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 <> 
Date: 3/12/18  9:51 PM  (GMT-10:00) To: MORPHMET <> 
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



    Obviously, having an idea of variation on your own data would be

    I hope this helps.






    On 3/12/2018 8:27 PM, Avi Koplovich

      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


          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 different 

          > 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 your 

          questions but keeping in mind that I'm not very knowledgeable

          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

          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

          direction tangent to the curve you want to approximate (i.e.,

          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 because

          >     it is docked on both X and Y axes while semi only on
          one of them

          >     (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 wrote:

          >     "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

          >     Jim mentioned this unbending function here before. I
          read the help

          >     about unbending specimens and thought I can use
          landmarks 20 (tail

          >     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 "helper"

          >     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

          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

          approach because it's more flexible (less stringent
          assumptions, which 

          obviously doesn't mean assumption-free) and therefore more

          applicable. But, of course, the approach in tpsUtil can be a

          solution if it's appropriate to your data.







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