FW364 Ecological Problem Solving
Wrap-Up/Review
Final Exam – Study Tips
Present work neatly & clearly on exam so I can give partial credit Do the practice exam! Try completing all problems before consulting key Practice exam (37 questions) is way longer than final exam Do the practice problems for predation and competition lectures Look through concept review posted on website- Many more questions on concept review than will be on the exam Look through PowerPoints for predation and competition
Final Exam – Study Tips Con’t
Practice working with figures that we covered in lecture Know the axes! Don’t need to memorize equations, but understand how they “operate” Understand how prey (resources) and predators (consumers) are linked Recognize density dependence from equations Recognize functional responses from equations General comments on the exam:
Not cumulative, but some concepts carrying over (e.g., density dependence) Can use calculators Mix of multiple choice and calculation problems Have two hours to complete exam
Final Exam: Tuesday, December 10 10am- 12pm Room 225 NR (normal classroom)
Emphasis is on a process
Observations Model Inference
Objectives: 1) Provide introduction to the quantitative analysis of natural
resources problems
2) Practice solving problems: provide tools to solve future problems you will encounter
FW364 – Wrap-Up
Remember the first day of class…
Strong critical thinking component (not as much memorization) Learning skills that are transferrable to your future work
“This is not your normal course”
Emphasis is on a process
Observations Model Inference
Objectives: 1) Provide introduction to the quantitative analysis of natural
resources problems
2) Practice solving problems: provide tools to solve future problems you will encounter
FW364 – Wrap-Up
Remember the first day of class…
Strong critical thinking component (not as much memorization) Learning skills that are transferrable to your future work
“This I not your normal course”
Outline for Today: Discuss how we’ve addressed Objective 1
Go over tools we’ve learned for Objective 2
Come back to Observations Model Inference
Objective 1: Provide introduction to quantitative analysis of natural resources problems
We’ve now covered nine conceptual groups of models at three different levels of the ecological hierarchy:
Populations
Exponential population growth Stochastic population growth Density dependent population growth Age-structured population growth Stage-structured population growth Spatial structure (metapopulations)
Communities (multiple species)
Predator-prey interactions Two-species resource competition
Ecosystems
Mass balance
Objective 1 Progress
Let’s look at our progression through these models…
Nt+1 = Nt + B - D
Objective 1 Progress
We began with a simple observation:
And what we then did was pretty spectacular:
From first principles, we derived a large set of equations that describe population and community dynamics
Exponential Population Growth
Nt+1 = Nt λ
dN/dt = rN
Exponential Population Growth
Nt+1 = Nt (λ ± errort)
Stochastic Population Growth Nt+1 = Nt (λmax)
(1-Nt/K)
Density Dependent Population Growth (Scramble)
xNt+1 = xNt L
Age / Stage-Structured Population Growth
Nt+1 = Nt λ
Nt+1 = Nt λ Nt+1 = Nt λ
Nt+1 = Nt λ
Metapopulation Growth
dV/dt = bvV - dvV - aVP
dP/dt = acVP - dpP
Predator-Prey Interactions
dP1/dt = a1c1RP1 – d1P1
dP2/dt = a2c2RP2 – d2P2
dR/dt = brR - drR – a1RP1 – a2RP2
Two-Species Resource Competition
Nt+1 = Nt λ
dN/dt = rN
Objective 1 Progress
Ecosystem
Plant
CO2
Herbivore
Detritus
Objective 1 Progress
We’ve seen management applications of every model:
Exponential Pop Growth: Species introductions
Stochastic Pop Growth: Endangered species
Dens Dependent Pop Growth: Fishery species (scramble)
Age-Structured Pop Growth: Endangered sub-species
Stage-Structured Pop Growth: Endangered species
Metapopulation Growth: Threatened sub-species
Objective 1 Progress
We’ve seen management applications of every model:
Predator-Prey Interactions: Species re-introductions
Two-Species Resource Competition: Invasive species
Objective 1 Progress
We’ve seen management applications of every model:
Ecosystem Models: Invasive species
Objective 1 Progress
Objective 1 Progress
The take home message for Objective 1:
Models are useful for natural resources management!
Models similar to the ones we built are used all the time for natural resource conservation and management
Uses include:
Fisheries and wildlife management Conservation of threatened and endangered species
Restoration of native species (species re-introductions) Understanding effects of invasive species
Objective 1: Provide introduction to quantitative analysis of natural resources problems
Objective 2: Provide tools to solve future problems you will encounter
“We are going to exercise our brains at something that is important in almost any discipline based on science”
~ Dr. Scott Peacor
Objective 2 Progress
We’ve spent a lot of time:
honing our critical thinking skills practicing quantitative problems
learning quantitative tools
…that are useful outside of class
Objective 2: Provide tools to solve future problems you will encounter
“We are going to exercise our brains at something that is important in almost any discipline based on science”
~ Dr. Scott Peacor
If Marshall has 3 oranges, and I give him 3 more oranges, how many oranges does Marshall have?
