Re: [R-sig-phylo] multiple traits measured within species
Hi, thanks Rafael and Emmanuel for further input into this problem. I have followed Rafael's advice and tried to use MCMCglmm with the help of Shinichi Nakagawa. This seems to provide again sensible results, however I would also be interested in following the procedure suggested by Emmanuel, since ideally I would like to see these results confirmed using different methods. I have just finished reading the new version of chapter 6 in the new book and am thinking how to implement this. I will probably contacting Emmanuel for further advice on that. Thanks again for all the help! best Kaspar On 12/03/2012 18:52, Emmanuel Paradis wrote: Hi Kaspar, Matt, Marguerite and others, I provide an overview of the issue of intraspecific variation in comparative methods in the 2nd edtion of my book. Specifically, there are functions pic.ortho and varCompPhylip (the latter requiring Phylip on your machine) which implement most of the methods described in Felsenstein (2008). I also describe how to implement Garland Ives's (2007) method (measurement-error model), and a few other things. Besides, I show how to expand a covariance matrix to include intraspecific covariance parameters (that should be able to be estimated with gls). I don't think this has been used yet. Kaspar, if you are interested in using this, you may contact me if you need more details. Best, Emmanuel Kaspar Delhey wrote on 12/03/2012 08:00: Hi Marguerite and Matt, thanks for your comments I should perhaps explain better the analysis I am trying to do which I tried to avoid first because it is lengthy and complicated (you have been warned continue reading at your own peril): The idea is to test for co-evolution between plumage colours and visual sensitivities in a clade of birds (fairy-wrens) where different species have different types of visual sensitivities. In birds this degree of variation in visual sensitivities within a small clade is rare and bird visual sensitivities fall into two main groups (U-type and V-type eyes, the former being more sensitive to ultraviolet light). This is a two-level factor in my analysis and invariant within species. In this particular clade there seems to be a correlation between having U-type eyes and presence of blue plumage (Ödeen et al. 2011 Proc. R. Soc. B), and the explanation behind this could be that U-type eyes are better at perceiving variation in blue colours than V-type eyes (which are also ancestral). Since for 12 species in this clade I had colour (reflectance) measurements of multiple males in breeding plumage I quantified, using visual models, whether U- or V-type eyes were better at uncovering the variability between male colours (as is expected of females choosing mates based on plumage colour). Given that variation in blue colours was hypothesised to be easier to perceive by U-type eyes, I tried to include as many colour patches as possible in order to compare blue vs. non-blue colours. Some species have both blue and non-blue colours, others only one type and some of them have fewer measured colour patches (due to technical reasons). Visual inspection of results indicate that in almost all cases U-type eyes are better than V-type eyes at discriminating colour variation between males and thus I computed the difference between U- and V-type eyes as an index of how much better U-type eyes performed. My expectation here was that it would be at discriminating blue colours. This was not the case as this difference was larger for non-blue colours. This trend is confirmed if instead of using the factor blue/non-blue we use a continuous descriptor of colours (which goes from red to ultraviolet) as explanatory variable and plot this against the difference in performance between U- and V-type eyes. What also becomes evident from this plot is that this difference in performance is larger for colours belonging to species with U-type eyes, no matter what type of colours. In other words, plumage colours of species with U-type eyes seem to show chromatic variation that appears well suited to be discriminated by U-type eyes, something we could expect from the coevolution between colours and visual sensitivities. If I would analyse these data ignoring phylogenetic relatedness I would use mixed models including, as fixed effects, eye type (a factor with two levels: U- or V-type) and a continuous covariate describing the colour (from red to UV). Species identity would be a random factor in order to control for multiple patches measured within each species. Results from such a model confirm the patterns described above. Off course I would like to see these results confirmed controlling for phylogenetic relatedness which prompted the attempt described in my previous e-mail to the list. I have also computed the species-specific averages and carried out the analyses on 12 data points while controllinh for phylogenetic relatedness. This analysis confirms the mixed model results but with
Re: [R-sig-phylo] multiple traits measured within species
