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Genetics, geographics, and prairie dogs:
error and accuracy in a validated
spatially-explicit dispersal model.
Abstract.- Genetic theory predicts that poplbtioas will diffaeatiate
besedmthegeographic~behveen~lmleassane
envhmmblfieatureaeatesabanier t o d q e a d . &wever,tbe
baniersareoftmio6enedh~fieetuteg,andrarelydiredly
testedfwtheirabilitytopredidgenetc~asaq,ressedby
peticdistances. ' Z b e r e i s a ~ t o d e v e b p ~ e x p l i c i t m o d e l s
validated by population dumtedics, such as genetics, to predict
population sub-division-animportant step in the canservation of a
species. Prairie dogs (Cynomys ludovciamcs),are wlonial fossorial
rodents that live in discrPte populati~f]~
which have distinctive signatures
in remotely-sensed images, providing a mecbanb to combine spgtia and
genetic databases into a single model. However, this combination of
spatial and &c
data complicates spatial error as spatial genetic
parameters, measured fiom protein difkedon, have associated error
around distaoce algorithms;while spatial databgses,such as elevation,
hydrology, and transportation, have error associated with plamnent. The
implications of testing spatial models on dorganisns at the laodscape
level are discussed
INTRODUCTION
Ecological modeling of animal populations with remotely-sensed data is a relatively
new field for conservation biologists (Johnson 1990). How animals move among
populations and how different environmental features affect population exchange and
stability are findmental questions for the conservation of patchy fiagmented habitats
(Johnson and Naiman 1987, Jensen et al. 1990). Given the current availability of
remotely-sensed databases along with the statistical tools to analyze those databases, there
is also an increasing need to address the accuracy and resolution of these landscape
databases when used at the scale of an individual animal (Costanza and Maxwell 1994).
Modeling population establishment and movement on a landscape level requires
using some remotely-sensed data (such as vegetation, elevation, or the like) to imply
where the animal populations may occur (Scott et al. 1993). However, the digital
databases expressing the environmental parameters contain sources of error associated
Natural Resource Specialist, Rocky Mountain System Support Office,National Park Service, Denver,
Colorado
with the scale, resolution and projection of the source map that can have important
implications when applied to ecological databases (Meenetemeyer and Box 1987, Lee et
al. 1992, Kemp 1993, Bolstad and Stowe 1994, Hodgson 1995). In addition, the unit of
scale of the landscape will change with the different ecological processes being examined
and will vary with different organisms as to the correct scale for expressing spatial
movements (Hunsacker et al. 1993 Cale and Hobbs 1994). At a certain point, the error
associated with the scale of the underlying database can overwhelm any potential to model
populations at finer resolutions (Brown and Bara 1994, Berry 1995). This point-of-noreturn can be expressed as an error term or through error management to evaluate model
performance (Hunter and Goodchild 1995).
Here I discuss the implications of scale and resolution on constructing a spatially
explicit model of animal dispersal, and how the validation of this model is limited by
discrepencies between the ecological scale (how far an individual animal can move on a
landscape) and the database scale (what are the limitations of resolution and projection on
the database accuracy for modeling the movements of small mammals).
BACKGROUND
Dispersal among populations is essential to maintain genetic homogeneity within a
population thus p r e s e ~ n gpopulation health and longetivity (Green 1994). As
populations become isolated through environmental or behavioral barriers, genetic
divergence occurs leading eventually towards speciation. The progress towards speciation
can be estimated on a shorter time scale by calculating the dispersal rates per generation
and creating a genetic distance (based on exchange as mirrored by genetic differentiation-Nei 1972) that can validate dispersal distances (a rate of exchange based on physical
separation).
To examine dispersal distances across realistic landscapes as a measure of population
conservation, each element of a landscape (elevation, vegetation, transportation,
hydrology) can be viewed as an independent treatments (single model runs) to be tested
against the predicted dispersal distances based on genetic differentiation (as a measure of
population persistence. The effects of environment elements (such as roads or
developments) on dispersing animals can be directly by calculating population parameters
(genetic differentiation) against an estimate of the exchange rate (a dispersal distance) that
creates a spatially-explicit dispersal model applicable for population conservation efforts.
Model Parameters
Three aspects of ecological model are directly affected by the scale and resolution of
the spatial databases themselves: the size of the area covered by the model; the size of the
species the model is designed to emulate; and the variablity in the landscape.
How big is the study area?
The first step in model construction is to define the size of the patch addressed by
the model. If the patch is a preserve or politically defined boundary, there may be
constraints defined by the boundary of that patch which should be included in any
modeling efforts. In addition, the size of the total area of consideration can determine the
resolution of the databases feasible given hardware and software limitations. Highly
mobile insects, for example, would required extremely high resolution data over large
areas that is beyond the storage capacity of many computers.
