Dear all,
I always feel a bit uneasy with the idea of simulating some "real shapes," subjecting them to Procrustes analysis, and then see what you get. One problem is that the simulations, such as Brownian motion, are usually based on the 2D or 3D coordinates of p landmarks (i.e., in 2p- or 3p-dimensional figure space, not in shape space). But shape space is of dimension 2p-4 or 3p-7, and Brownian motion in shape space does not translate into Brownian motion of shape coordinates because shape coordinates cannot vary independently. Note however, that isotropic variation or Brownian motion in figure space translates into isotropic or Brownian variation in shape space, which is an almost linear subspace of figure space (see, e.g., earlier work and morphmet postings of Bookstein), yet not into isotropic or Brownian variation of shape coordinates. This is clear without simulations. The easiest approach for simulations would be to stay in figure space, hence without any Procrustes analyses, which may be good enough for small variation. Given that Brownian motion is so far off from any reasonable developmental, genetic, or evolutionary model, the technical issue of Procrustes superimposition seems negligible to me. Alternatively, one may perform simulations directly along some basis vectors of shape space, e.g., the principal warps (see also the work of Bookstein and others). I agree with David's posting. One way of interpreting his nice figure is that the problem he depicts emerges from interpreting all six landmark coordinates (figure space) of the triangles, even though their shape has only two degrees of freedom. There simply is no "true" position or orientation unless additional geometric, histological, functional, etc. data are available. Best, Philipp Mitteroecker [email protected] schrieb am Mittwoch, 10. September 2025 um 10:57:31 UTC+2: > Hi David, Jim, Jacqueline and Manabu, > > Thank you so much for your responses! I have learned so much by reading > your replies and now I have an idea about how to progress from here. > > I am very grateful for the time you used to help me understand these > things better. > > Best regards, > Sofia > > > > On 9 Sep 2025, at 21.30, Polly, P. David <[email protected]> wrote: > > Hi Sofia, > > I do not personally know of simulation studies where the specific goal was > to determine the effect of Procrustes alignment on parameters of > evolutionary model fitting, but there have been some on its effects on > estimating covariance patterns and other parameters. I don't know all of > them off the top of my head, but I included one in this paper > <https://drive.google.com/file/d/1D1XCmLUYNYR3SZmgRL-zAVmRVzbh4V4I/view> on > testing for developmental correlations in teeth. Dean Adams did some > simulations of shapes in his 2014 paper on PGLS and high dimensional data > (Evolution, 68: 2675-2688). Goswami & Finarelli (2016) simulated shapes > for their EMMLi paper for analyzing modularity (Evolution, 70: 1622-1637). > I am sure there are many others. > > The problem is not straightforward, however. To rephrase the question, one > would be asking how does Procrustes alignment affect the covariance matrix > to which the evolutionary model is being fit compared to the "real" > alignment. If we simulate data, then we know the "real" alignment, but > arguably for most biological structures we do not know the real alignment, > and in many cases there probably is no such thing as a real alignment. If > we knew the real alignment then we wouldn't need Procrustes to place the > shapes into a common coordinate system. > > Simulating shape data also has its own limitations because we need some > sort of model of the covariances in order to generate stochastic states, > and the choices we make necessarily limit the generality of the results. > For example, in the paper linked above, I generated shapes based on the > predictions of a particular cascading model of development that has an > expectation for covariance patterns. In that model, the shapes are > developmentally aligned at one of the landmarks and cascade out > stochastically from there. In the model, the first landmark has no > variance and the distal ones in the sequence have the most variance and > their position covaries with the landmarks in their "ancestry" (much like > the expected covariance on a phylogeny). Procrustes redistributes the > variance across the landmarks, but actually does not much change the > covariance pattern. What may not be apparent from the text of the paper, > is that the degrees of freedom in the simulated data are much smaller than > in an empirical data set. Arguably that was appropriate for that > particular paper because the degrees of freedom match the developmental > model and (if that model applies) then the additional degrees of freedom in > real structures come from sources other than the developmental cascade > itself. The point is, however, that the same data could have been > simulated in many different ways, each of which would respond differently > to a Procrustes standardization. > > For the evolutionary model fitting, the phenotypic and phylogenetic > covariances will both be components in the Procrustes superimposed data. > Bookstein and Felsenstein have been working on likelihood methods for > joint Procrustes superimposition and phylogenetic reconstruction. I believe > the work is mostly in progress, but they have given several interesting > presentations about it, including this one in Copenhagen ( > https://youtu.be/otykxJ78oIw). > > An issue to always keep in mind for Procrustes problems is that there are > always an infinite number of "true" alignments that result in the same > Procrustes alignment. In other words, the relative positions of landmarks > can be measured, but their absolute location cannot. Therefore, it is > impossible to