Appendix D. Effect of multiple comparisons on detection of species groups using remote sensing.
We investigated whether our results relating remote-sensing indices to species richness results were an artifact of multiple comparisons. For clarity, we begin with a brief reiteration of the results. As described in the main text, we assessed the dependence of species on habitats through habitat-species association groups, where each was a species group (forest, generalist, agricultural, total) within a point count station type (forest, riparian strips, high-vertical-structure agriculture, abandoned fields, low-vertical-structure agriculture, and active pasture). There were 24 habitat-species association groups (Appendix D, Fig. D1).
|FIG. D1. The 24 habitat-species association groups.|
We assessed correlations between the richness of the 24 habitat-species association groups and the associated remotely-sensed wetness values (the results with remotely sensed brightness were extremely similar and are omitted for simplicity). For each disc radius (100500 m, 100 m increment), there were 24 such correlations between richness and wetness (one for each habitat-species association group), to which we added a 25th—forest-affiliated birds of the riparian strip and wetness calculated for the forest station type (Fig. D2). We included this type because the correlation of forest-affiliated birds of the riparian strip with the field-mapped measure of forest extent suggested that this habitat-species association group was responding to land cover variation centered about the forest fragment at the middle of each site, where the forest point count station was based (see Results section: Response of avian communities to fine-grained variation in land cover).
|FIG. D2. Illustration of correlations between habitat-species association groups and the remotely-sensed wetness index. There were 25 habitat-species association groups for which these correlations were calculated. One group is illustrated here (forest-affiliated species within forest stations).|
Out of a total of 125 correlations (5 disc radii by 25 habitat-species association groups), we found a total of 14 statistically significant correlations (P < 0.05) between species richness and wetness. Eleven of these correlations were spatially aggregated in three habitat-species association groups: agricultural species in forest stations (significant correlations across all five disc radii), forest species in forest stations, and forest species in riparian stations (the latter two exhibiting significant correlations across three adjacent disc radii). These correlations are shown in Fig. 5 of the main text. The habitat-species association groups in the remaining three significant correlations were: total species within forest stations (200 m disc, P = 0.040), agriculture-affiliated species within riparian stations (200 m disc, P = 0.045), and generalist species within low-vertical-structure stations (500 m disc, P = 0.035). We did not report these last three correlations in the main text, as we judged them to be spurious: the three were not spatially aggregated and they were not congruent with the results of the comparison of field-mapped land cover with species richness (see Results section: Response of avian communities to fine-grained variation in land cover).
As we calculated 125 correlations, finding some significant correlations could be expected by chance. Therefore, to determine the statistical significance of these results as a whole, we calculated the chance of achieving our results, assuming no true correlation between the remote sensing data and species richness. There were two parts to our calculation. First, we calculated the probability of detecting 14 or more significant correlations (P < 0.05) between habitat-species association groups and wetness at any of the five disc radii. If the data were independent, we would expect to find six significant correlations by chance (at P < 0.05 over 125 total correlations). However, the species data were not independent. We showed in the main text that forest-affiliated species richness within forest and riparian strip stations were correlated. The remote sensing data were also not independent, because we calculated wetness for each station with five nested discs of increasing width; clearly, the five wetness values for each station were dependent. Because of this data non-independence, we used a randomization approach to calculating the probability of detecting at least 14 significant correlations by chance (for details, see below).
The second part of calculating the chance of achieving our results, assuming no true correlation between the remote sensing and species richness, was to examine the spatial aggregation of significant correlations. In our results, we found that 11 significant correlations spatially aggregated in three clusters (significant correlations across all five disc radii for one habitat-species association group and two other groups with significant correlations across three adjacent disc radii). Because the threshold for “significant” spatial aggregation of correlations is somewhat arbitrary, we selected a conservative standard with less spatial aggregation than we actually found. We asked, what is the probability of finding at least one species-habitat association group significantly correlated with mean wetness across all five disc radii?
We calculated the probability of receiving our results by chance with a randomization approach. We conducted 10,000 trials, where we randomized the association between species richness and wetness, and then counted the number of trials where both of our threshold conditions held true (Fig. D3; Table 1; threshold conditions: > 13 significant correlations and at least one habitat-species association group significantly correlated with mean wetness across all five disc radii). For each trial, we randomized the site associated with the wetness value of each point count station (the site is the unit of replication within which point count stations were positioned). Additionally, for each trial, in order to maintain the spatial autocorrelation present within the remote sensing data, all station types within a single site were assigned the same (randomly assigned) site number. Only 267 trials met the two criteria that we set (P = 0.0267). Therefore, we rejected the null hypothesis that our results occurred by chance.
|FIG. D3. Illustration of the randomization method, showing the results obtained in a single trial for one habitat-species association group (forest-affiliated species within forest stations). The site number associated with the wetness values has been randomized; all wetness values within a single row received the same new site number, as can be seen by comparing this figure to Appendix D, Figure 2. The same random site order was used for all 25 habitat-species association groups in a single trial.|
TABLE D1. Illustration of determining whether threshold conditions have been met, using a single randomization trial as an example. In each of the 10,000 trials, we calculated 125 correlations between species richness and wetness. The table of correlations from one of the trials is shown here (significant correlations are circled and in bold). For each trial, we determined whether both of our threshold conditions held true (> 13 significant correlations and at least one habitat-species association group significantly correlated with mean wetness across all five disc radii). Here, neither condition holds true.
We further investigated this issue of multiple comparisons, by examining each of the three significant species-habitat association groups individually, using a similar randomization approach as just described. For each of the three components, we randomized the association between site and species richness and counted the number of replicates where all five disc radii showed significant correlation (in the case of agricultural species in forest stations) or where three adjacent disc radii showed significant correlation (in the cases of forest species in forest stations and forest species in riparian stations). All three groups were significant (forest species in forest stations: P = 0.0302, agricultural species in forest stations: P = 0.0038, forest species in riparian stations: P = 0.0258).