Population Biology Commons^™

Differential Equation Modeling For Sustainable Resource Management: A Steady-State Optimal Harvesting Approach, Iordanka N. Panayotova, Aleksei Talonov

CODEE Journal

Mathematical models based on differential equations provide a powerful framework for connecting real-world data to informed decision-making. In this work, we present a student-accessible project that uses an optimal-control framework to study the sustainable management of biological resources.

Motivated by fisheries management, we examine a predator--prey system in which harvesting decisions must balance ecological and economic considerations. The model is formulated as an optimal control problem that seeks to maximize the total discounted net revenue from harvesting. Rather than solving for the complete time-dependent harvesting trajectory, we restrict the analysis to positive controlled coexistence equilibria and characterize an interior stationary …

Modeling Population Growth With Logistic And Modified Logistic Equations, Mihil Dimpal Patel

Discovery Day - Daytona Beach

Population growth models are essential tools for understanding how biological populations change over time under environmental constraints. This study examines population dynamics by comparing the classical exponential growth model with the logistic growth model. While exponential growth assumes unlimited resources and results in unbounded population increase, the logistic model incorporates a carrying capacity that limits growth as resources become scarce. To better represent real-world conditions, the logistic model is extended by introducing modifications such as harvesting terms and time-varying carrying capacities, which account for external removal of individuals and changing environmental limits. The equilibria of these models are determined, and …

History And Distribution Of The Dark Ibises (Glossy Ibis Plegadis Falcinellus And White-Faced Ibis P. Chihi) In Arkansas, R. Tumlison, P. D. Rodriguez

Journal of the Arkansas Academy of Science

The Glossy Ibis (Plegadis falcinellus) and White-faced Ibis (P. chihi) sometimes are reported simply as Dark Ibises due to difficulty in identifying them when mature characters are not clearly visible. We evaluated reports verified on citizen science websites to examine the origins and distributions of these migratory species in Arkansas. The Glossy Ibis was first documented in Arkansas in 1956, has been reported in 21 of our 75 counties, and is found more commonly in eastern Arkansas. The White-faced Ibis was first reported in Arkansas in 1971, has been reported in 41 of our 75 counties, …

Remote Sensing To Detect Crop Damage By An Invasive Species, Cole Butler

Biology and Medicine Through Mathematics Conference

No abstract provided.

Incorporating Thermal Performance Curves Into Population Dynamic Models For The West Nile Vector, Culex Pipiens, Benjamin Bruncati, Helle Aronson, Chloé Lahondère, Michael A. Robert

Biology and Medicine Through Mathematics Conference

No abstract provided.

Enhancing Walleye (Ogaa) Recruitment: Evaluating Assisted Reproduction As A Mitigation Strategy, Douglass Keiser

Biology Graduate Theses

Over the past several decades, cold- and cool-water fish populations across the Upper Midwest, including Minnesota and Wisconsin, have shown troubling signs of decline. Among the most affected is the walleye/Ogaa (Sander vitreus), a species deeply embedded in the ecological balance, cultural identity, and economic vitality of the region, and central to the lifeways, treaty-reserved rights, and resource stewardship of Tribal Nations, including Ojibwe communities across the Upper Midwest. Despite ongoing stocking efforts and harvest regulations, many lake systems have experienced persistent declines in natural recruitment, prompting resource agencies to investigate the underlying causes. One such system is …

Tipping Points In Crayfish Management: Exploring Population Dynamics With The Bifurcations Activity In Slopes, Evan Inrig, Benjamin Lucas

Seaver College Research And Scholarly Achievement Symposium

Slopes is an interactive environment for exploring numerical methods and graphical solutions to ordinary differential equations. The app launched with five activities for exploration: slopefields, phase planes, oscillations, solutions to systems, and numerical methods for approximation. Bifurcations is a new sixth activity that we designed to investigate changes in the long term behavior of solutions to autonomous differential equations. This activity displays a slopefield and implements the ability to add solutions, but also introduces two new views that show how varying a single parameter impacts the values and stability of equilibrium solutions. We demonstrate the value of the new bifurcations …

Testing The Intermediate Disturbance Hypothesis On Anthropogenic Pressure In Central Alabama, Gavin Terrell

Theses

Biodiversity is fundamental to maintaining ecosystem structure and function globally. Prior to the late 20th century, ecological theory generally predicted that biodiversity would be highest in systems experiencing minimal disturbance. However, Joseph H. Connell challenged this view with the Intermediate Disturbance Hypothesis (IDH), which posits that species diversity peaks at intermediate levels of disturbance and declines under conditions of both low and high disturbance. Although widely cited, the applicability of the IDH to natural systems remains debated, particularly in the context of anthropogenic disturbances and when diversity is measured beyond species richness alone.

