stage-structured population models has significantly contributed to understanding energy flow and population dynamics of ecological systems. However, stage structure models fail to consider food quality in addition to food quantity. We develop a stoichiometric stage-structure producer-grazer model that considers co-limitation of nutrients, and parameterize the model for an algae-Daphnia food chain. Our findings emphasize the impact of stoichiometric constraints on structured population dynamics. By incorporating both food quantity and quality into maturation rates, we demonstrate how stage-structured dynamics can influence outcomes in variable environments.

Irakli Loladze

Bryan College of Health Sciences

"From Information Strings to Ocean Stoichiometry: Why Life's Atomic Constraints Drive Convergence to the Redfield Ratio"

The Redfield ratio (N:P ≈ 16), a cornerstone of marine biogeochemistry, represents a striking global pattern whose fundamental origins remain debated. Why this specific ratio? This talk presents a perspective rooted in the very nature of biological information. Unlike human technologies that often rely on elementary particles, biological information processing is fundamentally atom-bound. Specifically, genetic information is stored and processed using linear molecular strings – DNA, RNA, and associated proteins. Synthesizing these 'information-rich' molecules imposes non-negotiable demands for specific atoms, particularly nitrogen (N) for proteins and both N and phosphorus (P) for nucleic acids, in precise elemental ratios. These immutable atomic requirements constrain the core cellular machinery of information expression: the coupled synthesis of N-rich proteins and P-rich ribosomal RNA (rRNA). Mathematical modeling reveals that the interplay between translation and transcription creates a powerful biochemical attractor. Under optimal conditions, this balance naturally stabilizes at a protein:rRNA ratio corresponding to an elemental N:P stoichiometry remarkably close to the canonical Redfield value of 16. This biochemically optimal ratio is more than a cellular characteristic; it acts as a dynamic attractor on much larger scales. Incorporating evolutionary dynamics and biogeochemical feedbacks like nutrient recycling (mimicked by an iterative chemostat framework and analyzed using contraction mapping) demonstrates convergence towards N:P ≈ 16. This ratio emerges as an evolutionary stable strategy and a powerful stoichiometric attractor, pulling the system towards Redfield proportions even under varying nutrient limitations over ecological and evolutionary time. This talk proposes that the canonical Redfield ratio is a planetary-scale echo of the fundamental constraints imposed by the need to faithfully replicate and express genetic information using atoms. It shows how the deep rules governing information in biology can sculpt the chemistry of our planet.

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Annual Meeting for the Society for Mathematical Biology, 2025.