Testing LANDIS-II to stochastically model spatially abstract vegetation trends in the contiguous United States

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Content Copyright
2013

Austin
V.
Davis

TESTING
LANDIS-‐II
TO
STOCHASTICALLY

MODEL
SPATIALLY
ABSTRACT
VEGETATION

TRENDS
IN
THE
CONTIGUOUS
UNITED
STATES

By

Austin
V.
Davis

A
Thesis
Presented
to
the

FACULTY
OF
THE
USC
GRADUATE
SCHOOL

UNIVERSITY
OF
SOUTHERN
CALIFORNIA

In
Partial
Fulfillment
of
the

Requirements
for
the
Degree

MASTER
OF
SCIENCE

(GEOGRAPHIC
INFORMATION
SCIENCE
AND
TECHNOLOGY)

December
2013

ii

Dedication

To
the
men
and
women
of
the
United
States
Army.

iii

Acknowledgements

Special
thanks
to
Dr.
Travis
Longcore,
my
thesis
advisor,
for
putting
up
with

my
pesky
e-‐mail
and
supporting
me
in
this
effort.
Also,
I
deeply
appreciate
the

contributions
made
by
the
other
members
of
my
thesis
committee,
Dr.
Karen
Kemp

and
Dr.
Edward
Pultar,
despite
my
interruptions
to
their
summer
vacations.
Next,
I

acknowledge
my
Branch
Chief,
Mr.
Mark
Graves,
for
providing
a
set
of
footsteps
to

follow.
It
was
through
his
encouragement
that
I
pursue
this
degree
program
at
the

University
of
Southern
California.
On
that
note,
I
must
also
thank
the
Director
of
the

United
States
Army
Engineer
Research
and
Development
Center
Environmental

Laboratory,
Dr.
Beth
Fleming,
for
granting
her
unwavering
support
of
this
pursuit.

Dr.
Eric
Brizke,
Dr.
Nathan
Beane,
and
Mr.
Michael
Whitby
also
deserve
special

thanks
for
being
exceptional
research
partners
and
colleagues;
without
their

skepticism
this
project
would
never
have
existed.
Finally,
I
thank
my
mother
for

encouraging
me
to
read
and
write
before
I
thought
it
would
matter,
my
father
for

demonstrating
the
importance
of
life-‐long
education,
and
my
wife
for
not
giving
up

on
me.

iv

Table
of
Contents

Dedication..................................................................................................................................ii

Acknowledgements...............................................................................................................iii

Abstract......................................................................................................................................vi

Chapter
1:
Introduction.........................................................................................................1

Overview..................................................................................................................................................................1

Background.............................................................................................................................................................6

LANDIS......................................................................................................................................................................8

Chapter
2:
Methodology......................................................................................................12

Overview...............................................................................................................................................................12

Table
1:
LANDIS-‐II
Input
Files.....................................................................................................................12

Locality
Dataset..................................................................................................................................................19

Building
a
Landscape
Diversity
Database...............................................................................................21

Filtering
the
Dataset.........................................................................................................................................22

Generating
Ecological
Parameters
for
LANDIS-‐II................................................................................26

Extracting
Spatially
Explicit
Rasters.........................................................................................................30

Generating
Random
Rasters.........................................................................................................................31

Building
LANDIS-‐II
Input
Text-‐Files.........................................................................................................32

Executing
LANDIS-‐II.........................................................................................................................................33

Developing
Vegetation
Trends....................................................................................................................34

Statistical
Testing..............................................................................................................................................38

Chapter
3:
Results.................................................................................................................41

Chapter
4:
Discussion
and
Conclusion...........................................................................45

Discussion.............................................................................................................................................................45

Conclusion............................................................................................................................................................48

References...............................................................................................................................51

Appendix
A:
Pseudocode
for
LANDIS-II
Scenario
Server.........................................54

Appendix
B:
Pseudocode
for
LANDIS-II
Scenario
Client..........................................57

Appendix
C:
Pseudocode
for
Data
Analysis..................................................................61

v

List
of
Figures

Figure
1–
An
Example
of
the
Experimental
Variables
and
Iterations
Used
in
this

Research......................................................................................................................................................15

Figure
2–
Research
Overview............................................................................................................16

Figure
3
-‐
NatureServe
Dataset:
Ecological
Systems
of
the
United
States......................18

Figure
4
–
Candidate
Localities
Resulting
From
Hexagonal
Tessellation
of
the

Ecological
Systems
of
the
United
States
at
48-‐km
2

Scale.......................................................20

Figure
5
-‐
Landscape
Diversity
Based
On
The
Ecological
Systems
Of
The
United

States
Dataset
And
The
Candidate
Localities
At
The
12-‐km
2

Scale...................................22

Figure
6
–
The
Localities
Containing
Sets
Of
Vegetation
Communities
Used
To

Understand
The
Spatial
Sensitivity
Of
LANDIS-‐II......................................................................26

Figure
7
–
An
Example
Of
The
Three
Different
Spatial
Representations
Used
In
This

Experiment
And
Their
Associated
Succession
And
Output..................................................35

Figure
8
-‐
Chi-‐square
Equation..........................................................................................................39

Figure
9
-‐
Succession
Trajectory
Based
On
Initial
Area
Of
A
Vegetation
Community
.........................................................................................................................................................................42

Figure
10
-‐
Succession
Trajectory
Based
On
The
Total
Area
Of
A
Vegetation

Community.................................................................................................................................................43

Figure
11
-‐
End-‐State
Analysis...........................................................................................................44

vi

Abstract

The
second
generation
of
the
Landscape
Disturbance
and
Succession
model

(LANDIS-‐II)
is
frequently
used
to
understand
ecological
succession
on
the
landscape.

LANDIS-‐II
is
an
important
simulation
tool
but
it
can
be
difficult
to
parameterize

properly
in
data-‐poor
regions.
By
examining
the
spatial
sensitivity
of
LANDIS-‐II,
the

model’s
users
will
have
an
improved
understanding
of
the
data
required
to
properly

implement
the
model.
Existing
studies
have
tested
the
ecological
sensitivity
of

LANDIS-‐II
in
local
geographic
settings,
but
a
robust
test
of
the
model’s
spatial

sensitivity
has
not
been
completed.
This
research
tested
the
spatial
sensitivity
of
the

LANDIS-‐II
spatially
stochastic
landscape
model
using
a
broad
set
of
vegetation

communities
found
within
the
contiguous
United
States.
Thirty
spatially
explicit,

equal-‐area,
and
area-‐weighted
iterations
of
the
spatial
parameters
of
the
LANDIS-‐II

model
were
run
for
a
series
of
localities
in
the
contiguous
United
States,
where
the

areas
were
defined
by
the
spatial
composition
of
vegetation
community
values.

Ecological
attributes
were
derived
from
the
NatureServe
Ecological
Systems
of
the

United
States
dataset.
A
test
of
the
spatial
input
parameters
of
LANDIS-‐II

demonstrated
that
the
model
is
aspatial
under
certain
conditions.
Furthermore,

vegetation
community
interactions
may
be
effectively
represented
in
LANDIS-‐II
by
a

series
of
spatially
stochastic
input
rasters;
such
that
assessing
a
locality’s
vegetation

trend
is
possible
even
when
spatially
explicit
land
classification
information
is

unavailable,
thereby
facilitating
long-‐term
environmental
planning
in
data-‐poor

environments.

1

Chapter
1:
Introduction

Overview

Landscape
ecology
is
the
spatial-‐centric
sub-‐discipline
of
the
ecological

sciences
that
evolved
to
embrace
the
role
space
and
time
play
in
the
environment

(Turner
1989;
Watt
1947).
The
field
is
responsible
for
the
development
of
many

different
types
of
dynamic
landscape
models
including
models
with
dispersion-‐
based
drivers.
In
a
dispersion
model,
an
entity
is
represented
at
an
initial
position

and
its
replicates
are
propagated
to
surrounding
locations
during
a
series
of
time-‐
steps.
Model
parameters
can
be
used
to
attenuate
the
dispersion
process.
For

instance,
by
defining
a
maximum
dispersion
distance,
an
initial
entity
cannot
be

dispersed
farther
than
the
set
distance
in
the
model.

The
representation
of
dynamic
spatio-‐temporal
landscape
phenomena
has

been
an
ongoing
challenge
for
spatial
modelers.
A
common
method
for
modeling

these
phenomena
is
through
the
snapshot
method.
The
snapshot
method
represents

data
through
a
series
of
raster
grids,
one
for
each
time-‐step.
Each
raster
grid

displays
a
small
change
on
the
landscape;
the
temporally
ordered,
iterative
display

of
these
rasters
allows
the
modeler
to
visualize
the
temporal
processes
acting
in
the

model
(Pultar
et
al.
2009).
A
dispersion
model
adhering
to
the
snapshot
method

represents
an
initial
entity
as
a
single
cell,
or
series
of
cells,
on
the
initial
raster.
As

time
progresses,
new
raster
grids
are
generated
that
show
the
entity
spreading
to

more
cells
on
the
raster.

2

Most
landscape
models
use
spatially
explicit
knowledge
to
populate
the
input

conditions
of
the
model.
Spatially
explicit
knowledge
is
defined
here
as
the
digital

representation
of
the
real
world
that
maintains
a
recognizable
depiction
of
the
real

world’s
spatial
arrangement
and
composition.
Spatial
arrangement
is
the
unique

pattern
and
shape
of
an
entity
or
series
of
entities,
whereas,
spatial
composition
is

considered
the
proportion
of
area
each
entity
occupies
in
a
defined
space.
For

example,
a
spatially
explicit
dataset
representing
a
forested
landscape
maintains
the

shape
of
each
forest’s
boundary,
as
well
as
the
same
proportion
of
area
for
each

forest,
in
relation
to
the
spatial
extent
of
the
landscape
being
represented.

The
Landscape
Disturbance
and
Succession
family
of
models,
commonly

known
as
LANDIS
models,
were
developed
by
forest
ecologists
to
understand
forest

succession
across
a
broad
set
of
landscapes.
LANDIS
is
classified
as
a
dispersion

model
adhering
to
the
snapshot
method
to
represent
the
spatio-‐temporal
ecological

succession
occurring
in
the
model.
The
model
operator
defines
a
series
of
species

and
dispersion
parameters
to
represent
various
vegetation
communities
on
the

landscape.
In
most
(if
not
all)
studies
(Scheller
et
al.
2008;
Scheller
et
al.
2011;

Scheller
and
Mladenoff
2005;
Shang
et
al.
2004),
species
parameters
are
defined
by

iteratively
testing
a
set
of
observed
and
arbitrary
values
in
preliminary
LANDIS
runs,

and
then
selecting
parameters
that
the
operator
deems
most
representative
of
real

world
properties.
The
iterative
process
of
selecting
ideal
species
and
dispersion

parameters
is
known
as
ecological
parameter
optimization.
While
ecological

3

parameter
optimization
is
common,
a
robust
test
of
the
model’s
spatial
sensitivity
is

lacking.

Mlandenoff
and
He,
the
creators
of
the
original
LANDIS
model,
note
that
the

use
of
simulation
models
allow
researchers
the
opportunity
to
explore
the
effects
of

disturbance,
scale,
time,
and
ecological
complexity
on
an
environment.
While
both

claim
LANDIS
to
be
a
valid
tool
for
forest
related
research,
they
have
stated:

“…LANDIS
is
not
designed
to
predict
the
occurrence
of
a
given
event
or
change
on
a

single
real
location.
The
model
is
best
viewed
as
a
tool
for
projecting
plausible

landscape
patterns
resulting
from
different
simulated
assumptions
and
scenarios”

(pp.159,
Mladenoff
and
He
1999).
In
many
ways,
this
statement
sparked
the

development
of
this
research
project
because
it
highlights
a
direct
need
to

understand
the
model’s
spatial
sensitivity
before
accepting
its
results.

LANDIS
simulation
models
are
useful
for
understanding
landscape
level

succession
for
a
given
set
of
vegetation
communities.
In
this
research,
a
vegetation

community
is
considered
a
unique
set
of
collocated
plant
species
occurring
on
the

landscape,
regardless
of
their
spatial
properties
(e.g.
adjacency,
patchiness).
LANDIS

is
generally
used
to
determine
non-‐spatial
vegetation
trends
acting
in
the
model,

such
as
the
increase
or
decrease
of
a
given
species’
(or
vegetation
community’s)

percentage-‐area
shown
in
the
model’s
output.
An
example
of
aspatial
LANDIS
output

visualization
is
shown
in
LANDIS:
A
Spatial
Model
of
Forest,
Landscape
Disturbance,

Succession,
and
Management
(Mladenoff
et
al.
1996)
using
the
APACK
software

4

package
for
summarizing
landscape
metrics.
The
practice
of
chart
and
tabular

summaries
of
LANDIS
raster
output
is
still
in
use
(Scheller
et
al.
2007),
which

suggests
that
only
non-‐spatial
vegetation
trend
information
is
required
as
an
output

by
the
model’s
users.

