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.
Carmelo
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,
Avi
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
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 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
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
configurations
> (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
(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 Evolution
for a brief discussion). In your case:
- that you can consistently identify those points along an
hypothetical
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,
which
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.
Best,
Carmelo
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