Figure 1 (click here for high res.)
Using geographic information systems (GIS) to explore the spatial relationships of animal populations is a relatively new field for ecologists (Johnson 1990, Scott et al. 1993) and one untouched by population geneticists. GIS, as an environmental modelling tool, evolved from simple beginnings as a mapping program to a modelling and analysis engine for a variety of different disciplines (Goodchild 1993). GIS is well-established in habitat-based studies of animal populations to analyze remotely-sensed databases (Johnson and Naiman 1990) and as a predictive tool for animal or plant species distributions (Scott et al. 1993, Jensen et al. 1992). In addition, GIS is now used to create databases, manipulate spatially-explicit surfaces to represent specific parameters, and to displace spatial relationships through simulation modelling, hydrologic constructs, and species relationships (Keller 1990; Aspinall and Veitch 1993). One application still unexplored with GIS, despite the importance of spatial heterogeneity, is the animal population dynamics as expressed by genetic parameters.
Spatial heterogeneity is a complex phenomena involving patterns or mosaics of habitats at a landscape level (Kolasa and Rollo 1991, Turner and Gardner 1991, Dunning et al. 1992). The causes and consequences of spatial heterogeneity can be measured by examining patterns of variation in the population dynamics of an organism as recorded in the distribution and exchange of individuals. Environmental variables, as independent variables either abiotic or biotic, can control variation within "dependent taxonomic groups" (Karieva 1990; Green 1994) by influencing the movement of individuals among population units. Thus, the influence of those environmental features should be reflected in population measures such as genetic differentiation (Wayne et al. 1990; Patton and Smith 1992; Opdam 1991; Mitchell-Olds 1992; Lande 1988; Stewart et al 1993).
Two features of population dynamics, gene flow and genetic drift, are particularly sensitive to the spatial milieu in which populations are embedded. Populations persist in part through the exchange of individuals (gene flow) and maintance of genetic fitness (Slatkin 1981, 1985; Leberg 1990). In contrast, as populations become isolated and genetic mistakes occur and accumulate, the population drifts towards genetic differentiation and speciation (Leberg 1990, Slatkin 1993). As gene flow implies the migration of individuals between populations, genetic drift is a measure of the isolation or separation among populations (Wright 1965, Slatkin 1985, Weir and Cockerham 1984). In island models of genetic differentiation, the genetic separation among populations is analogous with their physical distances (Slatkin 1993). Genetic distance, as a measure of accumulated differences in allele frequencies among populations, is a single number (Jacquard 1970, Weir 1990) that characterizes populations by the genotype frequencies among members, condensed from information on the frequencies of various genes or alleles for the entire population (Jacquard 1970). Genetic distance, as a representation of linear distance, is an estimate as to how populations spatially organize themselves and is a data reducing device (Weir 1990) that can infer population groupings--phylogenetic trees or similarity cluster diagrams (Rogers 1991)--comparable to groups created by physical distances. Thus, euclidean distance (the linear distance or difference between two points characterized by many variables) approximates genetic distance when calculated across a simple landscape (Slatkin 1993).
In this study, theorectical dispersal paths were calculated using GIS first to build landscapes based on individual environmental features, then to redefine these landscapes with pre-conceived concepts on the ecological perspectives of a species. Spatially-explicit analyses use the physical path a dispersing animal follows across these newly-created landscapes to explain patterns of genetic differentiation among populations. The hypotheses for this study address the paths drawn across these ecologically-created landscapes:
Protein electrophoresis of alloyzmes from a fossorial colonial rodent (Cynomys ludovicianus) was used to determine genetic distances among different populations in Badlands National Park (BADL), South Dakota. Genetic distance was used as response variable in regression models where the predictors were dispersal paths created by Geographic Resources Analysis Support System (GRASS) version 4.1 GIS software across a variety of different environmental surfaces. Dispersal paths were tested in two steps: first each GIS-created path was compared with the Euclidean distance using two-way analysis of variance (ANOVA); second, each path was tested against the genetic distance (corrected to match the scale of the distance in meters) using multiple linear regression to find which set of paths best explained genetic distances.