Given
that
LANDIS-‐II
is
primarily
an
ecological
tool,
LANDIS-‐II’s
developers

and
users
have
focused
more
on
the
sensitivity
analysis
of
ecological
parameters
in

the
model
(He,
Larsen,
and
Mladenoff
2002)
instead
of
assessing
how
spatial

properties
influence
the
non-‐spatial
vegetation
trend
results.
This
research
tested

the
spatial
sensitivity
of
the
LANDIS-‐II
landscape
simulation
model
to
understand

the
influence
spatial
arrangement
and
spatial
composition
have
on
simulation

results.
This
study
posits
that
LANDIS-‐II’s
spatial
stochasticity
allows
it
to
accept

randomly
generated
spatial
input
parameters
and
produce
non-‐spatial
output

results
similar
to
those
found
when
spatially
explicit
input
parameters
are
used.

Certainly
non-‐spatially
explicit
input
layers
cannot
be
used
to
predict
spatially

explicit
trends
and
outcomes,
but
because
LANDIS
output
results
are
traditionally

reported
using
an
aspatial
method,
spatially
explicit
knowledge
may
not
be
needed.

Under
this
paradigm,
vegetation
communities
acting
within
LANDIS-‐II

simulations
are
contained
by
an
interaction
space
based
on
spatial
reality,
rather

than
an
explicit
representation
of
reality
itself.
If
this
paradigm
holds
true,
then

LANDIS-‐II
could
be
used
to
understand
vegetation
trends
in
data-‐poor

environments.

5

The
novelty
of
this
research
is
the
adaptive
application
of
the
LANDIS-‐II

model
to
understand
its
spatial
sensitivity.
In
previous
studies
(Scheller
and

Mladenoff
2005;
Scheller
et
al.
2011),
LANDIS-‐II
was
optimized
for
specific

ecological
regimes
using
the
ecological
parameter
optimization
technique
discussed

earlier,
and
applied
to
fixed,
spatially
explicit
input
layers
to
develop
a
set
of
non-‐
spatial
vegetation
trend
results.
In
this
research,
however,
the
results
of
spatially

explicit
output
based
on
generic
ecological
parameters
were
used
as
an

experimental
control
in
a
sensitivity
test
of
two
different,
random
spatial
variables.

Because
non-‐spatial
vegetation
trends
are
based
on
the
aggregation
of
spatial
data

within
a
spatial
extent,
the
experimental
design
of
this
research
also
assesses
the

spatial
sensitivity
of
three
different
aggregation
scales:
12km
2
,
24km
2
,
and
48km
2
.

The
Chi-‐square
statistic
was
used
to
compare
the
similarity
between
the
tabular

vegetation
trend
patterns
produced
by
the
experimental
control
and
both
variables

individually
at
each
scale.
After
all,
LANDIS-‐II
is
used
to
provide
non-‐spatial

vegetation
succession
trend
information
and
not
spatially
accurate
assessments
of

landscape
future
(Mladenoff
and
He
1999).
This
exploration
of
the
LANDIS-‐II
model

adds
to
the
current
body
of
knowledge.

Furthermore,
this
study
is
in
direct
support
of
U.S.
Army
research
operations

concerning
global
change,
land
management,
and
the
fate
of
contaminants
on

military
installations.
This
research
was
conducted
parallel
to
the
development
of
a

vegetation
trend
database
for
dominant,
natural,
upland
vegetation
in
the

6

contiguous
United
States.
Although
the
larger
research
project
is
not
outlined
in
this

study,
it
served
as
the
impetus
for
an
investigation
of
LANDIS-‐II,
provided
the

context
for
the
experimental
parameters
used,
and
served
as
an
opportunity
to

further
the
understanding
of
spatially
stochastic
modeling.

Background

The
study
of
spatially
variant
ecosystems
begins
with
Tansley’s
1935
paper,

The
Use
and
Abuse
of
Vegetation
Concepts
and
Terms
(Tansley
1935).
In
the
paper,

the
author
introduces
the
idea
of
ecosystems
as
being
a
web
of
inter-‐related
multi-‐
layered
natural
systems,
and
expounds
upon
the
concept
of
succession
found
in

these
systems.
By
1935,
ecologists
had
observed
that
not
only
do
plants
themselves

undergo
transitional
phases,
but
entire
vegetation
communities
undergo
a
series
of

transitions
as
well.
These
patterns
of
transition,
driving
one
ecosystem
to
transgress

upon
another,
are
referred
to
as
succession.

Watt
builds
on
Tansley’s
work
with
his
review
(Watt
1947)
of
vegetation

patterns
and
processes.
Contemporaries
of
Tansley
used
mathematical
and

population
models
to
describe,
predict,
and
understand
their
world
(Morris
1997).

Watt’s
work
is
striking
in
that
he
notices
the
importance
of
spatial
settings
on

vegetation,
and
describes
the
dynamic
phases
of
an
ecosystem
distributed
on
the

landscape.
In
the
19
th

century,
ecologists
believed
vegetation
and
ecosystems
were

distributed
uniformly
across
the
local
landscape,
but
advances
in
the
field
pointed
to

patchy
distributions
of
ecosystems
(Legendre
and
Fortin
1989).
Although
Watt’s

7

examples
largely
focus
on
the
patchiness
of
micro-‐communities
as
situated
on
a

local
hill-‐slope,
20
th

century
ecologists
would
begin
describing
the
spatial

relationships
and
ecological
settings
seen
in
the
environment.

Turner
(1989)
articulates
the
development
of
ecological
modeling
from
the

early
conceptual
understanding
provided
by
Watt.
The
notion
of
landscape
patches

in
different
phases
of
succession
and
the
influence
of
scale
on
biogeographic

understanding
are
discussed
in
more
detail
as
the
underpinning
of
modern
spatial

landscape
models.
The
quantitative
revolution
in
geography
brought
new
statistical

methods,
such
as
Moran’s
I,
for
describing
spatial
patterns.
A
spatial-‐centric

approach
to
ecology
became
formally
developed
and
Turner
presents
a
strong

argument
for
the
use
of
spatial
ecology
models
over
non-‐spatial
models,
which
may

not
capture
the
full
range
of
important
processes
in
the
environment.
Spatial

properties
and
drivers
play
an
important
role
in
ecosystems
and
should
be

represented
in
the
model
environment
because
spatial
patterns
do
affect
real
world

ecological
processes.

With
the
advent
of
the
personal
computers
becoming
more
available
at
lower

cost,
the
possibility
of
more
complex
modeling
efforts
was
slowly
realized.

Furthermore,
ecology
models
became
more
spatial-‐centric
and
incorporated
new

variables,
including
disturbance
and
human-‐ordered
land
management.
Paine
et
al.

(1998)
discuss
how
disturbances
affect
landscape
succession.
While
ecological

communities
often
rebound
following
routine
disturbances,
Paine
et
al.
note
that

8

after
a
catastrophic
disturbance,
or
series
of
disturbances,
the
landscape
enters
a

new
ecological
domain
by
undergoing
catastrophic
succession.
Once
this
process

has
occurred,
ecological
communities
rarely
rebound.

Although
this
research
tested
the
spatial
sensitivity
of
LANDIS-‐II
without

modeling
disturbances
or
land
management
decisions,
the
demand
for
these

variables
within
a
landscape
modeling
package
is
a
leading
reason
for
the

development,
evolution,
and
use
of
the
LANDIS
family
of
spatial
models.
Although

the
LANDIS
family
of
models
is
only
one
set
of
many,
it
is
widely
used
to
predict

species-‐specific
response
to
environmental
disturbances
and
is
portable
to
a
broad

range
of
landscapes
and
vegetation
regimes
(He,
H.
S.,
D.
R.
Larsen,
and
D.
J.

Mladenoff
2002).

LANDIS

LANDIS
is
a
dispersion-‐based
system
used
to
model
dynamic
ecological

succession
between
vegetation
communities.
The
model
internally
disperses
species

based
on
a
random-‐seed
value
that
determines
distance
and
direction,
provided
the

new
location
is
within
the
bounds
set
by
the
species
and
dispersion
parameters.

Mladenoff
et
al.
(1996)
describe
the
objectives
and
approach
used
in
the
design
and

production
of
the
original
LANDIS
model.
The
paper
provides
a
brief
background
of

the
original
research
goals,
model
description,
and
model
outputs.
The
creators
of

the
model
sought
to
develop
a
model
platform
able
to
capture
the
spatio-‐temporal

evolution
of
large
forested
landscapes.
The
developers
also
desired
a
model
capable

9

of
dynamically
modeling
ecological
disturbances
based
on
spatially
explicit
input

data.
The
LANDIS
developers
settled
on
a
dynamic,
spatially
stochastic,
dispersion-‐
based
platform
capable
of
meeting
their
research
needs.

He
et
al.
(2002)
present
a
persuasive
argument
for
the
use
of
the
LANDIS

family
of
models.
The
authors
describe
LANDIS
as
a
premier
system
in
the
ecological

modeling
field
and
consider
it
the
benchmark
for
future
landscape
model

development.
The
model
is
object
oriented
and
developed
in
C#
.Net
allowing

developers
to
extend
the
capabilities
of
the
system
using
a
modern
computing

language.
The
extensibility
of
the
model
through
the
use
of
open-‐source
extension

packages
is
a
leading
reason
for
its
prolific
use
(He,
Larsen,
and
Mladenoff
2002).

The
core
of
the
model,
however,
remains
proprietary.
It
is
this
proprietary
nature

that
makes
the
current
research
necessary.

LANDIS’s
design
as
a
spatially
stochastic
model
lends
itself
to
be
a
portable

and
adaptable
model
capable
of
investigating
a
broad
range
of
problems
(He,
Larsen,

and
Mladenoff
2002).
The
pedigree
of
LANDIS
and
its
many
applications
are

described
by
Mladenoff
(2004),
who
also
introduces
the
second
generation
LANDIS

model,
LANDIS-‐II.
LANDIS-‐II
includes
new
features
such
as
time-‐step
controls,
a

new
dispersal
method
(double
exponential
seed
dispersal),
and
increased

mechanistic
detail
within
the
model.

10

Like
LANDIS,
LANDIS-‐II’s
spatial
drivers
are
dispersion
based.
During

successive
temporal
iterations
of
the
model,
species
modeled
in
LANDIS-‐II
are

distributed
throughout
the
spatial
input
layer
(initial
communities
layer
model

parameter)
based
on
their
original
position
and
a
user-‐supplied
dispersion

parameter.
The
distance
and
direction
of
a
species’
dispersion
from
its
original

location
to
a
new
location
is
stochastically
determined.
The
probability
that
species’

establishment
will
occur
at
a
new
location
is
calculated
based
on
the
parameters

found
at
the
new
site
and
each
species’
establishment
probability.
If
establishment

occurs,
landscape
succession
has
occurred.
The
pattern
created
through
this

iterative
dispersion
process
is
considered
to
be
spatially
stochastic,
although
it
is

attenuated
by
the
model’s
parameters.

Schaller
et
al.
(2007)
present
LANDIS-‐II,
describing
the
model’s
basic

assumptions,
purpose,
features,
and
architecture.
The
model
is
designed
as
an

object-‐oriented
extendable
landscape
simulation
system
able
to
suggest
a
range
of

vegetation
succession
trajectories
that
may
occur
for
a
given
landscape.
LANDIS-‐II

does
make
broad
assumptions,
such
as,
soil,
elevation
regime,
solar
angle,
and

climate
conditions
are
considered
to
be
homogenous
across
the
input
grid.
In
an

effort
to
account
for
this
homogeneity,
many
LANDIS-‐II
users
define
different

ecoregions
for
a
study
area
based
on
local
microclimate
and
soil
patterns.
Each

species
in
each
ecoregion
is
then
assigned
different,
arbitrarily
assigned

establishment
probabilities.