Hi Marguerite and Matt, thanks for your comments I should perhaps explain better the analysis I am trying to do which I tried to avoid first because it is lengthy and complicated (you have been warned continue reading at your own peril): The idea is to test for co-evolution between plumage colours and visual sensitivities in a clade of birds (fairy-wrens) where different species have different types of visual sensitivities. In birds this degree of variation in visual sensitivities within a small clade is rare and bird visual sensitivities fall into two main groups (U-type and V-type eyes, the former being more sensitive to ultraviolet light). This is a two-level factor in my analysis and invariant within species. In this particular clade there seems to be a correlation between having U-type eyes and presence of blue plumage (Ödeen et al. 2011 Proc. R. Soc. B), and the explanation behind this could be that U-type eyes are better at perceiving variation in blue colours than V-type eyes (which are also ancestral). Since for 12 species in this clade I had colour (reflectance) measurements of multiple males in breeding plumage I quantified, using visual models, whether U- or V-type eyes were better at uncovering the variability between male colours (as is expected of females choosing mates based on plumage colour). Given that variation in blue colours was hypothesised to be easier to perceive by U-type eyes, I tried to include as many colour patches as possible in order to compare blue vs. non-blue colours. Some species have both blue and non-blue colours, others only one type and some of them have fewer measured colour patches (due to technical reasons). Visual inspection of results indicate that in almost all cases U-type eyes are better than V-type eyes at discriminating colour variation between males and thus I computed the difference between U- and V-type eyes as an index of how much better U-type eyes performed. My expectation here was that it would be at discriminating blue colours. This was not the case as this difference was larger for non-blue colours. This trend is confirmed if instead of using the factor blue/non-blue we use a continuous descriptor of colours (which goes from red to ultraviolet) as explanatory variable and plot this against the difference in performance between U- and V-type eyes. What also becomes evident from this plot is that this difference in performance is larger for colours belonging to species with U-type eyes, no matter what type of colours. In other words, plumage colours of species with U-type eyes seem to show chromatic variation that appears well suited to be discriminated by U-type eyes, something we could expect from the coevolution between colours and visual sensitivities. If I would analyse these data ignoring phylogenetic relatedness I would use mixed models including, as fixed effects, eye type (a factor with two levels: U- or V-type) and a continuous covariate describing the colour (from red to UV). Species identity would be a random factor in order to control for multiple patches measured within each species. Results from such a model confirm the patterns described above. Off course I would like to see these results confirmed controlling for phylogenetic relatedness which prompted the attempt described in my previous e-mail to the list. I have also computed the species-specific averages and carried out the analyses on 12 data points while controllinh for phylogenetic relatedness. This analysis confirms the mixed model results but with less power. I see Matt's point that we have no idea what evolutionary model accounts for differences within species in this case. Does this also preclude computing species-specific averages? What are we assuming then? I will explore the possibilities in the papers suggested by Matt but a first quick reading seems to indicate that there are designed to deal with between-individual variation and not variation between traits. Thanks again for the suggestions (and for reading so far!) and I certainly would appreciate any further ideas on how to analyse these data. best wishes Kaspar On 11/03/2012 16:23, Marguerite Butler wrote: Dear Kaspar, Are your traits the same? Basically, are the seven color patches on the same individual all one trait, or are they seven traits? Do all species have the seven color patches? Or are the number of color patches variable? (this could also be a character). I think before you attempt a comparative analysis, it is helpful to think about how you would set up a standard statistical analysis, for example some sort of ANOVA. I am not sure I understand your description clearly. It sort of sounds like you are considering the multiple color patches as repeated measures of color patch on the same individual, but then you want to include them all as separate traits in the analysis. You could consider them as repeated
Re: [R-sig-phylo] multiple traits measured within species
Hello Kaspar, I am new to phylogenetic comparative methods, so I may not be of much help, but I am dealing with similar questions that you are, so hopefully I can at least help the discussion in a useful way! First, I tried to sort out your main questions, which seem to be: - Are U- and V-type eyes better at sorting out colors? - Is this difference color-dependent; i.e. is the difference between U- and V-type eyes stronger for blue colors than for red colors? So it seems you have: - a response variable which says how discernible the color is (I'm guessing some deltaS measurement, between the color and the background or the color and the other colors in a bird's body?) - a predictor variable for eye type (U- or V-, factor, two levels) - a predictor variable for the color descriptor (a continuous variable, from blue to red) And you'd be particularly interested in the effect of eye type and its interaction with the color descriptor. So it seems to me that most models would be a problem for you because they assume some model of trait evolution across the phylogeny, which also relates to the within-species variability (as you pointed out, this is usually between-individual, within-species variation), which might become a problem. From a purely modeling perspective, however, the