Black-tailed prairie dog (Cynomys ludovicianus), a fossorial colonial rodent, populations from BADL were chosen because their colonies leave distinct scars on the landscape, easily mapped from low-level aerial photography (Schenbeck and Myhre 1990). These colonies can be aged by tracking scars back through time, using historical aerial photography, to minimize possible extinction and colonization effects on the genetic differentiation of focus colonies. Fourteen colonies were identified on aerial photography; seven were chosen for this study based on their age, stability, and size.
Genetic data was gathered from each colonies by live-trapping or destroying 20 individuals, each from separate family groups or coteries (Chesser 1983, Daley 1992). Blood samples were collected in hemphanized 250 microliter tubes and immediately stored on dry ice to prevent protein decay. Samples were shipped to the University of Missouri-St. Louis and analyzed for 21 presumptive proteins using horizontal starch-gel protein electrophoresis on three different (pH 7.1, 8.0, 9.1) buffer systems (Richardson et al. 1986, Pasteur et al. 1988, Aquaah 1990). Allele frequencies from seven polymorphic proteins were calculated along with genetic distances based on Modified Rogers' algorthim (Rogers 1991) using BIOSYS-1 software (Swofford and Selander 1981) on an IBM PC.
Models were created to build spatially-explicit dispersal paths among populations on complex ecologically-defined landscapes. The models themselves are translations of digital spatial data incorporated into GRASS and transformed by mathematical and ecological parameters using UNIX Bourne-shell scripts. Each model consists of several elements: (1) a transforming surface--a GIS layer based on a single environmental feature such as elevation, streams, roads, etc.; (2) a weighting protocol--weights are assigned to each element on the transforming surface based on a preconceived concept on the ecological impact of that feature on animal dispersal; (3) a cost surface--a surface created by the GIS that defines each pixel on the transforming surface based on it's cummulative weight (cost) from a chosen starting point like a population center, to a specific endpoint; and (4) a dispersal path--a route drawn across the cost surface based on choosing the lowest cummulative cost to move between two specified points on that surface.
Figure 1 (click here for high res.)
Digital databases used in the models included digital elevation model (DEM), digital line graph (DLG), vegetation (based on Soil Conservation Service DLG data), and landuse boundaries--based on Defense Mapping Agency data. From these databases, slope, elevation, aspect, hydrology, and roads, were extracted and separated into geographically referenced surfaces (Figure 1 elevation surface ). These surfaces, such as elevation, represent the biotic environment used as 'seed' surfaces for the dispersal models. Scanned and rectified aerial photography was overlaid on these digital databases and population centers were calculated by screen-digitizing colony scars visable in the photography. Residual Mean Square error (RMS) was calculated for each photograph and recorded along with the RMS of the base photograph or mapand the number of control points used.
Figure 2 (click here for high res.)
Every feature on a transforming surface was assigned a weight on a geometrically increasing scale, where the weights were based on a pre-conceived concept as to whether that feature consistutes a barrier or deterient to dispersing animals. The new weight surface bears little resemblance to the initial transforming surface as weights are now used to express 'height'. For example paved roads would be assigned a weight higher than a four-wheel drive track, but lower than an interstate highway--thus an interstate appears higher than a paved road on a three-diminsional representation of a transformed surface (Figure 2 weight surface)--giving a different appearance than the original transforming surface (Figure of elevation surface). The weights themselves were arbitrary (chosen in increments of tens or hundreds), and the rate of increase was consistent for all classes on a particular transforming surface. Thus an intermittent stream may have a weight of 10 on the stream transforming surface, and a foot-trail can also have a weight of 10 on the road surface, thus allowing for metric comparisions across surfaces and variables during the model analysis. Any features with no known impact on the ability of an animal to disperse was assigned a zero value. 'No data' values were assigned to missing variables or to areas outside the study area to reduce computer memory requirements. Finally, for surfaces containing habitat parameters (slope, vegetation, aspect) with information on the preferred habitats (based on back-tracking population position through 50 years of aerial photography), all preferred elements were assigned low weights based inversely on their occurrence within population boundaries over time. Thus areas not preferred would be assigned higher weights, but not high enough to completely deter dispersal (a discussion of using weights to compare variables and routes in GIS analysis is in Waggoner 1989; Dr. R. Root, Technology Transfer Center, National Biological Service, personal communication).
