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Title: Rich Dynamics of a General Producer–Grazer Interaction Model under Shared Multiple Resource Limitations
Organism growth is often determined by multiple resources interdependently. However, growth models based on the Droop cell quota framework have historically been built using threshold formulations, which means they intrinsically involve single-resource limitations. In addition, it is a daunting task to study the global dynamics of these models mathematically, since they employ minimum functions that are non-smooth (not differentiable). To provide an approach to encompass interactions of multiple resources, we propose a multiple-resource limitation growth function based on the Droop cell quota concept and incorporate it into an existing producer–grazer model. The formulation of the producer’s growth rate is based on cell growth process time-tracking, while the grazer’s growth rate is constructed based on optimal limiting nutrient allocation in cell transcription and translation phases. We show that the proposed model captures a wide range of experimental observations, such as the paradox of enrichment, the paradox of energy enrichment, and the paradox of nutrient enrichment. Together, our proposed formulation and the existing threshold formulation provide bounds on the expected growth of an organism. Moreover, the proposed model is mathematically more tractable, since it does not use the minimum functions as in other stoichiometric models.  more » « less
Award ID(s):
1930728
PAR ID:
10468216
Author(s) / Creator(s):
; ;
Publisher / Repository:
MDPI
Date Published:
Journal Name:
Applied Sciences
Edition / Version:
1
Volume:
13
Issue:
7
ISSN:
2076-3417
Page Range / eLocation ID:
4150
Subject(s) / Keyword(s):
multiple resource limitation Liebig’s law of the minimum colimitation producer–grazer predator–prey dynamics growth law ecological stoichiometry
Format(s):
Medium: X Size: 2.6MB Other: pdf
Size(s):
2.6MB
Sponsoring Org:
National Science Foundation
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