11

LANDIS-‐II
is
superior
to
LANDIS
because
it
is
designed
to
improve
its

portability
to
different
ecological
regimes
and
provides
greater
control
over
its

spatio-‐temporal
parameters.
This
is
evidenced
by
the
user-‐base
discussion
for

scaling-‐up
the
modeling
framework
to
run
at
the
regional
scale
(LANDIS-‐II
User

Community
2012).
Further,
its
modular
design
allows
it
to
interact
with
other

spatial
modeling
applications
(Scheller
and
Mladenoff
2005),
ultimately
influencing

the
results
of
other
models.

Ecologists
have
built
successive
generations
of
LANDIS
by
improving
its

ecological
parameters
and
adapting
its
geoprocessor
(e.g.
new
dispersal
method)

but
the
spatial
nature
of
the
model
has
not
been
robustly
examined.
Before

incorporating
LANDIS-‐II
into
further
spatial
modeling
workflows,
LANDIS-‐II’s

spatial
sensitivity
should
be
examined
in
detail.
This
research
examined
the
effects

of
spatial
arrangement
and
composition
within
the
model
by
performing
a
spatial

experiment.
This
experiment
compared
a
spatially
explict
control
case
against
two

spatial
variables
that
expressed
random
arrangement,
where
each
variable

expressed
a
different
degree
of
spatial
composition.

12

Chapter
2:
Methodology

Overview

LANDIS-‐II
operates
with
a
series
of
text
and
raster
files.
These
files
allow
the

model
operator
to
define
the
species-‐specific
parameters,
spatial
layer
parameters,

dispersion
parameters,
and
general
runtime
parameters
governing
the
model
(Table

1).
The
model
uses
two
spatial
layers:
the
initial
community
layer
that
defines
the

location
of
each
species,
and
the
ecoregions
layer
that
(in
this
research)
defines
the

active
and
inactive
areas
in
the
model.
These
are
discussed
in
greater
detail
in
a

later
section.

TABLE
1
-
LANDIS-II
INPUT
FILES

Input
File
Purpose
Type

Scenario.txt
Defines
overall
model
execution.
Text
File

Age-‐only-‐succession.txt
Defines
establishment
probabilities
of
each
species.
Text
File

Initial-‐Communities.txt
Defines
species’
age
cohorts
for
each
map-‐code.
Text
File

Reclass.txt
Defines
reclassification
coefficients.
Text
File

Species.txt
Defines
species’
ecological
attributes.
Text
File

Ecoregions.txt
Defines
active
state
of
each
ecoregion.
Text
File

Ecoregions.img
Defines
the
areas
of
each
ecoregion.
Raster

Initial-‐Communities.img
Defines
the
areas
of
each
vegetation
community

represented
by
its
associated
map-‐codes

Raster

The
spatial
experiment
executed
in
this
research
included
a
spatial
control

and
two
separate
spatial
variables.
Where
typical
LANDIS-‐II
studies
focus
on

determining
optimum
ecological
parameters
using
the
ecological
parameter

optimization
technique
described
earlier,
this
research
relied
on
a
variety
of
generic

ecological
parameters
to
represent
a
set
of
localities.
This
decision
was
made
for

13

three
reasons.
First,
it
is
a
requirement
of
the
concurrent
research
involving
the

development
of
a
vegetation
trend
database
to
process
a
broad
range
of
ecological

parameters.
Second,
the
experimental
results
using
different
ecological
regimes
only

serves
to
bolster
the
validity
of
the
results
because
ecological
parameters
can

remain
fixed.
Third,
ecological
parameter
sensitivity
is
not
the
focus
of
this
research,

but
rather
the
spatial
properties
of
the
underlying
datasets.
Therefore,
any

ecological
parameters
could
have
been
used
in
this
study,
provided
they
remained

constant
between
the
experimental
control
and
variables.

For
this
study,
ecological
regimes
were
defined
as
the
set
of
dominant,

natural,
terrestrial
vegetation
communities
within
the
boundaries
of
a
given
locality.

The
spatial
control
was
defined
as
the
spatial
composition
and
arrangement
of

vegetation
communities
at
each
locality.
Each
variable,
at
each
locality,
was

processed
by
LANDIS
using
thirty
separate
iterations
of
the
model
and
the
results

were
aggregated
for
more
robust
comparison.
The
spatial
control
variable
used
the

same
spatial
input
layer,
but
LANDIS’s
random-‐seed
value
was
changed.
The

random-‐seed
value
governs
the
stochasticity
of
the
model,
such
that
running

LANDIS-‐II
with
the
same
set
of
input
parameters,
layers,
and
random-‐seed
value

always
produces
the
same
result.
To
produce
a
range
of
results
with
the
same
input

parameters
and
layers,
the
random-‐seed
value
must
change.
Running
a
set
of
thirty

iterations
of
each
variable
at
each
locality
in
LANDIS-‐II
was
determined
to

effectively
capture
the
range
of
vegetation
trend
succession
occurring
for
each

14

instance
of
each
variable
at
each
locality.
This
acknowledges
Mlandenoff’s
earlier

quote
and
provides
a
stable
dataset
to
assess
vegetation
trends
for
each
variable.

The
control
is
compared
to
two
separate
spatial
variables.
The
first
spatial

variable,
area-‐weighted,
is
defined
by
fixed
ecological
spatial
composition
similar
to

the
control
and
random
spatial
arrangement.
That
is,
the
same
proportion
of
area

for
each
vegetation
community
found
in
the
control
was
represented
in
the
area-‐
weighted
variable
and
distributed
randomly
across
the
input
grid.
The
second

spatial
variable,
equal-‐area,
was
defined
by
equal
spatial
composition
and
random

spatial
arrangement.
The
equal-‐area
landscape
contained
an
equal
proportion
of

area
of
each
vegetation
community
on
the
input
grid,
but
was
distributed
randomly

(Figure
1).
Each
variable
had
a
subset
of
thirty
unique
input
grids
instead
of
thirty

different
random-‐seed
values
as
noted
in
the
control
runs.
Thus,
for
each
locality

investigated,
thirty
control
runs,
area-‐weighted
runs,
and
equal-‐area
runs
of
the

LANDIS-‐II
model
were
executed
before
final
analysis
and
trend
comparison

occurred
(Figure
2).

15

FIGURE
1–
AN
EXAMPLE
OF
THE
EXPERIMENTAL
VARIABLES
AND
ITERATIONS
USED
IN
THIS
RESEARCH

This
figure
diagrams
the
spatially
explicit
control
and
two
spatial
variables
used
to
test
the
spatial

sensitivity
of
LANDIS-‐II
in
this
research.
The
control
was
iterated
using
a
series
of
different
random-‐
seed
values
in
LANDIS-‐II.
The
two
variables
were
iterated
by
creating
thirty
different
input
grids.

16

FIGURE
2–
RESEARCH
OVERVIEW

This
figure
diagrams
the
approach
used
to
test
the
spatial
sensitivity
of
LANDIS-‐II
in
this
research.

Data
was
prepared
by
projecting
and
resampling
it
to
a
10
acre
resolution.
The
data
was
then

hexagonally
tessellated
into
localities.
Next,
the
vegetation
communities
were
extracted
from
each

locality
and
filtered
to
produce
the
final
set
of
localities
suitable
for
processing.
LANDIS-‐II
scenarios

were
generated
for
each
spatial
case,
at
each
locality,
and
the
results
were
analyzed
using
the
Chi-‐
square
statistic.

17

The
hypothesis
of
this
research
is
that,
significantly
more
often
than
not,

aspatial
vegetation
trends
produced
by
LANDIS-‐II
based
on
a
spatially
explicit
input

control
parameter
(i.e.
digital
representation
of
the
real
environment)
are
similar
to

trends
generated
using
the
area-‐weighted
variable.
Further,
succession
trends

generated
using
the
equal-‐area
variable
produce
trend
results
similar
to
the
control

case
significantly
more
often
than
not,
but
less
often
than
the
area-‐weighted
case.

Each
of
these
trend
comparisons
were
assessed
at
three
different
scales
to

determine
the
effect
locality
size
has
on
each
result
(Figure
1).

Testing
the
stochasticity
of
the
LANDIS-‐II
model
involves
a
significant

amount
of
computer
resources
and
data
handling.
This
research
used
the
python

programming
language
and
numerous
site-‐packages.
The
site-‐package
for
SQLite

(SQLite3)
was
used
to
store
large
datasets
that
were
easily
queried.
The
NumPy
and

SciPy
site-‐packages
were
used
to
generate
stochastic
spatial
arrangements
and

perform
the
final
analysis.
Esri’s
ArcPy
was
used
to
load,
convert,
and
store
a
variety

of
raster
file
formats.
Finally,
the
Python
language
was
instrumental
in
the

automation
of
LANDIS-‐II
simulations.
A
simple
client-‐server
environment
for

distributing
the
computing
load
across
multiple
machines
was
developed
for
this

project
(Figure
1).
Pseudo-‐code
used
to
implement
many
of
the
more
complex
tasks

is
available
in
the
appendicies.

18

Vegetation
Community
Dataset

A
single
dataset
was
used
to
provide
the
foundation
for
the
ecological

parameters
used
in
the
spatial
sensitivity
analysis.
NatureServe’s
Ecological
Systems

of
the
United
States
(NatureServe
2012)
provides
an
ecosystem
classification
map
of

vegetation
communities
distributed
throughout
the
contiguous
United
States

(Figure
3).
The
dataset
is
well
documented
and
provides
the
list
of
dominant
species

required
to
represent
each
vegetation
community
in
LANDIS-‐II.
The
NatureServe

dataset
has
been
used
in
conjunction
with
LANDIS-‐II
in
previous
studies
on
land
fire

(Scheller
et
al.
2008;
Scheller
et
al.
2011).

FIGURE
3
-
NATURESERVE
DATASET:
ECOLOGICAL
SYSTEMS
OF
THE
UNITED
STATES

NatureServe’s
Ecological
Systems
of
the
United
States
was
used
as
the
data
source
for
this
research.
It

contains
a
complete
land
classification
of
the
contiguous
United
States
and
identifies
individual

vegetation
communities
and
constituent
vegetation
species.
This
graphic
displays
a
broad

classification
of
the
dataset.

19

The
NatureServe
dataset
was
prepared
for
further
processing
by
first

projecting
it
into
the
Albers
Equal
Area
coordinate
system
(2012a)
such
that
each

locality
contained
an
equal
number
of
raster
cells.
The
concurrent
research
project

had
a
10-‐acre
minimum
mapping
area
requirement
(personal
communication
with

Dr.
Eric
Britzke);
therefore,
the
NatureServe
raster
was
resampled
from
a
30-‐m
2

spatial
resolution,
to
a
10-‐acre
spatial
resolution
using
a
majority-‐area
approach.

The
resampling
process
reduced
the
computational
intensity
of
this
study
by

limiting
the
time
required
to
calculate
each
locality’s
vegetation
community
regime.

It
should
be
noted
that
the
10-‐acre
resampling
procedure
slightly
accentuates

dominant
landscape
communities,
which
was
acceptable
given
the
research

preference
toward
dominant
communities.

Locality
Dataset

The
NatureServe
dataset
was
tessellated
into
three
continuous
hexagonal

polygon
shapefiles,
where
each
individual
polygon
represents
a
candidate
locality

suitable
for
investigation
(e.g.,
Figure
4).

20

FIGURE
4
–
CANDIDATE
LOCALITIES
RESULTING
FROM
HEXAGONAL
TESSELLATION
OF
THE
ECOLOGICAL
SYSTEMS

OF
THE
UNITED
STATES
AT
48-KM
2

SCALE

The
Contiguous
United
States
was
hexagonally
tessellated
into
localities
(48-‐km
2

shown
here)
to

define
sets
of
interacting
ecosystems
for
each
locality.

A
simple
python
script
was
used
to
tessellate
the
NatureServe
layer
using
the

ArcPy
site-‐package
and
its
result
was
further
refined
manually
in
ArcGIS.
First,
the

script
creates
a
series
of
evenly
distributed
points
across
the
input
dataset’s
spatial

extent.
The
user
specifies
the
distance
between
each
point
along
each
axis.
In
this

research,
the
script
was
executed
three
times
using
distance
values
of
12-‐kilometers,

24-‐kilometers,
and
48-‐kilometers
respectively
to
create
three
hexagonal
grids
of

varying
scale.
For
each
set
of
points,
Thiessen
polygons
were
generated
using
each

point
as
a
Thiessen
polygon
centroid.
The
result
of
the
process
yielded
three

hexagonal
grids
that
define
candidate
localities
at
different
scales.
Localities
were

21

considered
“candidate”
because
a
series
of
vegetation
filters
had
not
yet
been

applied
to
select
only
those
localities
meeting
a
series
of
target
criteria.

