Pearson (1991) watched (Spizella pusilla) and White-throated (Zonotrichia albicollis) feeding on artificial patches of three sizes. He compared the observed distributions of distances between nearest neighbors in small groups with computer-generated expected distributions. Two principal results were given (presented here in reverse order from Pearson's paper). First, both species occurred disproportionately often on portions of the patches near a nearby pile. Pearson concluded the birds were attracted to Second, observed distributions of distances between birds differed from Monte Carlo (computer-generated) distributions and differed between the two species for most combinations of group size and patch size. The Monte Carlo method was complete spatial randomness (CSR; Diggle 1983: 4), presumably accomplished by generating a pseudorandom X-value and Y-value for each point. The points were constrained only to be at least 1 cm apart; 1,000 nearest-neighbor distances were generated for each group size in this manner. Pearson's (1991) conclusions were derived from differences between the spacing of real and Monte Carlo-generated birds, although he stated that spacing behavior could not be separated from these birds' affinity for cover. The conclusions are valid only to the extent that CSR represents a realistic expectation of the birds' behavior in the absence of social interactions. However, because the birds were attracted to the pile, we know that they did not conform to CSR. In the absence of social interactions, one would expect nearest-neighbor distances on average to be less than those predicted by the purely random model, because the birds were bunched at one end. Fortunately, Pearson's (1991) detailed data allow construction of a more suitable alternative model. Values for X are computed pseudorandomly, as in Pearson's study. Values for Y are computed by using a weighted pseudorandom number generator (Robertson 1977), based on the known distributions in Pearson's figures 4 and 5. The weighted values cast birds on the plane with a preference for proximity to a brush pile at Y of zero; for instance, they place 72% of the computer-generated Field Sparrows within the closest 5 cm of a small patch when group size is two. The alternative model (Fig. 1) differs greatly from Pearson's (1991) figure 1. Although the mean may not be a meaningful measure of central tendency in these distributions, the recalculated means are 0.61 to 0.64 those of Pearson's model. They differ by 3 to 14 cm. Although Pearson's interesting conclusions about differences between spacing behaviors of the two species of sparrows may be unaffected, his conclusions about the degree of randomness in their spacing (Pearson 1991:fig. 3) are not supported by his data when a more realistic distribution of birds is used for comparison. The alternative model for random spacing with a preference for cover (Fig. 1) assumes that the sparrows have no overall preference for certain regions in the X direction, that the six zones described in Pearson (1991) are an accurate description of the birds' use of space, and that positions in X and Y are uncorrelated. Pearson did not test these assumptions, nor can they be tested from the published data. Comparison of the alternative weighted model with observed distributions, though more valid, is probably less powerful than comparison of Pearson's (1991) purely random model. This is because the birds' distribution in the Y direction is determined both by a known preference for Y of zero and by a suspected minimum or preferred distance between birds. Thus, using the observed Y distribution taints the model with an unknown component of social spacing itself. Monte Carlo methods allow testing for spatial patterning when conventional methods fail (Diggle 1983, Krebs 1989, Manly 1991). The technique of using weighted number generators (Larkin 1982) extends Monte Carlo methods to some situations in which distributions in one or more dimensions are not purely random.
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