How large is the organism?
The size of the species will dictate the required precision of any underlying map
layers (Brown and Bara 1994). Smaller species may be more sensitive to the resolution of
a spatial data than larger species and thus a model based on a coarser resolution data
could miss- or over-represent landscape features and their impact on animal movement.
The physical size of the species will also dictate how rapidly dispersal declines with
geographic distance, in which case modeling population placement may be more valid than
individual movement (even though this is fbndamentally a different question) and the
resolution of digital layers maybe unrealistic for that species (Cale and Hobbs 1994).
How variable is the study area?
Habitat variablity, especially as it Sects small animals, can be under-represented by
databases with coarse resolution. For example, small erosive features, long narrow gullies
or streambeds, may not be visible to a database with a minimum pixel size of 30meters. If
those gullies are barriers to the movement of small animals, the database may not be able
to detect those barriers and could mis-represent animal movement.
STUDY SITE
Black-tailed prairie dogs ( C ' y s ludbvicianus) are colonial fossorial rodents of
the Great Plains of North America. The prairie dog is considered a keystone species for
the North American plains because they form large colonies and actively modify the
environment within their colonies, creating unique ecosystems. The colonies with their
distinct vegetation are distinct in aerial photography (Schenbeck and Myre 1990) and thus
are ideal to demonstrate spatially-explicit dispersal models. Badlands National Park,
South Dakota has a number of large prairie dog colonies scattered throughout the park.
As the park has two distinct lobes with colonies on either end, predicted dispersal pattems
among colonies are colonies relatively close on one side of the park would be genetically
more similar than those on opposite (figure 1). These predictions (euclidean distances
describe population dispersal patterns) will serve to validate model predictions based on
the dispersal and genetic distances.
Figure 1. Cartoon of the distribution of major prairie dog populations in Badlands National Park,
South Dakota. Population abbreviations are: Baysinger @A), Burns Basin (BU),Bigfoot @I), Haybutte
(HA), Kocher Flats (KO), Tyree Basin (TY), Tyree South (TS).
MODEL CONSTRUCTION
Environmental layers such as Digital Elevation Model @EM- 1:24,000), Digital Line
Graph.(DLG-- 1:250,000), aerial photography (black and white and color hka-red:
1:24000), Soil Conservation Service (SCS DLG--1:250,000), vegetation (National Park
Service (NPS) database-- 1:24000) and landuse boundaries (NPS database- 1:250,000)
were entered into a GRASS4.1 GIs database on a Sun Sparkstation. All data were
rectified with GRASS program modules for geo-referencing (Clark66) and spheroid
corrections (NAD27). Additional corrections for resolution were done using C- and
Bourne-shell scripts and GRASS resampling. All model runs were generated by these
scripts and were run in the UNIX environment, calling the GRASS modules as needed.
A model run consisted of an individual GRASS surface (such as roads) redefined
based on user-assigned weights meant to symbolize the ease or difficulty for prairie dogs
to cross a particular environmental feature. Those weights are then expressed as a cost
surface (the curnmulative weights for moving fiom a particular point to any other point on
the surface) which is then used to generate a dispersal path (figure 2). Dispersal paths are
calculated using alogorithms fiom hydrology as water seeks the lowest path down a
drainage. The route water would follow then represents the least-cost path that an animal
would follow over an ecologically-defined surface (figure 3).
Dispersal paths were validated by using the genetic differentiation of proteins (as
determined by the horizontial gel-electrophoresis of polymorphic enzymes) to create a
genetic distance analogous to the physical separation (see Bowser 1996 for methods).
Genetic distance is a metric measure of the genetic differentiation of proteins among
679
population samples, and can be used as an independent measure to test for linear
associations with the paths generated by the dispersal models (Nei 1972, Slatkin 1985).
Genetic distances were calculated using BIOSYS- 1 (Swofford and Selander 1989) and
Weirs (1990) jack-knifing procedure.
L.,
'.
k.
I
Cost surface
Transforming
surfaces
Figure 2. Conceptual diagram of the cost path generation using surfaces consisting of single
environmental feature to create composite surfaces. Populations are represented by 'I' and 'j' and paths
are calculated from the centroids of i and j. Different polygons indicate ecological features on the
transforming surface that pose a barrier to dispersal.
All statistical tests were done using Splus3.3 in the UNIX environment after
corrections for normality and checks for autocorrelation. Each environmental surface was
seen as an independent model consisting of a single parameter such as roads, streams, etc.
