fw364 ecological problem solving...

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!