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closeDoubts about upper-bound regression
Posted by DiegoGil on 03 Dec 2009 at 12:49 GMT
The use of upper bound regression to detect a trade off seems reasonable once a STRONG negative relationship between two traits is detected, and when a triangular-shape "vacuum" of data points is found in a corner of the graph (e.g. the examples shown by Podos between trill rate and bandwidth in Emberizidae). In your case (Fig.2) I see little evidence of such a negative pattern, so I do not think that you are entitled to perform that regression. Not to mention that you base all this in just 6 individuals recorded several times, which is both insuficient and incorrect.
Furthermore, once you describe that relationship, the logical step would be to take deviations from that line in order to see if heterozygosity correlates with how close birds get to that trade-off. Otherwise, I see no reason for the analysis of the presumed trade-off.
I'm sorry to be so critical, your study suggests a fascinating story, but I fear that the small sample size and the incorrect analysis do not provide strong support for the hypothesis.
Best wishes,
Diego Gil (MNCN, CSIC, Madrid)
RE: Doubts about upper-bound regression
JohelChaves replied to DiegoGil on 05 Dec 2009 at 02:06 GMT
Figure 2 shows that the vocalizations with longest duration were performed at lower frequencies whereas the maximum duration of vocalizations performed at higher frequencies was relatively shorter. We simply used the upper bound regression analysis to describe this pattern. Our analysis includes data from all the individuals we had (13). After the binning process, the number of songs was reduced to seven, coming from six individuals. The result from the upper bound regression analysis remains unaltered if we only use one song per individual (i.e. six songs). It would have been nice to have enough data points to fill the gaps under the regression line and show a triangular shape, but the fact that the data points do not show a nice triangle does not invalidate what occurs at the “upper bound”. Jeff Podos was one of the reviewers of this manuscript and he agreed with our use of the method and with our interpretation.
You are right at pointing out that our sample size was low, which limited our power to detect other potentially significant relationships. We actually took deviations from the regression line (orthogonal distances) and used them in a correlation/regression analysis with heterozygosity. The analysis showed the trend predicted by the hypothesis but it was not significant, presumably due to lack of statistical power. We opted for only showing significant relationships in the manuscript. Overall, the results are consistent with our hypothesis but we do not claim we have provided a strong test of this hypothesis. We just wish our manuscript will motivate other researchers to test the hypothesis using a larger sample size and better analyses to either confirm it or reject it.
Thanks for your comment.