Figure 3 (click here for high res.)
Cost surfaces are representative surfaces of the cummulative cost (based on assigned pixel weights) of moving to each cell on a surface from a defined point (geographic coordinates). Each cell on the surface is reassigned a category value representative of the cost of traversing that cell (Awaida and Westervelt 1993). By using the centroids of each prairie dog colony as a starting point for a cost surface, seven new cost surfaces are generated for each transforming surface (Figure 3 cost surface. The pit in this surface represents the area of lowest cost from the starting point, accumulating cost as the distance from the starting point increases and the program encounters weights on the surface. The cost surface is defined from a starting point, and is analogous to an inverted peak which water will then be drained off of. An extra layer was then added to each surface to represent time. This layer consisted of concentric rings of increasing weights (the size was dependent on the resolution of the cost surface) originating at the starting centroid. These rings simulate time and prevent the program from backtracking or making wide detours. The time surface was meant to incorporate into the dispersal model the increasing risk to animals the longer they are outside colony boundaries.
Dispersal paths were created by defining an animals movement as a cummulative sum of cell values crossed as the animal moves between two points. Dispersal paths can be thought of as the path water follows to get to the lowest point on a surface. As water moves down from one point to another, it seeks the path with the least resistence and always chooses the downhill path. A dispersal path for animals is similar, assuming the animal always follows the easiest and quickest route, or 'least-cost' path for dispersal.
There are some construction restraints based on how GIS builds dispersal paths. Paths are constructed using the following equation:
where the first summation represents moving between two designated points (a and b) on the landscape; ij indicates scale of pixels containing features at scale-i and resolution-j. W is a measure of the weights for feature X or Y and the summuation of those features by scale, resolution, and accuracy will generate d--an actual distance going from a to b. Scale and Resolution (ij) are limited by the underlying databases and create a source of error around the placement of an individual point (a or b) for features (X, Y) on a given surface. However, there is also error associated with the calculation of each surface that involves the ability of the GIS to correct the surface and incorporate the data into a coordinate system (based on a reference surface) each with an associated error. For clarity, all of those sources of model construct error are summed into one term--accuracy (Z) for a map layer where the actual path constructed by the model may be represented by:
where the realized path (dr) is a function of the constructed path, d, the accuracy of that path for surface x (Zx) given the precision of surface X (P) to an actual ground location. Precision is the degree of detail in reporting a measurement or the arthematic calculation of scaling (Goodchild 1993). In model validating, the terms Z and P will be incorporated into the error term as representative of a sphere of error around each point on the surface that has a diameter determined by Z and P.
All statistical analysis was performed on a UNIX workstation with Splus3.2 software. There were three separate hypotheses tested by the statistical analysis:
Figure 4 (click here for high res.)
Seven colonies in or adjacent to BADL were used with 42 paths constructed (all possible pairs) per model run (Figure 4 badlands national park . Colony size ranged from 25-70,000 hectares with an estimated mean prairie dog density of 43 per hectare. The seven colonies were all at least 43 years old; some showed signs of budding and expansion (as sources for new populations) while others had neighbors go extinct (sink relationships--Green 1994). Both of these phenomena have implications important to the calculation of genetic distances that were not directly tested by this model.
Photography was scanned for one meter horizontal accuracy; however, the mean residual square error (RMS) from the photography (1:24,000) to the 1982 base photograph (1:250,000) used for rectification, ranged from 3.5 to 7 meters; while the RMS for the 1982 base to the USGS 7.5 minute topographic quadrant maps was 4.5 meters. As the topographic map had a minimum RMS of 11 meters, the minimum horizontal accuracy was approximately a 15 meter sphere around the centroid locations used to generate paths. This accuracy was considered a source of error in the models analogous to variance around each path constructed by the GIS model.
Models constructed from a single transforming surface (single surface models) were significantly different from those constructed using euclidean distance (two-way ANOVA, p=0.05). Some surfaces were quite different from euclidean distance (t-test, p=0.05) with roads (mean path length= 14903 pixels) and streams (mean path length= 15898 pixels) having dispersal paths significantly longer than those created by euclidean distances (mean path length = 13961 pixels). Pixel size for these layers was later adjusted to 30m per pixel to compare with ground measurements.
