I start with a "disclaimer" (and many apologies!): I read only the last two messages (by Jim and Carmelo), as I am stuck with teaching in this period.

I'd like only to suggest a reference on N vs the number of variables (in morphometrics but not necessarily only in this field). It's a difficult but very important and most interesting paper on this issue: Bookstein, 2017, Evolutionary Biology: A Newly Noticed Formula Enforces Fundamental Limits on Geometric Morphometric Analyses
DOI 10.1007/s11692-017-9424-9



On 14/03/18 04:05, f.james.rohlf wrote:
Actually the rule is that the number of specimens should be larger than the number of variables 2p-4 not p landmarks in the case of 2D data.

F. James Rohlf, Distinguished Prof. Emeritus
Dept. Anthropology and Ecology & Evolution
Stonybrook University

-------- Original message --------
From: Carmelo Fruciano <c.fruci...@unict.it>
Date: 3/12/18 9:51 PM (GMT-10:00)
To: MORPHMET <morphmet@morphometrics.org>
Subject: Re: ***SPAM*** [MORPHMET] Re: Digitizing landmarks on live larvae

Dear Avi,

I guess it's hard to formulate any rule of thumb.

Some analyses might not be defined if the number of variables exceed the number of observations. Some other analyses might be defined (there is many distance-based analyses nowadays which circumvent that problem).

However, whether a given analysis is defined doesn't mean that the inference is necessarily accurate. I guess it depends on what you plan to test/measure and the effect size you expect.

Andrea Cardini has some papers that can give you some hint on this, such as:

Cardini & Elton 2007 - Zoomorphology

Cardini et al. 2015 - Zoomorphology

Cardini & Elton 2017 - Hystrix

They should be downloadable from his website https://sites.google.com/site/alcardini/home/pubs

Obviously, having an idea of variation on your own data would be better.
I hope this helps.

On 3/12/2018 8:27 PM, Avi Koplovich wrote:
Hi Carmelo,
Thank you for those answers.
One more question please:
I know that the number of specimens should exceed the number of the total landmarks (fixed-landmarks + semi-landmarks). Is there a rule of thumb of by how much or what ratio between specimens to semi-landmarks one should keep?

Thank you,


On Sunday, March 11, 2018 at 5:15:24 PM UTC+2, Carmelo Fruciano wrote:

    Il 6/03/2018 4:44 PM, Avi Koplovich ha scritto:
    > Hi Carmelo,
    > Thank you for your answer.
    > My project tests for the influence of kairomones of a predator
    fish on
    > the morphology of Salamander larvae during its development. To
    do this,
    > I take pictures every other week of larvae spawned from six
    > females and assigned to 3 treatments: No fish, 3 caged fish, 6
    caged fish.

    Hi Avi,
    it sounds like an interesting experiment. I will try to answer to
    questions but keeping in mind that I'm not very knowledgeable on
    salamander development.

    >  1. I intend to use landmark 1 (dorsal connection of the tail
    fin) as a
    >     fixed factor. But I thought I may be able to use the tail tip
    >     (landmark 20) and head tip (landmark 48) as fixed landmarks
    as well.
    >     Do you think it's ok in an ontogeny experiment?

    I guess it will depend on how long into ontogeny you will track the
    larvae and whether or not that point will "disappear" over ontogeny
    and/or slide unreasonably (depends also on your question). You, being
    knowledgeable on their biology, are the best judge on that.

    > If not, do you think
    >     it's ok to slide all semi-landmarks of the tail on landmark
    1, and
    >     all head semi-landmarks on an eye landmark? Since the eye
    isn't part
    >     of the head contour, is it ok if I slide one semi-landmark
    to the
    >     eye and all rest semi-landmarks of the head one to each
    other as a
    >     closed shape?

    The point(s) slid relative to the eye won't be sliding along the
    direction tangent to the curve you want to approximate (i.e., the
    curvature of the head). A good starting point on the method could be
    Gunz & Mitteroecker 2013 - Hystrix

    >  2. Is it ok if landmarks 1 and 39 slid relative to each other
    as well
    >     as 41 and 55, since both describe a closed shape?

    It's not particularly desirable (see answer above).

    >  3. Another worry I have is that landmark 40 which I used to
    create the
    >     comb fan for both the tail and the head is too far from both
    of them
    >     so it doesn't bypass the bending.
    >  4. I'm affraid I don't fully understand why landmark 40 can not be
    >     treated as a fixed landmark. In the book of Zelditch 2004,
    she says
    >     that one of the basic differences between fixed-landmark and
    >     semi-landmark is the degree of freedom, while fixed has two
    >     it is docked on both X and Y axes while semi only on one of
    >     (depending on the nature of the specific fan). Please
    correct me if
    >     I'm wrong, but what if I use the side line of the larvae
    (which is
    >     an anatomical/homologous feature) as my X axis and use the Y
    >     component of landmark 1 (dorsal connection of the tail fin)
    to dock
    >     landmark 40 on the Y axis? Is it wrong because of the
    dependency of
    >     landmark 40 on landmark 1 regarding the Y coordinate?

    I think Don has covered these two very well.

    >  5. Emma Sherratt told me she straightened the bent tail-body
    using TPS
    >     software in her paper Sherratt et al. 2017 - Nature ecology &
    >     evolution. In the supplementary material of her paper she
    >     "To correct for dorso-ventral bending in the landmark
    >     (caused by the joint of the tail with the head/body), we
    used the
    >     ‘unbend specimens’ function of tpsUtil v.1.86 (Rohlf 2015). The
    >     landmark configurations for each specimen were transformed
    using the
    >     quadratic approach, straightening from the eye (1) along the
    >     notochord landmarks (46 to 55) to the tip of the tail (8)."
    >     Jim mentioned this unbending function here before. I read
    the help
    >     about unbending specimens and thought I can use landmarks 20
    >     tip), 48 (head tip) and several semi-landmarks I can
    digitize using
    >     the comb fan (equally spaced) along the side line of the
    larvae, in
    >     order to create the quadratic curve (while the side line
    >     semi-landmarks can be later omitted from the dataset - I saw
    >     Fruciano et al. 2016). Does this sound good?
    >     I bet that this can basically solve the problems I mentioned
    in 3 &
    >     4, since then I can digitized the whole body contour.

    That function is great but, as everything, relies on a set of
    assumptions (see also Fruciano 2016 - Development Genes and Evolution
    for a brief discussion). In your case:
    - that you can consistently identify those points along an
    line (which you would remove after the unbending)
    - that your arching is well represented by the chosen function

    You are the best judge on whether these assumptions are satisfied in
    your case or not.
    I suggested the Valentin et al. (2008 - Journal of Fish Biology)
    approach because it's more flexible (less stringent assumptions,
    obviously doesn't mean assumption-free) and therefore more generally
    applicable. But, of course, the approach in tpsUtil can be a great
    solution if it's appropriate to your data.


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Dr. Andrea Cardini
Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università di Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy
tel. 0039 059 2058472

Adjunct Associate Professor, School of Anatomy, Physiology and Human Biology, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia

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WEBPAGE: https://sites.google.com/site/alcardini/home/main

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