Ecosystem
Modeling
Danielle Rogers
Introduction
Ecosystem Modeling With an Emphasis on
Phytoplankton
Importance
Models
Equations
Resource Diagrams
How to get
coexistence
Danielle Rogers
Mississippi State University
Funded by the National Science Foundation and Texas A&M
July 25, 2013
Graphs
Introduction
Ecosystem
Modeling
Danielle Rogers
Introduction
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What are phytoplankton?
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Small phytosynthetic microorganisms
Motile but dependent on current
Importance
Models
Equations
Project focused on the growth rate of phytoplankton
communities
Resource Diagrams
How do we get multiple species using the same nutrient
without a clear “winner”?
Graphs
How to get
coexistence
Importance
Ecosystem
Modeling
Danielle Rogers
Introduction
Importance
Models
Equations
Resource Diagrams
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We want to understand how ecosystems work.
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Why do we have multiple “winners” in some ecosystems
but a clear “winner” in others?
If we understand more about how the species interact
we may be able to intervene without catastrophe.
How to get
coexistence
Graphs
Resource Models
Ecosystem
Modeling
Danielle Rogers
Introduction
Importance
Models
Equations
Resource Diagrams
How to get
coexistence
Graphs
Ecosystem
Modeling
Equations
Danielle Rogers
Introduction
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Population
Importance
Models
dNi
= µNi − νNi
dt
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Resource Diagrams
How to get
coexistence
Substrate or Nutrient
dS
= ν (Sin − Sj ) −
dt
Equations
n
X
Graphs
Qij µi Ni
i=1
Resource Dependent Growth
Equation
Sj
µi = µ̃i minj
Sj + kij
Resource Diagrams
Ecosystem
Modeling
Danielle Rogers
Introduction
Importance
Models
Equations
Resource Diagrams
How to get
coexistence
Graphs
Ecosystem
Modeling
Danielle Rogers
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dNi
= 0 equilibrium
dt
dNi
= µi Ni − νNi where µi = ν
dt
Sj
Plug ν into µi = µ̃i (
) if nutrient j is limiting
Sj + kij
Rij∗
)
ν = µ̃i ( ∗
Rij + kij
Rij∗ =
kij ν
µ̃i − ν
Introduction
Importance
Models
Equations
Resource Diagrams
How to get
coexistence
Graphs
Ecosystem
Modeling
In the following models all the parameters had the same
values except the amount of nutrient entering the
system (Sin ).
10
10
Sin =
Sin =
7.5
4.5
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Danielle Rogers
Introduction
Importance
Models
Equations
Resource Diagrams
How to get
coexistence
Graphs
Two Species with Two Substrates
Two Species with Two Substrates
25
25
pop 1
pop 2
pop 1
pop 2
20
log of the population
log of the population
20
15
10
5
0
15
10
5
0
10
20
30
40
50
time
60
70
80
90
100
0
0
10
20
30
40
50
time
60
70
80
90
100
Credits
Ecosystem
Modeling
Danielle Rogers
Introduction
Importance
Models
Equations
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Nutrient limitation models are from David Tilman’s
book Resource Competition and Community Structure.
Princeton University Press, Princeton, NJ. 1982.
Pictures of phytoplankton provided by
http://www.cof.orst.edu/project/plankton/truittr.html
and http://www.biologyreference.com/PhPo/Plankton.html
Resource Diagrams
How to get
coexistence
Graphs