This study evaluated the predictions of the …

Bird Population Response To Abiotic And Biotic Stresses In Urban & Restored Oak Savannah Habitat, Annabelle Ball

Posters - 2026

Birds are heavily impacted by urban development. Many experience habitat fragmentation and removal of food sources. However, other species can adapt to and even thrive in urban environments, thanks to certain tree species, bird feeders, and buildings. In North America, the house sparrow and the European starling are invasive species that benefit from urban environments (Bartelt, 2011; Fitzwater, 2014). Meanwhile, many habitats across the continent are experiencing restoration/rewilding efforts for the benefit of birds. One such habitat is the oak-savannah, which is characterized by 10-30% canopy cover and a mixture of prairie & woodland vegetation, supporting a high diversity of …

Optimal Control And Bifurcation Analysis Of A Predator–Prey Model With Self-Limiting Growth And Predator Disease, Dipo Aldila, Muhammad Akmal Fasya, Bevina D. Handari, Chidozie Williams Chukwu, Olumuyiwa James Peter

Mathematical Modelling and Numerical Simulation with Applications

We propose and analyze an eco-epidemiological predator–prey model that incorporates self-limitation and disease transmission within the predator population. The model is formulated as a system of ordinary differential equations describing logistic prey growth under the interspecific interaction with the predator. On the other hand, the predator population is divided into susceptible and infected classes, whose growth is constrained by prey availability. Three biologically relevant equilibria are identified: predator extinction, disease-free coexistence, and coexistence with endemic disease. The existence and stability of these equilibria are determined by key ecological and epidemiological thresholds, including the basic reproduction number. Using numerical continuation methods, …

Optimal Control Strategies For Infectious Diseases: A Numerical Simulation Approach, M. Abu Salek, Jannatun Nayeem, Romana Yesmin, M. Haider Ali Biswas, M. Humayun Kabir

Mathematical Modelling and Numerical Simulation with Applications

Various infectious diseases, such as Tuberculosis and Hepatitis B virus (HBV), caused by Mycobacterium bacteria and hepatitis B virus, respectively, pose serious threats worldwide. This paper examines the spread of these diseases using a mathematical model that incorporates control measures, including vaccination and awareness programs. We use a system of differential equations with control variables and apply Pontryagin's principle to determine optimal control strategies. The stability of the Disease Free Equilibrium (DFE) has been analysed and demonstrated to be both locally and globally asymptotically stable when the basic reproduction number remains below unity, thereby ensuring disease elimination. Furthermore, the Endemic …

Dynamical Analysis And Optimal Control Of The Mpox Transmission Model With Stratified Susceptibility, Tuhfatul Janan, Fatmawati Fatmawati, Cicik Alfiniyah, Santi Martini, Dipo Aldila, Agus Hasan

Mathematical Modelling and Numerical Simulation with Applications

This study develops a mathematical model of Mpox transmission that combines stratified susceptibility (low-risk and high-risk groups) with vaccinated and asymptomatically infected compartments. The analysis of the model begins with examining the well-posedness, boundedness, and nonnegativity conditions for the solutions. The local stabilities of the equilibria are examined through the Jacobian matrix and phase plane analysis, while the global stabilities are provided through Lyapunov functions. The estimated parameters are verified using epidemiological data on Mpox cases in the United States, with an MAPE of 2.20% and R_0 > 1, indicating that Mpox remains endemic. Sensitivity analysis indicates that the contact rate …

Trophic Structure And Mercury Bioaccumulation In Walleye And Yellow Perch In The Upper And Lower Red Lake Basins, Marissa Pribyl