Composite layers were created within GIs from combinations of single layers which were
then rescaled to account for changes in resolution and tested as a single independent
surface
RESULTS
Dispersal paths calculated for prairie dog populations in BADL were significantly
different than the Euclidean distances among the populations (table 1). All of the
environmental surfaces created longer paths than the Euclidean distances with the
exception of vegetation which was not significantly different. Loglinear regression on
splined distances showed that there were weak predictive relationships (p=0.05, r2=. 14)
for single models between the genetic distances and the dispersal distances (figure 4). The
best fitted model using step-wise regression was roads, streams, and park boundary
680
@=0.05, ?=0.33). Composite models were generally better at predicting the genetic
distances than single models using Principal Component Analysis; composite models
contributed the most to the first PCA axis which explained 86% of the variance in genetic
distances.
Figure 3. Cost surface for moving from one location (the pit) to any other point on the surface.
Cost re fers to the cummulative sum of pixel weights from a designated starting point to any other point
on the surface.
Table 1. ANOVA on single surface models as independent treatments against Euclidean distance
among populations of prairie dogs in Badlands National Park.
Model
df
f
P
sign
roads
1
64.55
0.00
**
streams
1
slope
elevation
vegetation
1
1
1
DISCUSSION
The validated dispersal models demonstrated here showed an ability to predict
another population parameter, genetic distance, which is an important measure of the
longetivity, exchange, and isolation of populations. As an exploratory model, the dispersal
model was able to demonstrate which environmental layer appear to best explain the
genetic patterns observed, as well as provide some insights as to which environmental
features may have little effect. Despite the presence of the badlands wall and other
erosion features within BADL, elevation was not a strong predictor of genetic distance.
68 1
In contrast, streams and roads together as a composite model was best able to explain the
genetic patterns over any single environmental feature.
Figure 3. Regression lines for each single surface tested using genetic distances as the dependent
variable. Graphs labels from the left: roads, streams,slope, vegetation, elevation, and park boundary.
The Influence of Error
There are two sources of error discussed here: error associated with the placement
of populations; and error associated with treatment affects during the model validation.
Population placement
The location of populations on the landscape for a dispersal model is critical as the
seed point for constructing paths on the cost surface. If a centroid position for a
population polygon is used as the starting point, the error associated with that centroid
only becomes important when referenced to ground measurements. Each centroid has a
sphere of error round it that represents the corrections due to population placement
(digitizing and interpretation error), RMS associated with the photograph rectification,
along with any error associated with
Treatment error
Treatment error builds on existing population placement error within the framework
of a statistical test. Location error can be analogous to the variance around each point
within a treatment. Testing the variance among treatments (assuming each treatment is a
different spatial layer), changes the total error incorporated within the statistical model
would be a combination of the variance among and within treatments--the first due to
population placement and the second due to the underlying precision and resolution of the
original environmental database. The combined errors reduce the power of a variance test
to explain the "background noise" resulting in low multiple r squared values.
CONCLUSIONS
Error, scale, and resolution can limit the ability of GIs to accurately model animal
682
movements across complex landscapes. When a model is validated by a population
measure (such as genetic distances) the error incorporated into spatial models fiom digital
databases and the assumptions of accuracy underlying those databases are elucidated. In
the dispersal model, the inability to explain more than 33% of the model variance in the
regression models yet still have a demonstratable relationship (and reproduce pattems
expected by the population parameters) suggests that the error in placement may distort
model results. The take-home message is that although the dispersal model did a modest
job in re-creating the genetic patterns and sorting through which environmental features
best explained those patterns, the accuracy, precision, and resolution of the underlying
databases must be discussed. In this model, the minimum resolution (30 meters) was
greater than most of the animal's home territories (and some colonies). Realistically, the
model requires the animal to move in jumps of at least one meter up to 30 meters
depending on the surface--a dficult task for an animal of 2-10 pounds. The fact that the
model still distinguished among surfaces and replicated genetic distance predictions is
intriging and will hopefblly generated m h e r exploration as to the effects of the accuracy
and error of spatial databases on ecological modeling.
ACKNOWLEDGEMENTS
Bette Loiselle and John Blake, my dissertation advisors from the University of
Missouri-St. Louis, provided strong support in the development of this project as a part of
my dissertation. Chip Harvey, Chris Theriault, and Michelle Gudorf of the National Park
Service provided excellent discussions on spatial error and ecological modeling. I
appreciate the efforts of Peter Strong, David Duran, and Bruce Powell of the National
Biological Service (NBS) to keep my computer running. Ralph Root and Susan Stitt
(NBS) provided excellent analytical support for the spatial analysis.
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BIOGRAPHICAL SKETCH
Gillian Bowser is a natural resource specialist with the National Park Service in
Denver, Colorado. She holds an MS from the University of Vermont in Zoology and is
currently a PhD candidate with the University of Missouri-St. Louis. Gillian provides
technical assistance and develops proposals in the sciences for national parks in the rocky
mountain area.