main issue you're trying to deal with is have residual error that is uncorrelated to phylogenetic relationships. So it seems to me that this is an issue similar to that faced by those attempting to conduct phylogenetic meta-analysis, where multiple effects obtained from each species also don't represent inter-individual variability, but a random sample from a population of effect sizes of that species. So, if in the same way, you can assume that your measurements of color discriminability are a random sample of effects for that species, your situation might be analogous, and the MCMCglmm implementation of Hadfield Nakagawa (detailed in the reference Matt pointed out earlier) might solve your problem, allowing you to add phylogenetic non-independence together with additional random effects in order to obtain your fixed effects estimates under uncorrelated residuals. However, I believe some (many?) will be uneasy with this approach, as it may have implicit assumptions about the model of trait evolution I am not considering, which may be problematic since the traits included are not homologous and the variation between samples within species are not being explicitly modeled in an evolutionary framework. Still, I hope it helps! And best of luck in the project - As a fellow bird-color enthusiast, I find it very interesting! ;) Abraços, Rafael Maia --- webpage: http://gozips.uakron.edu/~rm72 A little learning is a dangerous thing; drink deep, or taste not the Pierian spring. (A. Pope) Graduate Student - Integrated Bioscience University of Akron http://gozips.uakron.edu/~shawkey/ On Mar 11, 2012, at 9:00 PM, Kaspar Delhey wrote: Hi Marguerite and Matt, thanks for your comments I should perhaps explain better the analysis I am trying to do which I tried to avoid first because it is lengthy and complicated (you have been warned continue reading at your own peril): The idea is to test for co-evolution between plumage colours and visual sensitivities in a clade of birds (fairy-wrens) where different species have different types of visual sensitivities. In birds this degree of variation in visual sensitivities within a small clade is rare and bird visual sensitivities fall into two main groups (U-type and V-type eyes, the former being more sensitive to ultraviolet light). This is a two-level factor in my analysis and invariant within species. In this particular clade there seems to be a correlation between having U-type eyes and presence of blue plumage (Ödeen et al. 2011 Proc. R. Soc. B), and the explanation behind this could be that U-type eyes are better at perceiving variation in blue colours than V-type eyes (which are also ancestral). Since for 12 species in this clade I had colour (reflectance) measurements of multiple males in breeding plumage I quantified, using visual models, whether U- or V-type eyes were better at uncovering the variability between male colours (as is expected of females choosing mates based on plumage colour). Given that variation in blue colours was hypothesised to be easier to perceive by U-type eyes, I tried to include as many colour patches as possible in order to compare blue vs. non-blue colours. Some species have both blue and non-blue colours, others only one type and some of them have fewer measured colour patches (due to technical reasons). Visual inspection of results indicate that in almost all cases U-type eyes are better than V-type eyes at discriminating colour variation between males and thus I computed the difference between U- and V-type eyes as an index of how much better U-type eyes performed. My
Re: [R-sig-phylo] multiple traits measured within species
Dear Kaspar, Are your traits the same? Basically, are the seven color patches on the same individual all one trait, or are they seven traits? Do all species have the seven color patches? Or are the number of color patches variable? (this could also be a character). I think before you attempt a comparative analysis, it is helpful to think about how you would set up a standard statistical analysis, for example some sort of ANOVA. I am not sure I understand your description clearly. It sort of sounds like you are considering the multiple color patches as repeated measures of color patch on the same individual, but then you want to include them all as separate traits in the analysis. You could consider them as repeated measurements of a single color patch trait, in which case you would include the individual and species as factors in your analysis. Or you could consider each patch a different trait, and then compare them across species, so that each color patch is a separate dependent variable (in which case color patch 1 would be the same trait across individuals and species, etc.). Or you could take the mean of all color patches within an individual and use that in an analysis across individuals and species. Do you have any clues from development as to their identity? It seems like you want to consider them all to be replicates of the same measure. But then why measure so many? I assume there is variation among color patches within an individual? Ultimately you will have to decide if 3 color patches is one trait or if it is three traits. After you decide this, it will be much easier to design a comparative analysis. Good luck, Marguerite On Mar 6, 2012, at 2:42 PM, Kaspar Delhey wrote: Hello, I was wondering whether I could get some input into the following analysis: I am interested to test for the association between one dependent variable (continuous, normal) and one factor and a covariate while accounting for phylogenetic relatedness. In my analysis I have 12 