Building
a
Landscape
Diversity
Database

Before
the
set
of
candidate
localities
was
filtered,
the
vegetation
community

dataset
needed
to
be
configured
in
a
rapidly
queriable
manner.
For
each
locality,
the

ArcGIS
Extract
By
Mask
tool
(2012b)
extracted
the
set
of
NatureServe
community

values
found
within
the
hexagonal
extent.
The
ArcPy
RasterToNumPyArray
(2013b)

function
converted
the
extracted
result
into
an
array
suitable
for
evaluation
using

the
NumPy
Site-‐Package
(2013a).
The
NumPy
Unique
function
operated
on
the

returned
array
to
produce
the
set
of
unique
community
values
found
in
each

candidate
locality
under
investigation.
Each
community
value
and
its
associated
cell

count
(or
area
in
10-‐acre
units)
was
inserted
into
a
SQLite
table.
If
a
locality
was
not

contained
by
the
data
extent
of
the
NatureServe
raster,
it
was
ignored.

By
using
a
SQLite
table,
filtering
landscape
classification
data
to
determine

the
final
set
of
localities
can
be
performed
through
the
use
of
SQL
queries
rather

than
slower
more
complicated
raster
based
queries.
The
use
of
a
table
also
allows

the
researcher
to
retain
a
filter
identifier
that
specifies
the
criteria
used
to
remove
a

particular
locality
from
consideration.

As
byproduct
of
the
research
approach,
by
tallying
the
number
of
unique

communities
in
each
locality,
it
was
possible
to
create
a
landscape
diversity
map

(Figure
5).

22

FIGURE
5
-
LANDSCAPE
DIVERSITY
BASED
ON
THE
ECOLOGICAL
SYSTEMS
OF
THE
UNITED
STATES
DATASET
AND

THE
CANDIDATE
LOCALITIES
AT
THE
12-KM
2

SCALE

The
number
of
unique
land
classifications
taken
from
the
NatureServe
dataset
within
each
locality

was
calculated
for
each
scale
(12-‐km
2

shown
here).
This
created
a
landscape
diversity
map
for

further
filtering
to
define
only
dominant,
upland,
natural
vegetation
communities.

Filtering
the
Dataset

Each
locality
has
its
own
set
of
vegetation
communities
that
may
be
similar

to
other
localities’
vegetation
communities,
or
may
be
a
unique
set
of
vegetation

communities
found
only
in
the
locality
itself.
The
remaining
vegetation
communities,

post-‐filter,
were
used
to
define
species
parameters
for
any
given
run
of
LANDIS-‐II

that
used
those
vegetation
communities.
In
this
research,
the
only
vegetation

communities
under
investigation
were
those
that
exhibit
dominant,
natural,
and

terrestrial
properties.
As
a
result,
many
landscape
communities
contained
in
the

23

NatureServe
dataset
were
removed;
including,
agricultural
lands,
wetlands,
barren

lands,
and
urban
areas.

The
first
filter
removed
all
landscape
communities
that
did
not
represent

natural,
terrestrial
vegetation.
Of
the
remaining
landscape
communities
defined
by

the
NatureServe
dataset,
two
were
missing
appropriate
species
information
and

were
removed.

The
second
filter
focused
on
the
composition
of
each
candidate
locality.

Recall
that
vegetation
communities
are
the
set
of
collocated
species
occurring
on
the

landscape
as
classified
by
NatureServe.
For
the
given
set
of
vegetation
communities

contained
by
a
candidate
locality,
the
total
area
of
each
individual
vegetation

community
had
to
represent
at
least
3.34%
of
the
total
locality
area.
This
minimum

area
threshold
was
determined
by
calculating
the
total
area
of
each
vegetation

community
in
a
locality,
and
dividing
it
by
the
total
area
of
that
locality,
to
determine

the
proportional
area
of
each
vegetation
community
in
each
locality.
The
set
of

proportional
areas
for
all
vegetation
communities
in
all
localities
were
binned
into

thirty
bins,
where
the
first
bin
represented
the
smallest
proportional
areas
found

across
all
localities.
Thus,
the
first
bin
represented
vegetation
communities
on
the

local
landscape
considered
to
be
non-‐dominant
(i.e.
a
vegetation
community

occupied
less
than
3.34%
of
the
locality’s
area).
By
removing
the
non-‐dominant

communities
in
each
locality,
only
vegetation
communities
that
were
considered
to

24

be
dominant
(the
targets
of
this
research)
in
those
localities
remained,
regardless
of

their
patchiness
on
the
landscape.

The
third
filter
applied
acted
to
limit
the
number
of
communities
being

evaluated.
If
a
candidate
locality
had
more
than
six
unique
vegetation
communities

remaining
after
the
first
two
filters
were
applied,
it
was
removed
from

consideration.
Conceptually,
areas
of
real-‐world
landscape
that
exhibit
more
than

six
different
dominant
vegetation
communities
at
a
given
locality
are
highly
complex

and
may
be
driven
by
ecological
drivers
other
than
vegetation
dispersion;
such
as

elevation
regime
or
soil
patterns
(personal
communication,
Dr.
Eric
Britzke).
Seven

localities
were
removed
as
a
result
of
this
maximum
threshold
filter.

Also,
since
there
must
be
more
than
one
kind
of
vegetation
community

represented
in
LANDIS
to
fuel
succession,
all
localities
containing
only
one
kind
of

community
were
removed
from
further
consideration.

The
final
threshold
applied
to
the
dataset
ensured
that
candidate
localities

exhibited
natural,
terrestrial
connectivity
and
that
the
locality
was
dominated
by

natural
systems.
Candidate
localities
were
removed
from
further
processing
if
the

collective
set
of
remaining
communities
under
investigation
occupied
less
than
60%

of
the
total
area
of
the
locality.
The
60%
threshold
was
used
based
on
the

suggestions
of
percolation
theory
(Majewski
and
Malarz
2008).
Percolation
theory
is

a
branch
of
statistical
physics
that
explains
the
probability
of
connectivity
in
a
lattice.

25

The
theory
defines
a
set
of
percolation
thresholds,
that
when
met,
predict
the

existence
of
a
single
path
between
one
side
of
a
lattice
and
its
opposing
side,
passing

only
through
cells
of
the
same
value;
in
this
case,
cells
occupied
by
natural

vegetation.

The
final
set
of
localities
used
in
this
research
were
concentrated
in
New

England,
the
Appalachian
Mountains,
scattered
areas
in
the
Midwest,
and
much
of

the
public
land-‐dominated
regions
of
the
Intermountain
West,
and
open
spaces
of

the
West
Coast.
Areas
not
included
were
the
large
expanses
of
agriculture
and

silvicuture
in
the
Midwest
and
Southeast,
and
the
large
wetland
ecosystems
of
the

Gulf
Coastal
Plain
and
Florida
(Figure
6).

26

FIGURE
6
–
THE
LOCALITIES
CONTAINING
SETS
OF
VEGETATION
COMMUNITIES
USED
TO
UNDERSTAND
THE

SPATIAL
SENSITIVITY
OF
LANDIS-II

After
the
set
of
filters
was
applied
to
each
locality
scale,
the
remaining
localities
were
determined
to

be
acceptable
for
analysis.
The
brightest
green
areas
shown
on
this
map
are
regions
that
were

processed
for
all
scales
considered.
Lesser
green
shaded
regions
were
only
partially
processed
at

different
scales.

Generating
Ecological
Parameters
for
LANDIS-II

The
NatureServe
documentation
(2012c)
provides
a
list
of
species
that
are

considered
dominant
players
within
each
ecological
community
found
on
the

NatureServe
raster
(NatureServe
2012).
The
concurrent
research
provided
an
un-‐
published
version
of
generic
species
attributes
suitable
for
LANDIS-‐II
using
a

combination
of
expert
judgment
and
literature
review
(Beane,
Whitby,
and
Britzke

2013).
LANDIS-‐II’s
species
attributes
are
defined
using
the
species
text-‐file
input

27

parameter
and
govern
each
species’
behavior
at
runtime
(Scheller
and
Domingo

2011).

LANDIS-‐II’s
initial
communities
input
layer
is
a
raster
file
(e.g.
*.img,
*.gis)

that
defines
the
spatial
arrangement
and
distribution
of
vegetation
communities

(Scheller
and
Domingo
2011).
Each
cell
of
the
initial
communities
input
raster
may

contain
multiple
species
of
varying
ages
based
on
the
parameters
found
in
the
initial

communities
text
file.
In
this
research,
these
communities
were
identified
for

localities
within
the
contiguous
United
States;
where
each
locality
exhibited
a
given

set
of
vegetation
communities.
While
the
generation
of
initial
community
input

layers
is
discussed
in
a
latter
section,
its
associated
map-‐codes
are
discussed
here.

Vegetation
communities
in
natural
systems
are
composed
of
species
at

different
stages
of
their
lifecycles
(Watt
1947).
To
capture
age
diversity
in
the
real

landscape,
vegetation
communities
were
parsed
into
different
map-‐codes
by
the

researcher
to
allow
species
age
variability
to
be
appropriately
modeled
in
LANDIS-‐II.

For
each
vegetation
community,
a
set
of
twelve
map-‐codes
was
assigned
with

different
age
distributions
to
better
represent
the
range
of
vegetation
community

age
structures
found
on
the
landscape.
The
age
distributions
were
based
on
the

longevity
of
each
constituent
species.
Each
map-‐code
represents
an
equal

proportion
of
the
area
each
vegetation
community
represents
in
a
given
spatial

variable
or
control.
The
use
of
a
longevity-‐based
metric
was
chosen
over
a
sexual-‐

28

maturity
based
metric
because
the
forestry
profession
has
a
better
understanding
of

a
given
species
longevity
over
a
species’
sexual
maturity.

The
distribution
of
input
species
age
was
set
at
80%,
50%,
30%,
and
10%
of

each
species’
longevity.
In
LANDIS-‐II,
species
begin
to
die
after
their
age
was
greater

than
80%
of
that
species’
longevity.
This
age
class
was
used
to
represent
vegetation

communities
at
the
end
of
their
lifecycles.
The
50%
and
30%
of
longevity
age
classes

were
used
to
represent
two
different
mid-‐growth
stages.
The
10%
of
longevity
age

class
was
used
to
represent
a
community
early
in
its
lifecycle.

In
the
first
four,
out
of
twelve,
map-‐codes,
species
ages
were
assigned
as
80%,

50%,
30%,
or
10%
of
each
species’
longevity
to
create
four
homogenously
aged

cohorts.
The
next
four
map-‐codes
assigned
sets
of
age
classes
to
each
species
to

create
map-‐codes
with
mixed
ages.
The
sets
were:
80%
and
50%;
80%
and
30%;

10%
and
30%;
and
80%,
50%,
30%,
and
10%.
The
remaining
four
map-‐codes

randomly
assigned
species
ages,
or
sets
of
ages,
taken
from
the
first
eight
map-‐codes.

Map-‐code
generation
was
repeated
for
each
vegetation
community
at
each
locality

under
investigation.
Multiple
species
with
varying
ages
can
occur
in
each
cell
of
the

raster
used
to
represent
a
spatial
variable
or
the
experimental
control
to
comprise
a

vegetation
community.

LANDIS-‐II
uses
establishment
probabilities
to
determine
the
likelihood
that
a

particular
species
will
establish
itself
in
a
new
location
after
dispersal
(Scheller
and

29

Domingo
2011).
Often
these
values
are
optimized
for
extremely
site-‐specific
studies

using
the
ecological
parameter
optimization
process
discussed
earlier
to
take
into

account
soil
and
climatic
conditions.
Because
this
research
tested
LANDIS-‐II’s
spatial

sensitivity
at
thousands
of
different
sites,
all
establishment
probabilities
were
set
to

0.6
(on
a
0
to
1.0
scale).
This
ensured
all
species
are
more
likely
than
not
to
establish

themselves
at
new
locations
and
that
succession
was
more
likely
than
not
to
occur.

Further,
by
fixing
the
establishment
probability
for
all
species,
at
all
localities,
allows

for
a
clearer
picture
of
the
spatial
sensitivity
of
the
model
to
be
produced.

