Abstract
Spatial point pattern analysis is commonly used in ecology to examine the spatial distribution of individual organisms or events, which may shed light on the operation of underlying ecological processes driving the development of a spatial pattern. Commonly used quadrat-based methods of measuring spatial clustering or dispersion tend to be strongly influenced by the choice of quadrat size and population density. Using valley oak (Quercus lobata) stands at multiple sites, we show that values of the Morisita Index are sensitive to the choice of quadrat size, and that the comparative interpretation of the index for multiple sites or populations is problematic due to differences in scale and clustering intensity from site to site, which may call for different quadrat sizes for each site. We present a new method for analyzing the Morisita Index to estimate the appropriate quadrat size for a given site and to aid interpretation of the clustering index across multiple sites with local differences. By plotting the maximum clustering intensity (Imr) found across a range of quadrat sizes, we were able to describe how a spatial pattern changes when quadrat size varies and to identify scales of clustering and quadrat sizes for analysis of spatial patterns under different local conditions. Computing and plotting the instantaneous rate of change (first derivative of rMax), we were able to evaluate clustering across multiple sites on a standardized scale. The magnitude of the rMax first derivative is a useful tool to quantify the degree of crowding, dispersion, or random spatial distribution as a function of quadrat size.
Highlights
Spatial point pattern analysis is an approach commonly used in ecology to examine the spatial distribution—clustered, dispersed, or random—of individual organisms within a given area or in relation to other organisms, which can shed light on underlying ecological processes, e.g., resource competition or population dynamics [1,2,3,4]
Clustering peaked for CHE and was dubious for Paramount Ranch (PAR) in the 75 m grid, but increased to its highest level for Malibu Creek State Park (MAC) on the 100 m grid, though the rate of increase slowed between 75 m and 100 m
Examining the IMr graphs for points of comparison among the three sites, we observed that there appeared to be a common clustering or crowding threshold of approximately 20 stems when the 50 m quadrats were used and that clustering of more than 20 stems at this scale became less likely. Interpreting this value of 20 stems as a crowding threshold for valley oak in general is problematic because the stems at PAR are much more intensely crowded than at CHE or MAC, possibly indicating a difference in site-level spatial distribution rather than a meaningful comparison of crowding intensity
Summary
Spatial point pattern analysis is an approach commonly used in ecology to examine the spatial distribution—clustered, dispersed, or random—of individual organisms within a given area or in relation to other organisms, which can shed light on underlying ecological processes, e.g., resource competition or population dynamics [1,2,3,4]. Ecological processes can often be studied at multiple scales, and variables can occur at different spatial scales of variation in different places, making it difficult to find the “correct” scale. Given the importance of the chosen scale of analysis, ecological point-pattern analysis must be studied as the variation of organisms through different scales at the same time, where its effect may or may not to be consistent through different spatial frames of analysis [5,6]. The larger the scale of analysis, the more unpredictable the spatial pattern and there is no single, “correct” scale to study any population. If pattern depends on the scales of observation, it is possible to measure clustering or dispersion as a function of scale or distance
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