= + ?
Objective 2 Progress
Objective 2: Provide tools to solve future problems you will encounter
“We are going to exercise our brains at something that is important in almost any discipline based on science”
~ Dr. Scott Peacor
If Marshall has 3 oranges, and I give him 3 more oranges, how many oranges does Marshall have?
= + 6
Objective 2 Progress
Objective 2: Provide tools to solve future problems you will encounter
By answering this simple problem, you have done something important:
used a GENERAL quantitative tool (i.e., addition) to answer a specific question
You can use the same tool to answer other questions about:
apples, iPods, pandas, turtles, etc.
“We are going to exercise our brains at something that is important in almost any discipline based on science”
~ Dr. Scott Peacor
Objective 2 Progress
We have applied MANY general quantitative tools!
Simple Math: Addition Subtraction Multiplication Division
Trickier Math: Algebra Calculus
Conceptual Tools: Stock and flow diagrams
Focus: Applying quantitative tools in new ways
Objective 2 Progress
We have applied MANY general quantitative tools!
Simple Math: Addition Subtraction Multiplication Division
Trickier Math: Algebra Calculus
Conceptual Tools: Stock and flow diagrams
Focus: Applying quantitative tools in new ways
= - Change in Loggerhead
Population Size # Loggerhead Births # Loggerhead Deaths = -
Objective 2 Progress
Simple Math: Addition Subtraction Multiplication Division
Trickier Math: Algebra Calculus
Conceptual Tools: Stock and flow diagrams
Focus: Applying quantitative tools in new ways
0
5
10
15
20
0 5 10 15 20 25 30
Dist
ance
(mile
s)
Time (mins)
Abun
danc
e, N
(years)
Dingo pop growth after introduction to a new area
Objective 2 Progress
We have applied MANY general quantitative tools!
Simple Math: Addition Subtraction Multiplication Division
Trickier Math: Algebra Calculus
Conceptual Tools: Stock and flow diagrams
Focus: Applying quantitative tools in new ways
Consumption Respiration
C Input: C Output:
Stock Inflow Outflow
Objective 2 Progress
We have applied MANY general quantitative tools!
Simple Math: Addition Subtraction Multiplication Division
Trickier Math: Algebra Calculus
Conceptual Tools: Stock and flow diagrams
Focus: Applying quantitative tools in new ways
Important Question:
How can these tools be applied outside of this class?
Three specific tools (two equations, one conceptual):
Linear response Saturating response Stock and flow diagram
Objective 2 Progress
Those were some general quantitative tools we applied in this class…
We have applied MANY general quantitative tools!
Simple Math: Addition Subtraction Multiplication Division
Trickier Math: Algebra Calculus
Conceptual Tools: Stock and flow diagrams
Focus: Applying quantitative tools in new ways
Important Question:
How can these tools be applied outside of this class?
Three specific tools (two equations, one conceptual):
Linear response Saturating response Stock and flow diagram
Objective 2 Progress
Those were some general quantitative tools we applied in this class…
We have applied MANY general quantitative tools!
We’ll consider:
1. How we have used each tool already 2. New applications (outside of ecology) for each tool
Linear Response: Y = mX
X
Y
low
low high
high
Let’s look at some examples of how we have used linear responses …
Description: Two variables (X and Y) are related to each other linearly, with a slope, m
Objective 2 Progress
Linear Response: Y = mX
R
Feed
ing
rate
lo
w
0 many
high
f = aR
Type I functional response:
Where else might a linear response be used?
N
B
low
0 many
high
B = b’N
Number of births in a population:
Objective 2 Progress
Linear Response: Y = mX
Time
Dist
ance
lo
w
0 many
high
Distance traveled:
Distance = Velocity * Time
# Minutes talked
LD C
all C
ost
low
0 many
Long distance phone calls:
high
Cost = LD Calling Rate * # Minutes
Objective 2 Progress
Linear Response: Y = mX
# Dollars
# Eu
ros
# Euros = Exchange Rate * # Dollars
low
0 many
Exchange rate:
high
A common feature of these linear responses:
Involve inflexible rates
Objective 2 Progress
Let’s look at some examples of how we have used saturating responses …
Description: Two variables (X and Y) are related such that a maximum (threshold) Y is reached (Ymax), where half of Ymax occurs at a value of X called the half-saturation coefficient (h)
Y = Ymax X X + h
X
Y
low
low high
high
Ymax
h
Objective 2 Progress
Saturating Response:
Y = Ymax X X + h
Where else might a saturating response be used?
