1. FW364 Ecological Problem Solving Class 18: Spatial Structure
Nov. 4, 2013

2. Second Exam: Wednesday (Nov. 6)
Midterm II
Second Exam: Wednesday (Nov. 6)
Review session in lab tomorrow
Study items posted on website
Practice exams, Concept review, & Models and assumptions table
Test will cover material taught today
Topics covered will be:
Population regulation (i.e., density dependence)
Age structure
Stage structure
Spatial structure (i.e., metapopulations)
Can use your calculator on exam
I’ll cover general study tips during the lab review

3. Outline for Today
Shifting focus: No longer discussing a single population…
…Instead, a “population of populations”
Adding spatial structure to models
Objective from Last class:
Introduced spatial structure / metapopulation analysis
In-class demo of why spatial structure is good
Objectives for Today:
Cover more on metapopulation theory
Management of metapopulations
Text (optional reading):
Chapter 6

4. Metapopulation Theory
Basic components of metapopulation theory
Features of habitat within vs. outside of local populations
Factors affecting extinction probability of local populations
Factors affecting re-colonization of local populations
How spatial correlation affects metapopulation extinction

5. Metapopulation Theory
Basic components of metapopulation theory
Features of habitat within vs. outside of local populations
Factors affecting extinction probability of local populations
Factors affecting re-colonization of local populations
How spatial correlation affects metapopulation extinction

6. Metapopulation Theory - Habitat
Local populations occupy suitable habitat imbedded
in a matrix of unsuitable habitat
Fish in lakes in a landscape
Deer in an island chain
Sheep living on mountains
Birds in a fragmented forest
Mosquitoes in pitcher plants

7. Metapopulation Theory - Habitat
Local populations occupy suitable habitat imbedded
in a matrix of unsuitable habitat
California spotted owl
Dispersal among patches is key to metapopulation persistence

8. Metapopulation Theory
Basic components of metapopulation theory
Features of habitat within vs. outside of local populations
Factors affecting extinction probability of local populations
Factors affecting re-colonization of local populations
How spatial correlation affects metapopulation extinction

9. Metapopulation Theory – Local Extinction
Four factors affect probability of local extinction (pe)
You know three of these from other population growth lectures!
In-class challenge:
Talk to a neighbor and answer this question:
What factors affect probability of local extinction?
 Think about what effects extinction risk of single populations

10. Metapopulation Theory – Local Extinction
Four factors affect probability of local extinction (pe)
Population size within habitat patch (i.e., local population)
Strength of edge effects
Stability of dynamics within patch
Growth rate within patch

11. Metapopulation Theory – Local Extinction
Population size within habitat patch
Small populations more likely to fall below some extinction threshold
 demographic stochasticity
Genetic effects (inbreeding, lack of diversity)
Allee effects
Population size determined by:
size of habitat patch (i.e., spatial extent; contributes to carrying capacity)
quality of habitat in patch (contributes to productivity, carrying capacity)

12. Metapopulation Theory – Local Extinction
2. Strength of edge effects
Small patches have more edge, relative to internal (suitable) habitat
“What’s so bad about edges?”
Different environmental conditions in edges than within the patch
E.g., forest patch edge: more light and wind,
higher temperature, more human disturbance, etc.
Many small habitat patches have less suitable habitat than
a few larger patches of the same total area
Note: some species thrive in edge habitat…
… but these are not typically the species
we are concerned about
e.g., invasive kudzu loves edges

13. Metapopulation Theory – Local Extinction
2. Strength of edge effects
Big patch has same total habitat as 5 smaller patches, but more than double the suitable (interior) habitat:
>2x
Interior habitat in 5 km2 patch = 5 * 0.64 = 3.20 km2
Interior habitat in 1 km2 patch = 1 * 0.31 = 0.31 km2
* 5 = 1.55 km2

14. Metapopulation Theory – Local Extinction
3. Stability of dynamics within patch
Large fluctuations in population size increase extinction risk
What causes fluctuations?
Environmental variation
Type and strength of density dependence
Scramble (extreme effect)
Contest

15. Metapopulation Theory – Local Extinction
4. Growth rate within patch
Populations that are increasing (λ > 1) are less likely to go extinct
than populations that are decreasing (λ < 1)
Source: Local population where births are greater than deaths (λ > 1)
 Can persist on its own
Excess individuals are a source of colonists to other local pops
Alternative definition: Emigration > Immigration
Sink: Local population where births are less than deaths (λ < 1)
 Must be supplied with immigrants to persist
Alternative definition: Immigration > Emigration
Sink
λ < 1
Source λ > 1

16. Metapopulation Theory – Local Extinction
4. Growth rate within patch
Populations that are increasing (λ > 1) are less likely to go extinct
than populations that are decreasing (λ < 1)
Source: Local population where births are greater than deaths (λ > 1)
 Can persist on its own
Excess individuals are a source of colonists to other local pops
Alternative definition: Emigration > Immigration
Sink: Local population where births are less than deaths (λ < 1)
 Must be supplied with immigrants to persist
Alternative definition: Immigration > Emigration
There must be at least one source population
for the metapopulation to persist!

