Another, though non-statistical, approach to judge whether one has an appropriate number of landmarks or perhaps too many is to use the tpsSuper software.
One could start with many landmarks and confirm (one hopes) that the average unwarped image is clear implying that the landmarks have captured the variation of not only the landmarks but the structures around them. You can then remove landmarks and see whether the average looks fuzzier. If so, that reflects variation not well tracked by the chosen landmarks. If there is little change then the landmarks you removed are not really necessary to track the variation in the sample. One could then continue the process. Clearly the issue is not just the number of landmarks but where they are located relative to the variation among the specimens. This process could be automated to try combinations of landmarks such that some measure of variation in pixels of the unwarped images are minimized. I seem to remember that Mardia made a suggestion like that many years ago. _ _ _ _ _ _ _ _ _ F. James Rohlf, Distinguished Prof. Emeritus Stony Brook University Depts. of Anthropology and of Ecology & Evolution -----Original Message----- From: Murat Maga [mailto:m...@uw.edu] Sent: Wednesday, May 31, 2017 12:33 PM To: Mike Collyer <mlcoll...@gmail.com>; Lea Wolter <leawolter...@gmail.com> Cc: MORPHMET <email@example.com> Subject: RE: [MORPHMET] number of landmarks and sample size I want to chime in on Mike's comment about density of landmarking changing the effect size. Nicolas Navarro and I did something similar in context of quantitative genetics of mandible shape and came to a similar conclusion using 2D, 3D and 3D semi-landmarks sets on same dataset. Navarro N, Maga AM. 2016. Does 3D Phenotyping Yield Substantial Insights in the Genetics of the Mouse Mandible Shape? G3: Genes, Genomes, Genetics 6:1153–1163. -----Original Message----- From: Mike Collyer [mailto:mlcoll...@gmail.com] Sent: Wednesday, May 31, 2017 7:43 AM To: Lea Wolter <leawolter...@gmail.com> Cc: MORPHMET <firstname.lastname@example.org> Subject: Re: [MORPHMET] number of landmarks and sample size Dear Lea, I see others have responded to your inquiry, already. I thought I would add an additional perspective. Your question about statistical significance requires asking a follow-up question. What statistical methods would you intend to use to evaluate “significance”? If you are worried about the number of landmarks, your concern suggests you might be using parametric test statistics frequently associated with MANOVA, like Wilks lambda or Pilai trace. Indeed, when using these statistics and converting them to approximate F values, one must have many more specimens than landmarks (more error degrees of freedom than shape variables, to be more precise), if “significance” is to be inferred from probabilities associated with F-distributions. Therefore, limiting the number of landmarks might be a goal. When using resampling procedures to conduct ANOVA, using fewer landmarks can paradoxically decrease effect sizes, as an overly simplified definition of shape becomes implied. We demonstrated this in our paper: Collyer, M.L., D.J. Sekora, and D.C. Adams. 2015. A method for analysis of phenotypic change for phenotypes described by high-dimensional data. Heredity. 115: 357-365. This is consistent with Andrea’s comment about quality over quantity with the caveat that limited quantity precludes quality. In other words, too few landmarks translates to limited ability to discern shape differences, because the shape compared is basic. In the paper, we used two separate landmark configurations: one with few landmarks and the other with the same landmarks plus sliding semilandmarks between fixed points, on different populations of fish. We found that adding the semilandmarks increased the effect size for population differences and sexual dimorphism. But if we constrained our analyses to parametric MANOVA for our small samples, we would have to use the simpler landmark configurations and live with the results. I do not wish to suggest that adding more landmarks is better. Overkill is certainly a concern. I would suggest though that statistical power would be for me less of a concern than a proper characterization of the shape I wish to compare among samples. If I suspect curvature is important but am afraid to use (semi)landmarks that would allow me to assess the curvature differences among groups, opting instead to use just the endpoints of a structure because I am worried about statistical power, then I just allowed a statistical procedure to take me away from the biologically relevant question I sought to address. Andrea is correct that quality is better than quantity, but quantity can be a burden in either direction (too few or too many). Additionally, statistical power will vary among statistical methods. Reconsidering methods might be as important as reconsidering landmarks configurations. Regards! Mike > On May 4, 2017, at 5:19 AM, Lea Wolter <leawolter...@gmail.com> wrote: > > Hello everyone, > > I am new in the field of geometric morphometrics and have a question for my > bachelor thesis. > > I am not sure how many landmarks I should use at most in regard to the sample > size. I have a sample of about 22 individuals per population or maybe a bit > less (using sternum and epigyne of spiders) with 5 populations. > I have read a paper in which they use 18 landmarks with an even lower sample > size (3 populations with 20 individuals, 1 with 10). But I have also heard > that I should use twice as much individuals per population as land marks... > > Maybe there is some mathematical formula for it to know if it would be > statistically significant? Could you recommend some paper? > > Because of the symmetry of the epigyne I am now thinking of using just one > half of it for setting landmarks (so I get 5 instead of 9 landmarks). For the > sternum I thought about 7 or 9 landmarks, so at most I would also get 18 > landmarks like in the paper. > > I would also like to use two type specimens in the analysis, but I have just > this one individual per population... would it be totally nonesens in a > statistical point of view? > > Thanks very much for your help! > > Best regards > Lea > > -- > MORPHMET may be accessed via its webpage at http://www.morphometrics.org > --- > You received this message because you are subscribed to the Google Groups > "MORPHMET" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to morphmet+unsubscr...@morphometrics.org. -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org. -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org. -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org.