The
LANDIS-‐II
ecoregion
layer
parameter
allows
the
user
to
define
different

sets
of
establishment
probabilities
for
different
locations
on
the
initial
communities

input
layer.
It
also
allows
certain
areas
of
the
map
to
be
considered
inactive
in
the

model
(Scheller
and
Domingo
2011).
For
the
purposes
of
this
research,
areas
of
the

initial
communities
layer
containing
vegetation
communities
under
investigation

were
part
of
the
“alive”
region.
Areas
of
the
initial
communities
layer
containing

land
classification
values
not
under
investigation
(those
areas
removed
by
the
filter)

were
considered
part
of
the
“dead”
region.
The
“dead”
region
was
set
to
be
inactive

in
the
model.
Once
again,
to
simplify
the
ecological
parameters
and
focus
on
the

spatial
sensitivity
of
LANDIS-‐II
the
ecoregion
parameter
was
effectively
rendered

homogenous
for
each
locality
regardless
of
soil
and
microclimate.

The
final
ecological
parameter
defined
by
this
research
was
each
species’

reclassification
coefficient.
Reclassification
coefficients
allow
LANDIS-‐II
to

30

determine
which
vegetation
community
a
given
cell
should
belong
to
on
the
initial

communities
layer,
based
on
the
set
of
species
occurring
at
that
location.
In
this

research
the
succession
trajectory
of
vegetation
communities
and
not
species
was

assessed.
In
LANDIS-‐II
vegetation
communities
are
represented
by
their
constituent

species,
therefore,
vegetation
communities
must
be
parameterized
as
a
collection
of

species
in
LANDIS-‐II.
After
the
model
disperses
each
vegetation
community’s

constituent
species,
its
initial
community
layer
must
be
reclassified
to
determine
the

new
locations
and
areas
where
each
vegetation
community
resides.
If
all
species
are

given
equivalent
reclassification
values
for
each
community,
then
communities
have

an
equal
chance
of
being
assigned
to
a
cell
if
those
communities
happen
to
contain

the
same
species,
and
a
species
generally
used
for
community
discrimination
is
not

present
(Scheller
and
Domingo
2011).
All
reclassification
values
for
this
study
were

equal
in
value
(set
to
0.5
on
a
0
to
1.0
scale).

LANDIS-‐II’s
reclassification
calculation
also
considers
species
age
as
a

proportion
of
its
longevity.
Older
species
on
the
landscape
are
given
higher

reclassification
values
in
LANDIS-‐II
by
default.
By
structuring
the
parameter
as

described
above,
a
vegetation
community
must
complete
its
ecological
succession

before
it
is
reclassified
to
a
new
community.

Extracting
Spatially
Explicit
Rasters

The
spatially
explicit
rasters
required
for
the
experimental
control
were

extracted
using
a
python
script
that
iteratively
selected
a
given
locality
hexagon,

31

extracted
values
from
the
NatureServe
dataset
using
the
Extract
By
Mask
tool
and

classified
the
resulting
layer
using
the
NumPy
site-‐package.
The
classification

scheme
used
divides
each
vegetation
community
area
into
twelve
zones,
one
for

each
map-‐code,
to
represent
the
age
mixes
of
each
species
in
the
vegetation

community
in
LANDIS-‐II.
The
map-‐code
values
were
recycled
between
runs

representing
different
localities
with
different
sets
of
vegetation
communities.

Regions
of
the
grid
that
were
missing
vegetation
community
values,
or
exhibited

community
values
that
were
filtered
out,
were
given
a
value
of
zero
and
defined
as

inactive
areas
using
the
ecoregion
parameter
layer
in
LANDIS-‐II.
The
spatially

explicit
layer
was
processed
in
LANDIS-‐II
using
different
random-‐seed
values
for

each
run
to
capture
the
spatial
variation
of
model
results.
Every
extracted
raster

was
stored
in
its
own
uniquely
named
folder.

Generating
Random
Rasters

The
area-‐weighted
spatial
variable
maintains
the
proportion
of
area
each

ecological
community
represents
in
a
locality.
The
ecological
community

composition
was
extracted
from
the
SQLite
database
created
during
the
initial
phase

of
this
research.
The
spatial
arrangement
was
generated
randomly
using
the
NumPy

Random
Choice
function
of
the
NumPy
site-‐package.
The
total
number
of
cells
on
the

input
raster
was
equivalent
to
the
number
of
cells
contained
in
the
total
area
of
a

given
locality.
Thirty
different
area-‐weighted
spatial
scenarios
were
generated
for

each
locality
to
provide
a
range
of
inputs
into
the
model.

32

The
equal-‐area
variable
represents
equal
areas
of
vegetation
communities
in

a
locality
with
random
spatial
arrangement.
This
dataset
was
generated
in
a
similar

fashion
to
the
area-‐weighted
rasters;
the
exception
being,
post-‐filter
vegetation

communities
were
given
an
equivalent
amount
of
area
on
the
generated
raster.

Thirty
equal-‐area
spatial
scenarios
were
generated
for
each
locality
as
well.
Every

random
grid
generated
was
stored
in
its
own
uniquely
named
folder.

Building
LANDIS-II
Input
Text-Files

LANDIS-‐II
is
operated
using
a
series
of
text-‐files.
The
LANDIS-‐II
text-‐files

used
as
input
and
parameter
files
were
generated
for
each
uniquely
named
folder

containing
an
input
raster
(Table
1).
These
text-‐files
were
generated
using
object-‐
oriented
python
code
that
represented
each
text-‐file
as
a
different
method
within
a

LandisInput
class.
The
class
parsed
a
dictionary
of
model
variables
for
each
input

file
passed
to
the
script
as
input
arguments.
Then
a
Create
method
was
called
that

generated
all
of
the
input
text-‐files
and
saved
each
set
of
text-‐files
to
its
associated

uniquely
named
folder,
containing
its
initial
communities
input
raster.

An
ecoregion
raster
was
generated
for
each
initial
communities
raster
by

assigning
a
value
of
one
to
each
cell
that
was
not
equal
to
zero.
Each
initial

communities
raster
file
was
read-‐in
using
the
ArcPy
site-‐package.
It
was
then

converted
to
a
NumPy
array
for
further
processing.
Once
the
array
was
classified
as

one
or
zero
it
was
saved
as
a
different
filename.
This
created
the
spatial
parameter

33

that
defined
the
active
or
inactive
state
of
certain
areas
in
the
model
(i.e.
the

ecoregion
parameter
layer).

The
model
scenario
was
further
established
such
that
the
time-‐step
for

succession
in
the
model
occurred
every
3-‐years.
The
temporal
duration
of
the

scenario
was
set
to
80-‐years
to
match
the
time
horizon
of
the
concurrent
research

project.
The
Age
Reclass
Output
Extension
time-‐step
was
set
to
40-‐years
such
that

the
model
output
initial-‐state,
mid-‐state,
and
end-‐state
output.

Executing
LANDIS-II

The
large
number
of
LANDIS-‐II
runs
required
development
of
simple
server

and
client
scripts
in
python
to
distribute
the
processing
load
across
multiple

computers.
First,
all
of
the
folders
containing
LANDIS-‐II
input
files
were
copied
to
a

network
drive
that
all
computers
had
access
to.
Because
each
folder
represents
a

different
run
of
LANDIS-‐II,
the
server
script
built
the
list
of
required
LANDIS-‐II
runs

by
populating
a
list
of
folders
on
the
network
file-‐share.
Next,
the
server
script

extended
python’s
SocketServer
site-‐package
and
overrode
the
handle
method
to

handle
each
request
made
to
the
server.
When
a
client
computer
signaled
it
was

ready
to
process
a
LANDIS-‐II
run,
the
server
sent
a
filename
of
a
given
folder
on
the

network
share.
The
client
copied
the
folder
to
the
local
machine,
executed
the

LANDIS-‐II
run
and
copied
the
results
back
to
the
network
file-‐share.

The
client
was
also
able
to
execute
multiple
runs
of
LANDIS-‐II
simultaneously

by
using
python’s
multiprocessing
site-‐package.
A
pool
of
workers
was
defined
such

34

that
each
worker
downloaded
a
LANDIS-‐II
run
and
executed
it
in
a
sub-‐process.
This

allowed
the
client
to
take
advantage
of
the
multi-‐core
processors
found
on
each

computer.
For
any
given
scenario
of
the
LANDIS-‐II
model,
the
average
execution

time
was
approximately
4
seconds.
The
processing
of
all
runs
took
nearly
200
hours

on
eleven
different
machines.

The
server
and
client
code
is
shown
in
the
Appendicies
A
and
B.

Developing
Vegetation
Trends

The
spatially
explicit
control
case
was
represented
as
a
hexagon
due
to
the

tessellation
method
used.
The
spatial
variables
were
represented
as
square
rasters

to
reduce
computational
complexity
during
variable
generation.
The
shape
of
the

spatial
variables
is
considered
irrelevant
because
each
was
constructed
randomly

based
on
a
proportional
representation
of
ecological
communities.
As
an
example,

consider
a
locality
occupied
by
two
habitats;
Mediterranean
California
Lower

Montane
Black
Oak-‐Conifer
Forest
and
Woodland,
and
North
Pacific
Dry
Douglas-‐fir-‐
(Madrone)
Forest
and
Woodland
(Figure
7).
This
research
demonstrated
a
slight

increase
in
the
Mediterranean
California
Lower
Montane
Black
Oak-‐Conifer
Forest

and
Woodland
habitat
in
each
spatial
variable.
By
examining
the
proportional

representation
of
landscape
succession
trends
in
each
spatial
variable
and

comparing
it
to
the
proportional
representation
of
trends
in
the
spatial
control,
it
is

possible
to
demonstrate
that
the
trends
are
similar.

35

FIGURE
7
–
AN
EXAMPLE
OF
THE
THREE
DIFFERENT
SPATIAL
REPRESENTATIONS
USED
IN
THIS
EXPERIMENT
AND

THEIR
ASSOCIATED
SUCCESSION
AND
OUTPUT

The
type
of
succession
occurring
between
the
initial
and
final
time
steps
of
the
area-‐weighted
and

equal-‐area
variables
is
compared
to
the
succession
occurring
in
the
spatially
explicit
control.
Note

that
the
actual
analysis
used
an
aggregation
of
grids
at
each
locality
to
improve
the
robustness
of
the

analysis.
In
this
example,
Mediterranean
California
Lower
Montane
Black
Oak-‐Conifer
Forest
and

Woodland
is
shown
to
transgress
upon
habitat
previously
defined
as
North
Pacific
Dry
Douglas-‐fir-‐
(Madrone)
Forest
and
Woodland.
This
succession
trajectory
occurs
in
all
spatial
cases.
The
scale

shown
here
is
12-‐km
2
.

LANDIS-‐II
outputs
raster
results
for
its
initialization
(year
0)
and
end-‐state

(year
80)
through
the
Age
Reclass
Output
Extension.
These
outputs
were
classified

by
their
ecological
community
values.
This
means
that
the
twelve
map-‐codes

defined
to
generate
different
age
cohorts
and
species
mixes
for
a
particular

vegetation
community
were
assigned
the
same
value,
because
they
belong
to
the

same
community.
The
value
each
community
was
assigned
to
was
based
on
the

order
it
occured
in
the
reclass
text-‐file.
Because
the
community
values
for
the

initialization-‐state
output
and
the
end-‐state
output
were
classified
by
LANDIS-‐II

36

using
the
same
method,
the
comparison
between
the
two
layers
produced
the

switching
trend
for
each
LANDIS-‐II
run.

Because
the
maximum
number
of
communities
that
could
occur
on
an
output

raster
is
six
due
to
the
initial
filtering
procedure,
the
values
on
the
output
raster

were
always
less
than
or
equal
to
six.
The
initialization-‐state
raster
was
multiplied

by
ten
and
added
to
the
end-‐state
raster.
A
python
script
cast
each
raster
to
a

NumPy
array
to
complete
this
process.

The
result
produced
an
array
of
values,
where
the
first
digit
of
each
value

represents
the
initial
state
and
the
second
digit
of
each
value
represents
the
final

state.
Values
that
are
zero
represent
inactive
areas
of
the
grid.
Values
that
are

cleanly
divisible
by
ten
(e.g.,
10,
20,
30)
represent
areas
where
all
species

experienced
a
die-‐off,
and
succession
has
yet
to
occur.
This
comparison
was

completed
for
every
set
of
LANDIS-‐II
output.
In
these
experiments,
ecological

disturbances
were
not
modeled.
Isolated
incidences
of
a
few
cells
experiencing
a

die-‐off
due
to
a
species
reaching
its
maximum
age
may
occur;
but
in
reality,
discrete

ecological
transitions
are
rarely
seen
in
undisturbed
environments
and
were
an

artifact
of
the
model’s
representation
of
ecological
processes.