17. Metapopulation Theory
Basic components of metapopulation theory
Features of habitat within vs. outside of local populations
Factors affecting extinction probability of local populations
Factors affecting re-colonization of local populations
How spatial correlation affects metapopulation extinction

18. Metapopulation Theory – Re-colonization
Re-colonization of extinct local populations is
(typically) key to metapopulation persistence!
Re-colonization is a function of:
Distance to the nearest inhabited patch
 Longer distance decreases number of dispersing individuals
Population size of source populations
 Patches with high density often supply more colonists
more individuals
more reason to leave (competition)
For example:
Population with contest density-dependence:
At high N, more “floaters” as potential dispersers

19. Metapopulation Theory
Basic components of metapopulation theory
Features of habitat within vs. outside of local populations
Factors affecting extinction probability of local populations
Factors affecting re-colonization of local populations
How spatial correlation affects metapopulation extinction

20. Metapopulation Theory – Correlation
Spatial correlation:
Correlation in environmental and population fluctuation across space
 Affects how the probabilities of local extinction combine to determine the probability of metapopulation persistence or extinction
Fluctuations in populations close to each other will be more correlated
than fluctuations in populations far apart (i.e., less independent)
populations close together experience similar environmental conditions
Typically, less spatial correlation (greater independence)
means higher probability of metapopulation persistence

21. Metapopulation Theory – Correlation
Spatial correlation:
Correlation in environmental and population fluctuation across space
California spotted owl

22. Concept Check
How does distance among populations affect metapopulation persistence?
In class exercise: Add relationships to the figures below
Dispersal effects
Spatial correlation effects
Distance
Correlation
low
close
far
high
Persistence
Distance
Dispersal
low
close
far
high
Persistence

23. Concept Check
How does distance among populations affect metapopulation persistence?
In class exercise: Add relationships to the figures below
Dispersal effects
Spatial correlation effects
high
high
Dispersal
Correlation
low
low
high
high
close
far
close
far
Distance
Persistence
Distance
Persistence
low
low
close
far
close
far
high
high
Distance
Distance
Persistence
Persistence
low
low
low
high
low
high
Dispersal
Correlation

24. Concept Check
How does distance among populations affect metapopulation persistence?
In class exercise: Add relationships to the figures below
Dispersal effects
Spatial correlation effects
high
high
Persistence
Persistence
low
low
close
far
close
far
Distance
Distance
Distance among local populations has two opposing effects!
smaller distance means more dispersal = plus for persistence
smaller distance means greater correlation = minus for persistence
 Important complexity in metapopulation models

25. Metapopulation Management
Managing fragmented populations is becoming increasingly necessary
 Not an easy task!
Key metapopulation management questions:
1. How many (and what size) habitat reserves are needed?
2. How many (and what size) dispersal corridors are needed?
3. How do we handle future habitat fragmentation?

26. Metapopulation Management
1. How many (and what size) habitat reserves are needed?
Many small reserves may provide insurance against global extinction via the basic tenet of metapopulation theory
 Must have some degree of independence
 But also need dispersal among reserve (local) populations
A few large reserves means large local population size
 Less likely to go extinct due to bad luck
(series of bad recruitment years)
 Less likely to go extinct due to demographic stochasticity

27. Metapopulation Management
1. How many (and what size) habitat reserves are needed?
Many small reserves may provide insurance against global extinction via the basic tenet of metapopulation theory
 Must have some degree of independence
 But also need dispersal among reserve (local) populations
A few large reserves means large local population size
 Less likely to go extinct due to bad luck
(series of bad recruitment years)
 Less likely to go extinct due to demographic stochasticity
No (single) general answer will apply to all metapopulations!
Best options depend on specifics of metapopulation

28. Metapopulation Management
2. How many (and what size) dispersal corridors are needed?
Dispersal between suitable habitat patches is necessary for the metapopulation effect to work
BUT, there is a limit to how much dispersal is needed!
Do not want totally connected populations because then metapopulation is like one large population
What size & other attributes are needed to make a corridor usable?
Yellowstone to Yukon Initiative
Trying to link fragmented wildlife habitat
in the Rocky Mountains
e.g., link grizzly bears and wolves in Yellowstone
to larger populations in the Canadian Rockies

29. Metapopulation Management
3. How do we handle future habitat fragmentation?
In most cases, habitat fragmentation has a negative effect on populations
Loss of habitat (a bad thing)
Smaller populations (a bad thing)
Less dispersal due to matrix of unsuitable habitat (often bad)
Reality is that habitats are only going to get more fragmented
How low can we go before we’ve gone too far?

30. Metapopulation Models
To address these management questions,
we need metapopulation models
Simplest models predict fraction of local populations that are
extinct / not extinct
 Too simple for management
 But are good for understanding basic concepts
More complex models can be used to determine:
 Optimal number and size of reserves
 Optimal dispersal
And can be used to forecast effect of future fragmentation

31. End of material
on Midterm II

32. Predator-prey interactions (4 classes)
Looking Ahead
Next Unit:
Predator-prey interactions (4 classes)
Lab Tomorrow
REVIEW SESSION
Bring copy of practice exams (or download them onto your computer to work from) along with a calculator

33. Metapopulations