The G-O Rule and Waldmeier Effect in the Variations of the Numbers of Large and Small Sunspot Groups

We have analysed the combined Greenwich and Solar Optical Observing Network (SOON) sunspot group data during the period of 1874-2011 and determined variations in the annual numbers (counts) of the small, large and big sunspot groups (these classifications are made on the basis of the maximum areas of the sunspot groups). We found that the amplitude of an even-numbered cycle of the number of large groups is smaller than that of its immediately following odd-numbered cycle. This is consistent with the well known Gnevyshev and Ohl rule or G-O rule of solar cycles, generally described by using the Zurich sunspot number (Rz). During cycles 12-21 the G-O rule holds good for the variation in the number of small groups also, but it is violated by cycle pair (22, 23) as in the case of Rz. This behaviour of the variations in the small groups is largely responsible for the anomalous behaviour of Rz in cycle pair (22, 23). It is also found that the amplitude of an odd-numbered cycle of the number of small groups is larger than that of its immediately following even-numbered cycle. This can be called as `reverse G-O rule'. In the case of the number of the big groups, both cycle pairs (12, 13) and (22, 23) violated the G-O rule. In many cycles the positions of the peaks of the small, large, and big groups are different and considerably differ with respect to the corresponding positions of the Rz peaks. In the case of cycle 23, the corresponding cycles of the small and large groups are largely symmetric/less asymmetric (Waldmeier effect is weak/absent) with their maxima taking place two years later than that of Rz. The corresponding cycle of the big groups is more asymmetric (strong Waldmeier effect) with its maximum epoch taking place at the same time as that of Rz.Comment: 13 pages, 5 figures, 1 table, accepted by Solar Physic

Call diversity in the North Pacific killer whale populations: implications for dialect evolution and population history

Although killer whale, Orcinus orca, dialects have been studied in detail in several populations, little attempt has been made to compare dialect characteristics between populations. In this study we investigated geographical variation in monophonic and biphonic calls among four resident populations from the North Pacific Ocean: Northern and Southern residents from British Columbia and Washington State, southern Alaska residents, and eastern Kamchatka residents. We tested predictions generated by the hypothesis that call variation across populations is the result of an accumulation of random errors and innovation by vertical cultural transmission. Call frequency contours were extracted and compared using a dynamic time-warping algorithm. We found that the diversity of monophonic calls was substantially higher than that of biphonic calls for all populations. Repertoire diversity appeared to be related to population size: in larger populations, monophonic calls were more diverse and biphonic calls less diverse. We suggest that the evolution of both monophonic and biphonic calls is caused by an interaction between stochastic processes and directional selection, but the relative effect of directional selection is greater for biphonic calls. Our analysis revealed no direct correlation between call repertoire similarity and geographical distance. Call diversity within predefined call categories, types and subtypes, showed a high degree of correspondence between populations. Our results indicate that dialect evolution is a complex process influenced by an interaction among directional selection, horizontal transmission and founder effects. We suggest several scenarios for how this might have arisen and the implications of these scenarios for call evolution and population history