Clustering of sample sizes.
DSDP Site 214 Revisited 7 million year record of plankton size (G. Tumidia)

A particularly curious feature of the data is a clustering of sizes seen in the quantile plot as a stair step pattern, and in the histogram of sizes as a series of spikes ( figure A2). When displayed by themselves on the time line ( figure A3) the points of three of the clusters are found only in the transition period and the other four have points scattered throughout either the beginning or ending periods. None of the clusters are visible when the full time line is presented ( figure A1).

A clustering of points could certainly occur at random, but the considerable abnormality of the spikes in the histogram suggest that that may not be the case here. The implication is that these represent either sub-species, that coexist for either short or long periods, or recurrent states of the ecology. It does not seem at all unlikely that a long term evolutionary change would progress in stages, but the evidence here does not seem conclusive.

Work on the puzzle not shown here includes a considerable effort to find any correlation between these groups of points and clustering or other abnormality in the standard deviations of the same samples. The within sample standard deviations of the cluster points appear to be completely normal, neither larger nor smaller than those of the points falling outside the clusters. This suggest that the points within the clustered samples are not clustered within the sample themselves. The distribution of the standard deviations also shows some clustering, but these groups of points do not seem to strongly correlate with the clusters of sizes in the sample means.

The conflicting evidence may be resolvable by some other test, but seems more likely to remain unresolved until the distribution of the individual specimens can be examined, and any significant clusters of individual sizes studied for morphological congruence.

Abnormally great variation at the time of most rapid change.

Figure A4 presents a plot of the residual differences between the scale adjusted standard deviations and its polynomial fit. The pattern of residuals has a decided peak during the transition at -5.5 Myr, coinciding with the point of steepest slope on the polynomial. The fact that this is also the period of time when samples were taken with the greatest frequency does effect the appearance, and some caution is needed. For example, it would be possible to sample the series at a uniform frequency and just happen to miss all the divergent points, making the distribution of residuals appear constant. It seems quite unlikely , however, that such high variability is occurring throughout the other periods and being hidden by an accidents of sampling. The anomaly is probably a reliable fact. It is of further interest that it appears to have increasing and decreasing slopes on either side of the peak. This period of greater general population diversity appears fairly narrow, say a half to three quarters of a million years and suggests that the duration of the transition event as it appears in the polynomial fit is misrepresented.

The question, of course, is what does this unusual anomaly represent. A possible hypothesis is that the fundamental diversity of individual differences increased and then decreased during the period of rapid evolutionary change, that there was an increase in the rate and variety of mutations. There is also an appearance is that during this period that change in normal diversity of the population went through continuous progressions itself.

Figure A4 shows a quantile density contour plot which brings out another key question. Because the quantile contours at the peak are not centered on the axis, but are islanded on either side, there is an appearance that there may have been least two divergent strains in the evolving population, one leading and one following the norm, being alternately sampled, . This would be consistent with a scenario of species succession in which the active evolution is occurring in one niche of the species and gradually infusing others. If this were correct one might expect to see separate high and low curves in figure A1 , the low one fading out with fewer and fewer points on its path and the high curve appearing first less and then more frequently until it is all that is left. That is not what is seen and so some more complex scenario would seem more likely.