Dispersal
Landscape Ecology
Definitions

Dispersal
◦ Spreading of individuals away from others

Migration
◦ Mass directional movements of large numbers
of species from one location to another.
Question/Comments
Do all species disperse?

Yes…
◦ Some by choice, some by chance
 Chance can be influenced by evolution.
 E.g. dandelions sees are puffy for a “reason”.
Dispersal

Why disperse?
◦ Escape immediate environment.
 Relieve local congestion.
◦ Discovery Dispersal
 1) Exploring, picking, then settling
 2) Exploring, staying.
◦ Non-discovery dispersal
 Matter of change, e.g. seeds.
Do animal moves randomly?
Random
 Correlated random walk
 Memory – making a decision.
 Does it depend on patch type?

Do animal moves randomly?

Usually no….
◦ But that is as individuals, do they as a group?
Examples – Fire Ants
European Starling
How to model this spread?

What do we need to know about a
population?
◦ How far they move?
◦ How fast the population grows?
◦ Suitable Habitat?
Integrodifference Equation
Types of model?

Scientific or Statistical?

Analytical or Simulation?

Static or dynamic?
Modified diffusion equation
How to model this spread?

Diffusion equation?
2004 Distribution
Reservoirs in OK and KS in
Verdigis River basin
Lake Mead &
Havasu
80
100
120
Inland Lake Distance to Great Lakes
60
Frequency
2400
60
80
Inland Lake Distance to 1993 Distribution
40
quency
1700
Gravity Models – primary spread from the
Great Lakes
Scaling Factor
K
U

A
O
W
D

ij
i

1

d
i i j ij
Area
Number of Boats
Distance &
coefficient
Types of model?

Scientific or Statistical?

Analytical or Simulation?

Static or dynamic?
United States Gravity Model

Basic Information ◦ Based on 210 Watersheds
◦ Estimate # of boaters/watershed
◦ Sum lake area/watershed

How to parameterize?
◦ Boat surveys
◦ Local information

Primary Question –
◦ How many boaters from areas with zebra mussels are
traveling to western waters?
United States Gravity Model
From Bossenbroek et al. 2007 Conservation Biology
From Bossenbroek et al. 2007 Conservation Biology
2007 Distribution
Predict the spread of emerald ash borer
Local Dispersal
 Human-mediated Dispersal

Modeling Dispersal
Natural Spread
Linear Distance

Yr 1
Yr 2
Yr 3
Time
Modeling Dispersal
Long-distance spread
Yr 1
Yr 3
Linear Distance

Yr 2
Time
Predict the spread of emerald ash borer

Does natural dispersal account for the rapidity
with which the emerald ash borer has spread,
even at the county scale?
Diffusion Modeling

Used a derivation of
Skellam’s diffusion
equation
Toledo
 N  N 
N
 f ( N ) D 2  2 
t
y 
x
2
2
2004
VF  4rD
Croskey 2009 - Thesis
Can diffusion
explain this rate of
movement?
2005
Estimating Diffusion Model
Parameters

VF = velocity of the invasion front
◦ Observed in Lucas County Ohio
 16 – 40 km/year

D = diffusion coefficient
VF  4rD
◦ Reported movement capabilities of EAB
 0.8 – 20 km/year

r = intrinsic rate of increase
◦ r values for other beetles 
 0.1 – 9.1

Force the model to fit observations by solving
for r and D
Croskey 2009 - Thesis
Diffusion Model Alone Cannot
Explain EAB Spread
 When D is estimated (obs = 0.8 – 20 km/year)
 mean = 802.80 km/year

When r is estimated (obs = 0.1 – 9.0 ):
 mean = 76.04
Natural dispersal is not responsible for the rate at
which the emerald ash borer has spread
Croskey 2009 - Thesis
Predict the spread of emerald ash borer

Develop models for both:
◦ Local Dispersal
◦ Human-mediated Dispersal
Natural (or
local)
Dispersal of
EAB in
Ohio
Prasad et al. 2010
Predict the spread of emerald ash borer

Local Dispersal
◦ Flight (~2 km/yr)
◦ Local human spread (~20 km/yr)

Human-mediated dispersal
◦ Campers moving firewood
◦ Hitchhikers on cars, trucks, etc.
 i.e. road networks.
◦ Wood products industry
Predict the spread of emerald ash borer:
Human-mediated dispersal
K
U

A
O
W

ij
i
i
jD
ij

d
i

1
Campers with Firewood
Bossenbroek & Jerde – in review
Natural
and
HumanMediated
Dispersal
of EAB in
Ohio
Prasad et al. 2010
Compared model to known distribution
Examined the model predictions to the patterns of
the human factors included.
 We examined 11 of the major routes from Detroit,
MI, to major cities in Ohio

◦ And included one turn only onto an adjoining highway.
◦ Then buffered these highways at 1, 2, and 4 km.

Results:
◦ 52% of the known locations of EAB fell within 1 km
◦ 64% fell within 2 km
◦ 81% fell within 4 km
 these few roads that represent only 34.7% of the total road length
used in the modeling.
Prasad et al. 2010.
 This result highlights the importance of
the role of major highways that are in a
connected road network in spreading the
emerald ash borer.