The
result
of
each
comparison
was
compiled
in
a
SQLite
table.
The

comparison
table
used
scale,
locality,
run-‐type,
and
iteration
fields
to
uniquely

describe
each
run.
Values
for
the
scale
column
(i.e.,
12,
24,
and
48)
were
associated

37

to
the
spatial
extent
of
each
model
run.
The
locality
column
stored
the
feature

identifier
of
the
associated
initial
input
locality.
The
run-‐type
field
described

whether
or
not
the
run
was
spatially
explicit,
area-‐weighted,
or
equal-‐area.
The

iteration
column
held
a
value
that
noted
which
iteration
the
run
represented
(i.e.
1

through
30).
The
table
also
included
a
column
for
the
initial
vegetation
community

values,
final
vegetation
community
values,
and
the
area
of
each
change
between
an

initial
and
final
vegetation
community
pair.
These
changes
represent
the
landscape

succession.

By
storing
the
comparison
data
in
a
SQLite
table,
it
is
possible
to
perform

rapid
queries
for
each
unique
set
of
runs.
Each
experimental
variable
and
the

control
were
comprised
of
thirty
individual
runs
to
form
an
aggregate
assessment
of

vegetation
trends.
Aggregates
were
made
for
each
combination
of
scale,
locality,
and

run-‐type.
To
generate
the
aggregate
vegetation
community
succession
trend,
each

succession
trend’s
area
was
summed
for
all
thirty
runs
and
stored
in
an
aggregation

table;
such
that,
the
original
and
final
fields
in
the
aggregation
table
represented
the

total
number
of
cells
transitioning
from
the
initial
vegetation
community
to
the
final

vegetation
community
across
all
thirty
iterations.
An
analysis
of
these
trends

yielded
the
evidence
necessary
to
partially
accept
and
reject
the
research

hypotheses.

38

Statistical
Testing

Through
the
use
of
the
SQLite
and
SciPy
python
site-‐packages
it
was
possible

to
perform
a
Chi-‐square
analysis
at
each
locality
using
the
experimental
control
as

the
expected
value
and
each
experimental
variable
as
separate
observed
cases.
The

SQLite
table
containing
the
aggregated
values
of
vegetation
community
trends
for

each
locality
supplied
the
input
data
for
the
Chi-‐square
analyses.

Three
categories
of
Chi-‐square
analysis
were
used
to
compare
the

experimental
control
to
the
experimental
variables.
The
first
analysis
focused
on
the

succession
trajectory
of
the
landscape
by
assessing
each
trend
as
a
proportion
of
its

initial
starting
area.
The
second
Chi-‐square
analysis
considered
the
succession

trajectory
of
each
trend
as
a
proportion
of
the
total
landscape
area.
The
final
Chi-‐
square
analysis
evaluated
the
model
end-‐states
for
each
trend
to
determine
the

overall
sensitivity
of
the
model
using
the
end-‐state
proportion
of
each
vegetation

community
out
of
the
total
area.

By
comparing
proportions
instead
of
actual
cell
counts
it
was
possible
to

ignore
inactive
areas
in
the
spatially
explicit
experimental
control
and
focus
only
on

the
aspect
of
the
landscape
that
was
of
interest.

For
the
first
Chi-‐square
analysis
at
a
given
locality,
the
degrees
of
freedom

were
defined
as
the
total
number
of
succession
trends
occurring
across
all
spatial

cases
(spatially
explicit,
area-‐weighted,
equal-‐area)
at
a
particular
scale,
minus
one.

Next,
the
total
area
of
the
input
vegetation
community
at
its
initial
state
divided
the

39

area
represented
by
each
trend.
The
trends
generated
using
spatially
explicit
input

were
compared
to
the
trends
produced
in
the
area-‐weighted
variable,
and

separately
the
equal-‐area
variable
using
the
Chi-‐square
formula
(Figure
8).
This

analysis
was
carried
out
by
querying
the
SQLite
table
of
aggregated
data
in
Python,

calculating
the
degrees
of
freedom
and
the
Chi-‐square
statistic,
and
using
SciPy
to

determine
each
statistic’s
associated
alpha
value.
The
results
of
the
comparisons

were
stored
in
a
SQLite
table
and
represented
the
trajectory
of
landscape
change
as

a
proportion
of
each
vegetation
community’s
initial
state.

FIGURE
8
-
CHI-SQUARE
EQUATION

The
Chi-‐square
equation
was
used
to
determine
the
trends
produced
when
the
experimental
control

(i.e.
spatially
explicit
case)
was
compared
to
the
two
experimental
variables;
area-‐weighted
and

equal-‐area.

The
second
analysis
was
similar
to
the
first,
except
that
instead
of
calculating

the
initial
area
proportions
as
a
percentage
of
each
vegetation
community’s
initial

state,
the
calculation
represents
the
area
proportion
of
the
succession
trend
to
the

total
area
of
the
active
grid.
The
degrees
of
freedom
were
still
defined
by
the

number
of
succession
trends
across
all
runs
at
a
given
locality.
The
results
of
this

analysis
were
stored
in
a
separate
SQLite
table
and
represented
the
trajectory
of

succession
of
each
vegetation
community
as
a
proportion
of
the
total
area
of
the
grid.

The
final
analysis
compared
the
experimental
control
and
variables
at
the

output
end-‐state
to
determine
the
amount
of
equifinality
that
occurred
in
the
results.

40

The
aggregated
data
for
each
locality
was
extracted
from
the
SQLite
table.
The

proportion
each
vegetation
community
represented
as
a
ratio
to
the
total
active
area

of
the
grid
at
the
model’s
end-‐state
was
calculated.
This
calculation
was
made
by

summing
the
areas
of
each
vegetation
community
using
the
SQL
SUM
function
and

the
GROUP
BY
aggregator;
these
sums
were
further
divided
by
the
total
area
of
the

active
grid.
The
degrees
of
freedom
were
defined
by
the
total
number
of
unique

vegetation
communities
occurring
at
the
end-‐state
minus
one.
Next,
the
Chi-‐square

statistic
was
calculated
between
the
spatially
explicit
experimental
control
and
each

variable
and
the
result
was
stored
in
a
new
SQLite
table.

The
python
pseudocode
used
to
implement
these
analyses
may
be
found
in

Appendix
C.

41

Chapter
3:
Results

Recall
that
the
first
test
used
the
Chi-‐square
statistic
to
determine
the

similarity
between
the
spatially
explicit
case
and
the
two
spatial
variables

individually.
The
analysis
focused
on
the
succession
trajectories
as
a
proportion
of

each
vegetation
community’s
initial
area.
This
analysis
was
completed
at
every

locality
under
investigation
at
each
scale.
At
the
95%
confidence
level,
there
is
less

than
1%
difference
between
the
comparisons
of
each
spatial
variable
to
the
spatial

control
at
any
given
scale;
but,
there
is
approximately
a
10%
difference
between
the

results
at
each
scale.
The
results
also
indicate
that
a
dataset
containing
random

spatial
arrangements
and
percentage-‐area
compositions
can
substitute
for
spatially

explicit
data
between
40%
and
60%,
or
on
average
half,
of
the
time.
The
full
range
of

confidence
levels
for
the
chi-‐square
analysis
was
calculated
due
to
the
requirements

of
the
concurrent
research.
The
full
range
is
shown
here
to
indicate
a
slightly

decreasing
number
of
runs
considered
to
be
different
from
the
control
at
increasing

levels
of
confidence
(Figure
9).

42

FIGURE
9
-
SUCCESSION
TRAJECTORY
BASED
ON
INITIAL
AREA
OF
A
VEGETATION
COMMUNITY

This
graph
displays
the
result
of
the
succession
trajectory
analysis
based
on
the
proportion
of
initial

community
area
to
the
total
area.
It
is
the
result
of
the
Chi-‐square
analysis
calculated
for
a
range
of

confidence
values
(alpha).
As
confidence
increases,
the
number
of
localities
that
have
experimental

variables
that
are
significantly
different
from
the
experimental
control
decreases.

The
second
test
used
the
Chi-‐square
statistic
to
determine
the
similarity

between
the
experimental
control
and
both
experimental
variables
based
on
the

proportion
of
each
succession
trend
to
the
total
active
area
in
the
model.
This
test

was
also
used
at
each
scale
for
every
locality.
This
analysis,
as
expected,
yields

similar
succession
trajectory
results
as
those
shown
in
the
first
analysis
(Figure
9).

By
assessing
succession
trajectory
as
a
proportion
of
the
total
area,
LANDIS-‐II
is

shown
to
be
even
less
sensitive
to
spatial
arrangement
and
percentage-‐area
spatial

composition
at
every
confidence
level
(Figure
10).

43

FIGURE
10
-
SUCCESSION
TRAJECTORY
BASED
ON
THE
TOTAL
AREA
OF
A
VEGETATION
COMMUNITY

This
graph
displays
the
result
of
the
succession
trajectory
analysis
based
on
the
total
area.
It
is
the

result
of
the
Chi-‐square
analysis
being
calculated
for
a
range
of
confidence
values
(alpha).
As

confidence
increases,
the
number
of
localities
that
have
experimental
variables
that
are
significantly

different
from
the
experimental
control
decreases.

Finally,
the
third
test
used
the
Chi-‐square
statistic
to
determine
the
similarity

between
the
end-‐states
of
the
experimental
control
and
experimental
variables.
At

the
95%
confidence
level
it
is
shown
that
the
model
is
extremely
insensitive
to

spatial
arrangement
and
percentage-‐area
composition
over
80%
of
the
time.

Furthermore,
although
differences
in
succession
trajectory
were
shown
between

scales
(Figures
8
&
9),
at
the
95%
confidence
level
there
is
less
than
5%
difference

between
model
end-‐states
across
the
three
scales
evaluated
in
this
study.
At
the

99%
confidence
level
there
is
even
less
difference,
4%,
between
spatial
cases

(Figure
11).

44

FIGURE
11
-
END-STATE
ANALYSIS
COMPARING
MODEL
RUNS

This
graph
displays
the
result
of
the
end-‐state
analysis,
which
is
a
comparison
between
the

proportions
of
each
community
at
the
80-‐year
spatially
explicit
output
and
each
experimental

variable.
It
is
the
result
of
the
Chi-‐square
analysis
being
calculated
for
a
range
of
confidence
values

(alpha).
This
graph
shows
a
high
confidence
that
a
small
percentage
(e.g.
<20%)
of
localities
exhibit

differences
between
the
experimental
control
and
each
variable.

45

Chapter
4:
Discussion
and
Conclusion

Discussion

A
review
of
the
literature
on
the
LANDIS-‐II
model’s
use
and
application

suggests
that
the
spatial
sensitivity
of
the
model
has
largely
been
untested.
Although

the
current
research
does
not
test
every
possible
avenue
of
spatial
and
ecological

parameterization
of
the
LANDIS-‐II
model,
the
spatial
sensitivity
of
the
model’s

fundamental
spatial
function
(i.e.
dispersion)
has
been
assessed
for
a
range
of

spatial
and
ecological
settings
to
understand
the
processes
acting
within
the
model’s

proprietary
core.
The
results
suggest
that
LANDIS-‐II
is
a
spatially
insensitive
model

for
determining
vegetation
succession
trends.
While
the
model
does
produce
a

spatial
output
layer,
the
developer
and
user
communities
both
consider
it
to
be
an

imaginary
representation
of
reality,
rather
than
an
accurate
prediction
of
a
future

end-‐state
(Mladenoff
and
He
1999).

The
results
do
have
two
important
caveats.
On
further
review
of
the

underlying
LANDIS-‐II
runs
where
the
Chi-‐square
statistic
returned
a
value
of
zero,
it

appears
that
localities
exhibiting
only
grass
communities
experience
a
complete
die-‐
off
in
the
model.
Although
not
scientifically
sound,
it
occurs
in
all
spatial
cases.
By

slightly
adjusting
the
grass
species
parameters
to
have
maximum
dispersion

distances
greater
than
half
the
cell-‐size
(i.e.
>100m)
dispersion
occurs
and
species

die-‐off
no
longer
happens.
Also,
due
to
longevity
values
less
than
80
years
(the
time

horizon
of
this
analysis)
it
appears
that
the
grass
longevity
parameter
does
not

46

allow
the
grass
species
to
survive
in
an
undisturbed
environment
(one
of
the

assumptions
in
this
study).
While
this
caveat
points
to
a
flaw
in
the
generic
species

attributes
used
to
model
grass
species
in
this
research,
since
the
same
response

occurs
for
all
spatial
cases,
the
model
can
be
shown
to
be
spatially
insensitive
in

these
instances.
As
such,
the
result
is
still
valuable
to
this
analysis.

