Interpretation of scale in paired quadrat variance methods

Abstract Question: Previous interpretations of the variance plot of paired quadrat variance method (PQV) have been incomplete. The objective of this study was to clarify the interpretation of PQV, and to shed additional light on how different quadrat variance methods can be used, in concert, to measure scale in transect data. Methods: We used artificial and real data to examine how the PQV method elucidates spatial pattern. Two-term local quadrat variance (TTLQV) and new local variance (NLV) methods, together with their three-term counterparts, were also applied to the same data sets, and the results from all methods were compared. Results: When the mean gap size equalled the mean patch size along a transect, the first peak of the variance of PQV, NLV and TTLQV corresponded with the gap size (or patch size). However, if the mean gap size and patch size were unequal, the variance plot of PQV displayed a flat-topped plateau, in which the first inflection represented the mean size of the smaller phase and the second inflection represented the mean size of the larger phase; TTLQV showed a clear peak and NLV displayed a distinct first peak while the second inflection was dampened. The results also indicated than the three-term versions of quadrat variance methods did not consistently outperform their two-term counterparts, and often confused the interpretation of scale. Conclusions: The quadrat variance methods associated with the patch-gap measurements were able to efficiently detect not only the size of patches, but also the size of gaps. Abbreviations: NLV = New local variance; PQV = Paired quadrat variance; RPQV = random paired quadrat variance TQV = Triplet quadrat variance; TTLQV = Two-term local quadrat variance; 3TLQV = Three-term local quadrat variance; 3TNLV = Three-term new local variance.