R
Feed
ing
rate
lo
w
low high
high
h
fmax
f = fmax R R + h
Type II Feeding rate (f): # Resources consumed
per predator per time
R
Birt
h ra
te
low
low high
high
h
bmax
bp = bmax R R + h
Birth rate (bp): # Young born per
individual per time
Objective 2 Progress
Saturating Response:
Y = Ymax X X + h
Rain
Abso
rptio
n lo
w
low high
high
h
Amax
Rain Absorption by Ground:
Amount of rain absorbed per square foot per day
Irradiance
E pr
oduc
tion
low
low high
high
h
Amax
Solar Panel Energy Production:
Amount of energy produced per solar panel per day
Objective 2 Progress
Saturating Response:
Y = Ymax X X + h
# Saltines
Eatin
g ra
te
low
low high
high
h
Emax
Saltine Challenge!
Number of saltines eaten per person per minute
# Twisters
“Tw
istin
g” ra
te
low
low high
high
h
Tmax
Tongue Twisters:
Number of times “She sells seashells by the seashore”
repeated per person per minute
Objective 2 Progress
Saturating Response:
Y = Ymax X X + h
Resolution
Perc
eive
d pi
ctur
e qu
ality
low
low high
high
PQmax
h
Digital Camera – Megapixel Battle: Perceived picture quality as resolution increases
Let’s see if we can really tell the difference at the
highest resolutions
Exercise
The Science of Color
Objective 2 Progress
Saturating Response:
50 x 33 pixels
100 x 66 pixels
200 x 133 pixels
400 x 266 pixels
800 x 531 pixels
1600 x 1063 pixels
3200 x 2125 pixels
6400 x 4251 pixels
Saturating Response: Y = Ymax X X + h
The common feature of saturating responses:
Involve responses that eventually hit a maximum level (a saturation point)
At the saturation point:
It doesn’t matter how much the independent variable (X) increases, the response variable (Y) will not increase above a threshold
Y = Ymax X X + h
Fits a lot of situations!
Objective 2 Progress
Stock and Flow Diagram:
Let’s look at some examples of how we have used stock and flow diagrams…
Stock 2
Stock 5 Stock 4
Stock 3
Stock 1
Description: Illustrate connections of stocks via inflows and outflows More generally, are networks with nodes (~stocks) and connections (flows)
Objective 2 Progress
Stock Inflow Outflow
Carbon flow through an ecosystem
Stocks: Carbon reservoirs Flows: Processes that move C
Objective 2 Progress
Stock and Flow Diagram: Stock Inflow Outflow
Food webs:
Stocks: Species Flows: Consumption
Where else might a stock and flow diagram be used?
Objective 2 Progress
Stock and Flow Diagram: Stock Inflow Outflow
Stock Inflow Outflow
Road Networks
Stocks: Cities Flows: Vehicles on Roads
Cell Phone Networks
Stocks: Individual Phones / Towers Flows: Radio waves
Objective 2 Progress
Stock and Flow Diagram:
Neural Networks
Stocks: Neurons Flows: Neurotransmitters
Aquatic Landscapes
Stocks: Lakes Flows: Water in rivers
Objective 2 Progress
Stock and Flow Diagram: Stock Inflow Outflow
Social Networks
Stocks: People Flows: Communications
Objective 2 Progress
Stock and Flow Diagram: Stock Inflow Outflow
6 Degrees of Kevin Bacon
Stocks: People Flows: Working relationship
Coming Full Circle
The BIG PICTURE message:
You can apply the quantitative tools (equations, conceptual diagrams, etc.) you learned in this class in many different contexts!
The trick is in picking out the right tool for the job
e.g., picking the correct equation to describe a particular interaction
“How do we pick out the right tool?”
We make observations!
I.e., how do we know which quantitative tool to use in a particular context?
The BIG PICTURE message:
Making Observations - Example
Collect as many different Ys (values of response variable)… …for as many different Xs (values of independent variable) as possible
X
Y
low
low high
high
Linear response Saturating response See what fits best! Saturating response
Next: Try fitting multiple models (tools)
Coming Full Circle
The BIG PICTURE message:
Making Observations - Example
Collect as many different Ys (values of response variable)… …for as many different Xs (values of independent variable) as possible
X
Y
low
low high
high
Could predict:
What happens at X values not collected Functioning of other species or systems related to the system studied (i.e., use model to make general inferences)
Next: Can make predictions
Coming Full Circle
The BIG PICTURE message:
We just completed a important process!
Observations Model Inference
Take-Home Message
Coming Full Circle
We are back to where we started 4 months ago
What we did in this class was to use a general process that is applicable in MANY situations!
I hope you are able to use these skills beyond this course!
Final Thoughts
Thanks for a fun semester!
Best of luck and congrats to everyone that is graduating!
Enjoy your holiday break!