Biology Graduate Theses

Mercury is a persistent global contaminant that biomagnifies through aquatic food webs, with dietary and environmental factors serving as the primary drivers of accumulation in fishes. Trophic structure and methylmercury dynamics in Walleye (ogaa; Sander vitreus) and Yellow Perch (asaawens; Perca flavescens) were investigated in the Upper and Lower Red Lake basins in Red Lake, Minnesota, during 2024-2025. Diets of Walleye and Yellow Perch were assessed through stomach dissections, and tissue samples from both species were analyzed for total mercury concentrations. Additional analyses included shiners (gigoozens; Notropis spp., Hudsonius spp.) along with a variety of freshwater fish and …

Geographic Variation In Proteomic Responses To Ocean Acidification In A Cold-Water Coral (Balanophyllia Elegans), Keana A. Richmond

Cal Poly Humboldt theses and projects

In the face of a rapidly changing climate, assessing organismal responses to future stressors in the context of current, natural exposure to stress could provide key insights to understanding marine ecosystem resilience. I used Balanophyllia elegans, a cold-water, solitary, azooxanthellate coral as a model to better understand how varying oceanographic conditions across its geographic range have shaped its ability to tolerate and potentially adapt to current and future ocean acidification conditions. I collected B. elegans individuals from four sites across 2,500km of their range and subjected them to two pH treatments to investigate site-specific protein expression in response to …

Impacts Of Native And Nonnative Plant Species On Avian Community Diversity, Matty John Mackay, Steven Van Dang, Brandon Lee Corn

SPARK Symposium Presentations

Avian communities play an essential role in maintaining a healthy ecosystem dynamic by regulating insect populations, assisting in plant pollination, and seed dispersal. These contribute to the overall health of natural ecosystems and mitigate ecological disruptions that would arise in their absence. However, the introduction of non-native invasive plant species can interrupt the balance avian communities bring to ecosystems by reducing availability of food sources, altering habitat structures, increasing competition among individuals, and disrupting ecological relationships through rapid invasion of ecological spaces. Point count observations of birds at Shelby Bottoms Park, Nashville, Tennessee in areas dominated by non-native privet and …

Managing Multi-Drug Resistance: An Evolutionary Game Theory And Optimal Control Approach, Shukhrat Nasrulloev

Theses and Dissertations

Multi-drug resistance is an evolutionary process in which treatment eliminates sensitive cells, allowing resistant clones to dominate. This thesis investigates this process using a framework integrating population dynamics, evolutionary game theory, and optimal control theory. We develop a two-population logistic growth model describing competition between drug-sensitive and drug-resistant cells under treatment, construct dose-dependent payoff matrices and replicator dynamics to characterize evolutionary competition, and derive a critical drug level D_crit = (r_S - rR)/(dS - d_R) at which resistant cells gain a fitness advantage. An optimal control problem is formulated via Pontryagin's Maximum Principle to identify schedules …

Using Camera-Based Unmarked Spatial Capture-Recapture Modeling To Estimate Reintroduced Elk (Cervus Canadensis) Population Parameters And Distribution In Southeastern Kentucky, Claire Marie Muia

Theses and Dissertations--Forestry and Natural Resources

Estimation of population parameters is important for wildlife management decisions. Elk reintroduced to southeastern Kentucky experienced early irruptive population growth and are currently monitored using a statewide harvest-based statistical population reconstruction model (SPR) across the Kentucky Elk Restoration Zone (KERZ). Because the SPR model is spatially coarse and difficult to scale to the smaller management units comprising the KERZ, we conducted a spatially explicit capture-recapture study using a clustered camera-trapping array deployed for 10 weeks from June–August 2024 to estimate elk population parameters within Management Unit 4. Due to a lack of resights of GPS-marked elk, population parameters were estimated …

Effectiveness Of Walleye Stocking In Winter Kill Lakes, Tyler Haus

Journal of Earth and Life Science

Winter kill events, marked by extensive fish mortality due to hypoxic conditions under the ice, are a common phenomenon in shallow eutrophic lakes, especially in the northern lakes in the northern United States. These events can drastically alter fish communities and often result in the elimination of top predators. Though these lakes will typically slowly bounce back to what they were in a couple of years. This study evaluates the effectiveness of walleye, Sander vitreus, stocking in lakes after a winter kill. For this study, four known winter kill lakes that are consistently stocked with walleye were studied. Pre- …