Figure 5 (click here for high res.)
Single surface models did not individually explain genetic distance as a linear response. Each single surface model was tested individually against genetic distance and only two surfaces, roads and boundary were significant predictors of genetic distance (p=0.01, Figure 5 single surface regressions), but the regression models were both poor in their ability to explain the variance around the regression line (multiple r2=0.14). Residual plots on the other surfaces indicated non-linear responses and these models were tested by first applying a spline correction and loess smoother to the data and running loglinear regression. These smoothed models were better predictors (r2=0.33, Figure 5 single surface smoothed regression) suggesting non-linear relationships.
Figure 6 (click here for high res.)
Principal Component Analysis on five single surfaces showed 65% of the variance explained by the first principal component and vegetation contributed the most to that axis. High multicollinearity in the last two principal components suggests that some of the surfaces showed signs of auto-correlation probably based on use of common centroids for dispersal path construction. Because of this multi-collinearity a multiple regression using a stepwise selection procedure (using Mallows statistic for a selection criteria) was run on the least collinear surfaces and not the complete dataset. From this the best multiple surface run consists of roads, and streams; however the ability to explain variance declines to r2=0.14.
Groupings generated by PCA were weak and did not resemble those obtained by genetic distance alone, nor that expected by euclidean distance. The main source of disagreement appeared to be when GIS calculates paths from one town to another, the reverse path is not always the same length. These path reversals differed in the PCA grouping causing noticeably more scatter than in either the genetic distance or geographic distance groupings. PCA groupings on dispersal paths did have better grouping by starting locations such that loose groups for four of the seven locations were noted.
The dispersal paths tested provide some interesting insights to possible environmental influences population genetic characteristics. If population stability for 43 years is sufficient to stabilize genetic relationships (approximately 21 generations), then stable populations should be reflecting the processes of genetic drift and gene flow. For prairie dogs in BADL, gene flow seems to be most influenced by the presence of streams and roads and least influenced by the highly erosive cliffs characteristic of the badlands environment (Figure 1 elevation surface). These results lead to some interesting speculation. The model draws paths of different lengths (for a single pair of locations) depending on the direction of travel; however, if the dispersal paths are examined in light of environmental features, the difference appears to be related to when the drain program encounters a significant barrier. Because a time surface was imposed on top of the landscape, significant barriers encountered at the end of a dispersal path are less likely to divert the animal than one close in (when the time surface has the strongest effect). The ecological significance of this unexpected model artifact is that the placement of some features on a landscape will have differing effects dependent on the distance from the source population when that feature is encountered. To test this hypothesis is outside the current range of these dispersal models but warrants further exploration.
There are three sources of error in the dispersal models: (1) error associated with the ecological restraints of the animal; (2) error associated with database accuracy and precision; and (3) error due to the calculation of the predictor variable itself.
Ecological Error-- The ecological restraints of the study animal is a source of error and conflict between GIS databases--remotely sensed at large pixel sizes, and a mid-size rodent with a home-range often as small as the minimum pixel size. Prairie dogs weigh an average of 2-5 pounds and rarely disperse distances greater than 10 kilometers (Knowles 1985, Cincotta and Uresk 1986, Garret and Franklin 1988). Because of this small size, the resolution of the GIS map layers imposes an unrealistic decision-scale on the animals. The minimum pixel size had a resolution of one meter (park boundary and aerial photography); however, some databases had larger pixel sizes (5 to 30m). The cost surface is then based on a physical resolution determined by the databases and computational restrictions that do not match the dispersal capacity of a mid-sized rodent--prairie dogs cannot take 30 meter steps. Thus the ability to avoid barriers may be compromised with the model erring towards longer paths for linear features with high weights. By changing the weights of different classes of linear features (like roads). creating buffer zones around each linear feature (reducing edge effects), and mathematically enlarging features to match the pixel resolution, some of the path deviation is thought to be accounted for. However, some of the paths display jagged step-like movements, suggesting that some of the scale differences are still present.