estimate rates or modes of evolution for individual landmarks > that have been Procrustes aligned. I don't know I I can send attachments > through MorphMet but I am going to try -- the attached illustrates why this > is the case with an example similar to the classic "Pinocchio" problem. (if > the attachment doesn't come through, there is a similar illustration on > Slide 11 of the "Procrustes & PCA" lecture here > <https://www.pollylab.org/courses/geometric-morphometrics>). You should > be able to make inferences about the shape as a whole, however, if the > model fitting is appropriately multivariate. > > With best wishes, > David > > > P. David Polly > Indiana University > https://pollylab.org/ > https://github.com/pdpolly > personal: [email protected] > > On Sep 9, 2025, at 8:43 AM, 'F. James Rohlf' via Morphmet < > [email protected]> wrote: > > What is your alternative? Preserve in the analysis the arbitrary > positioning of specimens in a photo or scan? Procrustes does have biases > but it would have to be replaced with some other procedure. Perhaps one has > some known reference points but then variation in those points will become > very important. > > Jim > > __________________ > F. James Rohlf, Distinguished Prof. Emeritus > Dept. Anthropology and Ecology & Evolution > Stonybrook University > > > -------- Original message -------- > From: [email protected] > Date: 9/9/25 2:49 AM (GMT-05:00) > To: Jacqueline Silviria <[email protected]> > Cc: [email protected] > Subject: Re: [MORPHMET2] Effect of Procrustes alignment on parameter > estimates > > Dear Jacqueline > > Yes it could be for instance for ancestral state reconstruction. What I am > thinking about is whether anybody has done a simulation study where they > simulate shape data, procrustes align the data, infer some quantity of > interest (could be ancestral state, or something else) and then look at how > the estimated quantity compares to the true quantity (the one used for > simulation) with or without procrustes alignment. I would expect procrustes > alignment to have an effect as it is not really a part of any of the > stochastic models I am aware of. > > I am sorry if my question is very odd, I do not have a strong background > in geometric morphometrics so I might have misunderstood something. > > Thank you! > > Best regards, > Sofia > > On 9 Sep 2025, at 03.45, Jacqueline Silviria <[email protected]> wrote: > > Just to be clear, by parameter estimation for stochastic models, you mean > for the purpose of ancestral state reconstruction? > > *Jacqueline S. Silviria* > *she/her/hers* > *The Last King of the Jungle* > <https://protect.checkpoint.com/v2/r01/___https://discord.gg/m7KKkuKW___.YzJ1OnN0b255YnJvb2s6YzpnOmJiYjFlOWU2ZDE1YzNkOTg0NjllNjZmMmQzOGI5NTg1Ojc6NWE2Yzo1ZTc1Mzg1OWFjNDZlZDhhNmE3NjFjOTQyMmE4ZjZkNmRmMGI2ZDhlY2U3OTBmMDY4Mjk3YzJjNzc4YzYwNDc0Omg6VDpG> > > > > > * Department of Earth & Space Science University of Washington Seattle, > WA, USA [email protected], [email protected]* > > *ResearchGate profile > <https://protect.checkpoint.com/v2/r01/___https://www.researchgate.net/profile/J_Silviria___.YzJ1OnN0b255YnJvb2s6YzpnOmJiYjFlOWU2ZDE1YzNkOTg0NjllNjZmMmQzOGI5NTg1Ojc6OGMxYzo2NTI2YWIyNzM4NTYzNGUxYjA1ZmZiOTRiODcwYTBmOWQ4NTViOGEyMDMwOGU2MTk5NDlhMWU0MDVkOTU4ZjkyOmg6VDpG>* > > Sent from my iPhone > > On Sep 8, 2025, at 6:02 AM, Sofia Stroustrup <[email protected]> wrote: > > Dear all, > > I am wondering whether any of you are aware of a study that investigates > the effect of Procrustes alignment on parameter estimation for instance > under a Brownian motion or Ornstein-Uhlenbeck process? What I am thinking > about is, if we simulate data under a stochastic model, procrustes align > the data and then do parameter estimation how does Procrustes alignment > affect the estimates. I have not been able to find any study investigating > this. > > Thank you very much for your help! > > Best regards, > Sofia > (PhD student at University of Copenhagen) > > -- > 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 [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/morphmet2/695dcdb1-5844-420f-82ce-881a6ffe81f2n%40googlegroups.com > > <https://protect.checkpoint.com/v2/r01/___https://groups.google.com/d/msgid/morphmet2/695dcdb1-5844-420f-82ce-881a6ffe81f2n*40googlegroups.com?utm_medium=email&utm_source=footer___.YzJ1OnN0b255YnJvb2s6YzpnOmJiYjFlOWU2ZDE1YzNkOTg0NjllNjZmMmQzOGI5NTg1Ojc6NGQ4MTozMGNmZGZiMGY4ZWQzZjgzNDllODA4NDU3ZDExMDAyMzgyMTRkNTVjNDU4ZDRkNjMxMDhjYjRiNGRjMzM0YjA0Omg6VDpG> > . > > > > > -- > 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 [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/morphmet2/7F159313-FA85-45F7-93E6-611EBD78DADF%40gmail.com > > <https://protect.checkpoint.com/v2/r01/___https://groups.google.com/d/msgid/morphmet2/7F159313-FA85-45F7-93E6-611EBD78DADF*40gmail.com?utm_medium=email&utm_source=footer___.YzJ1OnN0b255YnJvb2s6YzpnOmJiYjFlOWU2ZDE1YzNkOTg0NjllNjZmMmQzOGI5NTg1Ojc6ZjAxYzpkYjVmZGU0Y2EyNTQ0NzU1YjQ3ODViZTU2YjA5MmE0MWNmNjBhNTZkZDA3NjAxOGE3ZmQ1ZDBkOTk2YmY3ZjZhOmg6VDpG> > . > > -- > 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 [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/morphmet2/68c020e8.050a0220.379554.2b88%40mx.google.com > > <https://groups.google.com/d/msgid/morphmet2/68c020e8.050a0220.379554.2b88%40mx.google.com?utm_medium=email&utm_source=footer> > . > > > > -- > 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 [email protected]. > > To view this discussion visit > https://groups.google.com/d/msgid/morphmet2/2C585800-1BE1-49D4-91E5-98506F715702%40iu.edu > > <https://groups.google.com/d/msgid/morphmet2/2C585800-1BE1-49D4-91E5-98506F715702%40iu.edu?utm_medium=email&utm_source=footer> > . > > -- You received this message because you are subscribed to the Google Groups "Morphmet" group. 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