Western Massasauga (Sistrurus Tergeminus): A Species Conservation Assessment For The Nebraska Natural Legacy Project, Colleen Rothe-Groleau, Melissa J. Panella

Nebraska Game and Parks Commission: Publications

The Nebraska Natural Legacy Project recognizes the western massasauga (Sistrurus tergeminus) as a Tier I at-risk species. Provided are some general management recommendations regarding western massasaugas. Conservation practitioners will need to use professional judgment to make specific management decisions based on objectives, location, and a multitude of variables. This resource was designed to share available knowledge of this at-risk species that will aid in the decision-making process or in identifying research needs to benefit the species.

Criteria for selection as Tier I: State listed, G3

Estimated Population in NE: 1,000–2,500

Estimate based on: Field surveys

Trends since 2005 …

Larval Crowding In Culex Pipiens Generates Cumulative Cascading Effects Under Changing Environmental Conditions, Sengul Talay, Zafer Sakaci, Michele C. Weigle, Bugrahan Regaip Kilinc, Jenah Parman, Holly Gaff, Deniz Sirin, Bulent Alten, Dennis Bente, Sirri Kar

Computer Science Faculty Publications

Density-dependent population regulation is a fundamental driver in the population dynamics of living systems, ensuring a balanced and sustainable maintenance in nature. It has been suggested that the adverse developmental and morphological effect of high larval density in container mosquitoes represents a significant limiting factor for population density, and the need to investigate this possible importance within the framework of field-based principles has been emphasized. This semi-field study, conducted under the natural thermal regime and using a natural population in Turkish Thrace, aimed to examine the effects of non-food-limiting larval density (crowding effect) in the mosquito species, Culex pipiens ( …

Taxonomy Of Endophytic Fungi Associated With Vallisneria Neotropicalis, Md. Arafat Rashid

Graduate Theses and Dissertations (2019 - present)

This study presents the first comprehensive taxonomic and ecological investigation of endophytic fungi (EF) associated with the submerged aquatic macrophyte Vallisneria neotropicalis in the southern United States. Over a 12 month period, from April 2023 to March 2024, leaf samples were collected from two distinct sites in Mobile Bay, Alabama a disturbed, brackish Causeway location and a cleaner, less impacted site at Meaher State Park. Using culture dependent methods, a total of 257 fungal endophytes were isolated from 1,200 leaf segments. All isolates belonged to the phylum Ascomycota, distributed across 3 classes, 6 orders, 10 families, and 19 taxa. The …

Following Carbon: Pathway And Flux Representations Of Ecosystems, Caner Kazanci

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

[Reev] Developing A Stage-Structure Stoichiometric Aquatic Tri-Trophic Food Chain Model, Ghislaine Niyodusenga, Cecilia Norris, Caroline Orza, Jing Li, Angela Peace, Greg Mayer, Rebecca A. Everett

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Analyzing The Effect Of A Holling Type Iii Functional Response On Predator-Prey Dynamics, Lawrence G. Seminario-Romero, Richard Rebarber, Brigitte Tenhumberg

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Metapopulation Model For Oyster Restoration, Leah Shaw

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

[Chu] Modelling The Effect Of Disturbed Blood-Feeding On Mosquito-Borne Disease Transmission, Kyle Dahlin, Michael Robert, Lauren Childs

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Understanding The Spread Of Black Sigatoka Disease: A Deterministic And Stochastic Modeling Approach, Bernard Asamoah Afful, Luis F. Gordillo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Compartmental Model For Diurnal Atlantic Stingray Migration, Rhianna Yates, Leah Glasser, Elena Wheatley, Christopher Hay-Jahans

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Compartmental Model For Periodic Animal Migration, Rhianna Yates, Leah Glasser, Elena Wheatley, Christopher Hay-Jahans

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Optimizing The Distribution Of Fruiting Agave On Bat-Friendly Tequila Plantations, Grace Gorreck, Clarissa Azurin, Lois Carpenter

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.