The
second
caveat
is
the
special
case
that
occurs
when
the
expected
area
of
a

succession
trend
is
zero
and
the
observed
succession
trend
area
is
greater
than
zero.

This
special
case
was
handled
by
adding
a
value
of
one
to
the
expected
and
observed

values
when
performing
the
Chi-‐square
evaluation.
The
squared
difference
between

the
adjusted-‐expected
and
adjusted-‐observed
value
in
the
Chi-‐square
statistic
was

divided
by
the
adjusted-‐expected
value
(one).
This
simplified
the
formula
to
be
the

square
of
the
original
observed
value.
This
case
“explodes”
the
Chi-‐square
results

and
inflated
the
perceived
differences
between
the
spatial
control
and
each
spatial

variable.
Thus,
differences
shown
in
the
results
are
artificially
inflated
as
a
direct

result
of
the
analytical
mechanism
used
(i.e.
the
Chi-‐square
statistic)
and
model

output
is
more
similar
than
these
results
suggest.
The
Chi-‐square
statistic
was

chosen
based
on
its
low
computational
intensity
and
its
ability
to
compare
sets
of

categories.
Although
the
use
of
Chi-‐square
is
shown
to
affect
the
results,
this
is

acceptable
because
the
elimination
of
the
inflated
values
would
only
serve
to

strengthen
trends
produced.

47

The
results
of
this
study
indicate
that
succession
trajectories
between
the

experimental
control
and
both
variables
are
likely
to
increase
in
difference
as
scale

increases.
This
is
consistent
with
expectation
because
dispersion
distance

parameters
for
any
given
species
cover
a
larger
proportion
of
the
small
12-‐km
2

grid

than
the
larger
24-‐km
2

grid.
Further,
the
differences
in
succession
trajectory
are

directly
related
to
scale
as
a
proportion
of
the
total
active
area,
and
as
a
proportion

of
the
initial
area
of
each
vegetation
community.

Although
the
succession
trends
seem
to
indicate
reduced
similarity
as
scale

increases,
the
end-‐state
analysis
suggests
that
the
end-‐states
are
very
similar

regardless
of
how
the
underlying
changes
are
occurring.
This
would
suggest
that

there
is
some
degree
of
equifinality
occurring
in
the
model.
The
differences
between

the
area-‐weighted
results
and
the
equal-‐area
results
are
very
small,
less
than
1%
at

the
99%
confidence
level
for
differences
between
runs.
This
end-‐state
metric
is

considered
to
be
more
important
because
the
proportion
of
vegetation
communities

occurring
at
the
end-‐state
condition
is
typically
used
to
document
succession
trends.

In
acknowledging
the
research
results,
it
appears
that
spatial
arrangement

and
percentage-‐area
composition
are
not
a
requirement
of
the
successful
use
of

LANDIS-‐II
approximately
80%
of
the
time
at
the
95%
confidence
level,
provided
the

ecological
communities
are
known.
These
results
represent
a
conservative
estimate,

because
of
the
artificial
inflation
of
the
Chi-‐square
statistic
discussed
earlier.
Stated

differently,
the
Chi-‐square
null
hypothesis
that
the
experimental
control
is
the
same

48

as
an
experimental
variable
was
rejected
roughly
20%
of
the
time
with
95%

confidence.

The
size
of
a
given
study
area,
however,
is
directly
related
to
the
method
of

succession
trajectory
the
vegetation
communities
undergo.
The
results
of
the
first

two
analyses
(Figures
8
&
9)
demonstrate
that
as
processing
area
increases,
the

difference
between
succession
trajectories
in
the
experimental
variables
and
the

spatial
control
increase
as
well.
Therefore,
as
the
size
of
a
study
area
increases,

succession
may
occur
differently
at
different
scales
but
the
final
end-‐state
results

will
be
similar.
Conclusion
This
research
assessed
the
spatial
sensitivity
of
the
LANDIS-‐II
model
to

spatial
arrangement
and
spatial
composition
in
homogenous
spatial
settings
(the

LANDIS-‐II
basic
assumptions).
No
effort
was
taken
to
capture
microclimate,
solar

angle,
elevation,
or
soils
using
variable
establishment
probabilities
and
ecoregions

to
ensure
all
ecological
parameters
in
the
model
remain
fixed.
The
research

approach
used
the
aggregate
of
thirty
runs
for
the
experimental
control
and
each

experimental
variable.
Further,
thousands
of
different
localities
were
assessed
with

different
generically
parameterized
dominant,
upland
vegetation
communities.

Although
the
results
of
this
research
point
to
caveats
in
the
generalization
of

ecological
parameters,
to
understand
the
spatial
sensitivity
of
the
model
in
a

simplified
environment
optimum
ecological
parameters
were
not
needed.

49

The
first
hypothesis
of
this
research
states
that
aspatial
end-‐state
vegetation

community
succession
trends
based
on
spatially
explicit
parameters
are
similar
to

results
produced
by
parameters
that
maintain
ecological
composition
but
possess

random
arrangement.
Given
the
result
of
the
end-‐state
Chi-‐square
analysis,
this

hypothesis
may
be
accepted.
The
second
hypothesis
of
this
research
states
that

aspatial
end-‐state
vegetation
community
succession
trends
based
on
spatially

explicit
parameters
are
similar
to
results
produced
by
parameters
that
do
not

maintain
ecological
composition
or
arrangement,
but
exhibit
less
comparison
than

the
area-‐weighted
case.
The
second
hypothesis
is
accepted
and
rejected
in
part.

The
equal-‐area
variable
did
produce
end-‐state
results
similar
to
that
of
the

spatially
explicit
control
and
in
this
sense
the
second
hypothesis
is
accepted
in
part.

The
equal-‐area
variable,
however,
was
not
shown
definitively
to
be
more
similar
to

the
control
case
than
the
area-‐weighted
variable,
therefore
the
second
hypothesis
is

rejected
in
part.

In
conclusion,
this
research
suggests
that
the
spatial
composition
and

arrangement
of
an
input
layer
into
the
LANDIS-‐II
model
may
not
be
as
important
as

originally
thought.
These
results
suggest
that
LANDIS-‐II
could
be
used
to
model

areas
where
spatially
explicit
information
is
poorly
known,
or
in
cases
where

producing
spatially
explicit
information
is
cost
prohibitive.
It
is
suggested
that

future
LANDIS-‐II
studies
assess
the
spatial
sensitivity
of
their
results
when
using

less
generic
ecological
parameters.
Future
spatial
tests
of
LANDIS-‐II
could
also
be

50

done
to
determine
the
effects
of
spatial
arrangement
and
composition
when

microclimate
or
soils
are
defined
by
ecoregions
and
variable
establishment

probabilities
are
used
in
the
model.
Finally,
successive
studies
may
also
see
value
in

assessing
spatial
sensitivity
for
longer
time
durations
and
different
scales
than
used

in
this
research.

51

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Copyright
2013

Austin
V.
Davis

Appendix
A:
Pseudocode
for
LANDIS-‐II
Scenario
Server

# load modules
import os, sys, ast, time, pickle
import threading as t
import Tkinter as tk

# set up address
HOST = sys.argv[1] # user specifies ip
PORT = 10003

# set up log file
log = r’pathToLogFile’

# load list of LANDIS-II scenarios
# this is a python list of LANDIS-II scenario paths on the
network drive
LandisPackages=[]
with open(‘ListAsPickle’,'r') as serializedRuns:
LandisPackages.extend( pickle.load( serializedRuns ) )

##########
# Functions #
##########
def LOGGER( msg ):
global log
fullmsg = '{%s} %s'%(time.asctime(), msg)
with open( log, 'a') as flog:
flog.write( fullmsg )

def CONNECT():
LOGGER('Server booted...\n')
server = SocketServer.TCPServer( (HOST, PORT),
LandisHandler)
server.serve_forever()

def JOINEVENT( ip ):
LOGGER('A Node Has Been Connected @%s\n'%(ip))

#########
# Run List #
#########
class LandisRoster( list ):
def __init__( self ):

55

super( LandisRoster, self )
global LandisPackages
for ix, package in enumerate(LandisPackages):
output = package+'_processed'
self.append( {ix:[package, output]})

# make the pop() user friendly
def pop(self):
p = super(LandisRoster, self).pop()
LOGGER('[*] Number of Runs Remaining: %s\n'%(len(self)))
return p

LIST_OF_RUNS = LandisRoster()
LOGGER( 'TOTAL: %s\n'%(len( LandisPackages )))

class LandisHandler(SocketServer.BaseRequestHandler):
def handle(self):
global LIST_OF_RUNS

rcv = str(self.request.recv(1024))
data = ast.literal_eval( rcv.strip() )

code = data.keys()[0]
payload = data.values()[0]

if code==0:
# show a join
JOINEVENT( payload )

elif code==1:
# completed a package
LOGGER('[*] DONE
ID: %s\n'%(payload.keys()[0]))
else:
# send a new package
try:
pkg = LIST_OF_RUNS.pop()

self.request.sendall( str(pkg)+'\n')
LOGGER('[+] SENT
ID: %s\n'%(pkg.keys()[0]))
except:
pass

56

if __name__ == "__main__":
CONNECT()

57

Appendix
B:
Pseudocode
for
LANDIS-‐II
Scenario
Client

# load modules
import os
import shutil
import getpass
import subprocess
import signal
import sys
import socket
import time
import ast
import tempfile
import multiprocessing as mp

#########
# Setup #
#########
# IP of server host and number of CPU on local
HOST, POOL = sys.argv[1:]
PORT = 10003
LOCK = mp.Lock()

USER = getpass.getuser()
WORKSPACE = os.path.join(r'C:\Users', USER, 'LandisClient')

#############
# Functions #
#############
def worker( run ):
global WORKSPACE, LOCK
# input looks like: {ix:[package, output]}
runNo = run.keys()[0]
landisinputdir = run.values()[0][0]
landisoutputdir= run.values()[0][1]
landisinputfiles= [os.path.join( landisinputdir, f) for
f in os.listdir( landisinputdir )]

# create workspace and outputdir
temp = tempfile.mkdtemp(suffix='_landis',dir=WORKSPACE)

if not os.path.exists( landisoutputdir ):
os.makedirs( landisoutputdir )

58

# copy to workspace and outputdir
for lif in landisinputfiles:
shutil.copy2( lif, temp )
shutil.copy2( lif, landisoutputdir )

# popen -- run landis
p = subprocess.Popen(['landis-ii',
'scenario.txt'],cwd=temp,
stdin=subprocess.PIPE,
stdout=subprocess.PIPE,
stderr=subprocess.PIPE,
shell=True)
while True:
line = p.stdout.readline()
if line =='' and p.poll()!=None:
break

LOCK.acquire()
if 'Error' not in line and ''!=line.strip():
sys.stdout.write( '{PID:%s} %s'%(p.pid,line ))
elif 'Error' in line:
sys.stderr.write('[!] LANDIS
ERROR: %s\n'%( landisinputdir ))
fobj =
open(os.path.join(landisoutputdir,'error.txt'),'w')
fobj.write(line)
fobj.close()
LOCK.release()
p.wait()
return
LOCK.release()

# wait for death
p.wait()

######################################################
# If you want to do something with the landis output #
# add that code here. #
######################################################

# copy landis output to outputdir
files = [ os.path.join(temp, of) for of in ['Landis-
log.txt', 'reclass\\reclass1-0.img', 'reclass\\reclass1-
40.img', 'reclass\\reclass1-80.img']]

59

for of in files:
shutil.copy2( of, landisoutputdir )

# delete workspace
shutil.rmtree( temp )

def Client():
global HOST, PORT, POOL
while True:
try:
## CONNECT CLIENT ##
sys.stdout.write('[+] CONNECT
TO: %s@%s...'%(HOST, PORT))
thisIP =
socket.gethostbyname(socket.gethostname())
sock = socket.socket( socket.AF_INET,
socket.SOCK_STREAM )
sys.stdout.write('SUCCESS!\n')

## MAKE FIRST PAYLOAD ##
data = '{0:"%s"}'%( thisIP )
sock.connect((HOST,PORT))
sock.sendall( data+'\n' )
sock.close()

PROCESSES = list()
for node in range( POOL ):
try:
data = '{2:"Acquire"}'

