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Stoichiometric producer-grazer models, incorporating the effects of excess food-nutrient content on grazer dynamics

Description
There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework…

There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework that produce rich dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon, known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, needs to be incorporated into mathematical models. Here we present Lotka-Volterra type models to investigate the growth response of Daphnia to algae of varying P:C ratios. Using a nonsmooth system of two ordinary differential equations (ODEs), we formulate the first model to incorporate the phenomenon of the stoichiometric knife edge. We then extend this stoichiometric model by mechanistically deriving and tracking free P in the environment. This resulting full knife edge model is a nonsmooth system of three ODEs. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, leads to quantitatively different predictions than previous models that neglect to track free nutrients. The full model shows that the grazer population is sensitive to excess nutrient concentrations as a dynamical free nutrient pool induces extreme grazer population density changes. These modeling efforts provide insight on the effects of excess nutrient content on grazer dynamics and deepen our understanding of the effects of stoichiometry on the mechanisms governing population dynamics and the interactions between trophic levels.
ContributorsPeace, Angela (Author) / Kuang, Yang (Thesis advisor) / Elser, James J (Committee member) / Baer, Steven (Committee member) / Tang, Wenbo (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Open Educational Resources from 2020 March Mammal Madness Tournament

2020 March Mammal Madness Educational Materials

Description

This packet includes:

2020 Bracket Common Name

2020 Bracket Latin Binomial

Pre-Tournament Research Lesson Plan (English)

Tournament Lesson Plan & Worksheets (English)

Visual Arts Lesson Plan (English)

Language Arts Lesson Plan (English)

2020 Bracket Common Name (Spanish)

Pre-Tournament Research Lesson Plan (Spanish)

Tournament Lesson Plan & Worksheets (Spanish)

ContributorsHinde, Katie (Author) / Schuttler, Stephanie (Author) / Henning, Charon (Illustrator) / Nuñez-de la Mora, Alejandra (Translator)
Created2020
2021 March Mammal Madness Educational Materials

2021 March Mammal Madness Educational Materials

Description

This packet includes:

 2021 Bracket Common Name 

2021 Bracket Latin Binomial 

Bracket FAQ (English) 

Pre-Tournament Research Lesson Plan (English) 

Tournament Lesson Plan & Worksheets (English) 

Visual Arts Lesson Plan (English) 

Language Arts Lesson Plan (English) 

Guide for Youngest Players (English)

JUMBO Bracket for Youngest Players (English)

2021 Bracket Common Name (Spanish) 

Pre-Tournament Research Lesson Plan (Spanish) 

Tournament Lesson Plan & Worksheets (Spanish) 

Visual…

This packet includes:

 2021 Bracket Common Name 

2021 Bracket Latin Binomial 

Bracket FAQ (English) 

Pre-Tournament Research Lesson Plan (English) 

Tournament Lesson Plan & Worksheets (English) 

Visual Arts Lesson Plan (English) 

Language Arts Lesson Plan (English) 

Guide for Youngest Players (English)

JUMBO Bracket for Youngest Players (English)

2021 Bracket Common Name (Spanish) 

Pre-Tournament Research Lesson Plan (Spanish) 

Tournament Lesson Plan & Worksheets (Spanish) 

Visual Arts Lesson Plan (Spanish)

Language Arts Lesson Plan (Spanish) 

JUMBO Bracket for Youngest Players (Spanish) 
ContributorsHinde, Katie (Author) / Schuttler, Stephanie (Author) / Henning, Charon (Illustrator) / Nuñez-de la Mora, Alejandra (Translator) / Kissel, Jenna (Author) / Nickley, William (Artist)
Created2021-02