species and I have measured the dependent variable and the covariate (which are both colour descriptors) on several patches per species (between 1 and 7 patches per species). The factor (the type of visual sensitivity) does not vary within species. Thus the repeated observations per species do not correspond to different individuals but are different patches of colour in the same individual, measured on the same scale and units (hence directly comparable). Does it make sense to make use of the whole dataset (i.e. without computing species averages) by replacing each tip in the phylogeny by a polytomy including all patches measured in that particular species? For example if I have this tree: (A, (B, C)) and I have measured two patches of colour in sp. A and three in spp B and C I could replace the tips in this tree by: ((A1,A2),((B1,B2,B3),(C1,C2,C3))) In this way I could use a gls approach with nlme and for example corPagel such as: model1-gls(dep.var~factor+covariate, correlation=Pagel, method=REML, data=data) The results that I obtain from such a model make sense and qualitatively agree with the results from a mixed model including species ID as a random factor but ignoring phylogenetic relatedness between species. My question then is whether there is a flaw in this analysis and whether it has been used before in other publications in order to be able to include references to back it up. Thanks in advance for any help. best kaspar -- Kaspar Delhey e-mail: kaspar.del...@monash.edu https://sites.google.com/site/kaspardelhey/ Tel:+61-(0)3-99020377 Bldg.18 School of Biological Sciences Monash University Clayton, 3800 Victoria Australia ___ R-sig-phylo mailing list R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo ___ R-sig-phylo mailing list R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
Re: [R-sig-phylo] multiple traits measured within species
Hi Kaspar and others, Sorry for responding so late to this. I am not sure if there exists any precedent for doing this but it seems problematic. We do not expect BM alone (or a variant thereof) to be a good model to account for variation within a species and I would strongly recommend against doing what you propose. However, there have been several methods published directly relevant to this that are worth checking out. Someone else on the list may have more insight than me on this (and please correct me if i am wrong). There exists a PGLS-esque method which I believe is available only in matlab... Ives, A.R., Midford, P.E. Garland, T. 2007. Within-species variation and measurement error in phylogenetic comparative methods. Syst. Biol. 56: 252270. And for a contrast-based approach, Felsenstein has developed machinery which has the advantage of simultaneously estimating the variances. It is coded up and availalbe in PHYLIP within the contrast program. Felsenstein, J. 2008. Comparative methods with sampling error and within-species variation: contrasts revisited and revised. Am. Nat. 171: 713725. There is also some discussion of this in: HADFIELD, J. D. and NAKAGAWA, S. (2010), General quantitative genetic methods for comparative biology: phylogenies, taxonomies and multi-trait models for continuous and categorical characters. Journal of Evolutionary Biology, 23: 494508. Hope this is helpful. cheers matt On Tue, Mar 6, 2012 at 4:42 PM, Kaspar Delhey kaspar.del...@monash.eduwrote: Hello, I was wondering whether I could get some input into the following analysis: I am interested to test for the association between one dependent variable (continuous, normal) and one factor and a covariate while accounting for phylogenetic relatedness. In my analysis I have 12 species and I have measured the dependent variable and the covariate (which are both colour descriptors) on several patches per species (between 1 and 7 patches per species). The factor (the type of visual sensitivity) does not vary within species. Thus the repeated observations per species do not correspond to different individuals but are different patches of colour in the same individual, measured on the same scale and units (hence directly comparable). Does it make sense to make use of the whole dataset (i.e. without computing species averages) by replacing each tip in the phylogeny by a polytomy including all patches measured in that particular species? For example if I have this tree: (A, (B, C)) and I have measured two patches of colour in sp. A and three in spp B and C I could replace the tips in this tree by: ((A1,A2),((B1,B2,B3),(C1,C2,**C3))) In this way I could use a gls approach with nlme and for example corPagel such as: model1-gls(dep.var~factor+**covariate, correlation=Pagel, method=REML, data=data) The results that I obtain from such a model make sense and qualitatively agree with the results from a mixed model including species ID as a random factor but ignoring phylogenetic relatedness between species. My question then is whether there is a flaw in this analysis and whether it has been used before in other publications in order to be able to include references to back it up. Thanks in advance for any help. best kaspar -- Kaspar Delhey e-mail: kaspar.del...@monash.edu https://sites.google.com/site/**kaspardelhey/https://sites.google.com/site/kaspardelhey/ Tel:+61-(0)3-99020377 Bldg.18 School of Biological Sciences Monash University Clayton, 3800 Victoria Australia __**_ R-sig-phylo mailing list R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/**listinfo/r-sig-phylohttps://stat.ethz.ch/mailman/listinfo/r-sig-phylo [[alternative HTML version deleted]] ___ R-sig-phylo mailing list R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