## COMMUNICATE ##
sock = socket.socket( socket.AF_INET,
socket.SOCK_STREAM )
sock.connect((HOST,PORT))
sock.sendall( data+'\n' )
rcvd = sock.recv(1024)
sock.close()

received = ast.literal_eval( rcvd )

sys.stdout.write(' [*] Acquired
(%s)\n'%(node))

PROCESSES.append( received )

60

except:
pass

if len( PROCESSES ) > 0:
# Process
pool = mp.Pool( POOL )
pool.map( worker, PROCESSES )
pool.terminate()
del pool

for node in range( POOL ):
data =
'{1:%s}'%( str(PROCESSES[node]) )

## COMMUNICATE ##
sock = socket.socket( socket.AF_INET,
socket.SOCK_STREAM )
sock.connect((HOST,PORT))
sock.sendall( data+'\n')
sock.close()

else:
sys.stderr.write('[!] FAIL: No Payload\n
[*] Recovering...\n')
time.sleep(10)

except:
sys.stderr.write('[!] FAIL: Connection\n [*]
Recovering...\n')
time.sleep( 10 )

if __name__=='__main__':
if not os.path.exists( WORKSPACE ):
os.makedirs( WORKSPACE )

# run client
Client()

61

Appendix
C:
Pseudocode
for
Data
Analysis

import sqlite3 as sql
import os,time
PATH = os.getcwd()

def FetchIter( cur ):
while True:
rows = cur.fetchmany( 1000 )
if not rows:
break
for row in rows:
yield row

def fetch( cur ):
data=[]
for item in FetchIter(cur):
data.append( item )
return data

def desc( cur ):
return map( lambda i:i[0], cur.description)

# connect
print 'connect...'
DB = PATH + os.sep + 'data.db'
db = sql.connect(DB)
cur=db.cursor()

# This script calculates a Chi-squared measure (o-e)/e for
each orig/final proportion
print 'Create metric 1...'
print ' -Aquire localities of interest'
cur.execute("SELECT scale, locality FROM dataset WHERE
filterid=0 GROUP BY scale, locality")
dataset=fetch( cur )
print ' -There are ', len( dataset ) ,' localities of
interest.'

records=[]
for scale, locality in dataset:

62

cur.execute("SELECT orig, final, ratio FROM
proportion_switch WHERE scale=? AND locality=? AND
runtype='SpatiallyExplicit'", (scale, locality))
se={}
for orig, final, ratio in fetch( cur ):
if ratio!=None:
se[(orig, final)]= ratio

cur.execute("SELECT orig, final, ratio FROM
proportion_switch WHERE scale=? AND locality=? AND
runtype='AreaWeighted'", (scale, locality))
aw={}
for orig, final, ratio in fetch( cur ):
if ratio!=None:
aw[(orig, final)]= ratio

cur.execute("SELECT orig, final, ratio FROM
proportion_switch WHERE scale=? AND locality=? AND
runtype='EqualArea'", (scale, locality))
ea={}
for orig, final, ratio in fetch( cur ):
if ratio!=None:
ea[(orig, final)]= ratio

# get all possible pairs
switches=se.keys()
switches.extend( aw.keys())
switches.extend( ea.keys())
switches=list( set( switches ))
for orig, final in switches:
# get expected
if (orig, final) not in se.keys():
E=0.0
else:
E=se[(orig, final)]

# get aw observed
if (orig, final) not in aw.keys():
AWO=0.0
else:
AWO=aw[(orig, final)]

# get ea observed
if (orig, final) not in ea.keys():
EAO=0.0

63

else:
EAO=ea[(orig, final)]

# calculate
if E==0:
# do a value shift o+1, E+1 for calculation
AW=(AWO)**2
EA=(EAO)**2
else:
AW = ((AWO-E)**2.)/float(E)
EA = ((EAO-E)**2.)/float(E)

# create rows
records.append( (scale, locality, 'AreaWeighted',
orig, final, AW) )
records.append( (scale, locality, 'EqualArea', orig,
final, EA) )

cur.execute("CREATE TABLE metric_1( scale int, locality
double, runtype string, orig double, final double, chisq
double)")
cur.executemany("INSERT INTO metric_1 VALUES (?,?,?,?,?,?)",
records)
cur.execute("CREATE INDEX metric_1_index ON metric_1(scale,
locality, runtype, orig, final)")
db.commit()

print 'Calculate Chisquare on metric 1...'

cur.executescript(
"""
CREATE TABLE chisquare_m1( scale int, locality double,
runtype string, x2 double, k int);

INSERT INTO chisquare_m1
SELECT scale, locality, runtype, SUM( chisq ) AS calc,
(COUNT(*)-1) AS degfree
FROM metric_1
GROUP BY scale, locality, runtype;

CREATE INDEX chisquare_m1_index ON chisquare_m1( scale,
locality, runtype);
""")

64

db.commit()

# metric 2
print 'Create metric 2...'
print ' -Aquire localities of interest'
cur.execute("SELECT scale, locality FROM dataset WHERE
filterid=0 GROUP BY scale, locality")
dataset=fetch( cur )
print ' -There are ', len( dataset ) ,' localities of
interest.'

records=[]
for scale, locality in dataset:
cur.execute("SELECT orig, final, ratio FROM
proportion_totalarea WHERE scale=? AND locality=? AND
runtype='SpatiallyExplicit'", (scale, locality))
se={}
for orig, final, ratio in fetch( cur ):
if ratio!=None:
se[(orig, final)]= ratio

cur.execute("SELECT orig, final, ratio FROM
proportion_totalarea WHERE scale=? AND locality=? AND
runtype='AreaWeighted'", (scale, locality))
aw={}
for orig, final, ratio in fetch( cur ):
if ratio!=None:
aw[(orig, final)]= ratio

cur.execute("SELECT orig, final, ratio FROM
proportion_totalarea WHERE scale=? AND locality=? AND
runtype='EqualArea'", (scale, locality))
ea={}
for orig, final, ratio in fetch( cur ):
if ratio!=None:
ea[(orig, final)]= ratio

# get all possible pairs
switches=se.keys()
switches.extend( aw.keys())
switches.extend( ea.keys())
switches=list( set( switches ))
for orig, final in switches:
# get expected

65

if (orig, final) not in se.keys():
E=0.0
else:
E=se[(orig, final)]

# get aw observed
if (orig, final) not in aw.keys():
AWO=0.0
else:
AWO=aw[(orig, final)]

# get ea observed
if (orig, final) not in ea.keys():
EAO=0.0
else:
EAO=ea[(orig, final)]

# calculate
if E==0:
# do a value shift o+1, E+1 for calculation
AW=(AWO)**2
EA=(EAO)**2
else:
AW = ((AWO-E)**2.)/float(E)
EA = ((EAO-E)**2.)/float(E)

# create rows
records.append( (scale, locality, 'AreaWeighted',
orig, final, AW) )
records.append( (scale, locality, 'EqualArea', orig,
final, EA) )

cur.execute("CREATE TABLE metric_2( scale int, locality
double, runtype string, orig double, final double, chisq
double)")
cur.executemany("INSERT INTO metric_2 VALUES (?,?,?,?,?,?)",
records)
cur.execute("CREATE INDEX metric_2_index ON metric_2(scale,
locality, runtype, orig, final)")
db.commit()

print 'Calculate Chisquare on metric 2...'

cur.executescript(
"""

66

CREATE TABLE chisquare_m2( scale int, locality double,
runtype string, x2 double, k int);

INSERT INTO chisquare_m2
SELECT scale, locality, runtype, SUM( chisq ) AS calc,
(COUNT(*)-1) AS degfree
FROM metric_2
GROUP BY scale, locality, runtype;

CREATE INDEX chisquare_m2_index ON chisquare_m2( scale,
locality, runtype);
""")
db.commit()

print 'Create metric 3...'
print ' -Aquire localities of interest'
cur.execute("SELECT scale, locality FROM dataset WHERE
filterid=0 GROUP BY scale, locality")
dataset=fetch( cur )
print ' -There are ', len( dataset ) ,' localities of
interest.'

records=[]
for scale, locality in dataset:
cur.execute("SELECT final, ratio FROM
proportion_endstate WHERE scale=? AND locality=? AND
runtype='SpatiallyExplicit'", (scale, locality))
se={}
for final, ratio in fetch( cur ):
if ratio!=None:
se[final]= ratio

cur.execute("SELECT final, ratio FROM
proportion_endstate WHERE scale=? AND locality=? AND
runtype='AreaWeighted'", (scale, locality))
aw={}
for final, ratio in fetch( cur ):
if ratio!=None:
aw[final]= ratio

cur.execute("SELECT final, ratio FROM
proportion_endstate WHERE scale=? AND locality=? AND
runtype='EqualArea'", (scale, locality))
ea={}
for final, ratio in fetch( cur ):

67

if ratio!=None:
ea[final]= ratio

# get all possible pairs
switches=se.keys()
switches.extend( aw.keys())
switches.extend( ea.keys())
switches=list( set( switches ))
for final in switches:
# get expected
if final not in se.keys():
E=0.0
else:
E=se[final]

# get aw observed
if final not in aw.keys():
AWO=0.0
else:
AWO=aw[final]

# get ea observed
if final not in ea.keys():
EAO=0.0
else:
EAO=ea[final]

# calculate
if E==0:
# do a value shift o+1, E+1 for calculation
AW=(AWO)**2
EA=(EAO)**2
else:
AW = ((AWO-E)**2.)/float(E)
EA = ((EAO-E)**2.)/float(E)

# create rows
records.append( (scale, locality, 'AreaWeighted',
final, AW) )
records.append( (scale, locality, 'EqualArea',
final, EA) )

cur.execute("CREATE TABLE metric_3( scale int, locality
double, runtype string, final double, chisq double)")

68

cur.executemany("INSERT INTO metric_3 VALUES (?,?,?,?,?)",
records)
cur.execute("CREATE INDEX metric_3_index ON metric_3(scale,
locality, runtype, final)")
db.commit()

print 'Calculate Chisquare on metric 3...'

cur.executescript(
"""
CREATE TABLE chisquare_m3( scale int, locality double,
runtype string, x2 double, k int);

INSERT INTO chisquare_m3
SELECT scale, locality, runtype, SUM( chisq ) AS calc,
(COUNT(*)-1) AS degfree
FROM metric_3
GROUP BY scale, locality, runtype;

CREATE INDEX chisquare_m3_index ON chisquare_m3( scale,
locality, runtype);
""")
db.commit()
db.close()

Asset Metadata

Creator Davis, Austin V. (author)

Core Title Testing LANDIS-II to stochastically model spatially abstract vegetation trends in the contiguous United States

Contributor Electronically uploaded by the author (provenance)

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geographic Information Science and Technology

Publication Date 09/13/2013

Defense Date 08/06/2013

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag LANDIS-II,OAI-PMH Harvest,spatial modeling,spatial sensitivity testing

Format application/pdf (imt)

Language English

Advisor Longcore, Travis R. (committee chair), Kemp, Karen K. (committee member), Pultar, Edward (committee member)

Creator Email austinda@usc.edu,austinvdavis@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-328099

Unique identifier UC11293580

Identifier etd-DavisAusti-2040.pdf (filename),usctheses-c3-328099 (legacy record id)

Legacy Identifier etd-DavisAusti-2040.pdf

Dmrecord 328099

Document Type Thesis

Format application/pdf (imt)

Rights Davis, Austin V.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Abstract (if available)

Abstract The second generation of the Landscape Disturbance and Succession model (LANDIS-II) is frequently used to understand ecological succession on the landscape. LANDIS-II is an important simulation tool but it can be difficult to parameterize properly in data-poor regions. By examining the spatial sensitivity of LANDIS-II, the model’s users will have an improved understanding of the data required to properly implement the model. Existing studies have tested the ecological sensitivity of LANDIS-II in local geographic settings, but a robust test of the model's spatial sensitivity has not been completed. This research tested the spatial sensitivity of the LANDIS-II spatially stochastic landscape model using a broad set of vegetation communities found within the contiguous United States. Thirty spatially explicit, equal-area, and area-weighted iterations of the spatial parameters of the LANDIS-II model were run for a series of localities in the contiguous United States, where the areas were defined by the spatial composition of vegetation community values. Ecological attributes were derived from the NatureServe Ecological Systems of the United States dataset. A test of the spatial input parameters of LANDIS-II demonstrated that the model is aspatial under certain conditions. Furthermore, vegetation community interactions may be effectively represented in LANDIS-II by a series of spatially stochastic input rasters