Spatial Error--The spheroid and projection errors as they relate to precision are particularly important to mention for BADL. BADL straddles two UTM zones (13 and 14) and when dispersal paths are drawn across this junction (corrected for in GRASS GIS) any distortion due to the bending of the UTM zones at their edges is incorporated into the dispersal paths. Another source of spatial error involves the construction of the model itself through a series of vector and raster data transformations (Hunter and Goodchild 1995). The cost surface in GRASS is constructed as a raster surface, but it must be translated into a vector surface to calculate the dispersal path length. The model script does this in several steps: first the cost surface is corrected for map resolution, then 'drained' using a raster-based program to find the least-cost path. Once the path is constructed, it is translated into a vector format using a thinning algorthim that sees only 45 degree angles. The algorthim reduces curves to a series of small vectors, each at an angle of of 0, 45, 90, etc. Round features or long curves around features (like mesa tables and buttes) are more likely to have some degradation of area due to vector-averaging than long linear features (such as roads); however, there is no easy mechanism to quantify these differences.
Calculations of genetic distances--The Rogers' genetic distance used in this study has several underlying assumptions that can influence the metric relationship to physical distance (Jacquard 1970, Weir 1990, Weir and Cockerham 1990). Rogers' genetic distance is a metric measure and is often used in spatial studies as an analog for geographic distances (Stewart et al. 1992, White and Svenson 1992). Rogers' distance is more sensitive to disjunct or private alleles, while other measures of genetic distance use an overall allele frequency; therefore, short time frame studies are more appropriate with Rogers than those studies looking at speciation or phylogeny (Rogers 1991, Britten and Brussard 1991). Whether the twenty-one generational span used in this study is sufficient to overcome biases associated with private alleles or disjunct frequencies is not clear; however there is some evidence of private alleles in two of the populations used in this study (Bowser, unpublished data) which may contribute to the different groupings noted in the PCA analysis. Some statistics were tested using several other measures of genetic distance (Neis and the original Rogers); there were no significant differences in results produced by these statistics as compared to the Modified Rogers. Finally, if additional polymorphic alleles were discovered and added to the analysis, there may be some increased power in the genetic database and thus in the genetic distance grouping. A proposal has been submitted to repeat this study using micro-satellite DNA frequencies to calculate genetic distances for 1996 funding.
The primary objective of this study was to demonstrate a new use for GIS technology by incorporating population genetics as a validation measure. Environmental features were shown to impact animal dispersal and thus create distances that were more similar to those predicted by the genetic measures. However, the overall model fit was poor suggesting that this exploration of GIS with genetics is still in its infancy and many bugs still need to be worked out. Dispersal paths, as a tool for understanding spatial relationships, may provide a key for understanding spatial relationships among populations on complex landscapes. Such models of animal movement and the impacts of such movement on long term population fitness are critical in the preservation of isolated species in preserves. As GIS develops into a management tool for the conservation of species, dispersal models can contribute to the realistic management of species--along with managing their genetic composition--on preserves into the next century.
This study used shell-scripts and UNIX to produce models; however, ideally these scripts should become tools portable to different ecosystems and species. As the park service is currently faced with several genetically isolated species, a model that looks directly at the impacts of different types of environmental features (including man-made features) on the genetics of a species can be immensely useful. I hope to expand this marriage of genetics and GIS to incorporate other databases, in new environments using different species--especially isolated or fragmented species. GIS, as an environmental modelling program, combined with genetics, as a measure of population dynamics, can be a powerful management tool and one with expanding application to preserves and parks.
I wish to thank my graduate advisors, Bette Loiselle and John Blake for their support and encouragement. The Technology Transfer Center of the National Biological Service provided assistance and equipment. Modelling advice and GIS expertise was generously provided by Ralph Root, Peter Strong, David Duran, and Susan Stitt of the NBS. Funding was provided by Dr. Bob Schiller of the National Park Service, Denver.
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Gillian Bowser, Natural Resource Specialist, Rocky Mountain System Support Office--National Park Service, 12795 W. Alameda Parkway, Denver, Colorado 80225.
phone: 303-969-2865
fax: 303-969-2644
email: gillian@rmro.nps.gov
url: http://www.nps.gov/wildlife/nat.resources/gillian/
