AVHRR 12 x 103 pixels Landsat TM 13 x 106 pixels 6 polygons33170 polygons

Delphacodes Kuscheli

| Examples of geostatistical representation. The Seeley-Swan watershed in Montana, United States, is depicted with 1-km2 raster cells on the left, by 30 x 30 m raster cells on the right, and with vector polygons defined from topographic analysis in the inset. The more heterogeneneous the landscape, the greater the number of cells required to provide an accurate assessment of spatial variation. From R. Waring and Running (1998). Please see extended permission list pg 570.

| Examples of geostatistical representation. The Seeley-Swan watershed in Montana, United States, is depicted with 1-km2 raster cells on the left, by 30 x 30 m raster cells on the right, and with vector polygons defined from topographic analysis in the inset. The more heterogeneneous the landscape, the greater the number of cells required to provide an accurate assessment of spatial variation. From R. Waring and Running (1998). Please see extended permission list pg 570.

An underlying assumption of geostatistics is that the degree of similarity between sample points is correlated with their proximity (Fig. 7.12) (Coulson et al. 1996, Gilbert and Grégoire 2003, Grilli and Gorla 1997, Liebhold et al. 1993, M. Smith et al. 2004). Population structure in a given cell is influenced by the population structures in neighboring cells more than by distant cells. An autocorrelation matrix can be developed from data for different distance classes (i.e., x and y coordinates differing by a given distance; Liebhold and Elkinton 1989). This spatial autocorrelation can be used to interpolate values for unsampled locations by taking a weighted linear average of available samples, a technique known as kriging (Gilbert and Grégoire 2003, Gribko et al. 1995, Grilli and Gorla 1997, Hohn et al. 1993, Liebhold et al. 1993). Kriging represents an advance over traditional methods of interpolation in several ways, but its most important provision is incorporation of several forms of information simultaneously. The joint spatial dependence of population density and factors such as climate, soil conditions, vegetation, etc. can be integrated to provide more accurate estimates than would be possible with any single variable.

Sampling Dendroctonus
Distance between sampling stations (km)
Sampling Dendroctonus
'20 40 60 80 100 120 140 160 180 200 220 Distance between sampling stations (km)

| Relationships for the temporal correlation of Delphacodes kuscheli density and the distance between sampling stations (top) and for the mean absolute difference in densities for pairs of sampling stations and the distance between sampling stations (bottom) in Argentina. From Grilli and Gorla (1997) with permission from CAB International.

Gilbert and Grégoire (2003) used these methods to evaluate factors affecting the spatial structure of the European bark beetle, Dendroctonus micans, in a French spruce forest (Fig. 7.13). They demonstrated that the D. micans population had a strong spatial structure, significantly related to tree density; average slope within a 250-m radius; and the number of the specialist predator, Rhi-zophagus grandis, released within a 300-m radius >6 years previously. D. Williams and Liebhold (1995) used these techniques to predict the spatial distribution of insect population densities under potential future climates (see Fig. 7.8).

Modeling of spatial dynamics in stream networks or montane topography with branched topology presents special challenges. In such networks, the distance between two points may not be represented adequately by Euclidean distance

Euclidean Distance

Spatial structure of proportion of trees attacked by Dendroctonus micans, based on two-dimensional omni-directional kriging, in a 600-ha spruce stand in France. From Gilbert and Grégoire (2003) with permission from the Royal Entomological Society. Please see extended permission list pg 570.

Attack Density

0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35

Spatial structure of proportion of trees attacked by Dendroctonus micans, based on two-dimensional omni-directional kriging, in a 600-ha spruce stand in France. From Gilbert and Grégoire (2003) with permission from the Royal Entomological Society. Please see extended permission list pg 570.

because of limitations to movement of aquatic organisms across land. Rather, the shortest distance from the perspective of aquatic organisms is along the stream channel (Fig. 7.14a). Ganio et al. (2005) described use of an empirical variogram, based on shortest distances along the network pathway between sample points, to evaluate spatial patterns and differences in spatial structure along stream networks in western Oregon, United States (Fig. 7.14b). Such new tools will contribute to modeling of spatial structure in aquatic populations.

Factors affecting the geographic distributions of populations have intrigued ecol-ogists for at least the past two centuries. Distributions can be described at different geographic scales. Six distinctive floral and faunal associations (biogeographic realms) can be identified, conforming roughly to continental boundaries but also reflecting the history of continental movement (plate tectonics). Topography also creates gradients in environmental conditions on mountains and temperature stratification with depth in aquatic ecosystems.

The distribution of species among islands intrigued early ecologists. The ability of populations to colonize oceanic islands was found to reflect the dispersal capacity of the species, the size of the island, and its distance from the population source. Although controversial, principles of island biogeography have been applied to colonization of terrestrial habitat islands (e.g., mountaintops and patches of unique habitat in otherwise inhospitable landscapes).

At more local scales, the spatial distribution of populations changes with population size. Growing populations expand over a larger area as individuals move from high-density patches to the fringe of the population. Rapidly expanding populations generate large numbers of dispersing individuals that maximize the

VI. SUMMARY

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Distance (km)

| A: Distance between points sj and s2 in a network can be measured either as Euclidean distance (de) or as distance along the network pathway (dn); B: Spatial distribution and empiric variograms of coastal cutthroat trout counts in Hinkle Creek in western Oregon. Variograms show semivariance as a function of network distance (dn) with 2.5th and 97.5th percentiles from 5000 permutations (green lines) for the entire watershed and for the North and South forks separately. From Ganio et al. (2005) with permission from the Ecological Society of America. Please see extended permission list pg 570.

colonization of new patches. Under favorable conditions, these satellite demes expand and coalesce with the main population, affecting ecosystem processes over large areas. Declining populations shrink into isolated refuges that maintain distinct demes of a metapopulation. The extent of movement of individuals among these demes determines genetic heterogeneity and ability to recolonize patches following local extinctions.

All populations are vulnerable to local extinctions as a result of changing environmental conditions and disturbances. Populations survive to the extent that their dispersal strategies facilitate recolonization and population movement over landscapes. Anthropogenic activities alter spatial distribution in several ways. Climate changes affect the geographic distribution of suitable habitats. However, the most serious anthropogenic effects on spatial patterns are habitat fragmentation, alteration and pollution of aquatic ecosystems, and redistribution (intentionally or unintentionally) of various species. Fragmentation increases isolation of demes and places many species at risk of extinction. At the same time, predators and parasites appear to be most vulnerable to fragmentation and habitat disturbances, often increasing opportunities for population growth by prey species. Humans also are responsible for the introduction of a large and growing number of plant and animal species to new regions as a result of transportation of commercial species and forest and agricultural products. Urban areas represent centers of commercial introductions and provide opportunities for exotic ornamental and associated species to become established and move into surrounding ecosystems. These species affect various ecosystem properties, often dramatically altering vegetation structure and competing with, or preying on, native species.

Modeling of spatial distribution patterns has been facilitated by development of GIS and geostatistical techniques. Early models represented population expansion as a simple diffusion process. Application of GIS techniques to the patch dynamics of metapopulations permits integration of data on population dynamics with data on other spatially varying factors across landscapes. Geosta-tistical techniques, such as kriging, permit interpolation of density data between sampling stations to improve mapping and projecting of population distributions. These techniques are improving our ability to evaluate population contributions to ecosystem properties across landscapes.

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